%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU186+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:27:10 AM UTC 2025
% Result : Theorem 6.54s 6.75s
% Output : Proof 6.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU186+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 06:18:20 EDT 2025
% 0.12/0.34 % CPUTime :
% 6.54/6.75 % SZS status Theorem
% 6.54/6.75 % SZS output start Proof
% 6.54/6.75 tff(in_type, type, (
% 6.54/6.75 in: ( $i * $i ) > $o)).
% 6.54/6.75 tff(relation_inverse_type, type, (
% 6.54/6.75 relation_inverse: $i > $i)).
% 6.54/6.75 tff(tptp_fun_A_46_type, type, (
% 6.54/6.75 tptp_fun_A_46: $i)).
% 6.54/6.75 tff(ordered_pair_type, type, (
% 6.54/6.75 ordered_pair: ( $i * $i ) > $i)).
% 6.54/6.75 tff(tptp_fun_C_29_type, type, (
% 6.54/6.75 tptp_fun_C_29: ( $i * $i ) > $i)).
% 6.54/6.75 tff(tptp_fun_A_36_type, type, (
% 6.54/6.75 tptp_fun_A_36: $i)).
% 6.54/6.75 tff(tptp_fun_D_28_type, type, (
% 6.54/6.75 tptp_fun_D_28: ( $i * $i ) > $i)).
% 6.54/6.75 tff(relation_type, type, (
% 6.54/6.75 relation: $i > $o)).
% 6.54/6.75 tff(empty_set_type, type, (
% 6.54/6.75 empty_set: $i)).
% 6.54/6.75 tff(empty_type, type, (
% 6.54/6.75 empty: $i > $o)).
% 6.54/6.75 tff(1,plain,
% 6.54/6.75 (((~(A!46 = empty_set)) & relation(A!46) & ![B: $i, C: $i] : (~in(ordered_pair(B, C), A!46))) <=> ((~(A!46 = empty_set)) & relation(A!46) & ![B: $i, C: $i] : (~in(ordered_pair(B, C), A!46)))),
% 6.54/6.75 inference(rewrite,[status(thm)],[])).
% 6.54/6.75 tff(2,plain,
% 6.54/6.75 ((~![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))))) <=> (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A)))))),
% 6.54/6.75 inference(rewrite,[status(thm)],[])).
% 6.54/6.75 tff(3,plain,
% 6.54/6.75 ((~![A: $i] : (relation(A) => (![B: $i, C: $i] : (~in(ordered_pair(B, C), A)) => (A = empty_set)))) <=> (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A)))))),
% 6.54/6.75 inference(rewrite,[status(thm)],[])).
% 6.54/6.75 tff(4,axiom,(~![A: $i] : (relation(A) => (![B: $i, C: $i] : (~in(ordered_pair(B, C), A)) => (A = empty_set)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t56_relat_1')).
% 6.54/6.75 tff(5,plain,
% 6.54/6.75 (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))))),
% 6.54/6.75 inference(modus_ponens,[status(thm)],[4, 3])).
% 6.54/6.75 tff(6,plain,
% 6.54/6.75 (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))))),
% 6.54/6.75 inference(modus_ponens,[status(thm)],[5, 2])).
% 6.54/6.75 tff(7,plain,
% 6.54/6.75 (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))))),
% 6.54/6.75 inference(modus_ponens,[status(thm)],[6, 2])).
% 6.54/6.75 tff(8,plain,
% 6.54/6.75 (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))))),
% 6.54/6.75 inference(modus_ponens,[status(thm)],[7, 2])).
% 6.54/6.75 tff(9,plain,
% 6.54/6.75 ((~(A!46 = empty_set)) & relation(A!46) & ![B: $i, C: $i] : (~in(ordered_pair(B, C), A!46))),
% 6.54/6.75 inference(modus_ponens,[status(thm)],[8, 1])).
% 6.54/6.75 tff(10,plain,
% 6.54/6.75 (relation(A!46)),
% 6.54/6.75 inference(and_elim,[status(thm)],[9])).
% 6.54/6.75 tff(11,plain,
% 6.54/6.75 (^[A: $i] : refl(((~relation(A)) | relation(relation_inverse(A))) <=> ((~relation(A)) | relation(relation_inverse(A))))),
% 6.54/6.75 inference(bind,[status(th)],[])).
% 6.54/6.75 tff(12,plain,
% 6.54/6.75 (![A: $i] : ((~relation(A)) | relation(relation_inverse(A))) <=> ![A: $i] : ((~relation(A)) | relation(relation_inverse(A)))),
% 6.54/6.75 inference(quant_intro,[status(thm)],[11])).
