%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU255+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:27:24 AM UTC 2025
% Result : Theorem 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU255+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:29:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.37 % SZS status Theorem
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 tff(in_type, type, (
% 0.20/0.37 in: ( $i * $i ) > $o)).
% 0.20/0.37 tff(tptp_fun_B_8_type, type, (
% 0.20/0.37 tptp_fun_B_8: $i)).
% 0.20/0.37 tff(ordered_pair_type, type, (
% 0.20/0.37 ordered_pair: ( $i * $i ) > $i)).
% 0.20/0.37 tff(tptp_fun_C_1_type, type, (
% 0.20/0.37 tptp_fun_C_1: $i > $i)).
% 0.20/0.37 tff(relation_restriction_type, type, (
% 0.20/0.37 relation_restriction: ( $i * $i ) > $i)).
% 0.20/0.37 tff(tptp_fun_A_9_type, type, (
% 0.20/0.37 tptp_fun_A_9: $i)).
% 0.20/0.37 tff(tptp_fun_B_2_type, type, (
% 0.20/0.37 tptp_fun_B_2: $i > $i)).
% 0.20/0.37 tff(cartesian_product2_type, type, (
% 0.20/0.37 cartesian_product2: ( $i * $i ) > $i)).
% 0.20/0.37 tff(relation_type, type, (
% 0.20/0.37 relation: $i > $o)).
% 0.20/0.37 tff(antisymmetric_type, type, (
% 0.20/0.37 antisymmetric: $i > $o)).
% 0.20/0.37 tff(1,plain,
% 0.20/0.37 ((~(antisymmetric(relation_restriction(B!8, A!9)) | (~relation(B!8)) | (~antisymmetric(B!8)))) <=> (~(antisymmetric(relation_restriction(B!8, A!9)) | (~relation(B!8)) | (~antisymmetric(B!8))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(2,plain,
% 0.20/0.37 ((~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))) <=> (~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(3,plain,
% 0.20/0.37 ((~![A: $i, B: $i] : (relation(B) => (antisymmetric(B) => antisymmetric(relation_restriction(B, A))))) <=> (~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(4,axiom,(~![A: $i, B: $i] : (relation(B) => (antisymmetric(B) => antisymmetric(relation_restriction(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t25_wellord1')).
% 0.20/0.37 tff(5,plain,
% 0.20/0.37 (~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.37 tff(6,plain,
% 0.20/0.37 (~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.20/0.37 tff(7,plain,
% 0.20/0.37 (~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.37 tff(8,plain,
% 0.20/0.37 (~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.20/0.37 tff(9,plain,(
% 0.20/0.37 ~(antisymmetric(relation_restriction(B!8, A!9)) | (~relation(B!8)) | (~antisymmetric(B!8)))),
% 0.20/0.37 inference(skolemize,[status(sab)],[8])).
% 0.20/0.37 tff(10,plain,
% 0.20/0.37 (~(antisymmetric(relation_restriction(B!8, A!9)) | (~relation(B!8)) | (~antisymmetric(B!8)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.20/0.37 tff(11,plain,
% 0.20/0.37 (relation(B!8)),
% 0.20/0.37 inference(or_elim,[status(thm)],[10])).
% 0.20/0.37 tff(12,plain,
% 0.20/0.37 (^[A: $i, B: $i, C: $i] : refl(((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B))))) <=> ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B))))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(13,plain,
% 0.20/0.37 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.37 tff(14,plain,
% 0.20/0.37 (^[A: $i, B: $i, C: $i] : rewrite(((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B))))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(15,plain,
% 0.20/0.37 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.37 tff(16,plain,
% 0.20/0.37 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(17,plain,
% 0.20/0.37 (^[A: $i, B: $i, C: $i] : rewrite((relation(C) => (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(18,plain,
% 0.20/0.37 (![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.37 tff(19,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t16_wellord1')).
% 0.20/0.37 tff(20,plain,
% 0.20/0.37 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.37 tff(21,plain,
% 0.20/0.37 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.20/0.37 tff(22,plain,(
% 0.20/0.37 ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.20/0.37 inference(skolemize,[status(sab)],[21])).
