%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUN066+1 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:22:36 AM UTC 2025
% Result : Theorem 56.06s 56.26s
% Output : Proof 56.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : NUN066+1 : TPTP v9.0.0. Released v7.3.0.
% 0.02/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n005.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 02:10:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 56.06/56.26 % SZS status Theorem
% 56.06/56.26 % SZS output start Proof
% 56.06/56.26 tff(r2_type, type, (
% 56.06/56.26 r2: ( $i * $i ) > $o)).
% 56.06/56.26 tff(tptp_fun_Y2_20_type, type, (
% 56.06/56.26 tptp_fun_Y2_20: $i > $i)).
% 56.06/56.26 tff(tptp_fun_Y21_1_type, type, (
% 56.06/56.26 tptp_fun_Y21_1: $i > $i)).
% 56.06/56.26 tff(elem_24_type, type, (
% 56.06/56.26 elem_24: $i)).
% 56.06/56.26 tff(tptp_fun_Y24_0_type, type, (
% 56.06/56.26 tptp_fun_Y24_0: $i)).
% 56.06/56.26 tff(id_type, type, (
% 56.06/56.26 id: ( $i * $i ) > $o)).
% 56.06/56.26 tff(tptp_fun_Y3_21_type, type, (
% 56.06/56.26 tptp_fun_Y3_21: $i > $i)).
% 56.06/56.26 tff(r1_type, type, (
% 56.06/56.26 r1: $i > $o)).
% 56.06/56.26 tff(tptp_fun_Y4_22_type, type, (
% 56.06/56.26 tptp_fun_Y4_22: $i > $i)).
% 56.06/56.26 tff(tptp_fun_Y5_23_type, type, (
% 56.06/56.26 tptp_fun_Y5_23: $i > $i)).
% 56.06/56.26 tff(tptp_fun_Y18_16_type, type, (
% 56.06/56.26 tptp_fun_Y18_16: $i > $i)).
% 56.06/56.26 tff(tptp_fun_Y9_12_type, type, (
% 56.06/56.26 tptp_fun_Y9_12: $i > $i)).
% 56.06/56.26 tff(tptp_fun_Y8_14_type, type, (
% 56.06/56.26 tptp_fun_Y8_14: $i > $i)).
% 56.06/56.26 tff(r4_type, type, (
% 56.06/56.26 r4: ( $i * $i * $i ) > $o)).
% 56.06/56.26 tff(tptp_fun_Y17_15_type, type, (
% 56.06/56.26 tptp_fun_Y17_15: $i > $i)).
% 56.06/56.26 tff(r3_type, type, (
% 56.06/56.26 r3: ( $i * $i * $i ) > $o)).
% 56.06/56.26 tff(tptp_fun_Y16_13_type, type, (
% 56.06/56.26 tptp_fun_Y16_13: $i > $i)).
% 56.06/56.26 tff(1,assumption,(~((~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))))), introduced(assumption)).
% 56.06/56.26 tff(2,plain,
% 56.06/56.26 (((~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24))))) | r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))),
% 56.06/56.26 inference(tautology,[status(thm)],[])).
% 56.06/56.26 tff(3,plain,
% 56.06/56.26 (r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))),
% 56.06/56.26 inference(unit_resolution,[status(thm)],[2, 1])).
% 56.06/56.26 tff(4,plain,
% 56.06/56.26 ((r1(tptp_fun_Y21_1(elem!24)) | r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24))))),
% 56.06/56.26 inference(tautology,[status(thm)],[])).
% 56.06/56.26 tff(5,plain,
% 56.06/56.26 (r1(tptp_fun_Y21_1(elem!24)) | r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))),
% 56.06/56.26 inference(unit_resolution,[status(thm)],[4, 3])).
% 56.06/56.26 tff(6,assumption,(![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y18_16(elem!24))))), introduced(assumption)).
% 56.06/56.26 tff(7,plain,
% 56.06/56.26 (^[X5: $i] : rewrite((r1(tptp_fun_Y17_15(X5)) & r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5)) & id(tptp_fun_Y8_14(X5), tptp_fun_Y18_16(X5)) & r1(tptp_fun_Y18_16(X5))) <=> (~((~r1(tptp_fun_Y17_15(X5))) | (~r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5))) | (~id(tptp_fun_Y8_14(X5), tptp_fun_Y18_16(X5))) | (~r1(tptp_fun_Y18_16(X5))))))),
% 56.06/56.26 inference(bind,[status(th)],[])).
% 56.06/56.26 tff(8,plain,
% 56.06/56.26 (![X5: $i] : (r1(tptp_fun_Y17_15(X5)) & r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5)) & id(tptp_fun_Y8_14(X5), tptp_fun_Y18_16(X5)) & r1(tptp_fun_Y18_16(X5))) <=> ![X5: $i] : (~((~r1(tptp_fun_Y17_15(X5))) | (~r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5))) | (~id(tptp_fun_Y8_14(X5), tptp_fun_Y18_16(X5))) | (~r1(tptp_fun_Y18_16(X5)))))),
% 56.06/56.26 inference(quant_intro,[status(thm)],[7])).
% 56.06/56.26 tff(9,plain,
% 56.06/56.26 (^[X5: $i] : rewrite(((r1(tptp_fun_Y17_15(X5)) & r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5))) & (id(tptp_fun_Y8_14(X5), tptp_fun_Y18_16(X5)) & r1(tptp_fun_Y18_16(X5)))) <=> (r1(tptp_fun_Y17_15(X5)) & r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5)) & id(tptp_fun_Y8_14(X5), tptp_fun_Y18_16(X5)) & r1(tptp_fun_Y18_16(X5))))),
% 56.06/56.26 inference(bind,[status(th)],[])).
% 56.06/56.26 tff(10,plain,
% 56.06/56.26 (![X5: $i] : ((r1(tptp_fun_Y17_15(X5)) & r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5))) & (id(tptp_fun_Y8_14(X5), tptp_fun_Y18_16(X5)) & r1(tptp_fun_Y18_16(X5)))) <=> ![X5: $i] : (r1(tptp_fun_Y17_15(X5)) & r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5)) & id(tptp_fun_Y8_14(X5), tptp_fun_Y18_16(X5)) & r1(tptp_fun_Y18_16(X5)))),
% 56.06/56.26 inference(quant_intro,[status(thm)],[9])).
% 56.06/56.26 tff(11,plain,
% 56.06/56.26 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (id(Y8, Y18) & r1(Y18))) <=> ![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (id(Y8, Y18) & r1(Y18)))),
% 56.06/56.26 inference(rewrite,[status(thm)],[])).
% 56.06/56.26 tff(12,axiom,(![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (id(Y8, Y18) & r1(Y18)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax','axiom_5a')).
% 56.06/56.26 tff(13,plain,
% 56.06/56.26 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (id(Y8, Y18) & r1(Y18)))),
% 56.06/56.26 inference(modus_ponens,[status(thm)],[12, 11])).
% 56.06/56.26 tff(14,plain,(
% 56.06/56.26 ![X5: $i] : ((r1(tptp_fun_Y17_15(X5)) & r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5))) & (id(tptp_fun_Y8_14(X5), tptp_fun_Y18_16(X5)) & r1(tptp_fun_Y18_16(X5))))),
% 56.06/56.26 inference(skolemize,[status(sab)],[13])).
% 56.06/56.26 tff(15,plain,
% 56.06/56.26 (![X5: $i] : (r1(tptp_fun_Y17_15(X5)) & r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5)) & id(tptp_fun_Y8_14(X5), tptp_fun_Y18_16(X5)) & r1(tptp_fun_Y18_16(X5)))),
% 56.06/56.26 inference(modus_ponens,[status(thm)],[14, 10])).
% 56.06/56.26 tff(16,plain,
% 56.06/56.26 (![X5: $i] : (~((~r1(tptp_fun_Y17_15(X5))) | (~r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5))) | (~id(tptp_fun_Y8_14(X5), tptp_fun_Y18_16(X5))) | (~r1(tptp_fun_Y18_16(X5)))))),
% 56.06/56.26 inference(modus_ponens,[status(thm)],[15, 8])).
% 56.06/56.26 tff(17,plain,
% 56.06/56.26 ((~![X5: $i] : (~((~r1(tptp_fun_Y17_15(X5))) | (~r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5))) | (~id(tptp_fun_Y8_14(X5), tptp_fun_Y18_16(X5))) | (~r1(tptp_fun_Y18_16(X5)))))) | (~((~r1(tptp_fun_Y17_15(elem!24))) | (~r4(elem!24, tptp_fun_Y17_15(elem!24), tptp_fun_Y8_14(elem!24))) | (~id(tptp_fun_Y8_14(elem!24), tptp_fun_Y18_16(elem!24))) | (~r1(tptp_fun_Y18_16(elem!24)))))),
% 56.06/56.26 inference(quant_inst,[status(thm)],[])).
% 56.06/56.26 tff(18,plain,
% 56.06/56.26 (~((~r1(tptp_fun_Y17_15(elem!24))) | (~r4(elem!24, tptp_fun_Y17_15(elem!24), tptp_fun_Y8_14(elem!24))) | (~id(tptp_fun_Y8_14(elem!24), tptp_fun_Y18_16(elem!24))) | (~r1(tptp_fun_Y18_16(elem!24))))),
% 56.06/56.26 inference(unit_resolution,[status(thm)],[17, 16])).
% 56.06/56.26 tff(19,plain,
% 56.06/56.26 (((~r1(tptp_fun_Y17_15(elem!24))) | (~r4(elem!24, tptp_fun_Y17_15(elem!24), tptp_fun_Y8_14(elem!24))) | (~id(tptp_fun_Y8_14(elem!24), tptp_fun_Y18_16(elem!24))) | (~r1(tptp_fun_Y18_16(elem!24)))) | r1(tptp_fun_Y18_16(elem!24))),
% 56.06/56.26 inference(tautology,[status(thm)],[])).
% 56.06/56.26 tff(20,plain,
% 56.06/56.26 (r1(tptp_fun_Y18_16(elem!24))),
% 56.06/56.26 inference(unit_resolution,[status(thm)],[19, 18])).
% 56.06/56.26 tff(21,plain,
% 56.06/56.26 ((r1(tptp_fun_Y18_16(elem!24)) | r1(tptp_fun_Y8_14(elem!24))) | (~r1(tptp_fun_Y18_16(elem!24)))),
% 56.06/56.26 inference(tautology,[status(thm)],[])).
% 56.06/56.26 tff(22,plain,
% 56.06/56.26 (r1(tptp_fun_Y18_16(elem!24)) | r1(tptp_fun_Y8_14(elem!24))),
% 56.06/56.26 inference(unit_resolution,[status(thm)],[21, 20])).
% 56.06/56.26 tff(23,plain,
% 56.06/56.26 (((~r1(tptp_fun_Y17_15(elem!24))) | (~r4(elem!24, tptp_fun_Y17_15(elem!24), tptp_fun_Y8_14(elem!24))) | (~id(tptp_fun_Y8_14(elem!24), tptp_fun_Y18_16(elem!24))) | (~r1(tptp_fun_Y18_16(elem!24)))) | id(tptp_fun_Y8_14(elem!24), tptp_fun_Y18_16(elem!24))),
% 56.06/56.26 inference(tautology,[status(thm)],[])).
% 56.06/56.26 tff(24,plain,
% 56.06/56.26 (id(tptp_fun_Y8_14(elem!24), tptp_fun_Y18_16(elem!24))),
% 56.06/56.26 inference(unit_resolution,[status(thm)],[23, 18])).
% 56.06/56.26 tff(25,plain,
% 56.06/56.26 (^[X26: $i, X27: $i] : refl(((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26)))) <=> ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26)))))),
% 56.06/56.26 inference(bind,[status(th)],[])).
% 56.06/56.26 tff(26,plain,
% 56.06/56.26 (![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26)))) <=> ![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))),
% 56.06/56.26 inference(quant_intro,[status(thm)],[25])).
% 56.06/56.26 tff(27,plain,
% 56.06/56.26 (^[X26: $i, X27: $i] : trans(monotonicity(rewrite((r1(X26) & r1(X27)) <=> (~((~r1(X27)) | (~r1(X26))))), rewrite(((~r1(X26)) & (~r1(X27))) <=> (~(r1(X27) | r1(X26)))), (((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27)))) <=> ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26)))))), rewrite(((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26)))) <=> ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))), (((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27)))) <=> ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))))),
% 56.06/56.26 inference(bind,[status(th)],[])).
% 56.06/56.26 tff(28,plain,
% 56.06/56.26 (![X26: $i, X27: $i] : ((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27)))) <=> ![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))),
% 56.06/56.26 inference(quant_intro,[status(thm)],[27])).
% 56.06/56.26 tff(29,plain,
% 56.06/56.26 (![X26: $i, X27: $i] : ((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27)))) <=> ![X26: $i, X27: $i] : ((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27))))),
% 56.06/56.26 inference(rewrite,[status(thm)],[])).
% 56.06/56.26 tff(30,plain,
% 56.06/56.26 (^[X26: $i, X27: $i] : rewrite((((~id(X26, X27)) | ((~r1(X26)) & (~r1(X27)))) | (r1(X26) & r1(X27))) <=> ((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27)))))),
% 56.06/56.26 inference(bind,[status(th)],[])).
% 56.06/56.26 tff(31,plain,
% 56.06/56.26 (![X26: $i, X27: $i] : (((~id(X26, X27)) | ((~r1(X26)) & (~r1(X27)))) | (r1(X26) & r1(X27))) <=> ![X26: $i, X27: $i] : ((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27))))),
% 56.06/56.26 inference(quant_intro,[status(thm)],[30])).
% 56.06/56.26 tff(32,axiom,(![X26: $i, X27: $i] : (((~id(X26, X27)) | ((~r1(X26)) & (~r1(X27)))) | (r1(X26) & r1(X27)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax','axiom_8')).
% 56.06/56.26 tff(33,plain,
% 56.06/56.26 (![X26: $i, X27: $i] : ((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27))))),
% 56.06/56.26 inference(modus_ponens,[status(thm)],[32, 31])).
% 56.06/56.26 tff(34,plain,
% 56.06/56.26 (![X26: $i, X27: $i] : ((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27))))),
% 56.06/56.26 inference(modus_ponens,[status(thm)],[33, 29])).
% 56.06/56.26 tff(35,plain,(
% 56.06/56.26 ![X26: $i, X27: $i] : ((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27))))),
% 56.06/56.26 inference(skolemize,[status(sab)],[34])).
% 56.06/56.26 tff(36,plain,
% 56.06/56.26 (![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))),
% 56.06/56.26 inference(modus_ponens,[status(thm)],[35, 28])).
% 56.06/56.26 tff(37,plain,
% 56.06/56.26 (![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))),
% 56.06/56.26 inference(modus_ponens,[status(thm)],[36, 26])).
% 56.06/56.26 tff(38,plain,
% 56.06/56.26 (((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | ((~id(tptp_fun_Y8_14(elem!24), tptp_fun_Y18_16(elem!24))) | (~((~r1(tptp_fun_Y18_16(elem!24))) | (~r1(tptp_fun_Y8_14(elem!24))))) | (~(r1(tptp_fun_Y18_16(elem!24)) | r1(tptp_fun_Y8_14(elem!24)))))) <=> ((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | (~id(tptp_fun_Y8_14(elem!24), tptp_fun_Y18_16(elem!24))) | (~((~r1(tptp_fun_Y18_16(elem!24))) | (~r1(tptp_fun_Y8_14(elem!24))))) | (~(r1(tptp_fun_Y18_16(elem!24)) | r1(tptp_fun_Y8_14(elem!24)))))),
% 56.06/56.26 inference(rewrite,[status(thm)],[])).
% 56.06/56.26 tff(39,plain,
% 56.06/56.26 ((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | ((~id(tptp_fun_Y8_14(elem!24), tptp_fun_Y18_16(elem!24))) | (~((~r1(tptp_fun_Y18_16(elem!24))) | (~r1(tptp_fun_Y8_14(elem!24))))) | (~(r1(tptp_fun_Y18_16(elem!24)) | r1(tptp_fun_Y8_14(elem!24)))))),
% 56.06/56.26 inference(quant_inst,[status(thm)],[])).
% 56.06/56.26 tff(40,plain,
% 56.06/56.26 ((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | (~id(tptp_fun_Y8_14(elem!24), tptp_fun_Y18_16(elem!24))) | (~((~r1(tptp_fun_Y18_16(elem!24))) | (~r1(tptp_fun_Y8_14(elem!24))))) | (~(r1(tptp_fun_Y18_16(elem!24)) | r1(tptp_fun_Y8_14(elem!24))))),
% 56.06/56.26 inference(modus_ponens,[status(thm)],[39, 38])).
% 56.06/56.26 tff(41,plain,
% 56.06/56.26 (~((~r1(tptp_fun_Y18_16(elem!24))) | (~r1(tptp_fun_Y8_14(elem!24))))),
% 56.06/56.26 inference(unit_resolution,[status(thm)],[40, 37, 24, 22])).
% 56.06/56.26 tff(42,plain,
% 56.06/56.26 (((~r1(tptp_fun_Y18_16(elem!24))) | (~r1(tptp_fun_Y8_14(elem!24)))) | r1(tptp_fun_Y8_14(elem!24))),
% 56.06/56.26 inference(tautology,[status(thm)],[])).
% 56.06/56.26 tff(43,plain,
% 56.06/56.26 (r1(tptp_fun_Y8_14(elem!24))),
% 56.06/56.26 inference(unit_resolution,[status(thm)],[42, 41])).
% 56.06/56.26 tff(44,plain,
% 56.06/56.26 (((~![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y18_16(elem!24))))) | ((~r1(tptp_fun_Y8_14(elem!24))) | (~id(tptp_fun_Y8_14(elem!24), tptp_fun_Y18_16(elem!24))))) <=> ((~![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y18_16(elem!24))))) | (~r1(tptp_fun_Y8_14(elem!24))) | (~id(tptp_fun_Y8_14(elem!24), tptp_fun_Y18_16(elem!24))))),
% 56.06/56.26 inference(rewrite,[status(thm)],[])).
% 56.06/56.26 tff(45,plain,
% 56.06/56.26 ((~![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y18_16(elem!24))))) | ((~r1(tptp_fun_Y8_14(elem!24))) | (~id(tptp_fun_Y8_14(elem!24), tptp_fun_Y18_16(elem!24))))),
% 56.06/56.26 inference(quant_inst,[status(thm)],[])).
% 56.06/56.26 tff(46,plain,
% 56.06/56.26 ((~![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y18_16(elem!24))))) | (~r1(tptp_fun_Y8_14(elem!24))) | (~id(tptp_fun_Y8_14(elem!24), tptp_fun_Y18_16(elem!24)))),
% 56.06/56.26 inference(modus_ponens,[status(thm)],[45, 44])).
% 56.06/56.26 tff(47,plain,
% 56.06/56.26 ($false),
% 56.06/56.26 inference(unit_resolution,[status(thm)],[46, 24, 43, 6])).
% 56.06/56.26 tff(48,plain,(~![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y18_16(elem!24))))), inference(lemma,lemma(discharge,[]))).
% 56.06/56.26 tff(49,assumption,(r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))), introduced(assumption)).
% 56.06/56.26 tff(50,plain,
% 56.06/56.26 (^[X7: $i, Y10: $i] : refl(((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))) <=> ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))))),
% 56.06/56.26 inference(bind,[status(th)],[])).
% 56.06/56.26 tff(51,plain,
% 56.06/56.26 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 56.06/56.26 inference(quant_intro,[status(thm)],[50])).
% 56.06/56.26 tff(52,plain,
% 56.06/56.26 (^[X7: $i, Y10: $i] : rewrite(((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))) <=> ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))))),
% 56.06/56.26 inference(bind,[status(th)],[])).
% 56.06/56.26 tff(53,plain,
% 56.06/56.26 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 56.06/56.26 inference(quant_intro,[status(thm)],[52])).
% 56.06/56.26 tff(54,plain,
% 56.06/56.26 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 56.06/56.26 inference(transitivity,[status(thm)],[53, 51])).
% 56.06/56.26 tff(55,plain,
% 56.06/56.26 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 56.06/56.26 inference(rewrite,[status(thm)],[])).
% 56.06/56.26 tff(56,plain,
% 56.06/56.26 (^[X7: $i, Y10: $i] : rewrite((![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))) | (~r2(X7, Y10))) <=> ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))))),
% 56.06/56.26 inference(bind,[status(th)],[])).
% 56.06/56.26 tff(57,plain,
% 56.06/56.26 (![X7: $i, Y10: $i] : (![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 56.06/56.26 inference(quant_intro,[status(thm)],[56])).
% 56.06/56.26 tff(58,axiom,(![X7: $i, Y10: $i] : (![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))) | (~r2(X7, Y10)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax','axiom_7a')).
% 56.06/56.26 tff(59,plain,
% 56.06/56.26 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 56.06/56.26 inference(modus_ponens,[status(thm)],[58, 57])).
% 56.06/56.26 tff(60,plain,
% 56.06/56.26 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 56.06/56.26 inference(modus_ponens,[status(thm)],[59, 55])).
% 56.06/56.26 tff(61,plain,(
% 56.06/56.26 ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 56.06/56.26 inference(skolemize,[status(sab)],[60])).
% 56.06/56.26 tff(62,plain,
% 56.06/56.26 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 56.06/56.26 inference(modus_ponens,[status(thm)],[61, 54])).
% 56.06/56.26 tff(63,plain,
% 56.06/56.26 (((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y18_16(elem!24)))))) <=> ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | (~r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y18_16(elem!24)))))),
% 56.06/56.26 inference(rewrite,[status(thm)],[])).
% 56.06/56.26 tff(64,plain,
% 56.06/56.26 (((~r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))) | ![Y20: $i] : ((~id(Y20, tptp_fun_Y18_16(elem!24))) | (~r1(Y20)))) <=> ((~r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y18_16(elem!24)))))),
% 56.06/56.26 inference(rewrite,[status(thm)],[])).
% 56.06/56.26 tff(65,plain,
% 56.06/56.26 (((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))) | ![Y20: $i] : ((~id(Y20, tptp_fun_Y18_16(elem!24))) | (~r1(Y20))))) <=> ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y18_16(elem!24))))))),
% 56.06/56.26 inference(monotonicity,[status(thm)],[64])).
% 56.06/56.26 tff(66,plain,
% 56.06/56.26 (((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))) | ![Y20: $i] : ((~id(Y20, tptp_fun_Y18_16(elem!24))) | (~r1(Y20))))) <=> ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | (~r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y18_16(elem!24)))))),
% 56.06/56.26 inference(transitivity,[status(thm)],[65, 63])).
% 56.06/56.26 tff(67,plain,
% 56.06/56.26 ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))) | ![Y20: $i] : ((~id(Y20, tptp_fun_Y18_16(elem!24))) | (~r1(Y20))))),
% 56.06/56.26 inference(quant_inst,[status(thm)],[])).
% 56.06/56.26 tff(68,plain,
% 56.06/56.26 ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | (~r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y18_16(elem!24))))),
% 56.06/56.26 inference(modus_ponens,[status(thm)],[67, 66])).
% 56.06/56.26 tff(69,plain,
% 56.06/56.26 ($false),
% 56.06/56.26 inference(unit_resolution,[status(thm)],[68, 62, 49, 48])).
% 56.06/56.26 tff(70,plain,(~r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))), inference(lemma,lemma(discharge,[]))).
% 56.06/56.26 tff(71,plain,
% 56.06/56.26 (((~r2(elem!24, Y24!0)) | (~r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24)))) | r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))),
% 56.06/56.26 inference(tautology,[status(thm)],[])).
% 56.06/56.26 tff(72,plain,
% 56.06/56.26 ((~r2(elem!24, Y24!0)) | (~r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24)))),
% 56.06/56.26 inference(unit_resolution,[status(thm)],[71, 70])).
% 56.06/56.26 tff(73,plain,
% 56.06/56.26 ((r1(tptp_fun_Y18_16(elem!24)) | id(tptp_fun_Y18_16(elem!24), Y24!0)) | (~r1(tptp_fun_Y18_16(elem!24)))),
% 56.06/56.26 inference(tautology,[status(thm)],[])).
