%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU255+2 : 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 0.50s 0.70s
% Output : Proof 0.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU255+2 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n006.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 06:29:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.50/0.70 % SZS status Theorem
% 0.50/0.70 % SZS output start Proof
% 0.50/0.70 tff(in_type, type, (
% 0.50/0.70 in: ( $i * $i ) > $o)).
% 0.50/0.70 tff(tptp_fun_B_103_type, type, (
% 0.50/0.70 tptp_fun_B_103: $i)).
% 0.50/0.70 tff(ordered_pair_type, type, (
% 0.50/0.70 ordered_pair: ( $i * $i ) > $i)).
% 0.50/0.70 tff(tptp_fun_C_82_type, type, (
% 0.50/0.70 tptp_fun_C_82: $i > $i)).
% 0.50/0.70 tff(relation_restriction_type, type, (
% 0.50/0.70 relation_restriction: ( $i * $i ) > $i)).
% 0.50/0.70 tff(tptp_fun_A_104_type, type, (
% 0.50/0.70 tptp_fun_A_104: $i)).
% 0.50/0.70 tff(tptp_fun_B_83_type, type, (
% 0.50/0.70 tptp_fun_B_83: $i > $i)).
% 0.50/0.70 tff(cartesian_product2_type, type, (
% 0.50/0.70 cartesian_product2: ( $i * $i ) > $i)).
% 0.50/0.70 tff(relation_type, type, (
% 0.50/0.70 relation: $i > $o)).
% 0.50/0.70 tff(antisymmetric_type, type, (
% 0.50/0.70 antisymmetric: $i > $o)).
% 0.50/0.70 tff(1,plain,
% 0.50/0.70 ((~(antisymmetric(relation_restriction(B!103, A!104)) | (~relation(B!103)) | (~antisymmetric(B!103)))) <=> (~(antisymmetric(relation_restriction(B!103, A!104)) | (~relation(B!103)) | (~antisymmetric(B!103))))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(2,plain,
% 0.50/0.70 ((~![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))))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(3,plain,
% 0.50/0.70 ((~![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))))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 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')).
% 0.50/0.70 tff(5,plain,
% 0.50/0.70 (~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.50/0.70 tff(6,plain,
% 0.50/0.70 (~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.50/0.70 tff(7,plain,
% 0.50/0.70 (~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.50/0.70 tff(8,plain,
% 0.50/0.70 (~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.50/0.70 tff(9,plain,(
% 0.50/0.70 ~(antisymmetric(relation_restriction(B!103, A!104)) | (~relation(B!103)) | (~antisymmetric(B!103)))),
% 0.50/0.70 inference(skolemize,[status(sab)],[8])).
% 0.50/0.70 tff(10,plain,
% 0.50/0.70 (~(antisymmetric(relation_restriction(B!103, A!104)) | (~relation(B!103)) | (~antisymmetric(B!103)))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.50/0.70 tff(11,plain,
% 0.50/0.70 (relation(B!103)),
% 0.50/0.70 inference(or_elim,[status(thm)],[10])).
% 0.50/0.70 tff(12,plain,
% 0.50/0.70 (^[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))))))),
% 0.50/0.70 inference(bind,[status(th)],[])).
% 0.50/0.70 tff(13,plain,
% 0.50/0.70 (![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)))))),
% 0.50/0.70 inference(quant_intro,[status(thm)],[12])).
% 0.50/0.70 tff(14,plain,
% 0.50/0.70 (^[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))))))),
% 0.50/0.70 inference(bind,[status(th)],[])).
% 0.50/0.70 tff(15,plain,
% 0.50/0.70 (![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)))))),
% 0.50/0.70 inference(quant_intro,[status(thm)],[14])).
% 0.50/0.70 tff(16,plain,
% 0.50/0.70 (![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)))))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(17,plain,
% 0.50/0.70 (^[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))))))),
% 0.50/0.70 inference(bind,[status(th)],[])).
% 0.50/0.70 tff(18,plain,
% 0.50/0.70 (![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)))))),
% 0.50/0.70 inference(quant_intro,[status(thm)],[17])).
% 0.50/0.70 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')).
% 0.50/0.70 tff(20,plain,
% 0.50/0.70 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.50/0.70 tff(21,plain,
% 0.50/0.70 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.50/0.70 tff(22,plain,(
% 0.50/0.70 ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.50/0.70 inference(skolemize,[status(sab)],[21])).