% 0.20/0.37 tff(23,plain,
% 0.20/0.37 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.20/0.37 tff(24,plain,
% 0.20/0.37 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.20/0.37 tff(25,plain,
% 0.20/0.37 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | ((~relation(B!8)) | (~(((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | (~relation(B!8)) | (~(((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(26,plain,
% 0.20/0.37 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | ((~relation(B!8)) | (~(((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(27,plain,
% 0.20/0.37 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | (~relation(B!8)) | (~(((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.37 tff(28,plain,
% 0.20/0.37 (~(((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[27, 24, 11])).
% 0.20/0.37 tff(29,plain,
% 0.20/0.37 (^[A: $i, B: $i] : refl(((~relation(A)) | relation(relation_restriction(A, B))) <=> ((~relation(A)) | relation(relation_restriction(A, B))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(30,plain,
% 0.20/0.37 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.37 tff(31,plain,
% 0.20/0.37 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(32,plain,
% 0.20/0.37 (^[A: $i, B: $i] : rewrite((relation(A) => relation(relation_restriction(A, B))) <=> ((~relation(A)) | relation(relation_restriction(A, B))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(33,plain,
% 0.20/0.37 (![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.37 tff(34,axiom,(![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_wellord1')).
% 0.20/0.37 tff(35,plain,
% 0.20/0.37 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.37 tff(36,plain,
% 0.20/0.37 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.20/0.37 tff(37,plain,(
% 0.20/0.37 ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.20/0.37 inference(skolemize,[status(sab)],[36])).
% 0.20/0.37 tff(38,plain,
% 0.20/0.37 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.20/0.37 tff(39,plain,
% 0.20/0.37 (((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | ((~relation(B!8)) | relation(relation_restriction(B!8, A!9)))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | (~relation(B!8)) | relation(relation_restriction(B!8, A!9)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(40,plain,
% 0.20/0.37 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | ((~relation(B!8)) | relation(relation_restriction(B!8, A!9)))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(41,plain,
% 0.20/0.37 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | (~relation(B!8)) | relation(relation_restriction(B!8, A!9))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.37 tff(42,plain,
% 0.20/0.37 (relation(relation_restriction(B!8, A!9))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[41, 38, 11])).
% 0.20/0.37 tff(43,plain,
% 0.20/0.37 (^[A: $i] : refl(((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))))))) <=> ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(44,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.38 tff(45,plain,
% 0.20/0.38 (^[A: $i] : rewrite(((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))))))) <=> ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(46,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.38 tff(47,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[46, 44])).
% 0.20/0.38 tff(48,plain,
% 0.20/0.38 (^[A: $i] : rewrite(((~relation(A)) | (((~antisymmetric(A)) | ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A))) | (B = C))) & (antisymmetric(A) | (~((~(in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) & in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A))))))) <=> ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(49,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | (((~antisymmetric(A)) | ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A))) | (B = C))) & (antisymmetric(A) | (~((~(in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) & in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.38 tff(50,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A))) | (B = C)))) <=> ![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A))) | (B = C))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(51,plain,
% 0.20/0.38 (^[A: $i] : trans(monotonicity(rewrite((antisymmetric(A) <=> ![B: $i, C: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A)) => (B = C))) <=> (antisymmetric(A) <=> ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A))) | (B = C)))), ((relation(A) => (antisymmetric(A) <=> ![B: $i, C: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A)) => (B = C)))) <=> (relation(A) => (antisymmetric(A) <=> ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A))) | (B = C)))))), rewrite((relation(A) => (antisymmetric(A) <=> ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A))) | (B = C)))) <=> ((~relation(A)) | (antisymmetric(A) <=> ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A))) | (B = C))))), ((relation(A) => (antisymmetric(A) <=> ![B: $i, C: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A)) => (B = C)))) <=> ((~relation(A)) | (antisymmetric(A) <=> ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A))) | (B = C))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(52,plain,
% 0.20/0.38 (![A: $i] : (relation(A) => (antisymmetric(A) <=> ![B: $i, C: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A)) => (B = C)))) <=> ![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A))) | (B = C))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.38 tff(53,axiom,(![A: $i] : (relation(A) => (antisymmetric(A) <=> ![B: $i, C: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A)) => (B = C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l3_wellord1')).