% 56.06/56.26 tff(74,plain,
% 56.06/56.26 (r1(tptp_fun_Y18_16(elem!24)) | id(tptp_fun_Y18_16(elem!24), Y24!0)),
% 56.06/56.26 inference(unit_resolution,[status(thm)],[73, 20])).
% 56.06/56.26 tff(75,plain,
% 56.06/56.26 (^[X19: $i] : refl(((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0)))) <=> ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0)))))),
% 56.06/56.26 inference(bind,[status(th)],[])).
% 56.06/56.26 tff(76,plain,
% 56.06/56.26 (![X19: $i] : ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0))))),
% 56.06/56.26 inference(quant_intro,[status(thm)],[75])).
% 56.06/56.26 tff(77,plain,
% 56.06/56.26 (^[X19: $i] : trans(monotonicity(rewrite((id(X19, Y24!0) & r1(X19)) <=> (~((~r1(X19)) | (~id(X19, Y24!0))))), rewrite(((~r1(X19)) & (~id(X19, Y24!0))) <=> (~(r1(X19) | id(X19, Y24!0)))), (((id(X19, Y24!0) & r1(X19)) | ((~r1(X19)) & (~id(X19, Y24!0)))) <=> ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0)))))), rewrite(((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0)))) <=> ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0))))), (((id(X19, Y24!0) & r1(X19)) | ((~r1(X19)) & (~id(X19, Y24!0)))) <=> ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0))))))),
% 56.06/56.26 inference(bind,[status(th)],[])).
% 56.06/56.26 tff(78,plain,
% 56.06/56.26 (![X19: $i] : ((id(X19, Y24!0) & r1(X19)) | ((~r1(X19)) & (~id(X19, Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0))))),
% 56.06/56.26 inference(quant_intro,[status(thm)],[77])).
% 56.06/56.26 tff(79,plain,
% 56.06/56.26 (?[Y24: $i] : ![X19: $i] : ((id(X19, Y24) & r1(X19)) | ((~r1(X19)) & (~id(X19, Y24)))) <=> ?[Y24: $i] : ![X19: $i] : ((id(X19, Y24) & r1(X19)) | ((~r1(X19)) & (~id(X19, Y24))))),
% 56.06/56.26 inference(rewrite,[status(thm)],[])).
% 56.06/56.26 tff(80,axiom,(?[Y24: $i] : ![X19: $i] : ((id(X19, Y24) & r1(X19)) | ((~r1(X19)) & (~id(X19, Y24))))), file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax','axiom_1')).
% 56.06/56.26 tff(81,plain,
% 56.06/56.26 (?[Y24: $i] : ![X19: $i] : ((id(X19, Y24) & r1(X19)) | ((~r1(X19)) & (~id(X19, Y24))))),
% 56.06/56.26 inference(modus_ponens,[status(thm)],[80, 79])).
% 56.06/56.26 tff(82,plain,(
% 56.06/56.26 $oeq(![X19: $i] : ((id(X19, Y24!0) & r1(X19)) | ((~r1(X19)) & (~id(X19, Y24!0)))), ![X19: $i] : ((id(X19, Y24!0) & r1(X19)) | ((~r1(X19)) & (~id(X19, Y24!0)))))),
% 56.06/56.26 inference(transitivity,[status(sab)],[81])).
% 56.06/56.26 tff(83,plain,
% 56.06/56.26 (![X19: $i] : ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0))))),
% 56.06/56.26 inference(modus_ponens,[status(thm)],[82, 78])).
% 56.06/56.26 tff(84,plain,
% 56.06/56.26 (![X19: $i] : ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0))))),
% 56.06/56.26 inference(modus_ponens,[status(thm)],[83, 76])).
% 56.06/56.26 tff(85,plain,
% 56.06/56.26 (((~![X19: $i] : ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0))))) | ((~((~r1(tptp_fun_Y18_16(elem!24))) | (~id(tptp_fun_Y18_16(elem!24), Y24!0)))) | (~(r1(tptp_fun_Y18_16(elem!24)) | id(tptp_fun_Y18_16(elem!24), Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0))))) | (~((~r1(tptp_fun_Y18_16(elem!24))) | (~id(tptp_fun_Y18_16(elem!24), Y24!0)))) | (~(r1(tptp_fun_Y18_16(elem!24)) | id(tptp_fun_Y18_16(elem!24), Y24!0))))),
% 56.06/56.26 inference(rewrite,[status(thm)],[])).
% 56.06/56.26 tff(86,plain,
% 56.06/56.26 ((~![X19: $i] : ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0))))) | ((~((~r1(tptp_fun_Y18_16(elem!24))) | (~id(tptp_fun_Y18_16(elem!24), Y24!0)))) | (~(r1(tptp_fun_Y18_16(elem!24)) | id(tptp_fun_Y18_16(elem!24), Y24!0))))),
% 56.06/56.26 inference(quant_inst,[status(thm)],[])).
% 56.06/56.26 tff(87,plain,
% 56.06/56.26 ((~![X19: $i] : ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0))))) | (~((~r1(tptp_fun_Y18_16(elem!24))) | (~id(tptp_fun_Y18_16(elem!24), Y24!0)))) | (~(r1(tptp_fun_Y18_16(elem!24)) | id(tptp_fun_Y18_16(elem!24), Y24!0)))),
% 56.06/56.26 inference(modus_ponens,[status(thm)],[86, 85])).
% 56.06/56.26 tff(88,plain,
% 56.06/56.26 (~((~r1(tptp_fun_Y18_16(elem!24))) | (~id(tptp_fun_Y18_16(elem!24), Y24!0)))),
% 56.06/56.26 inference(unit_resolution,[status(thm)],[87, 84, 74])).
% 56.06/56.26 tff(89,plain,
% 56.06/56.26 (((~r1(tptp_fun_Y18_16(elem!24))) | (~id(tptp_fun_Y18_16(elem!24), Y24!0))) | id(tptp_fun_Y18_16(elem!24), Y24!0)),
% 56.06/56.26 inference(tautology,[status(thm)],[])).
% 56.06/56.26 tff(90,plain,
% 56.06/56.26 (id(tptp_fun_Y18_16(elem!24), Y24!0)),
% 56.06/56.26 inference(unit_resolution,[status(thm)],[89, 88])).
% 56.06/56.26 tff(91,plain,
% 56.06/56.26 (^[X4: $i] : rewrite((id(tptp_fun_Y9_12(X4), X4) & r1(tptp_fun_Y16_13(X4)) & r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4))) <=> (~((~id(tptp_fun_Y9_12(X4), X4)) | (~r1(tptp_fun_Y16_13(X4))) | (~r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4))))))),
% 56.06/56.26 inference(bind,[status(th)],[])).
% 56.06/56.26 tff(92,plain,
% 56.06/56.26 (![X4: $i] : (id(tptp_fun_Y9_12(X4), X4) & r1(tptp_fun_Y16_13(X4)) & r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4))) <=> ![X4: $i] : (~((~id(tptp_fun_Y9_12(X4), X4)) | (~r1(tptp_fun_Y16_13(X4))) | (~r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4)))))),
% 56.06/56.26 inference(quant_intro,[status(thm)],[91])).
% 56.06/56.26 tff(93,plain,
% 56.06/56.26 (^[X4: $i] : rewrite((id(tptp_fun_Y9_12(X4), X4) & (r1(tptp_fun_Y16_13(X4)) & r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4)))) <=> (id(tptp_fun_Y9_12(X4), X4) & r1(tptp_fun_Y16_13(X4)) & r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4))))),
% 56.06/56.26 inference(bind,[status(th)],[])).
% 56.06/56.26 tff(94,plain,
% 56.06/56.26 (![X4: $i] : (id(tptp_fun_Y9_12(X4), X4) & (r1(tptp_fun_Y16_13(X4)) & r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4)))) <=> ![X4: $i] : (id(tptp_fun_Y9_12(X4), X4) & r1(tptp_fun_Y16_13(X4)) & r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4)))),
% 56.06/56.26 inference(quant_intro,[status(thm)],[93])).
% 56.06/56.26 tff(95,plain,
% 56.06/56.26 (![X4: $i] : ?[Y9: $i] : (id(Y9, X4) & ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9))) <=> ![X4: $i] : ?[Y9: $i] : (id(Y9, X4) & ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)))),
% 56.06/56.26 inference(rewrite,[status(thm)],[])).
% 56.06/56.26 tff(96,axiom,(![X4: $i] : ?[Y9: $i] : (id(Y9, X4) & ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax','axiom_4a')).
% 56.06/56.26 tff(97,plain,
% 56.06/56.26 (![X4: $i] : ?[Y9: $i] : (id(Y9, X4) & ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)))),
% 56.06/56.26 inference(modus_ponens,[status(thm)],[96, 95])).
% 56.06/56.26 tff(98,plain,(
% 56.06/56.26 ![X4: $i] : (id(tptp_fun_Y9_12(X4), X4) & (r1(tptp_fun_Y16_13(X4)) & r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4))))),
% 56.06/56.26 inference(skolemize,[status(sab)],[97])).
% 56.06/56.26 tff(99,plain,
% 56.06/56.26 (![X4: $i] : (id(tptp_fun_Y9_12(X4), X4) & r1(tptp_fun_Y16_13(X4)) & r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4)))),
% 56.06/56.26 inference(modus_ponens,[status(thm)],[98, 94])).
% 56.06/56.26 tff(100,plain,
% 56.06/56.26 (![X4: $i] : (~((~id(tptp_fun_Y9_12(X4), X4)) | (~r1(tptp_fun_Y16_13(X4))) | (~r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4)))))),
% 56.06/56.26 inference(modus_ponens,[status(thm)],[99, 92])).
% 56.06/56.26 tff(101,plain,
% 56.06/56.26 ((~![X4: $i] : (~((~id(tptp_fun_Y9_12(X4), X4)) | (~r1(tptp_fun_Y16_13(X4))) | (~r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4)))))) | (~((~id(tptp_fun_Y9_12(elem!24), elem!24)) | (~r1(tptp_fun_Y16_13(elem!24))) | (~r3(elem!24, tptp_fun_Y16_13(elem!24), tptp_fun_Y9_12(elem!24)))))),
% 56.06/56.26 inference(quant_inst,[status(thm)],[])).
% 56.06/56.26 tff(102,plain,
% 56.06/56.26 (~((~id(tptp_fun_Y9_12(elem!24), elem!24)) | (~r1(tptp_fun_Y16_13(elem!24))) | (~r3(elem!24, tptp_fun_Y16_13(elem!24), tptp_fun_Y9_12(elem!24))))),
% 56.06/56.26 inference(unit_resolution,[status(thm)],[101, 100])).
% 56.06/56.26 tff(103,plain,
% 56.06/56.26 (((~id(tptp_fun_Y9_12(elem!24), elem!24)) | (~r1(tptp_fun_Y16_13(elem!24))) | (~r3(elem!24, tptp_fun_Y16_13(elem!24), tptp_fun_Y9_12(elem!24)))) | id(tptp_fun_Y9_12(elem!24), elem!24)),
% 56.06/56.26 inference(tautology,[status(thm)],[])).
% 56.06/56.26 tff(104,plain,
% 56.06/56.26 (id(tptp_fun_Y9_12(elem!24), elem!24)),
% 56.06/56.26 inference(unit_resolution,[status(thm)],[103, 102])).
% 56.06/56.26 tff(105,plain,
% 56.06/56.26 (^[X28: $i, X29: $i, X30: $i, X31: $i] : refl(((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29)))) <=> ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29)))))),
% 56.06/56.26 inference(bind,[status(th)],[])).
% 56.06/56.26 tff(106,plain,
% 56.06/56.26 (![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29)))) <=> ![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))),
% 56.06/56.26 inference(quant_intro,[status(thm)],[105])).
% 56.06/56.26 tff(107,plain,
% 56.06/56.26 (^[X28: $i, X29: $i, X30: $i, X31: $i] : trans(monotonicity(rewrite((r2(X28, X29) & r2(X30, X31)) <=> (~((~r2(X30, X31)) | (~r2(X28, X29))))), rewrite(((~r2(X28, X29)) & (~r2(X30, X31))) <=> (~(r2(X30, X31) | r2(X28, X29)))), (((r2(X28, X29) & r2(X30, X31)) | ((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30))) <=> ((~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))) | (~id(X29, X31)) | (~id(X28, X30))))), rewrite(((~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))) | (~id(X29, X31)) | (~id(X28, X30))) <=> ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))), (((r2(X28, X29) & r2(X30, X31)) | ((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30))) <=> ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))))),
% 56.06/56.26 inference(bind,[status(th)],[])).
% 56.06/56.26 tff(108,plain,
% 56.06/56.26 (![X28: $i, X29: $i, X30: $i, X31: $i] : ((r2(X28, X29) & r2(X30, X31)) | ((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30))) <=> ![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))),
% 56.06/56.26 inference(quant_intro,[status(thm)],[107])).
% 56.06/56.26 tff(109,plain,
% 56.06/56.26 (![X28: $i, X29: $i, X30: $i, X31: $i] : ((r2(X28, X29) & r2(X30, X31)) | ((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30))) <=> ![X28: $i, X29: $i, X30: $i, X31: $i] : ((r2(X28, X29) & r2(X30, X31)) | ((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30)))),
% 56.06/56.26 inference(rewrite,[status(thm)],[])).
% 56.06/56.26 tff(110,plain,
% 56.06/56.26 (^[X28: $i, X29: $i, X30: $i, X31: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~id(X28, X30)) | (~id(X29, X31))) <=> ((~id(X29, X31)) | (~id(X28, X30)))), ((((~id(X28, X30)) | (~id(X29, X31))) | ((~r2(X28, X29)) & (~r2(X30, X31)))) <=> (((~id(X29, X31)) | (~id(X28, X30))) | ((~r2(X28, X29)) & (~r2(X30, X31)))))), rewrite((((~id(X29, X31)) | (~id(X28, X30))) | ((~r2(X28, X29)) & (~r2(X30, X31)))) <=> (((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30)))), ((((~id(X28, X30)) | (~id(X29, X31))) | ((~r2(X28, X29)) & (~r2(X30, X31)))) <=> (((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30))))), (((((~id(X28, X30)) | (~id(X29, X31))) | ((~r2(X28, X29)) & (~r2(X30, X31)))) | (r2(X28, X29) & r2(X30, X31))) <=> ((((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30))) | (r2(X28, X29) & r2(X30, X31))))), rewrite(((((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30))) | (r2(X28, X29) & r2(X30, X31))) <=> ((r2(X28, X29) & r2(X30, X31)) | ((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30)))), (((((~id(X28, X30)) | (~id(X29, X31))) | ((~r2(X28, X29)) & (~r2(X30, X31)))) | (r2(X28, X29) & r2(X30, X31))) <=> ((r2(X28, X29) & r2(X30, X31)) | ((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30)))))),
% 56.06/56.26 inference(bind,[status(th)],[])).
% 56.06/56.26 tff(111,plain,
% 56.06/56.26 (![X28: $i, X29: $i, X30: $i, X31: $i] : ((((~id(X28, X30)) | (~id(X29, X31))) | ((~r2(X28, X29)) & (~r2(X30, X31)))) | (r2(X28, X29) & r2(X30, X31))) <=> ![X28: $i, X29: $i, X30: $i, X31: $i] : ((r2(X28, X29) & r2(X30, X31)) | ((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30)))),
% 56.06/56.26 inference(quant_intro,[status(thm)],[110])).
% 56.06/56.26 tff(112,axiom,(![X28: $i, X29: $i, X30: $i, X31: $i] : ((((~id(X28, X30)) | (~id(X29, X31))) | ((~r2(X28, X29)) & (~r2(X30, X31)))) | (r2(X28, X29) & r2(X30, X31)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax','axiom_9')).
% 56.06/56.26 tff(113,plain,
% 56.06/56.26 (![X28: $i, X29: $i, X30: $i, X31: $i] : ((r2(X28, X29) & r2(X30, X31)) | ((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30)))),
% 56.06/56.26 inference(modus_ponens,[status(thm)],[112, 111])).
% 56.06/56.26 tff(114,plain,
% 56.06/56.26 (![X28: $i, X29: $i, X30: $i, X31: $i] : ((r2(X28, X29) & r2(X30, X31)) | ((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30)))),
% 56.06/56.26 inference(modus_ponens,[status(thm)],[113, 109])).
% 56.06/56.26 tff(115,plain,(
% 56.06/56.26 ![X28: $i, X29: $i, X30: $i, X31: $i] : ((r2(X28, X29) & r2(X30, X31)) | ((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30)))),
% 56.06/56.26 inference(skolemize,[status(sab)],[114])).
% 56.06/56.26 tff(116,plain,
% 56.06/56.26 (![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))),
% 56.06/56.26 inference(modus_ponens,[status(thm)],[115, 108])).
% 56.06/56.26 tff(117,plain,
% 56.06/56.26 (![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))),
% 56.06/56.26 inference(modus_ponens,[status(thm)],[116, 106])).
% 56.06/56.26 tff(118,plain,
% 56.06/56.26 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y9_12(elem!24), elem!24)) | (~id(tptp_fun_Y18_16(elem!24), Y24!0)) | (~((~r2(elem!24, Y24!0)) | (~r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))))) | (~(r2(elem!24, Y24!0) | r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24)))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(tptp_fun_Y9_12(elem!24), elem!24)) | (~id(tptp_fun_Y18_16(elem!24), Y24!0)) | (~((~r2(elem!24, Y24!0)) | (~r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))))) | (~(r2(elem!24, Y24!0) | r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24)))))),
% 56.06/56.26 inference(rewrite,[status(thm)],[])).
% 56.06/56.26 tff(119,plain,
% 56.06/56.27 (((~id(tptp_fun_Y18_16(elem!24), Y24!0)) | (~id(tptp_fun_Y9_12(elem!24), elem!24)) | (~((~r2(elem!24, Y24!0)) | (~r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))))) | (~(r2(elem!24, Y24!0) | r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))))) <=> ((~id(tptp_fun_Y9_12(elem!24), elem!24)) | (~id(tptp_fun_Y18_16(elem!24), Y24!0)) | (~((~r2(elem!24, Y24!0)) | (~r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))))) | (~(r2(elem!24, Y24!0) | r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24)))))),
% 56.06/56.27 inference(rewrite,[status(thm)],[])).
% 56.06/56.27 tff(120,plain,
% 56.06/56.27 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y18_16(elem!24), Y24!0)) | (~id(tptp_fun_Y9_12(elem!24), elem!24)) | (~((~r2(elem!24, Y24!0)) | (~r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))))) | (~(r2(elem!24, Y24!0) | r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24)))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y9_12(elem!24), elem!24)) | (~id(tptp_fun_Y18_16(elem!24), Y24!0)) | (~((~r2(elem!24, Y24!0)) | (~r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))))) | (~(r2(elem!24, Y24!0) | r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))))))),
% 56.06/56.27 inference(monotonicity,[status(thm)],[119])).
% 56.06/56.27 tff(121,plain,
% 56.06/56.27 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y18_16(elem!24), Y24!0)) | (~id(tptp_fun_Y9_12(elem!24), elem!24)) | (~((~r2(elem!24, Y24!0)) | (~r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))))) | (~(r2(elem!24, Y24!0) | r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24)))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(tptp_fun_Y9_12(elem!24), elem!24)) | (~id(tptp_fun_Y18_16(elem!24), Y24!0)) | (~((~r2(elem!24, Y24!0)) | (~r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))))) | (~(r2(elem!24, Y24!0) | r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24)))))),
% 56.06/56.27 inference(transitivity,[status(thm)],[120, 118])).
% 56.06/56.27 tff(122,plain,
% 56.06/56.27 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y18_16(elem!24), Y24!0)) | (~id(tptp_fun_Y9_12(elem!24), elem!24)) | (~((~r2(elem!24, Y24!0)) | (~r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))))) | (~(r2(elem!24, Y24!0) | r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24)))))),
% 56.06/56.27 inference(quant_inst,[status(thm)],[])).
% 56.06/56.27 tff(123,plain,
% 56.06/56.27 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(tptp_fun_Y9_12(elem!24), elem!24)) | (~id(tptp_fun_Y18_16(elem!24), Y24!0)) | (~((~r2(elem!24, Y24!0)) | (~r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))))) | (~(r2(elem!24, Y24!0) | r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))))),
% 56.06/56.27 inference(modus_ponens,[status(thm)],[122, 121])).
% 56.06/56.27 tff(124,plain,
% 56.06/56.27 ((~((~r2(elem!24, Y24!0)) | (~r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))))) | (~(r2(elem!24, Y24!0) | r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))))),
% 56.06/56.27 inference(unit_resolution,[status(thm)],[123, 117, 104, 90])).
% 56.06/56.27 tff(125,plain,
% 56.06/56.27 (~(r2(elem!24, Y24!0) | r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24)))),
% 56.06/56.27 inference(unit_resolution,[status(thm)],[124, 72])).
% 56.06/56.27 tff(126,plain,
% 56.06/56.27 ((r2(elem!24, Y24!0) | r2(tptp_fun_Y9_12(elem!24), tptp_fun_Y18_16(elem!24))) | (~r2(elem!24, Y24!0))),
% 56.06/56.27 inference(tautology,[status(thm)],[])).
% 56.06/56.27 tff(127,plain,
% 56.06/56.27 (~r2(elem!24, Y24!0)),
% 56.06/56.27 inference(unit_resolution,[status(thm)],[126, 125])).
% 56.06/56.27 tff(128,plain,
% 56.06/56.27 (((~r2(elem!24, Y24!0)) | (~id(Y24!0, tptp_fun_Y21_1(elem!24)))) | r2(elem!24, Y24!0)),
% 56.06/56.27 inference(tautology,[status(thm)],[])).
% 56.06/56.27 tff(129,plain,
% 56.06/56.27 ((~r2(elem!24, Y24!0)) | (~id(Y24!0, tptp_fun_Y21_1(elem!24)))),
% 56.06/56.27 inference(unit_resolution,[status(thm)],[128, 127])).
% 56.06/56.27 tff(130,plain,
% 56.06/56.27 (^[X11: $i, X12: $i] : refl(((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11))))) <=> ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11))))))),
% 56.06/56.27 inference(bind,[status(th)],[])).
% 56.06/56.27 tff(131,plain,
% 56.06/56.27 (![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11))))) <=> ![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))),
% 56.06/56.27 inference(quant_intro,[status(thm)],[130])).
% 56.06/56.27 tff(132,plain,
% 56.06/56.27 (^[X11: $i, X12: $i] : trans(monotonicity(rewrite((id(X12, tptp_fun_Y21_1(X11)) & r2(X11, X12)) <=> (~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11)))))), rewrite(((~r2(X11, X12)) & (~id(X12, tptp_fun_Y21_1(X11)))) <=> (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11))))), (((id(X12, tptp_fun_Y21_1(X11)) & r2(X11, X12)) | ((~r2(X11, X12)) & (~id(X12, tptp_fun_Y21_1(X11))))) <=> ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11))))))), rewrite(((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11))))) <=> ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))), (((id(X12, tptp_fun_Y21_1(X11)) & r2(X11, X12)) | ((~r2(X11, X12)) & (~id(X12, tptp_fun_Y21_1(X11))))) <=> ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))))),
% 56.06/56.27 inference(bind,[status(th)],[])).
% 56.06/56.27 tff(133,plain,
% 56.06/56.27 (![X11: $i, X12: $i] : ((id(X12, tptp_fun_Y21_1(X11)) & r2(X11, X12)) | ((~r2(X11, X12)) & (~id(X12, tptp_fun_Y21_1(X11))))) <=> ![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))),
% 56.06/56.27 inference(quant_intro,[status(thm)],[132])).
% 56.06/56.27 tff(134,plain,
% 56.06/56.27 (![X11: $i] : ![X12: $i] : ((id(X12, tptp_fun_Y21_1(X11)) & r2(X11, X12)) | ((~r2(X11, X12)) & (~id(X12, tptp_fun_Y21_1(X11))))) <=> ![X11: $i, X12: $i] : ((id(X12, tptp_fun_Y21_1(X11)) & r2(X11, X12)) | ((~r2(X11, X12)) & (~id(X12, tptp_fun_Y21_1(X11)))))),
% 56.06/56.27 inference(pull_quant,[status(thm)],[])).