% 6.54/6.75 tff(13,plain,
% 6.54/6.75 (![A: $i] : ((~relation(A)) | relation(relation_inverse(A))) <=> ![A: $i] : ((~relation(A)) | relation(relation_inverse(A)))),
% 6.54/6.75 inference(rewrite,[status(thm)],[])).
% 6.54/6.75 tff(14,plain,
% 6.54/6.75 (^[A: $i] : rewrite((relation(A) => relation(relation_inverse(A))) <=> ((~relation(A)) | relation(relation_inverse(A))))),
% 6.54/6.75 inference(bind,[status(th)],[])).
% 6.54/6.75 tff(15,plain,
% 6.54/6.75 (![A: $i] : (relation(A) => relation(relation_inverse(A))) <=> ![A: $i] : ((~relation(A)) | relation(relation_inverse(A)))),
% 6.54/6.75 inference(quant_intro,[status(thm)],[14])).
% 6.54/6.75 tff(16,axiom,(![A: $i] : (relation(A) => relation(relation_inverse(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k4_relat_1')).
% 6.54/6.75 tff(17,plain,
% 6.54/6.75 (![A: $i] : ((~relation(A)) | relation(relation_inverse(A)))),
% 6.54/6.75 inference(modus_ponens,[status(thm)],[16, 15])).
% 6.54/6.75 tff(18,plain,
% 6.54/6.75 (![A: $i] : ((~relation(A)) | relation(relation_inverse(A)))),
% 6.54/6.75 inference(modus_ponens,[status(thm)],[17, 13])).
% 6.54/6.75 tff(19,plain,(
% 6.54/6.75 ![A: $i] : ((~relation(A)) | relation(relation_inverse(A)))),
% 6.54/6.75 inference(skolemize,[status(sab)],[18])).
% 6.54/6.75 tff(20,plain,
% 6.54/6.75 (![A: $i] : ((~relation(A)) | relation(relation_inverse(A)))),
% 6.54/6.75 inference(modus_ponens,[status(thm)],[19, 12])).
% 6.54/6.75 tff(21,plain,
% 6.54/6.75 (((~![A: $i] : ((~relation(A)) | relation(relation_inverse(A)))) | ((~relation(A!46)) | relation(relation_inverse(A!46)))) <=> ((~![A: $i] : ((~relation(A)) | relation(relation_inverse(A)))) | (~relation(A!46)) | relation(relation_inverse(A!46)))),
% 6.54/6.75 inference(rewrite,[status(thm)],[])).
% 6.54/6.75 tff(22,plain,
% 6.54/6.75 ((~![A: $i] : ((~relation(A)) | relation(relation_inverse(A)))) | ((~relation(A!46)) | relation(relation_inverse(A!46)))),
% 6.54/6.75 inference(quant_inst,[status(thm)],[])).
% 6.54/6.75 tff(23,plain,
% 6.54/6.75 ((~![A: $i] : ((~relation(A)) | relation(relation_inverse(A)))) | (~relation(A!46)) | relation(relation_inverse(A!46))),
% 6.54/6.75 inference(modus_ponens,[status(thm)],[22, 21])).
% 6.54/6.75 tff(24,plain,
% 6.54/6.75 (relation(relation_inverse(A!46))),
% 6.54/6.75 inference(unit_resolution,[status(thm)],[23, 20, 10])).
% 6.54/6.75 tff(25,plain,
% 6.54/6.75 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A))))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A))))))))))),
% 6.54/6.75 inference(bind,[status(th)],[])).
% 6.54/6.75 tff(26,plain,
% 6.54/6.75 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))))))),
% 6.54/6.75 inference(quant_intro,[status(thm)],[25])).
% 6.54/6.75 tff(27,plain,
% 6.54/6.75 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A))))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A))))))))))),
% 6.54/6.75 inference(bind,[status(th)],[])).
% 6.54/6.75 tff(28,plain,
% 6.54/6.75 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))))))),
% 6.54/6.75 inference(quant_intro,[status(thm)],[27])).
% 6.54/6.75 tff(29,plain,
% 6.54/6.75 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))))))),
% 6.54/6.75 inference(transitivity,[status(thm)],[28, 26])).
% 6.54/6.75 tff(30,plain,
% 6.54/6.75 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((~relation(B)) | (((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))) & ((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A))))))))))),
% 6.54/6.75 inference(bind,[status(th)],[])).
% 6.54/6.75 tff(31,plain,
% 6.54/6.75 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))) & ((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))))))),
% 6.54/6.75 inference(quant_intro,[status(thm)],[30])).