% 0.50/0.70 tff(23,plain,
% 0.50/0.70 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.50/0.70 tff(24,plain,
% 0.50/0.70 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.50/0.70 tff(25,plain,
% 0.50/0.70 (((~![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!103)) | (~(((~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), cartesian_product2(A!104, A!104)))) <=> in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104)))))) <=> ((~![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!103)) | (~(((~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), cartesian_product2(A!104, A!104)))) <=> in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104)))))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(26,plain,
% 0.50/0.70 ((~![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!103)) | (~(((~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), cartesian_product2(A!104, A!104)))) <=> in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104)))))),
% 0.50/0.71 inference(quant_inst,[status(thm)],[])).
% 0.50/0.71 tff(27,plain,
% 0.50/0.71 ((~![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!103)) | (~(((~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), cartesian_product2(A!104, A!104)))) <=> in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.50/0.71 tff(28,plain,
% 0.50/0.71 (~(((~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), cartesian_product2(A!104, A!104)))) <=> in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104)))),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[27, 24, 11])).
% 0.50/0.71 tff(29,plain,
% 0.50/0.71 (^[A: $i, B: $i] : refl(((~relation(A)) | relation(relation_restriction(A, B))) <=> ((~relation(A)) | relation(relation_restriction(A, B))))),
% 0.50/0.71 inference(bind,[status(th)],[])).
% 0.50/0.71 tff(30,plain,
% 0.50/0.71 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.50/0.71 inference(quant_intro,[status(thm)],[29])).
% 0.50/0.71 tff(31,plain,
% 0.50/0.71 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(32,plain,
% 0.50/0.71 (^[A: $i, B: $i] : rewrite((relation(A) => relation(relation_restriction(A, B))) <=> ((~relation(A)) | relation(relation_restriction(A, B))))),
% 0.50/0.71 inference(bind,[status(th)],[])).
% 0.50/0.71 tff(33,plain,
% 0.50/0.71 (![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.50/0.71 inference(quant_intro,[status(thm)],[32])).
% 0.50/0.71 tff(34,axiom,(![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_wellord1')).
% 0.50/0.71 tff(35,plain,
% 0.50/0.71 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.50/0.71 tff(36,plain,
% 0.50/0.71 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.50/0.71 tff(37,plain,(
% 0.50/0.71 ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.50/0.71 inference(skolemize,[status(sab)],[36])).
% 0.50/0.71 tff(38,plain,
% 0.50/0.71 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.50/0.71 tff(39,plain,
% 0.50/0.71 (((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | ((~relation(B!103)) | relation(relation_restriction(B!103, A!104)))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | (~relation(B!103)) | relation(relation_restriction(B!103, A!104)))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(40,plain,
% 0.50/0.71 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | ((~relation(B!103)) | relation(relation_restriction(B!103, A!104)))),
% 0.50/0.71 inference(quant_inst,[status(thm)],[])).
% 0.50/0.71 tff(41,plain,
% 0.50/0.71 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | (~relation(B!103)) | relation(relation_restriction(B!103, A!104))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.50/0.71 tff(42,plain,
% 0.50/0.71 (relation(relation_restriction(B!103, A!104))),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[41, 38, 11])).
% 0.50/0.71 tff(43,plain,
% 0.50/0.71 (^[A: $i] : refl(((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A))))))))) <=> ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A))))))))))),
% 0.50/0.71 inference(bind,[status(th)],[])).
% 0.50/0.71 tff(44,plain,
% 0.50/0.71 (![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A)))))))))),
% 0.50/0.71 inference(quant_intro,[status(thm)],[43])).
% 0.50/0.71 tff(45,plain,
% 0.50/0.71 (^[A: $i] : rewrite(((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A))))))))) <=> ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A))))))))))),
% 0.50/0.71 inference(bind,[status(th)],[])).
% 0.50/0.71 tff(46,plain,
% 0.50/0.71 (![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A)))))))))),
% 0.50/0.71 inference(quant_intro,[status(thm)],[45])).
% 0.50/0.71 tff(47,plain,
% 0.50/0.71 (![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A)))))))))),
% 0.50/0.71 inference(transitivity,[status(thm)],[46, 44])).
% 0.50/0.71 tff(48,plain,
% 0.50/0.71 (^[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_83(A), tptp_fun_C_82(A)), A) & in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A))) | (tptp_fun_B_83(A) = tptp_fun_C_82(A))))))) <=> ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A))))))))))),
% 0.50/0.71 inference(bind,[status(th)],[])).