% 56.06/56.27 tff(135,plain,
% 56.06/56.27 (![X11: $i] : ?[Y21: $i] : ![X12: $i] : ((id(X12, Y21) & r2(X11, X12)) | ((~r2(X11, X12)) & (~id(X12, Y21)))) <=> ![X11: $i] : ?[Y21: $i] : ![X12: $i] : ((id(X12, Y21) & r2(X11, X12)) | ((~r2(X11, X12)) & (~id(X12, Y21))))),
% 56.06/56.27 inference(rewrite,[status(thm)],[])).
% 56.06/56.27 tff(136,axiom,(![X11: $i] : ?[Y21: $i] : ![X12: $i] : ((id(X12, Y21) & r2(X11, X12)) | ((~r2(X11, X12)) & (~id(X12, Y21))))), file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax','axiom_2')).
% 56.06/56.27 tff(137,plain,
% 56.06/56.27 (![X11: $i] : ?[Y21: $i] : ![X12: $i] : ((id(X12, Y21) & r2(X11, X12)) | ((~r2(X11, X12)) & (~id(X12, Y21))))),
% 56.06/56.27 inference(modus_ponens,[status(thm)],[136, 135])).
% 56.06/56.27 tff(138,plain,(
% 56.06/56.27 ![X11: $i] : ![X12: $i] : ((id(X12, tptp_fun_Y21_1(X11)) & r2(X11, X12)) | ((~r2(X11, X12)) & (~id(X12, tptp_fun_Y21_1(X11)))))),
% 56.06/56.27 inference(skolemize,[status(sab)],[137])).
% 56.06/56.27 tff(139,plain,
% 56.06/56.27 (![X11: $i, X12: $i] : ((id(X12, tptp_fun_Y21_1(X11)) & r2(X11, X12)) | ((~r2(X11, X12)) & (~id(X12, tptp_fun_Y21_1(X11)))))),
% 56.06/56.27 inference(modus_ponens,[status(thm)],[138, 134])).
% 56.06/56.27 tff(140,plain,
% 56.06/56.27 (![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))),
% 56.06/56.27 inference(modus_ponens,[status(thm)],[139, 133])).
% 56.06/56.27 tff(141,plain,
% 56.06/56.27 (![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))),
% 56.06/56.27 inference(modus_ponens,[status(thm)],[140, 131])).
% 56.06/56.27 tff(142,plain,
% 56.06/56.27 (((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | ((~((~r2(elem!24, Y24!0)) | (~id(Y24!0, tptp_fun_Y21_1(elem!24))))) | (~(r2(elem!24, Y24!0) | id(Y24!0, tptp_fun_Y21_1(elem!24)))))) <=> ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | (~((~r2(elem!24, Y24!0)) | (~id(Y24!0, tptp_fun_Y21_1(elem!24))))) | (~(r2(elem!24, Y24!0) | id(Y24!0, tptp_fun_Y21_1(elem!24)))))),
% 56.06/56.27 inference(rewrite,[status(thm)],[])).
% 56.06/56.27 tff(143,plain,
% 56.06/56.27 ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | ((~((~r2(elem!24, Y24!0)) | (~id(Y24!0, tptp_fun_Y21_1(elem!24))))) | (~(r2(elem!24, Y24!0) | id(Y24!0, tptp_fun_Y21_1(elem!24)))))),
% 56.06/56.27 inference(quant_inst,[status(thm)],[])).
% 56.06/56.27 tff(144,plain,
% 56.06/56.27 ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | (~((~r2(elem!24, Y24!0)) | (~id(Y24!0, tptp_fun_Y21_1(elem!24))))) | (~(r2(elem!24, Y24!0) | id(Y24!0, tptp_fun_Y21_1(elem!24))))),
% 56.06/56.27 inference(modus_ponens,[status(thm)],[143, 142])).
% 56.06/56.27 tff(145,plain,
% 56.06/56.27 (~(r2(elem!24, Y24!0) | id(Y24!0, tptp_fun_Y21_1(elem!24)))),
% 56.06/56.27 inference(unit_resolution,[status(thm)],[144, 141, 129])).
% 56.06/56.27 tff(146,plain,
% 56.06/56.27 ((r2(elem!24, Y24!0) | id(Y24!0, tptp_fun_Y21_1(elem!24))) | (~id(Y24!0, tptp_fun_Y21_1(elem!24)))),
% 56.06/56.27 inference(tautology,[status(thm)],[])).
% 56.06/56.27 tff(147,plain,
% 56.06/56.27 (~id(Y24!0, tptp_fun_Y21_1(elem!24))),
% 56.06/56.27 inference(unit_resolution,[status(thm)],[146, 145])).
% 56.06/56.27 tff(148,plain,
% 56.06/56.27 (^[X21: $i, X22: $i] : refl(((~id(X21, X22)) | id(X22, X21)) <=> ((~id(X21, X22)) | id(X22, X21)))),
% 56.06/56.27 inference(bind,[status(th)],[])).
% 56.06/56.27 tff(149,plain,
% 56.06/56.27 (![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21)) <=> ![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))),
% 56.06/56.27 inference(quant_intro,[status(thm)],[148])).
% 56.06/56.27 tff(150,plain,
% 56.06/56.27 (![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21)) <=> ![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))),
% 56.06/56.27 inference(rewrite,[status(thm)],[])).
% 56.06/56.27 tff(151,axiom,(![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))), file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax','axiom_6')).
% 56.06/56.27 tff(152,plain,
% 56.06/56.27 (![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))),
% 56.06/56.27 inference(modus_ponens,[status(thm)],[151, 150])).
% 56.06/56.27 tff(153,plain,(
% 56.06/56.27 ![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))),
% 56.06/56.27 inference(skolemize,[status(sab)],[152])).
% 56.06/56.27 tff(154,plain,
% 56.06/56.27 (![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))),
% 56.06/56.27 inference(modus_ponens,[status(thm)],[153, 149])).
% 56.06/56.27 tff(155,plain,
% 56.06/56.27 (((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | ((~id(tptp_fun_Y21_1(elem!24), Y24!0)) | id(Y24!0, tptp_fun_Y21_1(elem!24)))) <=> ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | (~id(tptp_fun_Y21_1(elem!24), Y24!0)) | id(Y24!0, tptp_fun_Y21_1(elem!24)))),
% 56.06/56.27 inference(rewrite,[status(thm)],[])).
% 56.06/56.27 tff(156,plain,
% 56.06/56.27 ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | ((~id(tptp_fun_Y21_1(elem!24), Y24!0)) | id(Y24!0, tptp_fun_Y21_1(elem!24)))),
% 56.06/56.27 inference(quant_inst,[status(thm)],[])).
% 56.06/56.27 tff(157,plain,
% 56.06/56.27 ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | (~id(tptp_fun_Y21_1(elem!24), Y24!0)) | id(Y24!0, tptp_fun_Y21_1(elem!24))),
% 56.06/56.27 inference(modus_ponens,[status(thm)],[156, 155])).
% 56.06/56.27 tff(158,plain,
% 56.06/56.27 (~id(tptp_fun_Y21_1(elem!24), Y24!0)),
% 56.06/56.27 inference(unit_resolution,[status(thm)],[157, 154, 147])).
% 56.06/56.27 tff(159,plain,
% 56.06/56.27 (((~r1(tptp_fun_Y21_1(elem!24))) | (~id(tptp_fun_Y21_1(elem!24), Y24!0))) | id(tptp_fun_Y21_1(elem!24), Y24!0)),
% 56.06/56.27 inference(tautology,[status(thm)],[])).
% 56.06/56.27 tff(160,plain,
% 56.06/56.27 ((~r1(tptp_fun_Y21_1(elem!24))) | (~id(tptp_fun_Y21_1(elem!24), Y24!0))),
% 56.06/56.27 inference(unit_resolution,[status(thm)],[159, 158])).
% 56.06/56.27 tff(161,plain,
% 56.06/56.27 (((~![X19: $i] : ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0))))) | ((~((~r1(tptp_fun_Y21_1(elem!24))) | (~id(tptp_fun_Y21_1(elem!24), Y24!0)))) | (~(r1(tptp_fun_Y21_1(elem!24)) | id(tptp_fun_Y21_1(elem!24), Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0))))) | (~((~r1(tptp_fun_Y21_1(elem!24))) | (~id(tptp_fun_Y21_1(elem!24), Y24!0)))) | (~(r1(tptp_fun_Y21_1(elem!24)) | id(tptp_fun_Y21_1(elem!24), Y24!0))))),
% 56.06/56.27 inference(rewrite,[status(thm)],[])).
% 56.06/56.27 tff(162,plain,
% 56.06/56.27 ((~![X19: $i] : ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0))))) | ((~((~r1(tptp_fun_Y21_1(elem!24))) | (~id(tptp_fun_Y21_1(elem!24), Y24!0)))) | (~(r1(tptp_fun_Y21_1(elem!24)) | id(tptp_fun_Y21_1(elem!24), Y24!0))))),
% 56.06/56.27 inference(quant_inst,[status(thm)],[])).
% 56.06/56.27 tff(163,plain,
% 56.06/56.27 ((~![X19: $i] : ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0))))) | (~((~r1(tptp_fun_Y21_1(elem!24))) | (~id(tptp_fun_Y21_1(elem!24), Y24!0)))) | (~(r1(tptp_fun_Y21_1(elem!24)) | id(tptp_fun_Y21_1(elem!24), Y24!0)))),
% 56.06/56.27 inference(modus_ponens,[status(thm)],[162, 161])).
% 56.06/56.27 tff(164,plain,
% 56.06/56.27 (~(r1(tptp_fun_Y21_1(elem!24)) | id(tptp_fun_Y21_1(elem!24), Y24!0))),
% 56.06/56.27 inference(unit_resolution,[status(thm)],[163, 84, 160])).
% 56.06/56.27 tff(165,plain,
% 56.06/56.27 ((r1(tptp_fun_Y21_1(elem!24)) | id(tptp_fun_Y21_1(elem!24), Y24!0)) | (~r1(tptp_fun_Y21_1(elem!24)))),
% 56.06/56.27 inference(tautology,[status(thm)],[])).
% 56.06/56.27 tff(166,plain,
% 56.06/56.27 (~r1(tptp_fun_Y21_1(elem!24))),
% 56.06/56.27 inference(unit_resolution,[status(thm)],[165, 164])).
% 56.06/56.27 tff(167,plain,
% 56.06/56.27 (((~r1(tptp_fun_Y21_1(elem!24))) | (~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24))))) | r1(tptp_fun_Y21_1(elem!24))),
% 56.06/56.27 inference(tautology,[status(thm)],[])).
% 56.06/56.27 tff(168,plain,
% 56.06/56.27 ((~r1(tptp_fun_Y21_1(elem!24))) | (~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24))))),
% 56.06/56.27 inference(unit_resolution,[status(thm)],[167, 166])).
% 56.06/56.27 tff(169,plain,
% 56.06/56.27 (((~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24))))) | id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))),
% 56.06/56.27 inference(tautology,[status(thm)],[])).
% 56.06/56.27 tff(170,plain,
% 56.06/56.27 (id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))),
% 56.06/56.27 inference(unit_resolution,[status(thm)],[169, 1])).
% 56.06/56.27 tff(171,plain,
% 56.06/56.27 (((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~((~r1(tptp_fun_Y21_1(elem!24))) | (~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))))) | (~(r1(tptp_fun_Y21_1(elem!24)) | r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24))))))) <=> ((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~((~r1(tptp_fun_Y21_1(elem!24))) | (~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))))) | (~(r1(tptp_fun_Y21_1(elem!24)) | r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.27 inference(rewrite,[status(thm)],[])).
% 56.06/56.27 tff(172,plain,
% 56.06/56.27 (((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~((~r1(tptp_fun_Y21_1(elem!24))) | (~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))))) | (~(r1(tptp_fun_Y21_1(elem!24)) | r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))))) <=> ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~((~r1(tptp_fun_Y21_1(elem!24))) | (~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))))) | (~(r1(tptp_fun_Y21_1(elem!24)) | r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.27 inference(rewrite,[status(thm)],[])).
% 56.06/56.27 tff(173,plain,
% 56.06/56.27 ((~(r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24))) | r1(tptp_fun_Y21_1(elem!24)))) <=> (~(r1(tptp_fun_Y21_1(elem!24)) | r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))))),
% 56.06/56.27 inference(rewrite,[status(thm)],[])).
% 56.06/56.27 tff(174,plain,
% 56.06/56.27 ((~((~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~r1(tptp_fun_Y21_1(elem!24))))) <=> (~((~r1(tptp_fun_Y21_1(elem!24))) | (~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.27 inference(rewrite,[status(thm)],[])).
% 56.06/56.27 tff(175,plain,
% 56.06/56.27 (((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~((~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~r1(tptp_fun_Y21_1(elem!24))))) | (~(r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24))) | r1(tptp_fun_Y21_1(elem!24))))) <=> ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~((~r1(tptp_fun_Y21_1(elem!24))) | (~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))))) | (~(r1(tptp_fun_Y21_1(elem!24)) | r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.27 inference(monotonicity,[status(thm)],[174, 173])).
% 56.06/56.27 tff(176,plain,
% 56.06/56.27 (((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~((~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~r1(tptp_fun_Y21_1(elem!24))))) | (~(r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24))) | r1(tptp_fun_Y21_1(elem!24))))) <=> ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~((~r1(tptp_fun_Y21_1(elem!24))) | (~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))))) | (~(r1(tptp_fun_Y21_1(elem!24)) | r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.27 inference(transitivity,[status(thm)],[175, 172])).
% 56.06/56.27 tff(177,plain,
% 56.06/56.27 (((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~((~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~r1(tptp_fun_Y21_1(elem!24))))) | (~(r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24))) | r1(tptp_fun_Y21_1(elem!24)))))) <=> ((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~((~r1(tptp_fun_Y21_1(elem!24))) | (~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))))) | (~(r1(tptp_fun_Y21_1(elem!24)) | r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))))))),
% 56.06/56.27 inference(monotonicity,[status(thm)],[176])).
% 56.06/56.27 tff(178,plain,
% 56.06/56.27 (((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~((~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~r1(tptp_fun_Y21_1(elem!24))))) | (~(r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24))) | r1(tptp_fun_Y21_1(elem!24)))))) <=> ((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~((~r1(tptp_fun_Y21_1(elem!24))) | (~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))))) | (~(r1(tptp_fun_Y21_1(elem!24)) | r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.27 inference(transitivity,[status(thm)],[177, 171])).
% 56.06/56.27 tff(179,plain,
% 56.06/56.27 ((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~((~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~r1(tptp_fun_Y21_1(elem!24))))) | (~(r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24))) | r1(tptp_fun_Y21_1(elem!24)))))),
% 56.06/56.27 inference(quant_inst,[status(thm)],[])).
% 56.06/56.27 tff(180,plain,
% 56.06/56.27 ((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~((~r1(tptp_fun_Y21_1(elem!24))) | (~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))))) | (~(r1(tptp_fun_Y21_1(elem!24)) | r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))))),
% 56.06/56.27 inference(modus_ponens,[status(thm)],[179, 178])).
% 56.06/56.27 tff(181,plain,
% 56.06/56.27 ($false),
% 56.06/56.27 inference(unit_resolution,[status(thm)],[180, 37, 170, 168, 5])).
% 56.06/56.27 tff(182,plain,((~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24))))), inference(lemma,lemma(discharge,[]))).
% 56.06/56.27 tff(183,plain,
% 56.06/56.27 (^[Y1: $i] : rewrite(((~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1))))) | (id(Y1, tptp_fun_Y2_20(Y1)) & r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) <=> ((~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1))))) | (~((~id(Y1, tptp_fun_Y2_20(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1)))))))),
% 56.06/56.27 inference(bind,[status(th)],[])).
% 56.06/56.27 tff(184,plain,
% 56.06/56.27 (![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1))))) | (id(Y1, tptp_fun_Y2_20(Y1)) & r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) <=> ![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1))))) | (~((~id(Y1, tptp_fun_Y2_20(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))),
% 56.06/56.27 inference(quant_intro,[status(thm)],[183])).
% 56.06/56.27 tff(185,plain,
% 56.06/56.27 (^[Y1: $i] : trans(monotonicity(rewrite((id(Y1, tptp_fun_Y2_20(Y1)) & (r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) <=> (id(Y1, tptp_fun_Y2_20(Y1)) & r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))), (((id(Y1, tptp_fun_Y2_20(Y1)) & (r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | (~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1)))))) <=> ((id(Y1, tptp_fun_Y2_20(Y1)) & r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1)))))) | (~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1)))))))), rewrite(((id(Y1, tptp_fun_Y2_20(Y1)) & r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1)))))) | (~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1)))))) <=> ((~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1))))) | (id(Y1, tptp_fun_Y2_20(Y1)) & r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1)))))))), (((id(Y1, tptp_fun_Y2_20(Y1)) & (r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | (~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1)))))) <=> ((~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1))))) | (id(Y1, tptp_fun_Y2_20(Y1)) & r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1)))))))))),
% 56.06/56.27 inference(bind,[status(th)],[])).
% 56.06/56.27 tff(186,plain,
% 56.06/56.27 (![Y1: $i] : ((id(Y1, tptp_fun_Y2_20(Y1)) & (r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | (~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1)))))) <=> ![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1))))) | (id(Y1, tptp_fun_Y2_20(Y1)) & r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1)))))))),
% 56.06/56.27 inference(quant_intro,[status(thm)],[185])).
% 56.06/56.27 tff(187,plain,
% 56.06/56.27 ((~?[Y1: $i] : (![Y2: $i] : ((~id(Y1, Y2)) | ![Y3: $i] : ((~r2(Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) & ![Y5: $i] : ((~r1(Y5)) | (~id(Y1, Y5))))) <=> (~?[Y1: $i] : (![Y2: $i] : ((~id(Y1, Y2)) | ![Y3: $i] : ((~r2(Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) & ![Y5: $i] : ((~r1(Y5)) | (~id(Y1, Y5)))))),
% 56.06/56.27 inference(rewrite,[status(thm)],[])).
% 56.06/56.27 tff(188,plain,
% 56.06/56.27 ((~?[Y1: $i] : (![Y2: $i] : (![Y3: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))) | (~r2(Y3, Y2))) | (~id(Y1, Y2))) & ![Y5: $i] : ((~id(Y1, Y5)) | (~r1(Y5))))) <=> (~?[Y1: $i] : (![Y2: $i] : ((~id(Y1, Y2)) | ![Y3: $i] : ((~r2(Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) & ![Y5: $i] : ((~r1(Y5)) | (~id(Y1, Y5)))))),
% 56.06/56.27 inference(rewrite,[status(thm)],[])).
% 56.06/56.27 tff(189,axiom,(~?[Y1: $i] : (![Y2: $i] : (![Y3: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))) | (~r2(Y3, Y2))) | (~id(Y1, Y2))) & ![Y5: $i] : ((~id(Y1, Y5)) | (~r1(Y5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','nonzerononetwoexistid')).
% 56.06/56.27 tff(190,plain,
% 56.06/56.27 (~?[Y1: $i] : (![Y2: $i] : ((~id(Y1, Y2)) | ![Y3: $i] : ((~r2(Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) & ![Y5: $i] : ((~r1(Y5)) | (~id(Y1, Y5))))),
% 56.06/56.27 inference(modus_ponens,[status(thm)],[189, 188])).
% 56.06/56.27 tff(191,plain,
% 56.06/56.27 (~?[Y1: $i] : (![Y2: $i] : ((~id(Y1, Y2)) | ![Y3: $i] : ((~r2(Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) & ![Y5: $i] : ((~r1(Y5)) | (~id(Y1, Y5))))),
% 56.06/56.27 inference(modus_ponens,[status(thm)],[190, 187])).
% 56.06/56.27 tff(192,plain,
% 56.06/56.27 (~?[Y1: $i] : (![Y2: $i] : ((~id(Y1, Y2)) | ![Y3: $i] : ((~r2(Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) & ![Y5: $i] : ((~r1(Y5)) | (~id(Y1, Y5))))),
% 56.06/56.27 inference(modus_ponens,[status(thm)],[191, 187])).
% 56.06/56.27 tff(193,plain,
% 56.06/56.27 (~?[Y1: $i] : (![Y2: $i] : ((~id(Y1, Y2)) | ![Y3: $i] : ((~r2(Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) & ![Y5: $i] : ((~r1(Y5)) | (~id(Y1, Y5))))),
% 56.06/56.27 inference(modus_ponens,[status(thm)],[192, 187])).
% 56.06/56.27 tff(194,plain,
% 56.06/56.27 (^[Y1: $i] : nnf_neg(trans(sk($oeq((~![Y2: $i] : ((~id(Y1, Y2)) | ![Y3: $i] : ((~r2(Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)))))), (~((~id(Y1, tptp_fun_Y2_20(Y1))) | ![Y3: $i] : ((~r2(Y3, tptp_fun_Y2_20(Y1))) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)))))))), nnf_neg(refl($oeq(id(Y1, tptp_fun_Y2_20(Y1)), id(Y1, tptp_fun_Y2_20(Y1)))), trans(sk($oeq((~![Y3: $i] : ((~r2(Y3, tptp_fun_Y2_20(Y1))) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))), (~((~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, tptp_fun_Y3_21(Y1)))))))), nnf_neg(refl($oeq(r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)), r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))), sk($oeq((~![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, tptp_fun_Y3_21(Y1))))), (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))), $oeq((~((~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, tptp_fun_Y3_21(Y1)))))), (r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1)))))))), $oeq((~![Y3: $i] : ((~r2(Y3, tptp_fun_Y2_20(Y1))) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))), (r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1)))))))), $oeq((~((~id(Y1, tptp_fun_Y2_20(Y1))) | ![Y3: $i] : ((~r2(Y3, tptp_fun_Y2_20(Y1))) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)))))), (id(Y1, tptp_fun_Y2_20(Y1)) & (r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))))), $oeq((~![Y2: $i] : ((~id(Y1, Y2)) | ![Y3: $i] : ((~r2(Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)))))), (id(Y1, tptp_fun_Y2_20(Y1)) & (r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))))), sk($oeq((~![Y5: $i] : ((~r1(Y5)) | (~id(Y1, Y5)))), (~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1))))))), $oeq((~(![Y2: $i] : ((~id(Y1, Y2)) | ![Y3: $i] : ((~r2(Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) & ![Y5: $i] : ((~r1(Y5)) | (~id(Y1, Y5))))), ((id(Y1, tptp_fun_Y2_20(Y1)) & (r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | (~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1))))))))),
% 56.06/56.27 inference(bind,[status(th)],[])).
% 56.06/56.27 tff(195,plain,(
% 56.06/56.27 ![Y1: $i] : ((id(Y1, tptp_fun_Y2_20(Y1)) & (r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | (~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1))))))),
% 56.06/56.27 inference(nnf-neg,[status(sab)],[193, 194])).
% 56.06/56.27 tff(196,plain,
% 56.06/56.27 (![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1))))) | (id(Y1, tptp_fun_Y2_20(Y1)) & r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1)))))))),
% 56.06/56.27 inference(modus_ponens,[status(thm)],[195, 186])).
% 56.06/56.27 tff(197,plain,
% 56.06/56.27 (![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1))))) | (~((~id(Y1, tptp_fun_Y2_20(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))),
% 56.06/56.27 inference(modus_ponens,[status(thm)],[196, 184])).
% 56.06/56.27 tff(198,plain,
% 56.06/56.27 (((~![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1))))) | (~((~id(Y1, tptp_fun_Y2_20(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | ((~((~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))))) <=> ((~![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1))))) | (~((~id(Y1, tptp_fun_Y2_20(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | (~((~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))))),
% 56.06/56.27 inference(rewrite,[status(thm)],[])).
% 56.06/56.27 tff(199,plain,
% 56.06/56.27 (((~((~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))))) | (~((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))) <=> ((~((~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))))),
% 56.06/56.27 inference(rewrite,[status(thm)],[])).