% 6.54/6.75 tff(32,plain,
% 6.54/6.75 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))))),
% 6.54/6.75 inference(rewrite,[status(thm)],[])).
% 6.54/6.75 tff(33,plain,
% 6.54/6.75 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite(((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))) <=> ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))), ((relation(B) => ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) <=> (relation(B) => ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))))), rewrite((relation(B) => ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) <=> ((~relation(B)) | ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))))), ((relation(B) => ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) <=> ((~relation(B)) | ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))))))), (![B: $i] : (relation(B) => ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) <=> ![B: $i] : ((~relation(B)) | ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))))), ((relation(A) => ![B: $i] : (relation(B) => ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))))) <=> (relation(A) => ![B: $i] : ((~relation(B)) | ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))))))), rewrite((relation(A) => ![B: $i] : ((~relation(B)) | ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))))), ((relation(A) => ![B: $i] : (relation(B) => ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))))))),
% 6.54/6.75 inference(bind,[status(th)],[])).
% 6.54/6.75 tff(34,plain,
% 6.54/6.75 (![A: $i] : (relation(A) => ![B: $i] : (relation(B) => ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))))),
% 6.54/6.75 inference(quant_intro,[status(thm)],[33])).
% 6.54/6.75 tff(35,axiom,(![A: $i] : (relation(A) => ![B: $i] : (relation(B) => ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d7_relat_1')).
% 6.54/6.75 tff(36,plain,
% 6.54/6.75 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))))),
% 6.54/6.75 inference(modus_ponens,[status(thm)],[35, 34])).
% 6.54/6.75 tff(37,plain,
% 6.54/6.75 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))))),
% 6.54/6.75 inference(modus_ponens,[status(thm)],[36, 32])).
% 6.54/6.75 tff(38,plain,(
% 6.54/6.75 ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))) & ((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))))),
% 6.54/6.75 inference(skolemize,[status(sab)],[37])).
% 6.54/6.75 tff(39,plain,
% 6.54/6.75 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))))))),
% 6.54/6.75 inference(modus_ponens,[status(thm)],[38, 31])).
% 6.54/6.75 tff(40,plain,
% 6.54/6.75 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))))))),
% 6.54/6.75 inference(modus_ponens,[status(thm)],[39, 29])).
% 6.54/6.75 tff(41,plain,
% 6.54/6.75 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))))))) | ((~relation(relation_inverse(A!46))) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46)))) | (B = relation_inverse(relation_inverse(A!46)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))))))) | (~relation(relation_inverse(A!46))) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46)))) | (B = relation_inverse(relation_inverse(A!46)))))))))),
% 6.54/6.75 inference(rewrite,[status(thm)],[])).
% 6.54/6.75 tff(42,plain,
% 6.54/6.75 (((~relation(relation_inverse(A!46))) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((B = relation_inverse(relation_inverse(A!46))) | (~(in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46)))))))))) <=> ((~relation(relation_inverse(A!46))) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46)))) | (B = relation_inverse(relation_inverse(A!46)))))))))),
% 6.54/6.75 inference(rewrite,[status(thm)],[])).
% 6.54/6.75 tff(43,plain,
% 6.54/6.75 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))))))) | ((~relation(relation_inverse(A!46))) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((B = relation_inverse(relation_inverse(A!46))) | (~(in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))))))) | ((~relation(relation_inverse(A!46))) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46)))) | (B = relation_inverse(relation_inverse(A!46))))))))))),
% 6.54/6.75 inference(monotonicity,[status(thm)],[42])).
% 6.54/6.75 tff(44,plain,
% 6.54/6.75 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))))))) | ((~relation(relation_inverse(A!46))) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((B = relation_inverse(relation_inverse(A!46))) | (~(in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))))))) | (~relation(relation_inverse(A!46))) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46)))) | (B = relation_inverse(relation_inverse(A!46)))))))))),
% 6.54/6.75 inference(transitivity,[status(thm)],[43, 41])).
% 6.54/6.75 tff(45,plain,
% 6.54/6.75 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))))))) | ((~relation(relation_inverse(A!46))) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((B = relation_inverse(relation_inverse(A!46))) | (~(in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46))))))))))),
% 6.54/6.75 inference(quant_inst,[status(thm)],[])).
% 6.54/6.75 tff(46,plain,
% 6.54/6.75 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))))))) | (~relation(relation_inverse(A!46))) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46)))) | (B = relation_inverse(relation_inverse(A!46))))))))),
% 6.54/6.75 inference(modus_ponens,[status(thm)],[45, 44])).