% 0.50/0.71 tff(49,plain,
% 0.50/0.71 (![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_83(A), tptp_fun_C_82(A)), A) & in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A))) | (tptp_fun_B_83(A) = tptp_fun_C_82(A))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A)))))))))),
% 0.50/0.71 inference(quant_intro,[status(thm)],[48])).
% 0.50/0.71 tff(50,plain,
% 0.50/0.71 (![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))))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(51,plain,
% 0.50/0.71 (^[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))))))),
% 0.50/0.71 inference(bind,[status(th)],[])).
% 0.50/0.71 tff(52,plain,
% 0.50/0.71 (![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))))),
% 0.50/0.71 inference(quant_intro,[status(thm)],[51])).
% 0.50/0.71 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')).
% 0.50/0.71 tff(54,plain,
% 0.50/0.71 (![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A))) | (B = C))))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.50/0.71 tff(55,plain,
% 0.50/0.71 (![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A))) | (B = C))))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.50/0.71 tff(56,plain,(
% 0.50/0.71 ![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_83(A), tptp_fun_C_82(A)), A) & in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A))) | (tptp_fun_B_83(A) = tptp_fun_C_82(A)))))))),
% 0.50/0.71 inference(skolemize,[status(sab)],[55])).
% 0.50/0.71 tff(57,plain,
% 0.50/0.71 (![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A)))))))))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.50/0.71 tff(58,plain,
% 0.50/0.71 (![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A)))))))))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[57, 47])).
% 0.50/0.71 tff(59,plain,
% 0.50/0.71 (((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A)))))))))) | ((~relation(relation_restriction(B!103, A!104))) | (~((~((~antisymmetric(relation_restriction(B!103, A!104))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), relation_restriction(B!103, A!104))) | (~in(ordered_pair(B, C), relation_restriction(B!103, A!104)))))) | (~(antisymmetric(relation_restriction(B!103, A!104)) | (~((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A)))))))))) | (~relation(relation_restriction(B!103, A!104))) | (~((~((~antisymmetric(relation_restriction(B!103, A!104))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), relation_restriction(B!103, A!104))) | (~in(ordered_pair(B, C), relation_restriction(B!103, A!104)))))) | (~(antisymmetric(relation_restriction(B!103, A!104)) | (~((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104))))))))))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(60,plain,
% 0.50/0.71 (((~relation(relation_restriction(B!103, A!104))) | (~((~((~antisymmetric(relation_restriction(B!103, A!104))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), relation_restriction(B!103, A!104))) | (~in(ordered_pair(B, C), relation_restriction(B!103, A!104)))))) | (~(antisymmetric(relation_restriction(B!103, A!104)) | (~((tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104)))))))))) <=> ((~relation(relation_restriction(B!103, A!104))) | (~((~((~antisymmetric(relation_restriction(B!103, A!104))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), relation_restriction(B!103, A!104))) | (~in(ordered_pair(B, C), relation_restriction(B!103, A!104)))))) | (~(antisymmetric(relation_restriction(B!103, A!104)) | (~((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104))))))))))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(61,plain,
% 0.50/0.71 (((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A)))))))))) | ((~relation(relation_restriction(B!103, A!104))) | (~((~((~antisymmetric(relation_restriction(B!103, A!104))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), relation_restriction(B!103, A!104))) | (~in(ordered_pair(B, C), relation_restriction(B!103, A!104)))))) | (~(antisymmetric(relation_restriction(B!103, A!104)) | (~((tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A)))))))))) | ((~relation(relation_restriction(B!103, A!104))) | (~((~((~antisymmetric(relation_restriction(B!103, A!104))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), relation_restriction(B!103, A!104))) | (~in(ordered_pair(B, C), relation_restriction(B!103, A!104)))))) | (~(antisymmetric(relation_restriction(B!103, A!104)) | (~((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104)))))))))))),
% 0.50/0.71 inference(monotonicity,[status(thm)],[60])).