% 56.06/56.27 tff(200,plain,
% 56.06/56.27 (((~![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1))))) | (~((~id(Y1, tptp_fun_Y2_20(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | ((~((~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))))) | (~((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))))) <=> ((~![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1))))) | (~((~id(Y1, tptp_fun_Y2_20(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | ((~((~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))))),
% 56.06/56.27 inference(monotonicity,[status(thm)],[199])).
% 56.06/56.27 tff(201,plain,
% 56.06/56.27 (((~![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1))))) | (~((~id(Y1, tptp_fun_Y2_20(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | ((~((~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))))) | (~((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))))) <=> ((~![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1))))) | (~((~id(Y1, tptp_fun_Y2_20(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | (~((~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))))),
% 56.06/56.27 inference(transitivity,[status(thm)],[200, 198])).
% 56.06/56.27 tff(202,plain,
% 56.06/56.27 ((~![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1))))) | (~((~id(Y1, tptp_fun_Y2_20(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | ((~((~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))))) | (~((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))))),
% 56.06/56.27 inference(quant_inst,[status(thm)],[])).
% 56.06/56.27 tff(203,plain,
% 56.06/56.27 ((~![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1))))) | (~((~id(Y1, tptp_fun_Y2_20(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | (~((~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.27 inference(modus_ponens,[status(thm)],[202, 201])).
% 56.06/56.27 tff(204,plain,
% 56.06/56.27 ((~((~r1(tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y5_23(tptp_fun_Y21_1(elem!24)))))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.27 inference(unit_resolution,[status(thm)],[203, 197])).
% 56.06/56.27 tff(205,plain,
% 56.06/56.27 (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))),
% 56.06/56.27 inference(unit_resolution,[status(thm)],[204, 182])).
% 56.06/56.27 tff(206,plain,
% 56.06/56.27 (((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))),
% 56.06/56.27 inference(tautology,[status(thm)],[])).
% 56.06/56.27 tff(207,plain,
% 56.06/56.27 (r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))),
% 56.06/56.27 inference(unit_resolution,[status(thm)],[206, 205])).
% 56.06/56.27 tff(208,plain,
% 56.06/56.27 (((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))) <=> ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.27 inference(rewrite,[status(thm)],[])).
% 56.06/56.27 tff(209,plain,
% 56.06/56.27 (((~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | ![Y20: $i] : ((~id(Y20, tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~r1(Y20)))) <=> ((~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.27 inference(rewrite,[status(thm)],[])).
% 56.06/56.27 tff(210,plain,
% 56.06/56.27 (((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | ![Y20: $i] : ((~id(Y20, tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~r1(Y20))))) <=> ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))))),
% 56.06/56.27 inference(monotonicity,[status(thm)],[209])).
% 56.06/56.27 tff(211,plain,
% 56.06/56.27 (((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | ![Y20: $i] : ((~id(Y20, tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~r1(Y20))))) <=> ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.27 inference(transitivity,[status(thm)],[210, 208])).
% 56.06/56.27 tff(212,plain,
% 56.06/56.27 ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | ![Y20: $i] : ((~id(Y20, tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~r1(Y20))))),
% 56.06/56.27 inference(quant_inst,[status(thm)],[])).
% 56.06/56.27 tff(213,plain,
% 56.06/56.27 ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))),
% 56.06/56.27 inference(modus_ponens,[status(thm)],[212, 211])).
% 56.06/56.27 tff(214,plain,
% 56.06/56.27 (![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))),
% 56.06/56.27 inference(unit_resolution,[status(thm)],[213, 62, 207])).
% 56.06/56.27 tff(215,plain,
% 56.06/56.27 (((~id(tptp_fun_Y9_12(elem!24), elem!24)) | (~r1(tptp_fun_Y16_13(elem!24))) | (~r3(elem!24, tptp_fun_Y16_13(elem!24), tptp_fun_Y9_12(elem!24)))) | r1(tptp_fun_Y16_13(elem!24))),
% 56.06/56.27 inference(tautology,[status(thm)],[])).
% 56.06/56.27 tff(216,plain,
% 56.06/56.27 (r1(tptp_fun_Y16_13(elem!24))),
% 56.06/56.27 inference(unit_resolution,[status(thm)],[215, 102])).
% 56.06/56.27 tff(217,plain,
% 56.06/56.27 ((r1(Y24!0) | r1(tptp_fun_Y16_13(elem!24))) | (~r1(tptp_fun_Y16_13(elem!24)))),
% 56.06/56.27 inference(tautology,[status(thm)],[])).
% 56.06/56.27 tff(218,plain,
% 56.06/56.27 (r1(Y24!0) | r1(tptp_fun_Y16_13(elem!24))),
% 56.06/56.27 inference(unit_resolution,[status(thm)],[217, 216])).
% 56.06/56.27 tff(219,plain,
% 56.06/56.27 ((r1(tptp_fun_Y16_13(elem!24)) | id(tptp_fun_Y16_13(elem!24), Y24!0)) | (~r1(tptp_fun_Y16_13(elem!24)))),
% 56.06/56.27 inference(tautology,[status(thm)],[])).
% 56.06/56.27 tff(220,plain,
% 56.06/56.27 (r1(tptp_fun_Y16_13(elem!24)) | id(tptp_fun_Y16_13(elem!24), Y24!0)),
% 56.06/56.27 inference(unit_resolution,[status(thm)],[219, 216])).
% 56.06/56.27 tff(221,plain,
% 56.06/56.27 (((~![X19: $i] : ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0))))) | ((~((~r1(tptp_fun_Y16_13(elem!24))) | (~id(tptp_fun_Y16_13(elem!24), Y24!0)))) | (~(r1(tptp_fun_Y16_13(elem!24)) | id(tptp_fun_Y16_13(elem!24), Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0))))) | (~((~r1(tptp_fun_Y16_13(elem!24))) | (~id(tptp_fun_Y16_13(elem!24), Y24!0)))) | (~(r1(tptp_fun_Y16_13(elem!24)) | id(tptp_fun_Y16_13(elem!24), Y24!0))))),
% 56.06/56.28 inference(rewrite,[status(thm)],[])).
% 56.06/56.28 tff(222,plain,
% 56.06/56.28 ((~![X19: $i] : ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0))))) | ((~((~r1(tptp_fun_Y16_13(elem!24))) | (~id(tptp_fun_Y16_13(elem!24), Y24!0)))) | (~(r1(tptp_fun_Y16_13(elem!24)) | id(tptp_fun_Y16_13(elem!24), Y24!0))))),
% 56.06/56.28 inference(quant_inst,[status(thm)],[])).
% 56.06/56.28 tff(223,plain,
% 56.06/56.28 ((~![X19: $i] : ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0))))) | (~((~r1(tptp_fun_Y16_13(elem!24))) | (~id(tptp_fun_Y16_13(elem!24), Y24!0)))) | (~(r1(tptp_fun_Y16_13(elem!24)) | id(tptp_fun_Y16_13(elem!24), Y24!0)))),
% 56.06/56.28 inference(modus_ponens,[status(thm)],[222, 221])).
% 56.06/56.28 tff(224,plain,
% 56.06/56.28 (~((~r1(tptp_fun_Y16_13(elem!24))) | (~id(tptp_fun_Y16_13(elem!24), Y24!0)))),
% 56.06/56.28 inference(unit_resolution,[status(thm)],[223, 84, 220])).
% 56.06/56.28 tff(225,plain,
% 56.06/56.28 (((~r1(tptp_fun_Y16_13(elem!24))) | (~id(tptp_fun_Y16_13(elem!24), Y24!0))) | id(tptp_fun_Y16_13(elem!24), Y24!0)),
% 56.06/56.28 inference(tautology,[status(thm)],[])).
% 56.06/56.28 tff(226,plain,
% 56.06/56.28 (id(tptp_fun_Y16_13(elem!24), Y24!0)),
% 56.06/56.28 inference(unit_resolution,[status(thm)],[225, 224])).
% 56.06/56.28 tff(227,plain,
% 56.06/56.28 (((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | ((~id(tptp_fun_Y16_13(elem!24), Y24!0)) | (~((~r1(Y24!0)) | (~r1(tptp_fun_Y16_13(elem!24))))) | (~(r1(Y24!0) | r1(tptp_fun_Y16_13(elem!24)))))) <=> ((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | (~id(tptp_fun_Y16_13(elem!24), Y24!0)) | (~((~r1(Y24!0)) | (~r1(tptp_fun_Y16_13(elem!24))))) | (~(r1(Y24!0) | r1(tptp_fun_Y16_13(elem!24)))))),
% 56.06/56.28 inference(rewrite,[status(thm)],[])).
% 56.06/56.28 tff(228,plain,
% 56.06/56.28 ((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | ((~id(tptp_fun_Y16_13(elem!24), Y24!0)) | (~((~r1(Y24!0)) | (~r1(tptp_fun_Y16_13(elem!24))))) | (~(r1(Y24!0) | r1(tptp_fun_Y16_13(elem!24)))))),
% 56.06/56.28 inference(quant_inst,[status(thm)],[])).
% 56.06/56.28 tff(229,plain,
% 56.06/56.28 ((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | (~id(tptp_fun_Y16_13(elem!24), Y24!0)) | (~((~r1(Y24!0)) | (~r1(tptp_fun_Y16_13(elem!24))))) | (~(r1(Y24!0) | r1(tptp_fun_Y16_13(elem!24))))),
% 56.06/56.28 inference(modus_ponens,[status(thm)],[228, 227])).
% 56.06/56.28 tff(230,plain,
% 56.06/56.28 (~((~r1(Y24!0)) | (~r1(tptp_fun_Y16_13(elem!24))))),
% 56.06/56.28 inference(unit_resolution,[status(thm)],[229, 37, 226, 218])).
% 56.06/56.28 tff(231,plain,
% 56.06/56.28 (((~r1(Y24!0)) | (~r1(tptp_fun_Y16_13(elem!24)))) | r1(Y24!0)),
% 56.06/56.28 inference(tautology,[status(thm)],[])).
% 56.06/56.28 tff(232,plain,
% 56.06/56.28 (r1(Y24!0)),
% 56.06/56.28 inference(unit_resolution,[status(thm)],[231, 230])).
% 56.06/56.28 tff(233,plain,
% 56.06/56.28 (((~![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))) | ((~r1(Y24!0)) | (~id(Y24!0, tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))) <=> ((~![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))) | (~r1(Y24!0)) | (~id(Y24!0, tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))),
% 56.06/56.28 inference(rewrite,[status(thm)],[])).
% 56.06/56.28 tff(234,plain,
% 56.06/56.28 ((~![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))) | ((~r1(Y24!0)) | (~id(Y24!0, tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))),
% 56.06/56.28 inference(quant_inst,[status(thm)],[])).
% 56.06/56.28 tff(235,plain,
% 56.06/56.28 ((~![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))) | (~r1(Y24!0)) | (~id(Y24!0, tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))),
% 56.06/56.28 inference(modus_ponens,[status(thm)],[234, 233])).
% 56.06/56.28 tff(236,plain,
% 56.06/56.28 (~id(Y24!0, tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))),
% 56.06/56.28 inference(unit_resolution,[status(thm)],[235, 232, 214])).
% 56.06/56.28 tff(237,plain,
% 56.06/56.28 (^[X3: $i, X10: $i] : refl((id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13))))) <=> (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13))))))),
% 56.06/56.28 inference(bind,[status(th)],[])).
% 56.06/56.28 tff(238,plain,
% 56.06/56.28 (![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13))))) <=> ![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))),
% 56.06/56.28 inference(quant_intro,[status(thm)],[237])).
% 56.06/56.28 tff(239,plain,
% 56.06/56.28 (^[X3: $i, X10: $i] : rewrite((id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13))))) <=> (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13))))))),
% 56.06/56.28 inference(bind,[status(th)],[])).
% 56.06/56.28 tff(240,plain,
% 56.06/56.28 (![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13))))) <=> ![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))),
% 56.06/56.28 inference(quant_intro,[status(thm)],[239])).
% 56.06/56.28 tff(241,plain,
% 56.06/56.28 (![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13))))) <=> ![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))),
% 56.06/56.28 inference(transitivity,[status(thm)],[240, 238])).
% 56.06/56.28 tff(242,plain,
% 56.06/56.28 (![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13))))) <=> ![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))),
% 56.06/56.28 inference(rewrite,[status(thm)],[])).
% 56.06/56.28 tff(243,plain,
% 56.06/56.28 (^[X3: $i, X10: $i] : trans(monotonicity(quant_intro(proof_bind(^[Y12: $i] : rewrite((![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13))) | (~r2(X10, Y12))) <=> ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))), (![Y12: $i] : (![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13))) | (~r2(X10, Y12))) <=> ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))), ((![Y12: $i] : (![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13))) | (~r2(X10, Y12))) | id(X3, X10)) <=> (![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))) | id(X3, X10)))), rewrite((![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))) | id(X3, X10)) <=> (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))), ((![Y12: $i] : (![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13))) | (~r2(X10, Y12))) | id(X3, X10)) <=> (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))))),
% 56.06/56.28 inference(bind,[status(th)],[])).
% 56.06/56.28 tff(244,plain,
% 56.06/56.28 (![X3: $i, X10: $i] : (![Y12: $i] : (![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13))) | (~r2(X10, Y12))) | id(X3, X10)) <=> ![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))),
% 56.06/56.28 inference(quant_intro,[status(thm)],[243])).
% 56.06/56.28 tff(245,axiom,(![X3: $i, X10: $i] : (![Y12: $i] : (![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13))) | (~r2(X10, Y12))) | id(X3, X10))), file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax','axiom_3a')).
% 56.06/56.28 tff(246,plain,
% 56.06/56.28 (![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))),
% 56.06/56.28 inference(modus_ponens,[status(thm)],[245, 244])).
% 56.06/56.28 tff(247,plain,
% 56.06/56.28 (![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))),
% 56.06/56.28 inference(modus_ponens,[status(thm)],[246, 242])).
% 56.06/56.28 tff(248,plain,(
% 56.06/56.28 ![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))),
% 56.06/56.28 inference(skolemize,[status(sab)],[247])).
% 56.06/56.28 tff(249,plain,
% 56.06/56.28 (![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))),
% 56.06/56.28 inference(modus_ponens,[status(thm)],[248, 241])).
% 56.06/56.28 tff(250,plain,
% 56.06/56.28 (((~![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))) | (id(Y24!0, tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))) | ![Y12: $i] : ((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(Y24!0, Y13)))))) <=> ((~![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))) | id(Y24!0, tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))) | ![Y12: $i] : ((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(Y24!0, Y13)))))),
% 56.06/56.28 inference(rewrite,[status(thm)],[])).
% 56.06/56.28 tff(251,plain,
% 56.06/56.28 ((~![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))) | (id(Y24!0, tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))) | ![Y12: $i] : ((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(Y24!0, Y13)))))),
% 56.06/56.28 inference(quant_inst,[status(thm)],[])).
% 56.06/56.28 tff(252,plain,
% 56.06/56.28 ((~![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))) | id(Y24!0, tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))) | ![Y12: $i] : ((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(Y24!0, Y13))))),
% 56.06/56.28 inference(modus_ponens,[status(thm)],[251, 250])).
% 56.06/56.28 tff(253,plain,
% 56.06/56.28 (![Y12: $i] : ((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(Y24!0, Y13))))),
% 56.06/56.28 inference(unit_resolution,[status(thm)],[252, 249, 236])).
% 56.06/56.28 tff(254,plain,
% 56.06/56.28 (((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))),
% 56.06/56.28 inference(tautology,[status(thm)],[])).
% 56.06/56.28 tff(255,plain,
% 56.06/56.28 (r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))),
% 56.06/56.28 inference(unit_resolution,[status(thm)],[254, 205])).
% 56.06/56.28 tff(256,plain,
% 56.06/56.28 ((r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))),
% 56.06/56.28 inference(tautology,[status(thm)],[])).
% 56.06/56.28 tff(257,plain,
% 56.06/56.28 (r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))),
% 56.06/56.28 inference(unit_resolution,[status(thm)],[256, 255])).
% 56.06/56.28 tff(258,plain,
% 56.06/56.28 (((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))),
% 56.06/56.28 inference(tautology,[status(thm)],[])).
% 56.06/56.28 tff(259,plain,
% 56.06/56.28 (id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))),
% 56.06/56.28 inference(unit_resolution,[status(thm)],[258, 205])).
% 56.06/56.28 tff(260,plain,
% 56.06/56.28 (((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24)))) <=> ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24)))),
% 56.06/56.28 inference(rewrite,[status(thm)],[])).
% 56.06/56.28 tff(261,plain,
% 56.06/56.28 ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24)))),
% 56.06/56.28 inference(quant_inst,[status(thm)],[])).
% 56.06/56.28 tff(262,plain,
% 56.06/56.28 ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))),
% 56.06/56.28 inference(modus_ponens,[status(thm)],[261, 260])).
% 56.06/56.28 tff(263,plain,
% 56.06/56.28 (id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))),
% 56.06/56.28 inference(unit_resolution,[status(thm)],[262, 154, 259])).
% 56.06/56.28 tff(264,plain,
% 56.06/56.28 ((r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))),
% 56.06/56.28 inference(tautology,[status(thm)],[])).
% 56.06/56.28 tff(265,plain,
% 56.06/56.28 (r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))),
% 56.06/56.28 inference(unit_resolution,[status(thm)],[264, 207])).
% 56.06/56.28 tff(266,plain,
% 56.06/56.28 (((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | ((~((~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))))) | (~(r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))))))) <=> ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | (~((~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))))) | (~(r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))))))),
% 56.06/56.28 inference(rewrite,[status(thm)],[])).
% 56.06/56.28 tff(267,plain,
% 56.06/56.28 ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | ((~((~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))))) | (~(r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))))))),
% 56.06/56.28 inference(quant_inst,[status(thm)],[])).
% 56.06/56.28 tff(268,plain,
% 56.06/56.28 ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | (~((~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))))) | (~(r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.28 inference(modus_ponens,[status(thm)],[267, 266])).
% 56.06/56.28 tff(269,plain,
% 56.06/56.28 (~((~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.28 inference(unit_resolution,[status(thm)],[268, 141, 265])).
% 56.06/56.28 tff(270,plain,
% 56.06/56.28 (((~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))))) | id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))),
% 56.06/56.28 inference(tautology,[status(thm)],[])).
% 56.06/56.28 tff(271,plain,
% 56.06/56.28 (id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))),
% 56.06/56.28 inference(unit_resolution,[status(thm)],[270, 269])).
% 56.06/56.28 tff(272,plain,
% 56.06/56.28 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.28 inference(rewrite,[status(thm)],[])).
% 56.06/56.28 tff(273,plain,
% 56.06/56.28 (((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))))) <=> ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.28 inference(rewrite,[status(thm)],[])).
% 56.06/56.28 tff(274,plain,
% 56.06/56.28 ((~(r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)) | r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) <=> (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))))),
% 56.06/56.28 inference(rewrite,[status(thm)],[])).
% 56.06/56.28 tff(275,plain,
% 56.06/56.28 ((~((~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) <=> (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)))))),
% 56.06/56.28 inference(rewrite,[status(thm)],[])).
% 56.06/56.28 tff(276,plain,
% 56.06/56.28 (((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)) | r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) <=> ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)))))),
% 56.06/56.28 inference(monotonicity,[status(thm)],[275, 274])).
% 56.06/56.28 tff(277,plain,
% 56.06/56.28 (((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)) | r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) <=> ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.28 inference(transitivity,[status(thm)],[276, 273])).
% 56.06/56.28 tff(278,plain,
% 56.06/56.28 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)) | r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))))))),
% 56.06/56.28 inference(monotonicity,[status(thm)],[277])).
% 56.06/56.28 tff(279,plain,
% 56.06/56.28 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)) | r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.28 inference(transitivity,[status(thm)],[278, 272])).
% 56.06/56.28 tff(280,plain,
% 56.06/56.28 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)) | r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.28 inference(quant_inst,[status(thm)],[])).
% 56.06/56.28 tff(281,plain,
% 56.06/56.28 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))))),
% 56.06/56.28 inference(modus_ponens,[status(thm)],[280, 279])).
% 56.06/56.28 tff(282,plain,
% 56.06/56.28 (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))))),
% 56.06/56.28 inference(unit_resolution,[status(thm)],[281, 117, 271, 263, 257])).
% 56.06/56.28 tff(283,plain,
% 56.06/56.28 (((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))),
% 56.06/56.28 inference(tautology,[status(thm)],[])).
% 56.06/56.28 tff(284,plain,
% 56.06/56.28 (r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))),
% 56.06/56.28 inference(unit_resolution,[status(thm)],[283, 282])).
% 56.06/56.28 tff(285,plain,
% 56.06/56.28 ((r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)))),
% 56.06/56.28 inference(tautology,[status(thm)],[])).
% 56.06/56.28 tff(286,plain,
% 56.06/56.28 (r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))),
% 56.06/56.28 inference(unit_resolution,[status(thm)],[285, 284])).
% 56.06/56.28 tff(287,plain,
% 56.06/56.28 ((r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))),
% 56.06/56.28 inference(tautology,[status(thm)],[])).
% 56.06/56.28 tff(288,plain,
% 56.06/56.28 (r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))),
% 56.06/56.28 inference(unit_resolution,[status(thm)],[287, 255])).
% 56.06/56.28 tff(289,plain,
% 56.06/56.28 (((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | ((~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))))) <=> ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))))),
% 56.06/56.28 inference(rewrite,[status(thm)],[])).
% 56.06/56.28 tff(290,plain,
% 56.06/56.28 ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | ((~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))))),
% 56.06/56.28 inference(quant_inst,[status(thm)],[])).
% 56.06/56.28 tff(291,plain,
% 56.06/56.28 ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.28 inference(modus_ponens,[status(thm)],[290, 289])).
% 56.06/56.28 tff(292,plain,
% 56.06/56.28 (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.28 inference(unit_resolution,[status(thm)],[291, 141, 288])).
% 56.06/56.28 tff(293,plain,
% 56.06/56.28 (((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))) | id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))),
% 56.06/56.28 inference(tautology,[status(thm)],[])).
% 56.06/56.28 tff(294,plain,
% 56.06/56.28 (id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))),
% 56.06/56.28 inference(unit_resolution,[status(thm)],[293, 292])).
% 56.06/56.28 tff(295,plain,
% 56.06/56.28 (![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24))) <=> ![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))),
% 56.06/56.28 inference(rewrite,[status(thm)],[])).
% 56.06/56.28 tff(296,plain,
% 56.06/56.28 (![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24))) <=> ![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))),
% 56.06/56.28 inference(rewrite,[status(thm)],[])).
% 56.06/56.28 tff(297,plain,
% 56.06/56.28 (^[X23: $i, X24: $i, X25: $i] : rewrite((((~id(X23, X24)) | id(X23, X25)) | (~id(X24, X25))) <=> ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24))))),
% 56.06/56.28 inference(bind,[status(th)],[])).
% 56.06/56.28 tff(298,plain,
% 56.06/56.28 (![X23: $i, X24: $i, X25: $i] : (((~id(X23, X24)) | id(X23, X25)) | (~id(X24, X25))) <=> ![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))),
% 56.06/56.28 inference(quant_intro,[status(thm)],[297])).
% 56.06/56.28 tff(299,axiom,(![X23: $i, X24: $i, X25: $i] : (((~id(X23, X24)) | id(X23, X25)) | (~id(X24, X25)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax','axiom_7')).
% 56.06/56.28 tff(300,plain,
% 56.06/56.28 (![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))),
% 56.06/56.28 inference(modus_ponens,[status(thm)],[299, 298])).
% 56.06/56.28 tff(301,plain,
% 56.06/56.28 (![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))),
% 56.06/56.28 inference(modus_ponens,[status(thm)],[300, 296])).
% 56.06/56.28 tff(302,plain,(
% 56.06/56.28 ![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))),
% 56.06/56.28 inference(skolemize,[status(sab)],[301])).