% 0.20/0.38 tff(54,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A))) | (B = C))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.38 tff(55,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A))) | (B = C))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.20/0.38 tff(56,plain,(
% 0.20/0.38 ![A: $i] : ((~relation(A)) | (((~antisymmetric(A)) | ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A))) | (B = C))) & (antisymmetric(A) | (~((~(in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) & in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)))))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[55])).
% 0.20/0.38 tff(57,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.20/0.38 tff(58,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[57, 47])).
% 0.20/0.38 tff(59,plain,
% 0.20/0.38 (((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))) | ((~relation(relation_restriction(B!8, A!9))) | (~((~((~antisymmetric(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), relation_restriction(B!8, A!9))) | (~in(ordered_pair(C, B), relation_restriction(B!8, A!9)))))) | (~(antisymmetric(relation_restriction(B!8, A!9)) | (~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))) | (~relation(relation_restriction(B!8, A!9))) | (~((~((~antisymmetric(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), relation_restriction(B!8, A!9))) | (~in(ordered_pair(C, B), relation_restriction(B!8, A!9)))))) | (~(antisymmetric(relation_restriction(B!8, A!9)) | (~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))))))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(60,plain,
% 0.20/0.38 (((~relation(relation_restriction(B!8, A!9))) | (~((~((~antisymmetric(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), relation_restriction(B!8, A!9))) | (~in(ordered_pair(C, B), relation_restriction(B!8, A!9)))))) | (~(antisymmetric(relation_restriction(B!8, A!9)) | (~((tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))))))) <=> ((~relation(relation_restriction(B!8, A!9))) | (~((~((~antisymmetric(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), relation_restriction(B!8, A!9))) | (~in(ordered_pair(C, B), relation_restriction(B!8, A!9)))))) | (~(antisymmetric(relation_restriction(B!8, A!9)) | (~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))))))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(61,plain,
% 0.20/0.38 (((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))) | ((~relation(relation_restriction(B!8, A!9))) | (~((~((~antisymmetric(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), relation_restriction(B!8, A!9))) | (~in(ordered_pair(C, B), relation_restriction(B!8, A!9)))))) | (~(antisymmetric(relation_restriction(B!8, A!9)) | (~((tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))) | ((~relation(relation_restriction(B!8, A!9))) | (~((~((~antisymmetric(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), relation_restriction(B!8, A!9))) | (~in(ordered_pair(C, B), relation_restriction(B!8, A!9)))))) | (~(antisymmetric(relation_restriction(B!8, A!9)) | (~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9)))))))))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[60])).
% 0.20/0.38 tff(62,plain,
% 0.20/0.38 (((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))) | ((~relation(relation_restriction(B!8, A!9))) | (~((~((~antisymmetric(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), relation_restriction(B!8, A!9))) | (~in(ordered_pair(C, B), relation_restriction(B!8, A!9)))))) | (~(antisymmetric(relation_restriction(B!8, A!9)) | (~((tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))) | (~relation(relation_restriction(B!8, A!9))) | (~((~((~antisymmetric(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), relation_restriction(B!8, A!9))) | (~in(ordered_pair(C, B), relation_restriction(B!8, A!9)))))) | (~(antisymmetric(relation_restriction(B!8, A!9)) | (~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))))))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[61, 59])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 ((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))) | ((~relation(relation_restriction(B!8, A!9))) | (~((~((~antisymmetric(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), relation_restriction(B!8, A!9))) | (~in(ordered_pair(C, B), relation_restriction(B!8, A!9)))))) | (~(antisymmetric(relation_restriction(B!8, A!9)) | (~((tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))))))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 ((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))) | (~relation(relation_restriction(B!8, A!9))) | (~((~((~antisymmetric(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), relation_restriction(B!8, A!9))) | (~in(ordered_pair(C, B), relation_restriction(B!8, A!9)))))) | (~(antisymmetric(relation_restriction(B!8, A!9)) | (~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9)))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 (~((~((~antisymmetric(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), relation_restriction(B!8, A!9))) | (~in(ordered_pair(C, B), relation_restriction(B!8, A!9)))))) | (~(antisymmetric(relation_restriction(B!8, A!9)) | (~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))))))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[64, 58, 42])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 (((~((~antisymmetric(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), relation_restriction(B!8, A!9))) | (~in(ordered_pair(C, B), relation_restriction(B!8, A!9)))))) | (~(antisymmetric(relation_restriction(B!8, A!9)) | (~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9)))))))) | (antisymmetric(relation_restriction(B!8, A!9)) | (~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 (antisymmetric(relation_restriction(B!8, A!9)) | (~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9)))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 (~antisymmetric(relation_restriction(B!8, A!9))),
% 0.20/0.39 inference(or_elim,[status(thm)],[10])).