% 0.50/0.71 tff(62,plain,
% 0.50/0.71 (((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A)))))))))) | ((~relation(relation_restriction(B!103, A!104))) | (~((~((~antisymmetric(relation_restriction(B!103, A!104))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), relation_restriction(B!103, A!104))) | (~in(ordered_pair(B, C), relation_restriction(B!103, A!104)))))) | (~(antisymmetric(relation_restriction(B!103, A!104)) | (~((tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A)))))))))) | (~relation(relation_restriction(B!103, A!104))) | (~((~((~antisymmetric(relation_restriction(B!103, A!104))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), relation_restriction(B!103, A!104))) | (~in(ordered_pair(B, C), relation_restriction(B!103, A!104)))))) | (~(antisymmetric(relation_restriction(B!103, A!104)) | (~((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104))))))))))),
% 0.50/0.71 inference(transitivity,[status(thm)],[61, 59])).
% 0.50/0.71 tff(63,plain,
% 0.50/0.71 ((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A)))))))))) | ((~relation(relation_restriction(B!103, A!104))) | (~((~((~antisymmetric(relation_restriction(B!103, A!104))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), relation_restriction(B!103, A!104))) | (~in(ordered_pair(B, C), relation_restriction(B!103, A!104)))))) | (~(antisymmetric(relation_restriction(B!103, A!104)) | (~((tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))))))))))),
% 0.50/0.71 inference(quant_inst,[status(thm)],[])).
% 0.50/0.71 tff(64,plain,
% 0.50/0.71 ((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A)))))))))) | (~relation(relation_restriction(B!103, A!104))) | (~((~((~antisymmetric(relation_restriction(B!103, A!104))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), relation_restriction(B!103, A!104))) | (~in(ordered_pair(B, C), relation_restriction(B!103, A!104)))))) | (~(antisymmetric(relation_restriction(B!103, A!104)) | (~((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104)))))))))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.50/0.71 tff(65,plain,
% 0.50/0.71 ((~relation(relation_restriction(B!103, A!104))) | (~((~((~antisymmetric(relation_restriction(B!103, A!104))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), relation_restriction(B!103, A!104))) | (~in(ordered_pair(B, C), relation_restriction(B!103, A!104)))))) | (~(antisymmetric(relation_restriction(B!103, A!104)) | (~((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104)))))))))),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[64, 58])).
% 0.50/0.71 tff(66,plain,
% 0.50/0.71 (~((~((~antisymmetric(relation_restriction(B!103, A!104))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), relation_restriction(B!103, A!104))) | (~in(ordered_pair(B, C), relation_restriction(B!103, A!104)))))) | (~(antisymmetric(relation_restriction(B!103, A!104)) | (~((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104))))))))),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[65, 42])).
% 0.50/0.71 tff(67,plain,
% 0.50/0.71 (((~((~antisymmetric(relation_restriction(B!103, A!104))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), relation_restriction(B!103, A!104))) | (~in(ordered_pair(B, C), relation_restriction(B!103, A!104)))))) | (~(antisymmetric(relation_restriction(B!103, A!104)) | (~((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104)))))))) | (antisymmetric(relation_restriction(B!103, A!104)) | (~((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104))))))),
% 0.50/0.71 inference(tautology,[status(thm)],[])).
% 0.50/0.71 tff(68,plain,
% 0.50/0.71 (antisymmetric(relation_restriction(B!103, A!104)) | (~((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104)))))),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.50/0.71 tff(69,plain,
% 0.50/0.71 (~antisymmetric(relation_restriction(B!103, A!104))),
% 0.50/0.71 inference(or_elim,[status(thm)],[10])).
% 0.50/0.71 tff(70,plain,
% 0.50/0.71 ((~(antisymmetric(relation_restriction(B!103, A!104)) | (~((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104))))))) | antisymmetric(relation_restriction(B!103, A!104)) | (~((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104)))))),
% 0.50/0.71 inference(tautology,[status(thm)],[])).
% 0.50/0.71 tff(71,plain,
% 0.50/0.71 ((~(antisymmetric(relation_restriction(B!103, A!104)) | (~((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104))))))) | (~((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104)))))),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.50/0.71 tff(72,plain,
% 0.50/0.71 (~((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104))))),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[71, 68])).
% 0.50/0.71 tff(73,plain,
% 0.50/0.71 (((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104)))) | in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))),
% 0.50/0.71 inference(tautology,[status(thm)],[])).
% 0.50/0.71 tff(74,plain,
% 0.50/0.71 (in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.50/0.71 tff(75,plain,
% 0.50/0.71 ((((~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), cartesian_product2(A!104, A!104)))) <=> in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~((~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), cartesian_product2(A!104, A!104))))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104)))),
% 0.50/0.71 inference(tautology,[status(thm)],[])).