% 56.06/56.28 tff(303,plain,
% 56.06/56.28 (![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))),
% 56.06/56.28 inference(modus_ponens,[status(thm)],[302, 295])).
% 56.06/56.28 tff(304,plain,
% 56.06/56.28 (((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))) <=> ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.28 inference(rewrite,[status(thm)],[])).
% 56.06/56.28 tff(305,plain,
% 56.06/56.28 (((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) <=> ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.28 inference(rewrite,[status(thm)],[])).
% 56.06/56.28 tff(306,plain,
% 56.06/56.28 (((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) <=> ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))))),
% 56.06/56.28 inference(monotonicity,[status(thm)],[305])).
% 56.06/56.28 tff(307,plain,
% 56.06/56.28 (((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) <=> ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.28 inference(transitivity,[status(thm)],[306, 304])).
% 56.06/56.28 tff(308,plain,
% 56.06/56.28 ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))),
% 56.06/56.28 inference(quant_inst,[status(thm)],[])).
% 56.06/56.28 tff(309,plain,
% 56.06/56.28 ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))),
% 56.06/56.28 inference(modus_ponens,[status(thm)],[308, 307])).
% 56.06/56.28 tff(310,plain,
% 56.06/56.28 (id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))),
% 56.06/56.28 inference(unit_resolution,[status(thm)],[309, 303, 259, 294])).
% 56.06/56.28 tff(311,plain,
% 56.06/56.28 (((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | ((~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | id(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) <=> ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | id(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))),
% 56.06/56.28 inference(rewrite,[status(thm)],[])).
% 56.06/56.28 tff(312,plain,
% 56.06/56.28 ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | ((~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | id(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))),
% 56.06/56.28 inference(quant_inst,[status(thm)],[])).
% 56.06/56.28 tff(313,plain,
% 56.06/56.28 ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | id(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))),
% 56.06/56.28 inference(modus_ponens,[status(thm)],[312, 311])).
% 56.06/56.28 tff(314,plain,
% 56.06/56.28 (id(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))),
% 56.06/56.28 inference(unit_resolution,[status(thm)],[313, 154, 271])).
% 56.06/56.28 tff(315,plain,
% 56.06/56.28 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.28 inference(rewrite,[status(thm)],[])).
% 56.06/56.28 tff(316,plain,
% 56.06/56.28 (((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))))) <=> ((~id(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.29 inference(rewrite,[status(thm)],[])).
% 56.06/56.29 tff(317,plain,
% 56.06/56.29 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)))))))),
% 56.06/56.29 inference(monotonicity,[status(thm)],[316])).
% 56.06/56.29 tff(318,plain,
% 56.06/56.29 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.29 inference(transitivity,[status(thm)],[317, 315])).
% 56.06/56.29 tff(319,plain,
% 56.06/56.29 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)))))),
% 56.06/56.29 inference(quant_inst,[status(thm)],[])).
% 56.06/56.29 tff(320,plain,
% 56.06/56.29 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)))))),
% 56.06/56.29 inference(modus_ponens,[status(thm)],[319, 318])).
% 56.06/56.29 tff(321,plain,
% 56.06/56.29 (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24))))),
% 56.06/56.29 inference(unit_resolution,[status(thm)],[320, 117, 314, 310, 286])).
% 56.06/56.29 tff(322,plain,
% 56.06/56.29 (((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(elem!24)))) | r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))),
% 56.06/56.29 inference(tautology,[status(thm)],[])).
% 56.06/56.29 tff(323,plain,
% 56.06/56.29 (r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))),
% 56.06/56.29 inference(unit_resolution,[status(thm)],[322, 321])).
% 56.06/56.29 tff(324,plain,
% 56.06/56.29 (((~![Y12: $i] : ((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(Y24!0, Y13))))) | ((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | ![Y13: $i] : ((~r2(Y24!0, Y13)) | (~id(Y13, tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))))) <=> ((~![Y12: $i] : ((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(Y24!0, Y13))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | ![Y13: $i] : ((~r2(Y24!0, Y13)) | (~id(Y13, tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))))),
% 56.06/56.29 inference(rewrite,[status(thm)],[])).
% 56.06/56.29 tff(325,plain,
% 56.06/56.29 (((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | ![Y13: $i] : ((~id(Y13, tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(Y24!0, Y13)))) <=> ((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | ![Y13: $i] : ((~r2(Y24!0, Y13)) | (~id(Y13, tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))))),
% 56.06/56.29 inference(rewrite,[status(thm)],[])).
% 56.06/56.29 tff(326,plain,
% 56.06/56.29 (((~![Y12: $i] : ((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(Y24!0, Y13))))) | ((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | ![Y13: $i] : ((~id(Y13, tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(Y24!0, Y13))))) <=> ((~![Y12: $i] : ((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(Y24!0, Y13))))) | ((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | ![Y13: $i] : ((~r2(Y24!0, Y13)) | (~id(Y13, tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))))),
% 56.06/56.29 inference(monotonicity,[status(thm)],[325])).
% 56.06/56.29 tff(327,plain,
% 56.06/56.29 (((~![Y12: $i] : ((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(Y24!0, Y13))))) | ((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | ![Y13: $i] : ((~id(Y13, tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(Y24!0, Y13))))) <=> ((~![Y12: $i] : ((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(Y24!0, Y13))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | ![Y13: $i] : ((~r2(Y24!0, Y13)) | (~id(Y13, tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))))),
% 56.06/56.29 inference(transitivity,[status(thm)],[326, 324])).
% 56.06/56.29 tff(328,plain,
% 56.06/56.29 ((~![Y12: $i] : ((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(Y24!0, Y13))))) | ((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | ![Y13: $i] : ((~id(Y13, tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(Y24!0, Y13))))),
% 56.06/56.29 inference(quant_inst,[status(thm)],[])).
% 56.06/56.29 tff(329,plain,
% 56.06/56.29 ((~![Y12: $i] : ((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(Y24!0, Y13))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | ![Y13: $i] : ((~r2(Y24!0, Y13)) | (~id(Y13, tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.29 inference(modus_ponens,[status(thm)],[328, 327])).
% 56.06/56.29 tff(330,plain,
% 56.06/56.29 (![Y13: $i] : ((~r2(Y24!0, Y13)) | (~id(Y13, tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.29 inference(unit_resolution,[status(thm)],[329, 323, 253])).
% 56.06/56.29 tff(331,plain,
% 56.06/56.29 (((~![Y13: $i] : ((~r2(Y24!0, Y13)) | (~id(Y13, tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))) | ((~r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))) <=> ((~![Y13: $i] : ((~r2(Y24!0, Y13)) | (~id(Y13, tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))) | (~r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.29 inference(rewrite,[status(thm)],[])).
% 56.06/56.29 tff(332,plain,
% 56.06/56.29 ((~![Y13: $i] : ((~r2(Y24!0, Y13)) | (~id(Y13, tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))) | ((~r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.29 inference(quant_inst,[status(thm)],[])).
% 56.06/56.29 tff(333,plain,
% 56.06/56.29 ((~![Y13: $i] : ((~r2(Y24!0, Y13)) | (~id(Y13, tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))) | (~r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))),
% 56.06/56.29 inference(modus_ponens,[status(thm)],[332, 331])).
% 56.06/56.29 tff(334,plain,
% 56.06/56.29 (~r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))),
% 56.06/56.29 inference(unit_resolution,[status(thm)],[333, 294, 330])).
% 56.06/56.29 tff(335,plain,
% 56.06/56.29 (((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))),
% 56.06/56.29 inference(tautology,[status(thm)],[])).
% 56.06/56.29 tff(336,plain,
% 56.06/56.29 ((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))),
% 56.06/56.29 inference(unit_resolution,[status(thm)],[335, 334])).
% 56.06/56.29 tff(337,plain,
% 56.06/56.29 (((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | (id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(elem!24)) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))))) <=> ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(elem!24)) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))))),
% 56.06/56.29 inference(rewrite,[status(thm)],[])).
% 56.06/56.29 tff(338,plain,
% 56.06/56.29 (((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(elem!24)) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) <=> (id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(elem!24)) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))))),
% 56.06/56.29 inference(rewrite,[status(thm)],[])).
% 56.06/56.29 tff(339,plain,
% 56.06/56.29 (((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(elem!24)) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) <=> ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | (id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(elem!24)) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24)))))),
% 56.06/56.29 inference(monotonicity,[status(thm)],[338])).
% 56.06/56.29 tff(340,plain,
% 56.06/56.29 (((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(elem!24)) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) <=> ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(elem!24)) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))))),
% 56.06/56.29 inference(transitivity,[status(thm)],[339, 337])).
% 56.06/56.29 tff(341,plain,
% 56.06/56.29 ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(elem!24)) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))),
% 56.06/56.29 inference(quant_inst,[status(thm)],[])).
% 56.06/56.29 tff(342,plain,
% 56.06/56.29 ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(elem!24)) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24)))),
% 56.06/56.29 inference(modus_ponens,[status(thm)],[341, 340])).
% 56.06/56.29 tff(343,plain,
% 56.06/56.29 (id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(elem!24))),
% 56.06/56.29 inference(unit_resolution,[status(thm)],[342, 303, 259, 263])).
% 56.06/56.29 tff(344,plain,
% 56.06/56.29 ((r2(elem!24, tptp_fun_Y21_1(elem!24)) | id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(elem!24))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(elem!24)))),
% 56.06/56.29 inference(tautology,[status(thm)],[])).
% 56.06/56.29 tff(345,plain,
% 56.06/56.29 (r2(elem!24, tptp_fun_Y21_1(elem!24)) | id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(elem!24))),
% 56.06/56.29 inference(unit_resolution,[status(thm)],[344, 343])).
% 56.06/56.29 tff(346,assumption,((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(elem!24)))), introduced(assumption)).
% 56.06/56.29 tff(347,plain,
% 56.06/56.29 (((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | ((~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(elem!24))))) | (~(r2(elem!24, tptp_fun_Y21_1(elem!24)) | id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(elem!24)))))) <=> ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | (~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(elem!24))))) | (~(r2(elem!24, tptp_fun_Y21_1(elem!24)) | id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(elem!24)))))),
% 56.06/56.29 inference(rewrite,[status(thm)],[])).
% 56.06/56.29 tff(348,plain,
% 56.06/56.29 ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | ((~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(elem!24))))) | (~(r2(elem!24, tptp_fun_Y21_1(elem!24)) | id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(elem!24)))))),
% 56.06/56.29 inference(quant_inst,[status(thm)],[])).
% 56.06/56.29 tff(349,plain,
% 56.06/56.29 ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | (~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(elem!24))))) | (~(r2(elem!24, tptp_fun_Y21_1(elem!24)) | id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(elem!24))))),
% 56.06/56.29 inference(modus_ponens,[status(thm)],[348, 347])).
% 56.06/56.29 tff(350,plain,
% 56.06/56.29 ($false),
% 56.06/56.29 inference(unit_resolution,[status(thm)],[349, 141, 346, 345])).
% 56.06/56.29 tff(351,plain,(~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(elem!24))))), inference(lemma,lemma(discharge,[]))).
% 56.06/56.29 tff(352,plain,
% 56.06/56.29 (((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y21_1(elem!24)))) | r2(elem!24, tptp_fun_Y21_1(elem!24))),
% 56.06/56.29 inference(tautology,[status(thm)],[])).
% 56.06/56.29 tff(353,plain,
% 56.06/56.29 (r2(elem!24, tptp_fun_Y21_1(elem!24))),
% 56.06/56.29 inference(unit_resolution,[status(thm)],[352, 351])).
% 56.06/56.29 tff(354,plain,
% 56.06/56.29 ((r2(elem!24, tptp_fun_Y21_1(elem!24)) | r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(elem!24, tptp_fun_Y21_1(elem!24)))),
% 56.06/56.29 inference(tautology,[status(thm)],[])).
% 56.06/56.29 tff(355,plain,
% 56.06/56.29 (r2(elem!24, tptp_fun_Y21_1(elem!24)) | r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))),
% 56.06/56.29 inference(unit_resolution,[status(thm)],[354, 353])).
% 56.06/56.29 tff(356,assumption,(~((~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24))) | (~r1(tptp_fun_Y4_22(elem!24))) | (~r2(tptp_fun_Y4_22(elem!24), tptp_fun_Y3_21(elem!24))))), introduced(assumption)).
% 56.06/56.29 tff(357,plain,
% 56.06/56.29 (((~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24))) | (~r1(tptp_fun_Y4_22(elem!24))) | (~r2(tptp_fun_Y4_22(elem!24), tptp_fun_Y3_21(elem!24)))) | r2(tptp_fun_Y4_22(elem!24), tptp_fun_Y3_21(elem!24))),
% 56.06/56.29 inference(tautology,[status(thm)],[])).
% 56.06/56.29 tff(358,plain,
% 56.06/56.29 (r2(tptp_fun_Y4_22(elem!24), tptp_fun_Y3_21(elem!24))),
% 56.06/56.29 inference(unit_resolution,[status(thm)],[357, 356])).
% 56.06/56.29 tff(359,plain,
% 56.06/56.29 (((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(tptp_fun_Y4_22(elem!24), tptp_fun_Y3_21(elem!24))) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y3_21(elem!24)))))) <=> ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | (~r2(tptp_fun_Y4_22(elem!24), tptp_fun_Y3_21(elem!24))) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y3_21(elem!24)))))),
% 56.06/56.29 inference(rewrite,[status(thm)],[])).
% 56.06/56.29 tff(360,plain,
% 56.06/56.29 (((~r2(tptp_fun_Y4_22(elem!24), tptp_fun_Y3_21(elem!24))) | ![Y20: $i] : ((~id(Y20, tptp_fun_Y3_21(elem!24))) | (~r1(Y20)))) <=> ((~r2(tptp_fun_Y4_22(elem!24), tptp_fun_Y3_21(elem!24))) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y3_21(elem!24)))))),
% 56.06/56.29 inference(rewrite,[status(thm)],[])).
% 56.06/56.29 tff(361,plain,
% 56.06/56.29 (((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(tptp_fun_Y4_22(elem!24), tptp_fun_Y3_21(elem!24))) | ![Y20: $i] : ((~id(Y20, tptp_fun_Y3_21(elem!24))) | (~r1(Y20))))) <=> ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(tptp_fun_Y4_22(elem!24), tptp_fun_Y3_21(elem!24))) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y3_21(elem!24))))))),
% 56.06/56.29 inference(monotonicity,[status(thm)],[360])).
% 56.06/56.29 tff(362,plain,
% 56.06/56.29 (((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(tptp_fun_Y4_22(elem!24), tptp_fun_Y3_21(elem!24))) | ![Y20: $i] : ((~id(Y20, tptp_fun_Y3_21(elem!24))) | (~r1(Y20))))) <=> ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | (~r2(tptp_fun_Y4_22(elem!24), tptp_fun_Y3_21(elem!24))) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y3_21(elem!24)))))),
% 56.06/56.29 inference(transitivity,[status(thm)],[361, 359])).
% 56.06/56.29 tff(363,plain,
% 56.06/56.29 ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(tptp_fun_Y4_22(elem!24), tptp_fun_Y3_21(elem!24))) | ![Y20: $i] : ((~id(Y20, tptp_fun_Y3_21(elem!24))) | (~r1(Y20))))),
% 56.06/56.29 inference(quant_inst,[status(thm)],[])).
% 56.06/56.29 tff(364,plain,
% 56.06/56.29 ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | (~r2(tptp_fun_Y4_22(elem!24), tptp_fun_Y3_21(elem!24))) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y3_21(elem!24))))),
% 56.06/56.29 inference(modus_ponens,[status(thm)],[363, 362])).
% 56.06/56.29 tff(365,plain,
% 56.06/56.29 (![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y3_21(elem!24))))),
% 56.06/56.29 inference(unit_resolution,[status(thm)],[364, 62, 358])).
% 56.06/56.29 tff(366,plain,
% 56.06/56.29 (((~![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y3_21(elem!24))))) | ((~r1(tptp_fun_Y18_16(elem!24))) | (~id(tptp_fun_Y18_16(elem!24), tptp_fun_Y3_21(elem!24))))) <=> ((~![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y3_21(elem!24))))) | (~r1(tptp_fun_Y18_16(elem!24))) | (~id(tptp_fun_Y18_16(elem!24), tptp_fun_Y3_21(elem!24))))),
% 56.06/56.29 inference(rewrite,[status(thm)],[])).
% 56.06/56.29 tff(367,plain,
% 56.06/56.29 ((~![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y3_21(elem!24))))) | ((~r1(tptp_fun_Y18_16(elem!24))) | (~id(tptp_fun_Y18_16(elem!24), tptp_fun_Y3_21(elem!24))))),
% 56.06/56.29 inference(quant_inst,[status(thm)],[])).
% 56.06/56.29 tff(368,plain,
% 56.06/56.29 ((~![Y20: $i] : ((~r1(Y20)) | (~id(Y20, tptp_fun_Y3_21(elem!24))))) | (~r1(tptp_fun_Y18_16(elem!24))) | (~id(tptp_fun_Y18_16(elem!24), tptp_fun_Y3_21(elem!24)))),
% 56.06/56.29 inference(modus_ponens,[status(thm)],[367, 366])).
% 56.06/56.29 tff(369,plain,
% 56.06/56.29 (~id(tptp_fun_Y18_16(elem!24), tptp_fun_Y3_21(elem!24))),
% 56.06/56.29 inference(unit_resolution,[status(thm)],[368, 20, 365])).
% 56.06/56.29 tff(370,plain,
% 56.06/56.29 (((~![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))) | (id(tptp_fun_Y18_16(elem!24), tptp_fun_Y3_21(elem!24)) | ![Y12: $i] : ((~r2(tptp_fun_Y3_21(elem!24), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(tptp_fun_Y18_16(elem!24), Y13)))))) <=> ((~![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))) | id(tptp_fun_Y18_16(elem!24), tptp_fun_Y3_21(elem!24)) | ![Y12: $i] : ((~r2(tptp_fun_Y3_21(elem!24), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(tptp_fun_Y18_16(elem!24), Y13)))))),
% 56.06/56.29 inference(rewrite,[status(thm)],[])).
% 56.06/56.29 tff(371,plain,
% 56.06/56.29 ((~![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))) | (id(tptp_fun_Y18_16(elem!24), tptp_fun_Y3_21(elem!24)) | ![Y12: $i] : ((~r2(tptp_fun_Y3_21(elem!24), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(tptp_fun_Y18_16(elem!24), Y13)))))),
% 56.06/56.29 inference(quant_inst,[status(thm)],[])).
% 56.06/56.29 tff(372,plain,
% 56.06/56.29 ((~![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))) | id(tptp_fun_Y18_16(elem!24), tptp_fun_Y3_21(elem!24)) | ![Y12: $i] : ((~r2(tptp_fun_Y3_21(elem!24), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(tptp_fun_Y18_16(elem!24), Y13))))),
% 56.06/56.29 inference(modus_ponens,[status(thm)],[371, 370])).
% 56.06/56.29 tff(373,plain,
% 56.06/56.29 (![Y12: $i] : ((~r2(tptp_fun_Y3_21(elem!24), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(tptp_fun_Y18_16(elem!24), Y13))))),
% 56.06/56.29 inference(unit_resolution,[status(thm)],[372, 249, 369])).
% 56.06/56.29 tff(374,plain,
% 56.06/56.29 (((~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24))) | (~r1(tptp_fun_Y4_22(elem!24))) | (~r2(tptp_fun_Y4_22(elem!24), tptp_fun_Y3_21(elem!24)))) | r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24))),
% 56.06/56.29 inference(tautology,[status(thm)],[])).
% 56.06/56.29 tff(375,plain,
% 56.06/56.29 (r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24))),
% 56.06/56.29 inference(unit_resolution,[status(thm)],[374, 356])).
% 56.06/56.29 tff(376,plain,
% 56.06/56.29 (((~![Y12: $i] : ((~r2(tptp_fun_Y3_21(elem!24), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(tptp_fun_Y18_16(elem!24), Y13))))) | ((~r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24))) | ![Y13: $i] : ((~id(Y13, tptp_fun_Y2_20(elem!24))) | (~r2(tptp_fun_Y18_16(elem!24), Y13))))) <=> ((~![Y12: $i] : ((~r2(tptp_fun_Y3_21(elem!24), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(tptp_fun_Y18_16(elem!24), Y13))))) | (~r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24))) | ![Y13: $i] : ((~id(Y13, tptp_fun_Y2_20(elem!24))) | (~r2(tptp_fun_Y18_16(elem!24), Y13))))),
% 56.06/56.29 inference(rewrite,[status(thm)],[])).
% 56.06/56.29 tff(377,plain,
% 56.06/56.29 ((~![Y12: $i] : ((~r2(tptp_fun_Y3_21(elem!24), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(tptp_fun_Y18_16(elem!24), Y13))))) | ((~r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24))) | ![Y13: $i] : ((~id(Y13, tptp_fun_Y2_20(elem!24))) | (~r2(tptp_fun_Y18_16(elem!24), Y13))))),
% 56.06/56.29 inference(quant_inst,[status(thm)],[])).
% 56.06/56.29 tff(378,plain,
% 56.06/56.29 ((~![Y12: $i] : ((~r2(tptp_fun_Y3_21(elem!24), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(tptp_fun_Y18_16(elem!24), Y13))))) | (~r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24))) | ![Y13: $i] : ((~id(Y13, tptp_fun_Y2_20(elem!24))) | (~r2(tptp_fun_Y18_16(elem!24), Y13)))),
% 56.06/56.29 inference(modus_ponens,[status(thm)],[377, 376])).
% 56.06/56.29 tff(379,plain,
% 56.06/56.29 (![Y13: $i] : ((~id(Y13, tptp_fun_Y2_20(elem!24))) | (~r2(tptp_fun_Y18_16(elem!24), Y13)))),
% 56.06/56.29 inference(unit_resolution,[status(thm)],[378, 375, 373])).
% 56.06/56.29 tff(380,plain,
% 56.06/56.29 ((~![X4: $i] : (~((~id(tptp_fun_Y9_12(X4), X4)) | (~r1(tptp_fun_Y16_13(X4))) | (~r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4)))))) | (~((~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r1(tptp_fun_Y16_13(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~r3(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y16_13(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))))),
% 56.06/56.29 inference(quant_inst,[status(thm)],[])).
% 56.06/56.29 tff(381,plain,
% 56.06/56.29 (~((~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r1(tptp_fun_Y16_13(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~r3(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y16_13(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))),
% 56.06/56.29 inference(unit_resolution,[status(thm)],[380, 100])).
% 56.06/56.29 tff(382,plain,
% 56.06/56.29 (((~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r1(tptp_fun_Y16_13(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~r3(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y16_13(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) | id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))),
% 56.06/56.29 inference(tautology,[status(thm)],[])).
% 56.06/56.29 tff(383,plain,
% 56.06/56.29 (id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))),
% 56.06/56.29 inference(unit_resolution,[status(thm)],[382, 381])).
% 56.06/56.29 tff(384,plain,
% 56.06/56.29 (((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | ((~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) <=> ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | (~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))),
% 56.06/56.29 inference(rewrite,[status(thm)],[])).
% 56.06/56.29 tff(385,plain,
% 56.06/56.29 ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | ((~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))),
% 56.06/56.29 inference(quant_inst,[status(thm)],[])).
% 56.06/56.29 tff(386,plain,
% 56.06/56.29 ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | (~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))),
% 56.06/56.29 inference(modus_ponens,[status(thm)],[385, 384])).
% 56.06/56.29 tff(387,plain,
% 56.06/56.29 (id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))),
% 56.06/56.29 inference(unit_resolution,[status(thm)],[386, 154, 383])).
% 56.06/56.29 tff(388,plain,
% 56.06/56.29 (((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) <=> ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | (~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))),
% 56.06/56.29 inference(rewrite,[status(thm)],[])).
% 56.06/56.29 tff(389,plain,
% 56.06/56.29 (((~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) <=> ((~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))),
% 56.06/56.29 inference(rewrite,[status(thm)],[])).
% 56.06/56.29 tff(390,plain,
% 56.06/56.29 (((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))) <=> ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))),
% 56.06/56.29 inference(monotonicity,[status(thm)],[389])).