% 0.20/0.39 tff(69,plain,
% 0.20/0.39 ((~(antisymmetric(relation_restriction(B!8, A!9)) | (~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))))))) | antisymmetric(relation_restriction(B!8, A!9)) | (~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9)))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 ((~(antisymmetric(relation_restriction(B!8, A!9)) | (~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))))))) | (~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9)))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.20/0.39 tff(71,plain,
% 0.20/0.39 (~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[70, 67])).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 (((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9)))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(73,plain,
% 0.20/0.39 (in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.20/0.39 tff(74,plain,
% 0.20/0.39 ((((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(75,plain,
% 0.20/0.39 ((((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.20/0.39 tff(76,plain,
% 0.20/0.39 (~((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[75, 28])).
% 0.20/0.39 tff(77,plain,
% 0.20/0.39 (((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(78,plain,
% 0.20/0.39 (in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.20/0.39 tff(79,plain,
% 0.20/0.39 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | ((~relation(B!8)) | (~(((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | (~relation(B!8)) | (~(((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(80,plain,
% 0.20/0.39 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | ((~relation(B!8)) | (~(((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(81,plain,
% 0.20/0.39 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | (~relation(B!8)) | (~(((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.39 tff(82,plain,
% 0.20/0.39 (~(((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[81, 24, 11])).
% 0.20/0.39 tff(83,plain,
% 0.20/0.39 (((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9)))) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(84,plain,
% 0.20/0.39 (in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[83, 71])).
% 0.20/0.39 tff(85,plain,
% 0.20/0.39 ((((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))))) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(86,plain,
% 0.20/0.39 ((((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) <=> in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.20/0.39 tff(87,plain,
% 0.20/0.39 (~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[86, 82])).
% 0.20/0.40 tff(88,plain,
% 0.20/0.40 (((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(89,plain,
% 0.20/0.40 (in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.20/0.40 tff(90,plain,
% 0.20/0.40 (((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9)))) | (~(tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(91,plain,
% 0.20/0.40 (~(tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[90, 71])).
% 0.20/0.40 tff(92,plain,
% 0.20/0.40 (((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))) | ((~relation(B!8)) | (~((~((~antisymmetric(B!8)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), B!8)) | (~in(ordered_pair(C, B), B!8))))) | (~(antisymmetric(B!8) | (~((~in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8)) | (~in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8)) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))) | (~relation(B!8)) | (~((~((~antisymmetric(B!8)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), B!8)) | (~in(ordered_pair(C, B), B!8))))) | (~(antisymmetric(B!8) | (~((~in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8)) | (~in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8)) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(93,plain,
% 0.20/0.40 (((~relation(B!8)) | (~((~((~antisymmetric(B!8)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), B!8)) | (~in(ordered_pair(C, B), B!8))))) | (~(antisymmetric(B!8) | (~((tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | (~in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8)) | (~in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8))))))))) <=> ((~relation(B!8)) | (~((~((~antisymmetric(B!8)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), B!8)) | (~in(ordered_pair(C, B), B!8))))) | (~(antisymmetric(B!8) | (~((~in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8)) | (~in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8)) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(94,plain,
% 0.20/0.40 (((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))) | ((~relation(B!8)) | (~((~((~antisymmetric(B!8)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), B!8)) | (~in(ordered_pair(C, B), B!8))))) | (~(antisymmetric(B!8) | (~((tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | (~in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8)) | (~in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8)))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))) | ((~relation(B!8)) | (~((~((~antisymmetric(B!8)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), B!8)) | (~in(ordered_pair(C, B), B!8))))) | (~(antisymmetric(B!8) | (~((~in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8)) | (~in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8)) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8))))))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[93])).