% 0.50/0.71 tff(76,plain,
% 0.50/0.71 ((((~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), cartesian_product2(A!104, A!104)))) <=> in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~((~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), cartesian_product2(A!104, A!104)))))),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.50/0.71 tff(77,plain,
% 0.50/0.71 (~((~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), cartesian_product2(A!104, A!104))))),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[76, 28])).
% 0.50/0.72 tff(78,plain,
% 0.50/0.72 (((~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), cartesian_product2(A!104, A!104)))) | in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), B!103)),
% 0.50/0.72 inference(tautology,[status(thm)],[])).
% 0.50/0.72 tff(79,plain,
% 0.50/0.72 (in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), B!103)),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.50/0.72 tff(80,plain,
% 0.50/0.72 (((~![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!103)) | (~(((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), cartesian_product2(A!104, A!104)))) <=> in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104)))))) <=> ((~![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!103)) | (~(((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), cartesian_product2(A!104, A!104)))) <=> in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104)))))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(81,plain,
% 0.50/0.72 ((~![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!103)) | (~(((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), cartesian_product2(A!104, A!104)))) <=> in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104)))))),
% 0.50/0.72 inference(quant_inst,[status(thm)],[])).
% 0.50/0.72 tff(82,plain,
% 0.50/0.72 ((~![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!103)) | (~(((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), cartesian_product2(A!104, A!104)))) <=> in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))))),
% 0.50/0.72 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.50/0.72 tff(83,plain,
% 0.50/0.72 (~(((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), cartesian_product2(A!104, A!104)))) <=> in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104)))),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[82, 24, 11])).
% 0.50/0.72 tff(84,plain,
% 0.50/0.72 (((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104)))) | in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))),
% 0.50/0.72 inference(tautology,[status(thm)],[])).
% 0.50/0.72 tff(85,plain,
% 0.50/0.72 (in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[84, 72])).
% 0.50/0.72 tff(86,plain,
% 0.50/0.72 ((((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), cartesian_product2(A!104, A!104)))) <=> in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), cartesian_product2(A!104, A!104))))) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104)))),
% 0.50/0.72 inference(tautology,[status(thm)],[])).
% 0.50/0.72 tff(87,plain,
% 0.50/0.72 ((((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), cartesian_product2(A!104, A!104)))) <=> in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), cartesian_product2(A!104, A!104)))))),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.50/0.72 tff(88,plain,
% 0.50/0.72 (~((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), cartesian_product2(A!104, A!104))))),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[87, 83])).
% 0.50/0.72 tff(89,plain,
% 0.50/0.72 (((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), cartesian_product2(A!104, A!104)))) | in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), B!103)),
% 0.50/0.72 inference(tautology,[status(thm)],[])).
% 0.50/0.72 tff(90,plain,
% 0.50/0.72 (in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), B!103)),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.50/0.72 tff(91,plain,
% 0.50/0.72 (((~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), relation_restriction(B!103, A!104))) | (tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104)))) | (~(tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104))))),
% 0.50/0.72 inference(tautology,[status(thm)],[])).
% 0.50/0.72 tff(92,plain,
% 0.50/0.72 (~(tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104)))),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[91, 72])).