% 56.06/56.29 tff(391,plain,
% 56.06/56.29 (((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))) <=> ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | (~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))),
% 56.06/56.29 inference(transitivity,[status(thm)],[390, 388])).
% 56.06/56.29 tff(392,plain,
% 56.06/56.29 ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))),
% 56.06/56.29 inference(quant_inst,[status(thm)],[])).
% 56.06/56.29 tff(393,plain,
% 56.06/56.29 ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | (~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))),
% 56.06/56.29 inference(modus_ponens,[status(thm)],[392, 391])).
% 56.06/56.29 tff(394,plain,
% 56.06/56.29 (id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))),
% 56.06/56.29 inference(unit_resolution,[status(thm)],[393, 303, 383, 387])).
% 56.06/56.29 tff(395,plain,
% 56.06/56.29 ((r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))),
% 56.06/56.29 inference(tautology,[status(thm)],[])).
% 56.06/56.29 tff(396,plain,
% 56.06/56.29 (r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))),
% 56.06/56.29 inference(unit_resolution,[status(thm)],[395, 394])).
% 56.06/56.29 tff(397,assumption,((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))), introduced(assumption)).
% 56.06/56.29 tff(398,plain,
% 56.06/56.29 (((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | ((~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) | (~(r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))) <=> ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | (~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) | (~(r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))),
% 56.06/56.29 inference(rewrite,[status(thm)],[])).
% 56.06/56.29 tff(399,plain,
% 56.06/56.29 ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | ((~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) | (~(r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))),
% 56.06/56.29 inference(quant_inst,[status(thm)],[])).
% 56.06/56.29 tff(400,plain,
% 56.06/56.29 ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | (~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) | (~(r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))),
% 56.06/56.29 inference(modus_ponens,[status(thm)],[399, 398])).
% 56.06/56.30 tff(401,plain,
% 56.06/56.30 ($false),
% 56.06/56.30 inference(unit_resolution,[status(thm)],[400, 141, 397, 396])).
% 56.06/56.30 tff(402,plain,(~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))), inference(lemma,lemma(discharge,[]))).
% 56.06/56.30 tff(403,plain,
% 56.06/56.30 (((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))),
% 56.06/56.30 inference(tautology,[status(thm)],[])).
% 56.06/56.30 tff(404,plain,
% 56.06/56.30 (r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))),
% 56.06/56.30 inference(unit_resolution,[status(thm)],[403, 402])).
% 56.06/56.30 tff(405,plain,
% 56.06/56.30 ((r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))),
% 56.06/56.30 inference(tautology,[status(thm)],[])).
% 56.06/56.30 tff(406,plain,
% 56.06/56.30 (r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))),
% 56.06/56.30 inference(unit_resolution,[status(thm)],[405, 404])).
% 56.06/56.30 tff(407,plain,
% 56.06/56.30 (((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | ((~id(tptp_fun_Y16_13(elem!24), Y24!0)) | id(Y24!0, tptp_fun_Y16_13(elem!24)))) <=> ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | (~id(tptp_fun_Y16_13(elem!24), Y24!0)) | id(Y24!0, tptp_fun_Y16_13(elem!24)))),
% 56.06/56.30 inference(rewrite,[status(thm)],[])).
% 56.06/56.30 tff(408,plain,
% 56.06/56.30 ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | ((~id(tptp_fun_Y16_13(elem!24), Y24!0)) | id(Y24!0, tptp_fun_Y16_13(elem!24)))),
% 56.06/56.30 inference(quant_inst,[status(thm)],[])).
% 56.06/56.30 tff(409,plain,
% 56.06/56.30 ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | (~id(tptp_fun_Y16_13(elem!24), Y24!0)) | id(Y24!0, tptp_fun_Y16_13(elem!24))),
% 56.06/56.30 inference(modus_ponens,[status(thm)],[408, 407])).
% 56.06/56.30 tff(410,plain,
% 56.06/56.30 (id(Y24!0, tptp_fun_Y16_13(elem!24))),
% 56.06/56.30 inference(unit_resolution,[status(thm)],[409, 154, 226])).
% 56.06/56.30 tff(411,plain,
% 56.06/56.30 (((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(tptp_fun_Y18_16(elem!24), Y24!0)) | (~id(Y24!0, tptp_fun_Y16_13(elem!24))) | id(tptp_fun_Y18_16(elem!24), tptp_fun_Y16_13(elem!24)))) <=> ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | (~id(tptp_fun_Y18_16(elem!24), Y24!0)) | (~id(Y24!0, tptp_fun_Y16_13(elem!24))) | id(tptp_fun_Y18_16(elem!24), tptp_fun_Y16_13(elem!24)))),
% 56.06/56.30 inference(rewrite,[status(thm)],[])).
% 56.06/56.30 tff(412,plain,
% 56.06/56.30 (((~id(Y24!0, tptp_fun_Y16_13(elem!24))) | id(tptp_fun_Y18_16(elem!24), tptp_fun_Y16_13(elem!24)) | (~id(tptp_fun_Y18_16(elem!24), Y24!0))) <=> ((~id(tptp_fun_Y18_16(elem!24), Y24!0)) | (~id(Y24!0, tptp_fun_Y16_13(elem!24))) | id(tptp_fun_Y18_16(elem!24), tptp_fun_Y16_13(elem!24)))),
% 56.06/56.30 inference(rewrite,[status(thm)],[])).
% 56.06/56.30 tff(413,plain,
% 56.06/56.30 (((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(Y24!0, tptp_fun_Y16_13(elem!24))) | id(tptp_fun_Y18_16(elem!24), tptp_fun_Y16_13(elem!24)) | (~id(tptp_fun_Y18_16(elem!24), Y24!0)))) <=> ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(tptp_fun_Y18_16(elem!24), Y24!0)) | (~id(Y24!0, tptp_fun_Y16_13(elem!24))) | id(tptp_fun_Y18_16(elem!24), tptp_fun_Y16_13(elem!24))))),
% 56.06/56.30 inference(monotonicity,[status(thm)],[412])).
% 56.06/56.30 tff(414,plain,
% 56.06/56.30 (((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(Y24!0, tptp_fun_Y16_13(elem!24))) | id(tptp_fun_Y18_16(elem!24), tptp_fun_Y16_13(elem!24)) | (~id(tptp_fun_Y18_16(elem!24), Y24!0)))) <=> ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | (~id(tptp_fun_Y18_16(elem!24), Y24!0)) | (~id(Y24!0, tptp_fun_Y16_13(elem!24))) | id(tptp_fun_Y18_16(elem!24), tptp_fun_Y16_13(elem!24)))),
% 56.06/56.30 inference(transitivity,[status(thm)],[413, 411])).
% 56.06/56.30 tff(415,plain,
% 56.06/56.30 ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(Y24!0, tptp_fun_Y16_13(elem!24))) | id(tptp_fun_Y18_16(elem!24), tptp_fun_Y16_13(elem!24)) | (~id(tptp_fun_Y18_16(elem!24), Y24!0)))),
% 56.06/56.30 inference(quant_inst,[status(thm)],[])).
% 56.06/56.30 tff(416,plain,
% 56.06/56.30 ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | (~id(tptp_fun_Y18_16(elem!24), Y24!0)) | (~id(Y24!0, tptp_fun_Y16_13(elem!24))) | id(tptp_fun_Y18_16(elem!24), tptp_fun_Y16_13(elem!24))),
% 56.06/56.30 inference(modus_ponens,[status(thm)],[415, 414])).
% 56.06/56.30 tff(417,plain,
% 56.06/56.30 (id(tptp_fun_Y18_16(elem!24), tptp_fun_Y16_13(elem!24))),
% 56.06/56.30 inference(unit_resolution,[status(thm)],[416, 303, 90, 410])).
% 56.06/56.30 tff(418,plain,
% 56.06/56.30 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y18_16(elem!24), tptp_fun_Y16_13(elem!24))) | (~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) | (~(r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(tptp_fun_Y18_16(elem!24), tptp_fun_Y16_13(elem!24))) | (~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) | (~(r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))),
% 56.06/56.30 inference(rewrite,[status(thm)],[])).
% 56.06/56.30 tff(419,plain,
% 56.06/56.30 (((~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(tptp_fun_Y18_16(elem!24), tptp_fun_Y16_13(elem!24))) | (~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) | (~(r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) <=> ((~id(tptp_fun_Y18_16(elem!24), tptp_fun_Y16_13(elem!24))) | (~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) | (~(r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))),
% 56.06/56.30 inference(rewrite,[status(thm)],[])).
% 56.06/56.30 tff(420,plain,
% 56.06/56.30 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(tptp_fun_Y18_16(elem!24), tptp_fun_Y16_13(elem!24))) | (~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) | (~(r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y18_16(elem!24), tptp_fun_Y16_13(elem!24))) | (~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) | (~(r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))),
% 56.06/56.30 inference(monotonicity,[status(thm)],[419])).
% 56.06/56.30 tff(421,plain,
% 56.06/56.30 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(tptp_fun_Y18_16(elem!24), tptp_fun_Y16_13(elem!24))) | (~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) | (~(r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(tptp_fun_Y18_16(elem!24), tptp_fun_Y16_13(elem!24))) | (~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) | (~(r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))),
% 56.06/56.30 inference(transitivity,[status(thm)],[420, 418])).
% 56.06/56.30 tff(422,plain,
% 56.06/56.30 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(tptp_fun_Y18_16(elem!24), tptp_fun_Y16_13(elem!24))) | (~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) | (~(r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))),
% 56.06/56.30 inference(quant_inst,[status(thm)],[])).
% 56.06/56.30 tff(423,plain,
% 56.06/56.30 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(tptp_fun_Y18_16(elem!24), tptp_fun_Y16_13(elem!24))) | (~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) | (~(r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))),
% 56.06/56.30 inference(modus_ponens,[status(thm)],[422, 421])).
% 56.06/56.30 tff(424,plain,
% 56.06/56.30 ((~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) | (~(r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))),
% 56.06/56.30 inference(unit_resolution,[status(thm)],[423, 117, 417, 394])).
% 56.06/56.30 tff(425,plain,
% 56.06/56.30 (~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))),
% 56.06/56.30 inference(unit_resolution,[status(thm)],[424, 406])).
% 56.06/56.30 tff(426,plain,
% 56.06/56.30 (((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))),
% 56.06/56.30 inference(tautology,[status(thm)],[])).
% 56.06/56.30 tff(427,plain,
% 56.06/56.30 (r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))),
% 56.06/56.30 inference(unit_resolution,[status(thm)],[426, 425])).
% 56.06/56.30 tff(428,plain,
% 56.06/56.30 (((~![Y13: $i] : ((~id(Y13, tptp_fun_Y2_20(elem!24))) | (~r2(tptp_fun_Y18_16(elem!24), Y13)))) | ((~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(elem!24))) | (~r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) <=> ((~![Y13: $i] : ((~id(Y13, tptp_fun_Y2_20(elem!24))) | (~r2(tptp_fun_Y18_16(elem!24), Y13)))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(elem!24))) | (~r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))),
% 56.06/56.30 inference(rewrite,[status(thm)],[])).
% 56.06/56.30 tff(429,plain,
% 56.06/56.30 ((~![Y13: $i] : ((~id(Y13, tptp_fun_Y2_20(elem!24))) | (~r2(tptp_fun_Y18_16(elem!24), Y13)))) | ((~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(elem!24))) | (~r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))),
% 56.06/56.30 inference(quant_inst,[status(thm)],[])).
% 56.06/56.30 tff(430,plain,
% 56.06/56.30 ((~![Y13: $i] : ((~id(Y13, tptp_fun_Y2_20(elem!24))) | (~r2(tptp_fun_Y18_16(elem!24), Y13)))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(elem!24))) | (~r2(tptp_fun_Y18_16(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))),
% 56.06/56.30 inference(modus_ponens,[status(thm)],[429, 428])).
% 56.06/56.30 tff(431,plain,
% 56.06/56.30 (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(elem!24))),
% 56.06/56.30 inference(unit_resolution,[status(thm)],[430, 427, 379])).
% 56.06/56.30 tff(432,plain,
% 56.06/56.30 (((~![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))) | (id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(elem!24)) | ![Y12: $i] : ((~r2(tptp_fun_Y2_20(elem!24), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13)))))) <=> ((~![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(elem!24)) | ![Y12: $i] : ((~r2(tptp_fun_Y2_20(elem!24), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13)))))),
% 56.06/56.30 inference(rewrite,[status(thm)],[])).
% 56.06/56.30 tff(433,plain,
% 56.06/56.30 ((~![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))) | (id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(elem!24)) | ![Y12: $i] : ((~r2(tptp_fun_Y2_20(elem!24), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13)))))),
% 56.06/56.30 inference(quant_inst,[status(thm)],[])).
% 56.06/56.30 tff(434,plain,
% 56.06/56.30 ((~![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(elem!24)) | ![Y12: $i] : ((~r2(tptp_fun_Y2_20(elem!24), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13))))),
% 56.06/56.30 inference(modus_ponens,[status(thm)],[433, 432])).
% 56.06/56.30 tff(435,plain,
% 56.06/56.30 (![Y12: $i] : ((~r2(tptp_fun_Y2_20(elem!24), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13))))),
% 56.06/56.30 inference(unit_resolution,[status(thm)],[434, 249, 431])).
% 56.06/56.30 tff(436,plain,
% 56.06/56.30 ((r2(elem!24, tptp_fun_Y21_1(elem!24)) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(elem!24, tptp_fun_Y21_1(elem!24)))),
% 56.06/56.30 inference(tautology,[status(thm)],[])).
% 56.06/56.30 tff(437,plain,
% 56.06/56.30 (r2(elem!24, tptp_fun_Y21_1(elem!24)) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))),
% 56.06/56.30 inference(unit_resolution,[status(thm)],[436, 353])).
% 56.06/56.30 tff(438,plain,
% 56.06/56.30 (((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | ((~id(tptp_fun_Y9_12(elem!24), elem!24)) | id(elem!24, tptp_fun_Y9_12(elem!24)))) <=> ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | (~id(tptp_fun_Y9_12(elem!24), elem!24)) | id(elem!24, tptp_fun_Y9_12(elem!24)))),
% 56.06/56.30 inference(rewrite,[status(thm)],[])).
% 56.06/56.30 tff(439,plain,
% 56.06/56.30 ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | ((~id(tptp_fun_Y9_12(elem!24), elem!24)) | id(elem!24, tptp_fun_Y9_12(elem!24)))),
% 56.06/56.30 inference(quant_inst,[status(thm)],[])).
% 56.06/56.30 tff(440,plain,
% 56.06/56.30 ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | (~id(tptp_fun_Y9_12(elem!24), elem!24)) | id(elem!24, tptp_fun_Y9_12(elem!24))),
% 56.06/56.30 inference(modus_ponens,[status(thm)],[439, 438])).
% 56.06/56.30 tff(441,plain,
% 56.06/56.30 (id(elem!24, tptp_fun_Y9_12(elem!24))),
% 56.06/56.30 inference(unit_resolution,[status(thm)],[440, 154, 104])).
% 56.06/56.30 tff(442,plain,
% 56.06/56.30 (((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(tptp_fun_Y9_12(elem!24), elem!24)) | (~id(elem!24, tptp_fun_Y9_12(elem!24))) | id(elem!24, elem!24))) <=> ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | (~id(tptp_fun_Y9_12(elem!24), elem!24)) | (~id(elem!24, tptp_fun_Y9_12(elem!24))) | id(elem!24, elem!24))),
% 56.06/56.30 inference(rewrite,[status(thm)],[])).
% 56.06/56.30 tff(443,plain,
% 56.06/56.30 (((~id(tptp_fun_Y9_12(elem!24), elem!24)) | id(elem!24, elem!24) | (~id(elem!24, tptp_fun_Y9_12(elem!24)))) <=> ((~id(tptp_fun_Y9_12(elem!24), elem!24)) | (~id(elem!24, tptp_fun_Y9_12(elem!24))) | id(elem!24, elem!24))),
% 56.06/56.30 inference(rewrite,[status(thm)],[])).
% 56.06/56.30 tff(444,plain,
% 56.06/56.30 (((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(tptp_fun_Y9_12(elem!24), elem!24)) | id(elem!24, elem!24) | (~id(elem!24, tptp_fun_Y9_12(elem!24))))) <=> ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(tptp_fun_Y9_12(elem!24), elem!24)) | (~id(elem!24, tptp_fun_Y9_12(elem!24))) | id(elem!24, elem!24)))),
% 56.06/56.30 inference(monotonicity,[status(thm)],[443])).
% 56.06/56.30 tff(445,plain,
% 56.06/56.30 (((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(tptp_fun_Y9_12(elem!24), elem!24)) | id(elem!24, elem!24) | (~id(elem!24, tptp_fun_Y9_12(elem!24))))) <=> ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | (~id(tptp_fun_Y9_12(elem!24), elem!24)) | (~id(elem!24, tptp_fun_Y9_12(elem!24))) | id(elem!24, elem!24))),
% 56.06/56.30 inference(transitivity,[status(thm)],[444, 442])).
% 56.06/56.30 tff(446,plain,
% 56.06/56.30 ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(tptp_fun_Y9_12(elem!24), elem!24)) | id(elem!24, elem!24) | (~id(elem!24, tptp_fun_Y9_12(elem!24))))),
% 56.06/56.30 inference(quant_inst,[status(thm)],[])).
% 56.06/56.30 tff(447,plain,
% 56.06/56.30 ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | (~id(tptp_fun_Y9_12(elem!24), elem!24)) | (~id(elem!24, tptp_fun_Y9_12(elem!24))) | id(elem!24, elem!24)),
% 56.06/56.30 inference(modus_ponens,[status(thm)],[446, 445])).
% 56.06/56.30 tff(448,plain,
% 56.06/56.30 (id(elem!24, elem!24)),
% 56.06/56.30 inference(unit_resolution,[status(thm)],[447, 303, 104, 441])).
% 56.06/56.30 tff(449,plain,
% 56.06/56.30 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(elem!24, elem!24)) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~(r2(elem!24, tptp_fun_Y21_1(elem!24)) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(elem!24, elem!24)) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~(r2(elem!24, tptp_fun_Y21_1(elem!24)) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))))),
% 56.06/56.30 inference(rewrite,[status(thm)],[])).
% 56.06/56.30 tff(450,plain,
% 56.06/56.30 (((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(elem!24, elem!24)) | (~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(elem!24, tptp_fun_Y21_1(elem!24)) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) <=> ((~id(elem!24, elem!24)) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~(r2(elem!24, tptp_fun_Y21_1(elem!24)) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))))),
% 56.06/56.30 inference(rewrite,[status(thm)],[])).
% 56.06/56.30 tff(451,plain,
% 56.06/56.30 ((~(r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(elem!24, tptp_fun_Y21_1(elem!24)))) <=> (~(r2(elem!24, tptp_fun_Y21_1(elem!24)) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))),
% 56.06/56.30 inference(rewrite,[status(thm)],[])).
% 56.06/56.30 tff(452,plain,
% 56.06/56.30 ((~((~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(elem!24, tptp_fun_Y21_1(elem!24))))) <=> (~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.30 inference(rewrite,[status(thm)],[])).
% 56.06/56.30 tff(453,plain,
% 56.06/56.30 (((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(elem!24, elem!24)) | (~((~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(elem!24, tptp_fun_Y21_1(elem!24))))) | (~(r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(elem!24, tptp_fun_Y21_1(elem!24))))) <=> ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(elem!24, elem!24)) | (~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(elem!24, tptp_fun_Y21_1(elem!24)) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.30 inference(monotonicity,[status(thm)],[452, 451])).
% 56.06/56.30 tff(454,plain,
% 56.06/56.30 (((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(elem!24, elem!24)) | (~((~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(elem!24, tptp_fun_Y21_1(elem!24))))) | (~(r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(elem!24, tptp_fun_Y21_1(elem!24))))) <=> ((~id(elem!24, elem!24)) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~(r2(elem!24, tptp_fun_Y21_1(elem!24)) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))))),
% 56.06/56.30 inference(transitivity,[status(thm)],[453, 450])).
% 56.06/56.30 tff(455,plain,
% 56.06/56.30 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(elem!24, elem!24)) | (~((~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(elem!24, tptp_fun_Y21_1(elem!24))))) | (~(r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(elem!24, tptp_fun_Y21_1(elem!24)))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(elem!24, elem!24)) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~(r2(elem!24, tptp_fun_Y21_1(elem!24)) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))))),
% 56.06/56.30 inference(monotonicity,[status(thm)],[454])).
% 56.06/56.30 tff(456,plain,
% 56.06/56.30 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(elem!24, elem!24)) | (~((~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(elem!24, tptp_fun_Y21_1(elem!24))))) | (~(r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(elem!24, tptp_fun_Y21_1(elem!24)))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(elem!24, elem!24)) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~(r2(elem!24, tptp_fun_Y21_1(elem!24)) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))))),
% 56.06/56.30 inference(transitivity,[status(thm)],[455, 449])).
% 56.06/56.30 tff(457,plain,
% 56.06/56.30 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(elem!24, elem!24)) | (~((~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(elem!24, tptp_fun_Y21_1(elem!24))))) | (~(r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(elem!24, tptp_fun_Y21_1(elem!24)))))),
% 56.06/56.30 inference(quant_inst,[status(thm)],[])).
% 56.06/56.30 tff(458,plain,
% 56.06/56.30 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(elem!24, elem!24)) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~(r2(elem!24, tptp_fun_Y21_1(elem!24)) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.30 inference(modus_ponens,[status(thm)],[457, 456])).
% 56.06/56.30 tff(459,plain,
% 56.06/56.30 ((~(r2(elem!24, tptp_fun_Y21_1(elem!24)) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.30 inference(unit_resolution,[status(thm)],[458, 117, 448, 259])).
% 56.06/56.30 tff(460,plain,
% 56.06/56.30 (~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))),
% 56.06/56.30 inference(unit_resolution,[status(thm)],[459, 437])).
% 56.06/56.30 tff(461,plain,
% 56.06/56.30 (((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))),
% 56.06/56.30 inference(tautology,[status(thm)],[])).
% 56.06/56.30 tff(462,plain,
% 56.06/56.30 (r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))),
% 56.06/56.30 inference(unit_resolution,[status(thm)],[461, 460])).
% 56.06/56.30 tff(463,plain,
% 56.06/56.30 ((r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))),
% 56.06/56.30 inference(tautology,[status(thm)],[])).
% 56.06/56.30 tff(464,plain,
% 56.06/56.30 (r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))),
% 56.06/56.30 inference(unit_resolution,[status(thm)],[463, 462])).
% 56.06/56.30 tff(465,plain,
% 56.06/56.30 ((r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))),
% 56.06/56.30 inference(tautology,[status(thm)],[])).
% 56.06/56.30 tff(466,plain,
% 56.06/56.30 (r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))),
% 56.06/56.30 inference(unit_resolution,[status(thm)],[465, 462])).
% 56.06/56.30 tff(467,plain,
% 56.06/56.30 (((~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24))) | (~r1(tptp_fun_Y4_22(elem!24))) | (~r2(tptp_fun_Y4_22(elem!24), tptp_fun_Y3_21(elem!24)))) | id(elem!24, tptp_fun_Y2_20(elem!24))),
% 56.06/56.30 inference(tautology,[status(thm)],[])).
% 56.06/56.30 tff(468,plain,
% 56.06/56.30 (id(elem!24, tptp_fun_Y2_20(elem!24))),
% 56.06/56.30 inference(unit_resolution,[status(thm)],[467, 356])).
% 56.06/56.30 tff(469,plain,
% 56.06/56.30 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))))),
% 56.06/56.30 inference(rewrite,[status(thm)],[])).
% 56.06/56.30 tff(470,plain,
% 56.06/56.30 (((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))) | (~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) <=> ((~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))))),
% 56.06/56.30 inference(rewrite,[status(thm)],[])).
% 56.06/56.30 tff(471,plain,
% 56.06/56.30 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))) | (~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24)))))),
% 56.06/56.30 inference(monotonicity,[status(thm)],[470])).
% 56.06/56.30 tff(472,plain,
% 56.06/56.30 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))) | (~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))))),
% 56.06/56.30 inference(transitivity,[status(thm)],[471, 469])).