% 6.54/6.75 tff(47,plain,
% 6.54/6.75 (![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46)))) | (B = relation_inverse(relation_inverse(A!46))))))))),
% 6.54/6.75 inference(unit_resolution,[status(thm)],[46, 40, 24])).
% 6.54/6.75 tff(48,plain,
% 6.54/6.75 (((~![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46)))) | (B = relation_inverse(relation_inverse(A!46))))))))) | ((~relation(A!46)) | (~((~((~(A!46 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(A!46, relation_inverse(A!46)), tptp_fun_D_28(A!46, relation_inverse(A!46))), A!46) <=> in(ordered_pair(tptp_fun_D_28(A!46, relation_inverse(A!46)), tptp_fun_C_29(A!46, relation_inverse(A!46))), relation_inverse(A!46)))) | (A!46 = relation_inverse(relation_inverse(A!46))))))))) <=> ((~![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46)))) | (B = relation_inverse(relation_inverse(A!46))))))))) | (~relation(A!46)) | (~((~((~(A!46 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(A!46, relation_inverse(A!46)), tptp_fun_D_28(A!46, relation_inverse(A!46))), A!46) <=> in(ordered_pair(tptp_fun_D_28(A!46, relation_inverse(A!46)), tptp_fun_C_29(A!46, relation_inverse(A!46))), relation_inverse(A!46)))) | (A!46 = relation_inverse(relation_inverse(A!46))))))))),
% 6.54/6.75 inference(rewrite,[status(thm)],[])).
% 6.54/6.75 tff(49,plain,
% 6.54/6.75 ((~![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46)))) | (B = relation_inverse(relation_inverse(A!46))))))))) | ((~relation(A!46)) | (~((~((~(A!46 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(A!46, relation_inverse(A!46)), tptp_fun_D_28(A!46, relation_inverse(A!46))), A!46) <=> in(ordered_pair(tptp_fun_D_28(A!46, relation_inverse(A!46)), tptp_fun_C_29(A!46, relation_inverse(A!46))), relation_inverse(A!46)))) | (A!46 = relation_inverse(relation_inverse(A!46))))))))),
% 6.54/6.75 inference(quant_inst,[status(thm)],[])).
% 6.54/6.75 tff(50,plain,
% 6.54/6.75 ((~![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46)))) | (B = relation_inverse(relation_inverse(A!46))))))))) | (~relation(A!46)) | (~((~((~(A!46 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(A!46, relation_inverse(A!46)), tptp_fun_D_28(A!46, relation_inverse(A!46))), A!46) <=> in(ordered_pair(tptp_fun_D_28(A!46, relation_inverse(A!46)), tptp_fun_C_29(A!46, relation_inverse(A!46))), relation_inverse(A!46)))) | (A!46 = relation_inverse(relation_inverse(A!46)))))))),
% 6.54/6.75 inference(modus_ponens,[status(thm)],[49, 48])).
% 6.54/6.75 tff(51,plain,
% 6.54/6.75 (~((~((~(A!46 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(A!46, relation_inverse(A!46)), tptp_fun_D_28(A!46, relation_inverse(A!46))), A!46) <=> in(ordered_pair(tptp_fun_D_28(A!46, relation_inverse(A!46)), tptp_fun_C_29(A!46, relation_inverse(A!46))), relation_inverse(A!46)))) | (A!46 = relation_inverse(relation_inverse(A!46))))))),
% 6.54/6.75 inference(unit_resolution,[status(thm)],[50, 10, 47])).
% 6.54/6.75 tff(52,plain,
% 6.54/6.75 (((~((~(A!46 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(A!46, relation_inverse(A!46)), tptp_fun_D_28(A!46, relation_inverse(A!46))), A!46) <=> in(ordered_pair(tptp_fun_D_28(A!46, relation_inverse(A!46)), tptp_fun_C_29(A!46, relation_inverse(A!46))), relation_inverse(A!46)))) | (A!46 = relation_inverse(relation_inverse(A!46)))))) | ((~(A!46 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46))))),
% 6.54/6.75 inference(tautology,[status(thm)],[])).
% 6.54/6.75 tff(53,plain,
% 6.54/6.75 ((~(A!46 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46)))),
% 6.54/6.75 inference(unit_resolution,[status(thm)],[52, 51])).
% 6.54/6.75 tff(54,plain,
% 6.54/6.75 (^[A: $i] : refl(((~relation(A)) | (relation_inverse(relation_inverse(A)) = A)) <=> ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A)))),
% 6.54/6.75 inference(bind,[status(th)],[])).