% 0.20/0.40 tff(95,plain,
% 0.20/0.40 (((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))) | ((~relation(B!8)) | (~((~((~antisymmetric(B!8)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), B!8)) | (~in(ordered_pair(C, B), B!8))))) | (~(antisymmetric(B!8) | (~((tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | (~in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8)) | (~in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8)))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))) | (~relation(B!8)) | (~((~((~antisymmetric(B!8)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), B!8)) | (~in(ordered_pair(C, B), B!8))))) | (~(antisymmetric(B!8) | (~((~in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8)) | (~in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8)) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)))))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[94, 92])).
% 0.20/0.40 tff(96,plain,
% 0.20/0.40 ((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))) | ((~relation(B!8)) | (~((~((~antisymmetric(B!8)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), B!8)) | (~in(ordered_pair(C, B), B!8))))) | (~(antisymmetric(B!8) | (~((tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | (~in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8)) | (~in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8)))))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(97,plain,
% 0.20/0.40 ((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, B), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_2(A) = tptp_fun_C_1(A)) | (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) | (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))) | (~relation(B!8)) | (~((~((~antisymmetric(B!8)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), B!8)) | (~in(ordered_pair(C, B), B!8))))) | (~(antisymmetric(B!8) | (~((~in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8)) | (~in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8)) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.40 tff(98,plain,
% 0.20/0.40 (~((~((~antisymmetric(B!8)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), B!8)) | (~in(ordered_pair(C, B), B!8))))) | (~(antisymmetric(B!8) | (~((~in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8)) | (~in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8)) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[97, 58, 11])).
% 0.20/0.40 tff(99,plain,
% 0.20/0.40 (((~((~antisymmetric(B!8)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), B!8)) | (~in(ordered_pair(C, B), B!8))))) | (~(antisymmetric(B!8) | (~((~in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8)) | (~in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8)) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8))))))) | ((~antisymmetric(B!8)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), B!8)) | (~in(ordered_pair(C, B), B!8))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(100,plain,
% 0.20/0.40 ((~antisymmetric(B!8)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), B!8)) | (~in(ordered_pair(C, B), B!8)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.20/0.40 tff(101,plain,
% 0.20/0.40 (antisymmetric(B!8)),
% 0.20/0.40 inference(or_elim,[status(thm)],[10])).
% 0.20/0.40 tff(102,plain,
% 0.20/0.40 ((~((~antisymmetric(B!8)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), B!8)) | (~in(ordered_pair(C, B), B!8))))) | (~antisymmetric(B!8)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), B!8)) | (~in(ordered_pair(C, B), B!8)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(103,plain,
% 0.20/0.40 ((~((~antisymmetric(B!8)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), B!8)) | (~in(ordered_pair(C, B), B!8))))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), B!8)) | (~in(ordered_pair(C, B), B!8)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.20/0.40 tff(104,plain,
% 0.20/0.40 (![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), B!8)) | (~in(ordered_pair(C, B), B!8)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[103, 100])).
% 0.20/0.40 tff(105,plain,
% 0.20/0.40 (((~![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), B!8)) | (~in(ordered_pair(C, B), B!8)))) | ((tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)))) <=> ((~![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), B!8)) | (~in(ordered_pair(C, B), B!8)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(106,plain,
% 0.20/0.40 ((~![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), B!8)) | (~in(ordered_pair(C, B), B!8)))) | ((tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(107,plain,
% 0.20/0.40 ((~![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), B!8)) | (~in(ordered_pair(C, B), B!8)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.40 tff(108,plain,
% 0.20/0.40 ((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[107, 104, 91])).
% 0.20/0.40 tff(109,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[108, 89, 78])).
% 0.20/0.40 % SZS output end Proof
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------