% 56.06/56.30 tff(473,plain,
% 56.06/56.30 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24))) | (~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))),
% 56.06/56.30 inference(quant_inst,[status(thm)],[])).
% 56.06/56.30 tff(474,plain,
% 56.06/56.30 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(elem!24)))),
% 56.16/56.31 inference(modus_ponens,[status(thm)],[473, 472])).
% 56.16/56.31 tff(475,plain,
% 56.16/56.31 (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))),
% 56.16/56.31 inference(unit_resolution,[status(thm)],[474, 117, 468, 263, 466])).
% 56.16/56.31 tff(476,plain,
% 56.16/56.31 (((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))),
% 56.16/56.31 inference(tautology,[status(thm)],[])).
% 56.16/56.31 tff(477,plain,
% 56.16/56.31 (r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))),
% 56.16/56.31 inference(unit_resolution,[status(thm)],[476, 475])).
% 56.16/56.31 tff(478,plain,
% 56.16/56.31 ((r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)) | r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)))),
% 56.16/56.31 inference(tautology,[status(thm)],[])).
% 56.16/56.31 tff(479,plain,
% 56.16/56.31 (r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)) | r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))),
% 56.16/56.31 inference(unit_resolution,[status(thm)],[478, 477])).
% 56.16/56.31 tff(480,plain,
% 56.16/56.31 ((r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24)) | id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))) | (~r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24)))),
% 56.16/56.31 inference(tautology,[status(thm)],[])).
% 56.16/56.31 tff(481,plain,
% 56.16/56.31 (r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24)) | id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))),
% 56.16/56.31 inference(unit_resolution,[status(thm)],[480, 375])).
% 56.16/56.31 tff(482,plain,
% 56.16/56.31 (((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | ((~((~r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24))) | (~id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))) | (~(r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24)) | id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))) <=> ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | (~((~r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24))) | (~id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))) | (~(r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24)) | id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))),
% 56.16/56.31 inference(rewrite,[status(thm)],[])).
% 56.16/56.31 tff(483,plain,
% 56.16/56.31 ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | ((~((~r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24))) | (~id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))) | (~(r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24)) | id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))),
% 56.16/56.31 inference(quant_inst,[status(thm)],[])).
% 56.16/56.31 tff(484,plain,
% 56.16/56.31 ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | (~((~r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24))) | (~id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))) | (~(r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24)) | id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))),
% 56.16/56.31 inference(modus_ponens,[status(thm)],[483, 482])).
% 56.16/56.31 tff(485,plain,
% 56.16/56.31 (~((~r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24))) | (~id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))),
% 56.16/56.31 inference(unit_resolution,[status(thm)],[484, 141, 481])).
% 56.16/56.31 tff(486,plain,
% 56.16/56.31 (((~r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24))) | (~id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))),
% 56.16/56.31 inference(tautology,[status(thm)],[])).
% 56.16/56.31 tff(487,plain,
% 56.16/56.31 (id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))),
% 56.16/56.31 inference(unit_resolution,[status(thm)],[486, 485])).
% 56.16/56.31 tff(488,plain,
% 56.16/56.31 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~(r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)) | r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~(r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)) | r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))))),
% 56.16/56.31 inference(rewrite,[status(thm)],[])).
% 56.16/56.31 tff(489,plain,
% 56.16/56.31 (((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))) | (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)) | r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) <=> ((~id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~(r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)) | r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))))),
% 56.16/56.31 inference(rewrite,[status(thm)],[])).
% 56.16/56.31 tff(490,plain,
% 56.16/56.31 ((~(r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)))) <=> (~(r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)) | r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))),
% 56.16/56.31 inference(rewrite,[status(thm)],[])).
% 56.16/56.31 tff(491,plain,
% 56.16/56.31 ((~((~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))))) <=> (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))),
% 56.16/56.31 inference(rewrite,[status(thm)],[])).
% 56.16/56.31 tff(492,plain,
% 56.16/56.31 (((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))))) <=> ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))) | (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)) | r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))),
% 56.16/56.31 inference(monotonicity,[status(thm)],[491, 490])).
% 56.16/56.31 tff(493,plain,
% 56.16/56.31 (((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))))) <=> ((~id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~(r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)) | r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))))),
% 56.16/56.31 inference(transitivity,[status(thm)],[492, 489])).
% 56.16/56.31 tff(494,plain,
% 56.16/56.31 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~(r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)) | r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))))),
% 56.16/56.31 inference(monotonicity,[status(thm)],[493])).
% 56.16/56.31 tff(495,plain,
% 56.16/56.31 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~(r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)) | r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))))),
% 56.16/56.31 inference(transitivity,[status(thm)],[494, 488])).
% 56.16/56.31 tff(496,plain,
% 56.16/56.31 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)))))),
% 56.16/56.31 inference(quant_inst,[status(thm)],[])).
% 56.16/56.31 tff(497,plain,
% 56.16/56.31 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~(r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24)) | r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))),
% 56.16/56.31 inference(modus_ponens,[status(thm)],[496, 495])).
% 56.16/56.31 tff(498,plain,
% 56.16/56.31 (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))),
% 56.16/56.31 inference(unit_resolution,[status(thm)],[497, 117, 259, 487, 479])).
% 56.16/56.31 tff(499,plain,
% 56.16/56.31 (((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(elem!24))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))),
% 56.16/56.31 inference(tautology,[status(thm)],[])).
% 56.16/56.31 tff(500,plain,
% 56.16/56.31 (r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))),
% 56.16/56.31 inference(unit_resolution,[status(thm)],[499, 498])).
% 56.16/56.31 tff(501,plain,
% 56.16/56.31 ((r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))),
% 56.16/56.31 inference(tautology,[status(thm)],[])).
% 56.16/56.31 tff(502,plain,
% 56.16/56.31 (r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))),
% 56.16/56.31 inference(unit_resolution,[status(thm)],[501, 500])).
% 56.16/56.31 tff(503,plain,
% 56.16/56.31 (((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | ((~(r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))))) <=> ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))))),
% 56.16/56.31 inference(rewrite,[status(thm)],[])).
% 56.16/56.31 tff(504,plain,
% 56.16/56.31 (((~((~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))) <=> ((~(r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))))),
% 56.16/56.31 inference(rewrite,[status(thm)],[])).
% 56.16/56.31 tff(505,plain,
% 56.16/56.31 (((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | ((~((~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))))) <=> ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | ((~(r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))))))),
% 56.16/56.31 inference(monotonicity,[status(thm)],[504])).
% 56.16/56.31 tff(506,plain,
% 56.16/56.31 (((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | ((~((~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))))) <=> ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))))),
% 56.16/56.31 inference(transitivity,[status(thm)],[505, 503])).
% 56.16/56.31 tff(507,plain,
% 56.16/56.31 ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | ((~((~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))))),
% 56.16/56.31 inference(quant_inst,[status(thm)],[])).
% 56.16/56.31 tff(508,plain,
% 56.16/56.31 ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))))),
% 56.16/56.31 inference(modus_ponens,[status(thm)],[507, 506])).
% 56.16/56.31 tff(509,plain,
% 56.16/56.31 (~((~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))),
% 56.16/56.31 inference(unit_resolution,[status(thm)],[508, 141, 502])).
% 56.16/56.31 tff(510,plain,
% 56.16/56.31 (((~r2(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))) | id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))),
% 56.16/56.31 inference(tautology,[status(thm)],[])).
% 56.16/56.31 tff(511,plain,
% 56.16/56.31 (id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))),
% 56.16/56.31 inference(unit_resolution,[status(thm)],[510, 509])).
% 56.16/56.31 tff(512,plain,
% 56.16/56.31 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~(r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))) | (~((~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~(r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))) | (~((~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))),
% 56.16/56.31 inference(rewrite,[status(thm)],[])).
% 56.16/56.31 tff(513,plain,
% 56.16/56.31 (((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | (~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~((~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))) | (~(r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))) <=> ((~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~(r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))) | (~((~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))),
% 56.16/56.31 inference(rewrite,[status(thm)],[])).
% 56.16/56.31 tff(514,plain,
% 56.16/56.31 ((~(r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) <=> (~(r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))),
% 56.16/56.31 inference(rewrite,[status(thm)],[])).
% 56.16/56.31 tff(515,plain,
% 56.16/56.31 ((~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) <=> (~((~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))))),
% 56.16/56.31 inference(rewrite,[status(thm)],[])).
% 56.16/56.31 tff(516,plain,
% 56.16/56.31 (((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | (~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) <=> ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | (~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~((~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))) | (~(r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))))),
% 56.16/56.31 inference(monotonicity,[status(thm)],[515, 514])).
% 56.16/56.31 tff(517,plain,
% 56.16/56.31 (((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | (~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) <=> ((~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~(r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))) | (~((~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))),
% 56.16/56.31 inference(transitivity,[status(thm)],[516, 513])).
% 56.16/56.31 tff(518,plain,
% 56.16/56.31 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | (~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~(r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))) | (~((~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))))),
% 56.16/56.31 inference(monotonicity,[status(thm)],[517])).
% 56.16/56.31 tff(519,plain,
% 56.16/56.31 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | (~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~(r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))) | (~((~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))),
% 56.16/56.31 inference(transitivity,[status(thm)],[518, 512])).
% 56.16/56.31 tff(520,plain,
% 56.16/56.31 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | (~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | (~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))) | r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))),
% 56.16/56.31 inference(quant_inst,[status(thm)],[])).
% 56.16/56.31 tff(521,plain,
% 56.16/56.31 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~(r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))) | (~((~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))),
% 56.16/56.31 inference(modus_ponens,[status(thm)],[520, 519])).
% 56.16/56.31 tff(522,plain,
% 56.16/56.31 (~((~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))),
% 56.16/56.31 inference(unit_resolution,[status(thm)],[521, 117, 468, 511, 464])).
% 56.16/56.31 tff(523,plain,
% 56.16/56.31 (((~r2(elem!24, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))) | r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))),
% 56.16/56.31 inference(tautology,[status(thm)],[])).
% 56.16/56.31 tff(524,plain,
% 56.16/56.31 (r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))),
% 56.16/56.31 inference(unit_resolution,[status(thm)],[523, 522])).
% 56.16/56.31 tff(525,plain,
% 56.16/56.31 (((~![Y12: $i] : ((~r2(tptp_fun_Y2_20(elem!24), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13))))) | ((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | ![Y13: $i] : ((~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13)) | (~id(Y13, tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))))) <=> ((~![Y12: $i] : ((~r2(tptp_fun_Y2_20(elem!24), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13))))) | (~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | ![Y13: $i] : ((~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13)) | (~id(Y13, tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))))),
% 56.16/56.31 inference(rewrite,[status(thm)],[])).
% 56.16/56.31 tff(526,plain,
% 56.16/56.31 (((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | ![Y13: $i] : ((~id(Y13, tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13)))) <=> ((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | ![Y13: $i] : ((~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13)) | (~id(Y13, tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))))),
% 56.16/56.31 inference(rewrite,[status(thm)],[])).
% 56.16/56.31 tff(527,plain,
% 56.16/56.31 (((~![Y12: $i] : ((~r2(tptp_fun_Y2_20(elem!24), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13))))) | ((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | ![Y13: $i] : ((~id(Y13, tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13))))) <=> ((~![Y12: $i] : ((~r2(tptp_fun_Y2_20(elem!24), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13))))) | ((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | ![Y13: $i] : ((~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13)) | (~id(Y13, tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))))),
% 56.16/56.31 inference(monotonicity,[status(thm)],[526])).
% 56.16/56.31 tff(528,plain,
% 56.16/56.31 (((~![Y12: $i] : ((~r2(tptp_fun_Y2_20(elem!24), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13))))) | ((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | ![Y13: $i] : ((~id(Y13, tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13))))) <=> ((~![Y12: $i] : ((~r2(tptp_fun_Y2_20(elem!24), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13))))) | (~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | ![Y13: $i] : ((~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13)) | (~id(Y13, tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))))),
% 56.16/56.31 inference(transitivity,[status(thm)],[527, 525])).
% 56.16/56.31 tff(529,plain,
% 56.16/56.31 ((~![Y12: $i] : ((~r2(tptp_fun_Y2_20(elem!24), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13))))) | ((~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | ![Y13: $i] : ((~id(Y13, tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13))))),
% 56.16/56.31 inference(quant_inst,[status(thm)],[])).
% 56.16/56.31 tff(530,plain,
% 56.16/56.31 ((~![Y12: $i] : ((~r2(tptp_fun_Y2_20(elem!24), Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13))))) | (~r2(tptp_fun_Y2_20(elem!24), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))) | ![Y13: $i] : ((~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13)) | (~id(Y13, tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))),
% 56.16/56.31 inference(modus_ponens,[status(thm)],[529, 528])).
% 56.16/56.31 tff(531,plain,
% 56.16/56.31 (![Y13: $i] : ((~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13)) | (~id(Y13, tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))),
% 56.16/56.31 inference(unit_resolution,[status(thm)],[530, 524, 435])).
% 56.16/56.31 tff(532,plain,
% 56.16/56.31 ((r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))),
% 56.16/56.31 inference(tautology,[status(thm)],[])).
% 56.16/56.31 tff(533,plain,
% 56.16/56.31 (r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))),
% 56.16/56.31 inference(unit_resolution,[status(thm)],[532, 255])).
% 56.16/56.31 tff(534,plain,
% 56.16/56.31 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))))),
% 56.16/56.31 inference(rewrite,[status(thm)],[])).
% 56.16/56.31 tff(535,plain,
% 56.16/56.31 (((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))) <=> ((~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))))),
% 56.16/56.31 inference(rewrite,[status(thm)],[])).
% 56.16/56.31 tff(536,plain,
% 56.16/56.31 ((~(r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) <=> (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))),
% 56.16/56.31 inference(rewrite,[status(thm)],[])).
% 56.16/56.31 tff(537,plain,
% 56.16/56.31 ((~((~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) <=> (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))))),
% 56.16/56.31 inference(rewrite,[status(thm)],[])).
% 56.16/56.31 tff(538,plain,
% 56.16/56.31 (((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) <=> ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))))),
% 56.16/56.31 inference(monotonicity,[status(thm)],[537, 536])).
% 56.16/56.31 tff(539,plain,
% 56.16/56.31 (((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) <=> ((~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))))),
% 56.16/56.32 inference(transitivity,[status(thm)],[538, 535])).
% 56.16/56.32 tff(540,plain,
% 56.16/56.32 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))))))),
% 56.16/56.32 inference(monotonicity,[status(thm)],[539])).
% 56.16/56.32 tff(541,plain,
% 56.16/56.32 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))))),
% 56.16/56.32 inference(transitivity,[status(thm)],[540, 534])).
% 56.16/56.32 tff(542,plain,
% 56.16/56.32 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))),
% 56.16/56.32 inference(quant_inst,[status(thm)],[])).
% 56.16/56.32 tff(543,plain,
% 56.16/56.32 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~(r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))) | (~id(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))))),
% 56.16/56.32 inference(modus_ponens,[status(thm)],[542, 541])).
% 56.16/56.32 tff(544,plain,
% 56.16/56.32 (~((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))),
% 56.16/56.32 inference(unit_resolution,[status(thm)],[543, 117, 271, 294, 533])).
% 56.16/56.32 tff(545,plain,
% 56.16/56.32 (((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))),
% 56.16/56.32 inference(tautology,[status(thm)],[])).
% 56.16/56.32 tff(546,plain,
% 56.16/56.32 (r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))),
% 56.16/56.32 inference(unit_resolution,[status(thm)],[545, 544])).
% 56.16/56.32 tff(547,plain,
% 56.16/56.32 ((r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))),
% 56.16/56.32 inference(tautology,[status(thm)],[])).
% 56.16/56.32 tff(548,plain,
% 56.16/56.32 (r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))),
% 56.16/56.32 inference(unit_resolution,[status(thm)],[547, 546])).
% 56.16/56.32 tff(549,plain,
% 56.16/56.32 ((r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))),
% 56.16/56.32 inference(tautology,[status(thm)],[])).
% 56.16/56.32 tff(550,plain,
% 56.16/56.32 (r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))),
% 56.16/56.32 inference(unit_resolution,[status(thm)],[549, 404])).
% 56.16/56.32 tff(551,plain,
% 56.16/56.32 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(Y24!0, tptp_fun_Y16_13(elem!24))) | (~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))) | (~(r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(Y24!0, tptp_fun_Y16_13(elem!24))) | (~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))) | (~(r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))))),
% 56.16/56.32 inference(rewrite,[status(thm)],[])).
% 56.16/56.32 tff(552,plain,
% 56.16/56.32 (((~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(Y24!0, tptp_fun_Y16_13(elem!24))) | (~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))) | (~(r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))) <=> ((~id(Y24!0, tptp_fun_Y16_13(elem!24))) | (~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))) | (~(r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))))),
% 56.16/56.32 inference(rewrite,[status(thm)],[])).
% 56.16/56.32 tff(553,plain,
% 56.16/56.32 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(Y24!0, tptp_fun_Y16_13(elem!24))) | (~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))) | (~(r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(Y24!0, tptp_fun_Y16_13(elem!24))) | (~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))) | (~(r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))))),
% 56.16/56.32 inference(monotonicity,[status(thm)],[552])).
% 56.16/56.32 tff(554,plain,
% 56.16/56.32 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(Y24!0, tptp_fun_Y16_13(elem!24))) | (~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))) | (~(r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(Y24!0, tptp_fun_Y16_13(elem!24))) | (~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))) | (~(r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))))),
% 56.16/56.32 inference(transitivity,[status(thm)],[553, 551])).
% 56.16/56.32 tff(555,plain,
% 56.16/56.32 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(Y24!0, tptp_fun_Y16_13(elem!24))) | (~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))) | (~(r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))))),
% 56.16/56.32 inference(quant_inst,[status(thm)],[])).
% 56.16/56.32 tff(556,plain,
% 56.16/56.32 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(Y24!0, tptp_fun_Y16_13(elem!24))) | (~id(tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))) | (~(r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))),
% 56.16/56.32 inference(modus_ponens,[status(thm)],[555, 554])).
% 56.16/56.32 tff(557,plain,
% 56.16/56.32 ((~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))) | (~(r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))),
% 56.16/56.32 inference(unit_resolution,[status(thm)],[556, 117, 410, 383])).
% 56.16/56.32 tff(558,plain,
% 56.16/56.32 (~((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))),
% 56.16/56.32 inference(unit_resolution,[status(thm)],[557, 550])).
% 56.16/56.32 tff(559,plain,
% 56.16/56.32 (((~r2(tptp_fun_Y16_13(elem!24), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) | r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))),
% 56.16/56.32 inference(tautology,[status(thm)],[])).
% 56.16/56.32 tff(560,plain,
% 56.16/56.32 (r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))),
% 56.16/56.32 inference(unit_resolution,[status(thm)],[559, 558])).
% 56.16/56.32 tff(561,plain,
% 56.16/56.32 ((r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))),
% 56.16/56.32 inference(tautology,[status(thm)],[])).
% 56.16/56.32 tff(562,plain,
% 56.16/56.32 (r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))),
% 56.16/56.32 inference(unit_resolution,[status(thm)],[561, 560])).
% 56.16/56.32 tff(563,plain,
% 56.16/56.32 (((~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))),
% 56.16/56.32 inference(tautology,[status(thm)],[])).
% 56.16/56.32 tff(564,plain,
% 56.16/56.32 (r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))),
% 56.16/56.32 inference(unit_resolution,[status(thm)],[563, 205])).
% 56.16/56.32 tff(565,plain,
% 56.16/56.32 ((r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0)) | (~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))),
% 56.16/56.32 inference(tautology,[status(thm)],[])).
% 56.16/56.32 tff(566,plain,
% 56.16/56.32 (r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0)),
% 56.16/56.32 inference(unit_resolution,[status(thm)],[565, 564])).
% 56.16/56.32 tff(567,plain,
% 56.16/56.32 (((~![X19: $i] : ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0))))) | ((~((~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0)))) | (~(r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0))))) | (~((~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0)))) | (~(r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0))))),
% 56.16/56.32 inference(rewrite,[status(thm)],[])).
% 56.16/56.32 tff(568,plain,
% 56.16/56.32 ((~![X19: $i] : ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0))))) | ((~((~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0)))) | (~(r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0))))),
% 56.16/56.32 inference(quant_inst,[status(thm)],[])).
% 56.16/56.32 tff(569,plain,
% 56.16/56.32 ((~![X19: $i] : ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0))))) | (~((~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0)))) | (~(r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))) | id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0)))),
% 56.16/56.32 inference(modus_ponens,[status(thm)],[568, 567])).
% 56.16/56.32 tff(570,plain,
% 56.16/56.32 (~((~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0)))),
% 56.16/56.32 inference(unit_resolution,[status(thm)],[569, 84, 566])).
% 56.16/56.32 tff(571,plain,
% 56.16/56.32 (((~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0))) | id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0)),
% 56.16/56.32 inference(tautology,[status(thm)],[])).
% 56.16/56.32 tff(572,plain,
% 56.16/56.32 (id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0)),
% 56.16/56.32 inference(unit_resolution,[status(thm)],[571, 570])).
% 56.16/56.32 tff(573,plain,
% 56.16/56.32 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0)) | (~(r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~((~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0)) | (~(r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~((~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))))),
% 56.16/56.32 inference(rewrite,[status(thm)],[])).
% 56.16/56.32 tff(574,plain,
% 56.16/56.32 (((~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0)) | (~((~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) | (~(r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) <=> ((~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0)) | (~(r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~((~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))))),
% 56.16/56.32 inference(rewrite,[status(thm)],[])).
% 56.16/56.32 tff(575,plain,
% 56.16/56.32 ((~(r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) <=> (~(r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))),
% 56.16/56.32 inference(rewrite,[status(thm)],[])).
% 56.16/56.32 tff(576,plain,
% 56.16/56.32 ((~((~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) <=> (~((~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))),
% 56.16/56.32 inference(rewrite,[status(thm)],[])).
% 56.16/56.32 tff(577,plain,
% 56.16/56.32 (((~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0)) | (~((~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) | (~(r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) <=> ((~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0)) | (~((~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) | (~(r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))),
% 56.16/56.32 inference(monotonicity,[status(thm)],[576, 575])).
% 56.16/56.32 tff(578,plain,
% 56.16/56.32 (((~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0)) | (~((~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) | (~(r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) <=> ((~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0)) | (~(r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~((~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))))),
% 56.16/56.32 inference(transitivity,[status(thm)],[577, 574])).
% 56.16/56.32 tff(579,plain,
% 56.16/56.32 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0)) | (~((~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) | (~(r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0)) | (~(r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~((~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))))),
% 56.16/56.32 inference(monotonicity,[status(thm)],[578])).
% 56.16/56.32 tff(580,plain,
% 56.16/56.32 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0)) | (~((~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) | (~(r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0)) | (~(r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~((~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))))),
% 56.16/56.32 inference(transitivity,[status(thm)],[579, 573])).
% 56.16/56.32 tff(581,plain,
% 56.16/56.32 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0)) | (~((~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))) | (~(r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))),
% 56.16/56.32 inference(quant_inst,[status(thm)],[])).
% 56.16/56.32 tff(582,plain,
% 56.16/56.32 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~id(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), Y24!0)) | (~(r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~((~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))))),
% 56.16/56.32 inference(modus_ponens,[status(thm)],[581, 580])).
% 56.16/56.32 tff(583,plain,
% 56.16/56.32 (~((~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))))),
% 56.16/56.32 inference(unit_resolution,[status(thm)],[582, 117, 387, 572, 562])).
% 56.16/56.32 tff(584,plain,
% 56.16/56.32 (((~r2(Y24!0, tptp_fun_Y9_12(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))) | r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))),
% 56.16/56.32 inference(tautology,[status(thm)],[])).
% 56.16/56.32 tff(585,plain,
% 56.16/56.32 (r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))),
% 56.16/56.32 inference(unit_resolution,[status(thm)],[584, 583])).
% 56.16/56.32 tff(586,plain,
% 56.16/56.32 ((r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))))),
% 56.16/56.32 inference(tautology,[status(thm)],[])).