% 0.50/0.72 tff(93,plain,
% 0.50/0.72 (((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A)))))))))) | ((~relation(B!103)) | (~((~((~antisymmetric(B!103)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103))))) | (~(antisymmetric(B!103) | (~((~in(ordered_pair(tptp_fun_C_82(B!103), tptp_fun_B_83(B!103)), B!103)) | (~in(ordered_pair(tptp_fun_B_83(B!103), tptp_fun_C_82(B!103)), B!103)) | (tptp_fun_B_83(B!103) = tptp_fun_C_82(B!103)))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A)))))))))) | (~relation(B!103)) | (~((~((~antisymmetric(B!103)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103))))) | (~(antisymmetric(B!103) | (~((~in(ordered_pair(tptp_fun_C_82(B!103), tptp_fun_B_83(B!103)), B!103)) | (~in(ordered_pair(tptp_fun_B_83(B!103), tptp_fun_C_82(B!103)), B!103)) | (tptp_fun_B_83(B!103) = tptp_fun_C_82(B!103)))))))))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(94,plain,
% 0.50/0.72 (((~relation(B!103)) | (~((~((~antisymmetric(B!103)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103))))) | (~(antisymmetric(B!103) | (~((tptp_fun_B_83(B!103) = tptp_fun_C_82(B!103)) | (~in(ordered_pair(tptp_fun_B_83(B!103), tptp_fun_C_82(B!103)), B!103)) | (~in(ordered_pair(tptp_fun_C_82(B!103), tptp_fun_B_83(B!103)), B!103))))))))) <=> ((~relation(B!103)) | (~((~((~antisymmetric(B!103)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103))))) | (~(antisymmetric(B!103) | (~((~in(ordered_pair(tptp_fun_C_82(B!103), tptp_fun_B_83(B!103)), B!103)) | (~in(ordered_pair(tptp_fun_B_83(B!103), tptp_fun_C_82(B!103)), B!103)) | (tptp_fun_B_83(B!103) = tptp_fun_C_82(B!103)))))))))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(95,plain,
% 0.50/0.72 (((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A)))))))))) | ((~relation(B!103)) | (~((~((~antisymmetric(B!103)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103))))) | (~(antisymmetric(B!103) | (~((tptp_fun_B_83(B!103) = tptp_fun_C_82(B!103)) | (~in(ordered_pair(tptp_fun_B_83(B!103), tptp_fun_C_82(B!103)), B!103)) | (~in(ordered_pair(tptp_fun_C_82(B!103), tptp_fun_B_83(B!103)), B!103)))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A)))))))))) | ((~relation(B!103)) | (~((~((~antisymmetric(B!103)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103))))) | (~(antisymmetric(B!103) | (~((~in(ordered_pair(tptp_fun_C_82(B!103), tptp_fun_B_83(B!103)), B!103)) | (~in(ordered_pair(tptp_fun_B_83(B!103), tptp_fun_C_82(B!103)), B!103)) | (tptp_fun_B_83(B!103) = tptp_fun_C_82(B!103))))))))))),
% 0.50/0.72 inference(monotonicity,[status(thm)],[94])).
% 0.50/0.72 tff(96,plain,
% 0.50/0.72 (((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A)))))))))) | ((~relation(B!103)) | (~((~((~antisymmetric(B!103)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103))))) | (~(antisymmetric(B!103) | (~((tptp_fun_B_83(B!103) = tptp_fun_C_82(B!103)) | (~in(ordered_pair(tptp_fun_B_83(B!103), tptp_fun_C_82(B!103)), B!103)) | (~in(ordered_pair(tptp_fun_C_82(B!103), tptp_fun_B_83(B!103)), B!103)))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A)))))))))) | (~relation(B!103)) | (~((~((~antisymmetric(B!103)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103))))) | (~(antisymmetric(B!103) | (~((~in(ordered_pair(tptp_fun_C_82(B!103), tptp_fun_B_83(B!103)), B!103)) | (~in(ordered_pair(tptp_fun_B_83(B!103), tptp_fun_C_82(B!103)), B!103)) | (tptp_fun_B_83(B!103) = tptp_fun_C_82(B!103)))))))))),
% 0.50/0.72 inference(transitivity,[status(thm)],[95, 93])).
% 0.50/0.72 tff(97,plain,
% 0.50/0.72 ((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A)))))))))) | ((~relation(B!103)) | (~((~((~antisymmetric(B!103)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103))))) | (~(antisymmetric(B!103) | (~((tptp_fun_B_83(B!103) = tptp_fun_C_82(B!103)) | (~in(ordered_pair(tptp_fun_B_83(B!103), tptp_fun_C_82(B!103)), B!103)) | (~in(ordered_pair(tptp_fun_C_82(B!103), tptp_fun_B_83(B!103)), B!103)))))))))),
% 0.50/0.72 inference(quant_inst,[status(thm)],[])).