% 56.16/56.32 tff(587,plain,
% 56.16/56.32 (r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))),
% 56.16/56.32 inference(unit_resolution,[status(thm)],[586, 585])).
% 56.16/56.32 tff(588,plain,
% 56.16/56.32 (((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | ((~((~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))))) | (~(r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))))))) <=> ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | (~((~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))))) | (~(r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))))))),
% 56.16/56.32 inference(rewrite,[status(thm)],[])).
% 56.16/56.32 tff(589,plain,
% 56.16/56.32 ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | ((~((~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))))) | (~(r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))))))),
% 56.16/56.32 inference(quant_inst,[status(thm)],[])).
% 56.16/56.32 tff(590,plain,
% 56.16/56.32 ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | (~((~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))))) | (~(r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))))),
% 56.16/56.32 inference(modus_ponens,[status(thm)],[589, 588])).
% 56.16/56.32 tff(591,plain,
% 56.16/56.32 (~((~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))))),
% 56.16/56.32 inference(unit_resolution,[status(thm)],[590, 141, 587])).
% 56.16/56.32 tff(592,plain,
% 56.16/56.32 (((~r2(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24)))))) | id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))),
% 56.16/56.32 inference(tautology,[status(thm)],[])).
% 56.16/56.32 tff(593,plain,
% 56.16/56.32 (id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))),
% 56.16/56.32 inference(unit_resolution,[status(thm)],[592, 591])).
% 56.16/56.32 tff(594,plain,
% 56.16/56.32 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))),
% 56.16/56.32 inference(rewrite,[status(thm)],[])).
% 56.16/56.32 tff(595,plain,
% 56.16/56.32 (((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))) <=> ((~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))),
% 56.16/56.32 inference(rewrite,[status(thm)],[])).
% 56.16/56.32 tff(596,plain,
% 56.16/56.32 ((~(r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) <=> (~(r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))),
% 56.16/56.32 inference(rewrite,[status(thm)],[])).
% 56.16/56.32 tff(597,plain,
% 56.16/56.32 ((~((~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) <=> (~((~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))))),
% 56.16/56.32 inference(rewrite,[status(thm)],[])).
% 56.16/56.32 tff(598,plain,
% 56.16/56.32 (((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) <=> ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))))),
% 56.16/56.32 inference(monotonicity,[status(thm)],[597, 596])).
% 56.16/56.32 tff(599,plain,
% 56.16/56.32 (((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) <=> ((~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))),
% 56.16/56.32 inference(transitivity,[status(thm)],[598, 595])).
% 56.16/56.32 tff(600,plain,
% 56.16/56.32 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))))),
% 56.16/56.32 inference(monotonicity,[status(thm)],[599])).
% 56.16/56.32 tff(601,plain,
% 56.16/56.32 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))),
% 56.16/56.32 inference(transitivity,[status(thm)],[600, 594])).
% 56.16/56.32 tff(602,plain,
% 56.16/56.32 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))) | r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))),
% 56.16/56.32 inference(quant_inst,[status(thm)],[])).
% 56.16/56.32 tff(603,plain,
% 56.16/56.32 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))),
% 56.16/56.32 inference(modus_ponens,[status(thm)],[602, 601])).
% 56.16/56.32 tff(604,plain,
% 56.16/56.32 (~((~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24))))))),
% 56.16/56.32 inference(unit_resolution,[status(thm)],[603, 117, 294, 593, 548])).
% 56.16/56.32 tff(605,plain,
% 56.16/56.32 (((~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y21_1(elem!24))), tptp_fun_Y21_1(tptp_fun_Y3_21(tptp_fun_Y21_1(elem!24)))))) | r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))),
% 56.16/56.33 inference(tautology,[status(thm)],[])).
% 56.16/56.33 tff(606,plain,
% 56.16/56.33 (r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))),
% 56.16/56.33 inference(unit_resolution,[status(thm)],[605, 604])).
% 56.16/56.33 tff(607,plain,
% 56.16/56.33 (((~![Y13: $i] : ((~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13)) | (~id(Y13, tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))) | ((~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))) <=> ((~![Y13: $i] : ((~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13)) | (~id(Y13, tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))),
% 56.16/56.33 inference(rewrite,[status(thm)],[])).
% 56.16/56.33 tff(608,plain,
% 56.16/56.33 ((~![Y13: $i] : ((~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13)) | (~id(Y13, tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))) | ((~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))),
% 56.16/56.33 inference(quant_inst,[status(thm)],[])).
% 56.16/56.33 tff(609,plain,
% 56.16/56.33 ((~![Y13: $i] : ((~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), Y13)) | (~id(Y13, tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24))))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y16_13(elem!24)), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y3_21(elem!24)))))),
% 56.16/56.33 inference(modus_ponens,[status(thm)],[608, 607])).
% 56.16/56.33 tff(610,plain,
% 56.16/56.33 ($false),
% 56.16/56.33 inference(unit_resolution,[status(thm)],[609, 606, 511, 531])).
% 56.16/56.33 tff(611,plain,((~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24))) | (~r1(tptp_fun_Y4_22(elem!24))) | (~r2(tptp_fun_Y4_22(elem!24), tptp_fun_Y3_21(elem!24)))), inference(lemma,lemma(discharge,[]))).
% 56.16/56.33 tff(612,plain,
% 56.16/56.33 (((~![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1))))) | (~((~id(Y1, tptp_fun_Y2_20(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | ((~((~r1(tptp_fun_Y5_23(elem!24))) | (~id(elem!24, tptp_fun_Y5_23(elem!24))))) | (~((~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24))) | (~r1(tptp_fun_Y4_22(elem!24))) | (~r2(tptp_fun_Y4_22(elem!24), tptp_fun_Y3_21(elem!24))))))) <=> ((~![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1))))) | (~((~id(Y1, tptp_fun_Y2_20(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | (~((~r1(tptp_fun_Y5_23(elem!24))) | (~id(elem!24, tptp_fun_Y5_23(elem!24))))) | (~((~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24))) | (~r1(tptp_fun_Y4_22(elem!24))) | (~r2(tptp_fun_Y4_22(elem!24), tptp_fun_Y3_21(elem!24))))))),
% 56.16/56.33 inference(rewrite,[status(thm)],[])).
% 56.16/56.33 tff(613,plain,
% 56.16/56.33 ((~![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1))))) | (~((~id(Y1, tptp_fun_Y2_20(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | ((~((~r1(tptp_fun_Y5_23(elem!24))) | (~id(elem!24, tptp_fun_Y5_23(elem!24))))) | (~((~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24))) | (~r1(tptp_fun_Y4_22(elem!24))) | (~r2(tptp_fun_Y4_22(elem!24), tptp_fun_Y3_21(elem!24))))))),
% 56.16/56.33 inference(quant_inst,[status(thm)],[])).
% 56.16/56.33 tff(614,plain,
% 56.16/56.33 ((~![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~id(Y1, tptp_fun_Y5_23(Y1))))) | (~((~id(Y1, tptp_fun_Y2_20(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | (~((~r1(tptp_fun_Y5_23(elem!24))) | (~id(elem!24, tptp_fun_Y5_23(elem!24))))) | (~((~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24))) | (~r1(tptp_fun_Y4_22(elem!24))) | (~r2(tptp_fun_Y4_22(elem!24), tptp_fun_Y3_21(elem!24)))))),
% 56.16/56.33 inference(modus_ponens,[status(thm)],[613, 612])).
% 56.16/56.33 tff(615,plain,
% 56.16/56.33 ((~((~r1(tptp_fun_Y5_23(elem!24))) | (~id(elem!24, tptp_fun_Y5_23(elem!24))))) | (~((~id(elem!24, tptp_fun_Y2_20(elem!24))) | (~r2(tptp_fun_Y3_21(elem!24), tptp_fun_Y2_20(elem!24))) | (~r1(tptp_fun_Y4_22(elem!24))) | (~r2(tptp_fun_Y4_22(elem!24), tptp_fun_Y3_21(elem!24)))))),
% 56.16/56.33 inference(unit_resolution,[status(thm)],[614, 197])).
% 56.16/56.33 tff(616,plain,
% 56.16/56.33 (~((~r1(tptp_fun_Y5_23(elem!24))) | (~id(elem!24, tptp_fun_Y5_23(elem!24))))),
% 56.16/56.33 inference(unit_resolution,[status(thm)],[615, 611])).
% 56.16/56.33 tff(617,assumption,(~((~r1(tptp_fun_Y5_23(elem!24))) | (~id(elem!24, tptp_fun_Y5_23(elem!24))))), introduced(assumption)).
% 56.16/56.33 tff(618,plain,
% 56.16/56.33 (((~r1(tptp_fun_Y5_23(elem!24))) | (~id(elem!24, tptp_fun_Y5_23(elem!24)))) | r1(tptp_fun_Y5_23(elem!24))),
% 56.16/56.33 inference(tautology,[status(thm)],[])).
% 56.16/56.33 tff(619,plain,
% 56.16/56.33 (r1(tptp_fun_Y5_23(elem!24))),
% 56.16/56.33 inference(unit_resolution,[status(thm)],[618, 617])).
% 56.16/56.33 tff(620,plain,
% 56.16/56.33 ((r1(elem!24) | r1(tptp_fun_Y5_23(elem!24))) | (~r1(tptp_fun_Y5_23(elem!24)))),
% 56.16/56.33 inference(tautology,[status(thm)],[])).
% 56.16/56.33 tff(621,plain,
% 56.16/56.33 (r1(elem!24) | r1(tptp_fun_Y5_23(elem!24))),
% 56.16/56.33 inference(unit_resolution,[status(thm)],[620, 619])).
% 56.16/56.33 tff(622,assumption,(~r1(elem!24)), introduced(assumption)).
% 56.16/56.33 tff(623,plain,
% 56.16/56.33 (((~r1(elem!24)) | (~r1(tptp_fun_Y5_23(elem!24)))) | r1(elem!24)),
% 56.16/56.33 inference(tautology,[status(thm)],[])).
% 56.16/56.33 tff(624,plain,
% 56.16/56.33 ((~r1(elem!24)) | (~r1(tptp_fun_Y5_23(elem!24)))),
% 56.16/56.33 inference(unit_resolution,[status(thm)],[623, 622])).
% 56.16/56.33 tff(625,plain,
% 56.16/56.33 (((~r1(tptp_fun_Y5_23(elem!24))) | (~id(elem!24, tptp_fun_Y5_23(elem!24)))) | id(elem!24, tptp_fun_Y5_23(elem!24))),
% 56.16/56.33 inference(tautology,[status(thm)],[])).
% 56.16/56.33 tff(626,plain,
% 56.16/56.33 (id(elem!24, tptp_fun_Y5_23(elem!24))),
% 56.16/56.33 inference(unit_resolution,[status(thm)],[625, 617])).
% 56.16/56.33 tff(627,plain,
% 56.16/56.33 (((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | ((~id(elem!24, tptp_fun_Y5_23(elem!24))) | (~((~r1(elem!24)) | (~r1(tptp_fun_Y5_23(elem!24))))) | (~(r1(elem!24) | r1(tptp_fun_Y5_23(elem!24)))))) <=> ((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | (~id(elem!24, tptp_fun_Y5_23(elem!24))) | (~((~r1(elem!24)) | (~r1(tptp_fun_Y5_23(elem!24))))) | (~(r1(elem!24) | r1(tptp_fun_Y5_23(elem!24)))))),
% 56.16/56.33 inference(rewrite,[status(thm)],[])).
% 56.16/56.33 tff(628,plain,
% 56.16/56.33 (((~id(elem!24, tptp_fun_Y5_23(elem!24))) | (~((~r1(elem!24)) | (~r1(tptp_fun_Y5_23(elem!24))))) | (~(r1(elem!24) | r1(tptp_fun_Y5_23(elem!24))))) <=> ((~id(elem!24, tptp_fun_Y5_23(elem!24))) | (~((~r1(elem!24)) | (~r1(tptp_fun_Y5_23(elem!24))))) | (~(r1(elem!24) | r1(tptp_fun_Y5_23(elem!24)))))),
% 56.16/56.33 inference(rewrite,[status(thm)],[])).
% 56.16/56.33 tff(629,plain,
% 56.16/56.33 ((~(r1(tptp_fun_Y5_23(elem!24)) | r1(elem!24))) <=> (~(r1(elem!24) | r1(tptp_fun_Y5_23(elem!24))))),
% 56.16/56.33 inference(rewrite,[status(thm)],[])).
% 56.16/56.33 tff(630,plain,
% 56.16/56.33 ((~((~r1(tptp_fun_Y5_23(elem!24))) | (~r1(elem!24)))) <=> (~((~r1(elem!24)) | (~r1(tptp_fun_Y5_23(elem!24)))))),
% 56.16/56.33 inference(rewrite,[status(thm)],[])).
% 56.16/56.33 tff(631,plain,
% 56.16/56.33 (((~id(elem!24, tptp_fun_Y5_23(elem!24))) | (~((~r1(tptp_fun_Y5_23(elem!24))) | (~r1(elem!24)))) | (~(r1(tptp_fun_Y5_23(elem!24)) | r1(elem!24)))) <=> ((~id(elem!24, tptp_fun_Y5_23(elem!24))) | (~((~r1(elem!24)) | (~r1(tptp_fun_Y5_23(elem!24))))) | (~(r1(elem!24) | r1(tptp_fun_Y5_23(elem!24)))))),
% 56.16/56.33 inference(monotonicity,[status(thm)],[630, 629])).
% 56.16/56.33 tff(632,plain,
% 56.16/56.33 (((~id(elem!24, tptp_fun_Y5_23(elem!24))) | (~((~r1(tptp_fun_Y5_23(elem!24))) | (~r1(elem!24)))) | (~(r1(tptp_fun_Y5_23(elem!24)) | r1(elem!24)))) <=> ((~id(elem!24, tptp_fun_Y5_23(elem!24))) | (~((~r1(elem!24)) | (~r1(tptp_fun_Y5_23(elem!24))))) | (~(r1(elem!24) | r1(tptp_fun_Y5_23(elem!24)))))),
% 56.16/56.33 inference(transitivity,[status(thm)],[631, 628])).
% 56.16/56.33 tff(633,plain,
% 56.16/56.33 (((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | ((~id(elem!24, tptp_fun_Y5_23(elem!24))) | (~((~r1(tptp_fun_Y5_23(elem!24))) | (~r1(elem!24)))) | (~(r1(tptp_fun_Y5_23(elem!24)) | r1(elem!24))))) <=> ((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | ((~id(elem!24, tptp_fun_Y5_23(elem!24))) | (~((~r1(elem!24)) | (~r1(tptp_fun_Y5_23(elem!24))))) | (~(r1(elem!24) | r1(tptp_fun_Y5_23(elem!24))))))),
% 56.16/56.33 inference(monotonicity,[status(thm)],[632])).
% 56.16/56.33 tff(634,plain,
% 56.16/56.33 (((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | ((~id(elem!24, tptp_fun_Y5_23(elem!24))) | (~((~r1(tptp_fun_Y5_23(elem!24))) | (~r1(elem!24)))) | (~(r1(tptp_fun_Y5_23(elem!24)) | r1(elem!24))))) <=> ((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | (~id(elem!24, tptp_fun_Y5_23(elem!24))) | (~((~r1(elem!24)) | (~r1(tptp_fun_Y5_23(elem!24))))) | (~(r1(elem!24) | r1(tptp_fun_Y5_23(elem!24)))))),
% 56.16/56.33 inference(transitivity,[status(thm)],[633, 627])).
% 56.16/56.33 tff(635,plain,
% 56.16/56.33 ((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | ((~id(elem!24, tptp_fun_Y5_23(elem!24))) | (~((~r1(tptp_fun_Y5_23(elem!24))) | (~r1(elem!24)))) | (~(r1(tptp_fun_Y5_23(elem!24)) | r1(elem!24))))),
% 56.16/56.33 inference(quant_inst,[status(thm)],[])).
% 56.16/56.33 tff(636,plain,
% 56.16/56.33 ((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | (~id(elem!24, tptp_fun_Y5_23(elem!24))) | (~((~r1(elem!24)) | (~r1(tptp_fun_Y5_23(elem!24))))) | (~(r1(elem!24) | r1(tptp_fun_Y5_23(elem!24))))),
% 56.16/56.33 inference(modus_ponens,[status(thm)],[635, 634])).
% 56.16/56.33 tff(637,plain,
% 56.16/56.33 ($false),
% 56.16/56.33 inference(unit_resolution,[status(thm)],[636, 37, 626, 624, 621])).
% 56.16/56.33 tff(638,plain,(((~r1(tptp_fun_Y5_23(elem!24))) | (~id(elem!24, tptp_fun_Y5_23(elem!24)))) | r1(elem!24)), inference(lemma,lemma(discharge,[]))).
% 56.16/56.33 tff(639,plain,
% 56.16/56.33 (r1(elem!24)),
% 56.16/56.33 inference(unit_resolution,[status(thm)],[638, 616])).
% 56.16/56.33 tff(640,plain,
% 56.16/56.33 ((r1(elem!24) | id(elem!24, Y24!0)) | (~r1(elem!24))),
% 56.16/56.33 inference(tautology,[status(thm)],[])).
% 56.16/56.33 tff(641,plain,
% 56.16/56.33 (r1(elem!24) | id(elem!24, Y24!0)),
% 56.16/56.33 inference(unit_resolution,[status(thm)],[640, 639])).
% 56.16/56.33 tff(642,plain,
% 56.16/56.33 (((~![X19: $i] : ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0))))) | ((~((~r1(elem!24)) | (~id(elem!24, Y24!0)))) | (~(r1(elem!24) | id(elem!24, Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0))))) | (~((~r1(elem!24)) | (~id(elem!24, Y24!0)))) | (~(r1(elem!24) | id(elem!24, Y24!0))))),
% 56.16/56.33 inference(rewrite,[status(thm)],[])).
% 56.16/56.33 tff(643,plain,
% 56.16/56.33 ((~![X19: $i] : ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0))))) | ((~((~r1(elem!24)) | (~id(elem!24, Y24!0)))) | (~(r1(elem!24) | id(elem!24, Y24!0))))),
% 56.16/56.33 inference(quant_inst,[status(thm)],[])).
% 56.16/56.33 tff(644,plain,
% 56.16/56.33 ((~![X19: $i] : ((~((~r1(X19)) | (~id(X19, Y24!0)))) | (~(r1(X19) | id(X19, Y24!0))))) | (~((~r1(elem!24)) | (~id(elem!24, Y24!0)))) | (~(r1(elem!24) | id(elem!24, Y24!0)))),
% 56.16/56.33 inference(modus_ponens,[status(thm)],[643, 642])).
% 56.16/56.33 tff(645,plain,
% 56.16/56.33 ((~((~r1(elem!24)) | (~id(elem!24, Y24!0)))) | (~(r1(elem!24) | id(elem!24, Y24!0)))),
% 56.16/56.33 inference(unit_resolution,[status(thm)],[644, 84])).
% 56.16/56.33 tff(646,plain,
% 56.16/56.33 (~((~r1(elem!24)) | (~id(elem!24, Y24!0)))),
% 56.16/56.33 inference(unit_resolution,[status(thm)],[645, 641])).
% 56.16/56.33 tff(647,plain,
% 56.16/56.33 (((~r1(elem!24)) | (~id(elem!24, Y24!0))) | id(elem!24, Y24!0)),
% 56.16/56.33 inference(tautology,[status(thm)],[])).
% 56.16/56.33 tff(648,plain,
% 56.16/56.33 (id(elem!24, Y24!0)),
% 56.16/56.33 inference(unit_resolution,[status(thm)],[647, 646])).
% 56.16/56.33 tff(649,plain,
% 56.16/56.33 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(elem!24, Y24!0)) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~(r2(elem!24, tptp_fun_Y21_1(elem!24)) | r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(elem!24, Y24!0)) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~(r2(elem!24, tptp_fun_Y21_1(elem!24)) | r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))))),
% 56.16/56.33 inference(rewrite,[status(thm)],[])).
% 56.16/56.33 tff(650,plain,
% 56.16/56.33 (((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(elem!24, Y24!0)) | (~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(elem!24, tptp_fun_Y21_1(elem!24)) | r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) <=> ((~id(elem!24, Y24!0)) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~(r2(elem!24, tptp_fun_Y21_1(elem!24)) | r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))))),
% 56.16/56.33 inference(rewrite,[status(thm)],[])).
% 56.16/56.33 tff(651,plain,
% 56.16/56.33 ((~(r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(elem!24, tptp_fun_Y21_1(elem!24)))) <=> (~(r2(elem!24, tptp_fun_Y21_1(elem!24)) | r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))),
% 56.16/56.33 inference(rewrite,[status(thm)],[])).
% 56.16/56.33 tff(652,plain,
% 56.16/56.33 ((~((~r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(elem!24, tptp_fun_Y21_1(elem!24))))) <=> (~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))),
% 56.16/56.33 inference(rewrite,[status(thm)],[])).
% 56.16/56.33 tff(653,plain,
% 56.16/56.33 (((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(elem!24, Y24!0)) | (~((~r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(elem!24, tptp_fun_Y21_1(elem!24))))) | (~(r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(elem!24, tptp_fun_Y21_1(elem!24))))) <=> ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(elem!24, Y24!0)) | (~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))) | (~(r2(elem!24, tptp_fun_Y21_1(elem!24)) | r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))),
% 56.16/56.33 inference(monotonicity,[status(thm)],[652, 651])).
% 56.16/56.33 tff(654,plain,
% 56.16/56.33 (((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(elem!24, Y24!0)) | (~((~r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(elem!24, tptp_fun_Y21_1(elem!24))))) | (~(r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(elem!24, tptp_fun_Y21_1(elem!24))))) <=> ((~id(elem!24, Y24!0)) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~(r2(elem!24, tptp_fun_Y21_1(elem!24)) | r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))))),
% 56.16/56.33 inference(transitivity,[status(thm)],[653, 650])).
% 56.16/56.33 tff(655,plain,
% 56.16/56.33 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(elem!24, Y24!0)) | (~((~r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(elem!24, tptp_fun_Y21_1(elem!24))))) | (~(r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(elem!24, tptp_fun_Y21_1(elem!24)))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(elem!24, Y24!0)) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~(r2(elem!24, tptp_fun_Y21_1(elem!24)) | r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))))),
% 56.16/56.36 inference(monotonicity,[status(thm)],[654])).
% 56.16/56.36 tff(656,plain,
% 56.16/56.36 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(elem!24, Y24!0)) | (~((~r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(elem!24, tptp_fun_Y21_1(elem!24))))) | (~(r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(elem!24, tptp_fun_Y21_1(elem!24)))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(elem!24, Y24!0)) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~(r2(elem!24, tptp_fun_Y21_1(elem!24)) | r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))))))),
% 56.16/56.36 inference(transitivity,[status(thm)],[655, 649])).
% 56.16/56.36 tff(657,plain,
% 56.16/56.36 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~id(elem!24, Y24!0)) | (~((~r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~r2(elem!24, tptp_fun_Y21_1(elem!24))))) | (~(r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))) | r2(elem!24, tptp_fun_Y21_1(elem!24)))))),
% 56.16/56.36 inference(quant_inst,[status(thm)],[])).
% 56.16/56.36 tff(658,plain,
% 56.16/56.36 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(elem!24, Y24!0)) | (~id(tptp_fun_Y21_1(elem!24), tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24)))) | (~(r2(elem!24, tptp_fun_Y21_1(elem!24)) | r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))) | (~((~r2(elem!24, tptp_fun_Y21_1(elem!24))) | (~r2(Y24!0, tptp_fun_Y2_20(tptp_fun_Y21_1(elem!24))))))),
% 56.16/56.36 inference(modus_ponens,[status(thm)],[657, 656])).
% 56.16/56.36 tff(659,plain,
% 56.16/56.36 ($false),
% 56.16/56.36 inference(unit_resolution,[status(thm)],[658, 117, 648, 259, 355, 336])).
% 56.16/56.36 % SZS output end Proof
% 56.16/56.38 % E exiting
%------------------------------------------------------------------------------