% 0.50/0.72 tff(98,plain,
% 0.50/0.72 ((~![A: $i] : ((~relation(A)) | (~((~((~antisymmetric(A)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), A)) | (~in(ordered_pair(B, C), A))))) | (~(antisymmetric(A) | (~((tptp_fun_B_83(A) = tptp_fun_C_82(A)) | (~in(ordered_pair(tptp_fun_B_83(A), tptp_fun_C_82(A)), A)) | (~in(ordered_pair(tptp_fun_C_82(A), tptp_fun_B_83(A)), A)))))))))) | (~relation(B!103)) | (~((~((~antisymmetric(B!103)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103))))) | (~(antisymmetric(B!103) | (~((~in(ordered_pair(tptp_fun_C_82(B!103), tptp_fun_B_83(B!103)), B!103)) | (~in(ordered_pair(tptp_fun_B_83(B!103), tptp_fun_C_82(B!103)), B!103)) | (tptp_fun_B_83(B!103) = tptp_fun_C_82(B!103))))))))),
% 0.50/0.72 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.50/0.72 tff(99,plain,
% 0.50/0.72 (~((~((~antisymmetric(B!103)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103))))) | (~(antisymmetric(B!103) | (~((~in(ordered_pair(tptp_fun_C_82(B!103), tptp_fun_B_83(B!103)), B!103)) | (~in(ordered_pair(tptp_fun_B_83(B!103), tptp_fun_C_82(B!103)), B!103)) | (tptp_fun_B_83(B!103) = tptp_fun_C_82(B!103)))))))),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[98, 58, 11])).
% 0.50/0.72 tff(100,plain,
% 0.50/0.72 (((~((~antisymmetric(B!103)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103))))) | (~(antisymmetric(B!103) | (~((~in(ordered_pair(tptp_fun_C_82(B!103), tptp_fun_B_83(B!103)), B!103)) | (~in(ordered_pair(tptp_fun_B_83(B!103), tptp_fun_C_82(B!103)), B!103)) | (tptp_fun_B_83(B!103) = tptp_fun_C_82(B!103))))))) | ((~antisymmetric(B!103)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103))))),
% 0.50/0.72 inference(tautology,[status(thm)],[])).
% 0.50/0.72 tff(101,plain,
% 0.50/0.72 ((~antisymmetric(B!103)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103)))),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.50/0.72 tff(102,plain,
% 0.50/0.72 (antisymmetric(B!103)),
% 0.50/0.72 inference(or_elim,[status(thm)],[10])).
% 0.50/0.72 tff(103,plain,
% 0.50/0.72 ((~((~antisymmetric(B!103)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103))))) | (~antisymmetric(B!103)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103)))),
% 0.50/0.72 inference(tautology,[status(thm)],[])).
% 0.50/0.72 tff(104,plain,
% 0.50/0.72 ((~((~antisymmetric(B!103)) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103))))) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103)))),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.50/0.72 tff(105,plain,
% 0.50/0.72 (![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103)))),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[104, 101])).
% 0.50/0.72 tff(106,plain,
% 0.50/0.72 (((~![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103)))) | ((tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), B!103)))) <=> ((~![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103)))) | (tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), B!103)))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(107,plain,
% 0.50/0.72 (((tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), B!103))) <=> ((tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), B!103)))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(108,plain,
% 0.50/0.72 (((~![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103)))) | ((tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), B!103)))) <=> ((~![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103)))) | ((tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), B!103))))),
% 0.58/0.73 inference(monotonicity,[status(thm)],[107])).
% 0.58/0.73 tff(109,plain,
% 0.58/0.73 (((~![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103)))) | ((tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), B!103)))) <=> ((~![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103)))) | (tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), B!103)))),
% 0.58/0.73 inference(transitivity,[status(thm)],[108, 106])).
% 0.58/0.73 tff(110,plain,
% 0.58/0.73 ((~![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103)))) | ((tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), B!103)))),
% 0.58/0.73 inference(quant_inst,[status(thm)],[])).
% 0.58/0.73 tff(111,plain,
% 0.58/0.73 ((~![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(C, B), B!103)) | (~in(ordered_pair(B, C), B!103)))) | (tptp_fun_B_83(relation_restriction(B!103, A!104)) = tptp_fun_C_82(relation_restriction(B!103, A!104))) | (~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), B!103))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.58/0.74 tff(112,plain,
% 0.58/0.74 ((~in(ordered_pair(tptp_fun_B_83(relation_restriction(B!103, A!104)), tptp_fun_C_82(relation_restriction(B!103, A!104))), B!103)) | (~in(ordered_pair(tptp_fun_C_82(relation_restriction(B!103, A!104)), tptp_fun_B_83(relation_restriction(B!103, A!104))), B!103))),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[111, 105, 92])).
% 0.58/0.74 tff(113,plain,
% 0.58/0.74 ($false),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[112, 90, 79])).
% 0.58/0.74 % SZS output end Proof
% 0.58/0.74 % E exiting
%------------------------------------------------------------------------------