% 6.54/6.75 tff(55,plain,
% 6.54/6.75 (![A: $i] : ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A)) <=> ![A: $i] : ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A))),
% 6.54/6.75 inference(quant_intro,[status(thm)],[54])).
% 6.54/6.75 tff(56,plain,
% 6.54/6.75 (![A: $i] : ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A)) <=> ![A: $i] : ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A))),
% 6.54/6.75 inference(rewrite,[status(thm)],[])).
% 6.54/6.75 tff(57,plain,
% 6.54/6.75 (^[A: $i] : rewrite((relation(A) => (relation_inverse(relation_inverse(A)) = A)) <=> ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A)))),
% 6.54/6.75 inference(bind,[status(th)],[])).
% 6.54/6.75 tff(58,plain,
% 6.54/6.75 (![A: $i] : (relation(A) => (relation_inverse(relation_inverse(A)) = A)) <=> ![A: $i] : ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A))),
% 6.54/6.75 inference(quant_intro,[status(thm)],[57])).
% 6.54/6.75 tff(59,axiom,(![A: $i] : (relation(A) => (relation_inverse(relation_inverse(A)) = A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','involutiveness_k4_relat_1')).
% 6.54/6.75 tff(60,plain,
% 6.54/6.75 (![A: $i] : ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A))),
% 6.54/6.75 inference(modus_ponens,[status(thm)],[59, 58])).
% 6.54/6.75 tff(61,plain,
% 6.54/6.75 (![A: $i] : ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A))),
% 6.54/6.75 inference(modus_ponens,[status(thm)],[60, 56])).
% 6.54/6.75 tff(62,plain,(
% 6.54/6.75 ![A: $i] : ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A))),
% 6.54/6.75 inference(skolemize,[status(sab)],[61])).
% 6.54/6.75 tff(63,plain,
% 6.54/6.75 (![A: $i] : ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A))),
% 6.54/6.75 inference(modus_ponens,[status(thm)],[62, 55])).
% 6.54/6.75 tff(64,plain,
% 6.54/6.75 (((~![A: $i] : ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A))) | ((~relation(A!46)) | (relation_inverse(relation_inverse(A!46)) = A!46))) <=> ((~![A: $i] : ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A))) | (~relation(A!46)) | (relation_inverse(relation_inverse(A!46)) = A!46))),
% 6.54/6.75 inference(rewrite,[status(thm)],[])).
% 6.54/6.75 tff(65,plain,
% 6.54/6.75 ((~![A: $i] : ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A))) | ((~relation(A!46)) | (relation_inverse(relation_inverse(A!46)) = A!46))),
% 6.54/6.75 inference(quant_inst,[status(thm)],[])).
% 6.54/6.75 tff(66,plain,
% 6.54/6.75 ((~![A: $i] : ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A))) | (~relation(A!46)) | (relation_inverse(relation_inverse(A!46)) = A!46)),
% 6.54/6.75 inference(modus_ponens,[status(thm)],[65, 64])).
% 6.54/6.75 tff(67,plain,
% 6.54/6.75 (relation_inverse(relation_inverse(A!46)) = A!46),
% 6.54/6.75 inference(unit_resolution,[status(thm)],[66, 63, 10])).
% 6.54/6.75 tff(68,plain,
% 6.54/6.75 (A!46 = relation_inverse(relation_inverse(A!46))),
% 6.54/6.75 inference(symmetry,[status(thm)],[67])).
% 6.54/6.75 tff(69,plain,
% 6.54/6.75 ((~((~(A!46 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~(A!46 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46)))),
% 6.54/6.75 inference(tautology,[status(thm)],[])).
% 6.54/6.75 tff(70,plain,
% 6.54/6.75 ((~((~(A!46 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46)))),
% 6.54/6.75 inference(unit_resolution,[status(thm)],[69, 68])).
% 6.54/6.75 tff(71,plain,
% 6.54/6.75 (![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46)))),
% 6.54/6.75 inference(unit_resolution,[status(thm)],[70, 53])).
% 6.54/6.75 tff(72,plain,
% 6.54/6.75 ((~![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46)))) | (in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!46) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46)))),
% 6.54/6.75 inference(quant_inst,[status(thm)],[])).
% 6.54/6.75 tff(73,plain,
% 6.54/6.75 (in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!46) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46))),
% 6.54/6.75 inference(unit_resolution,[status(thm)],[72, 71])).
% 6.54/6.75 tff(74,plain,
% 6.54/6.75 (^[B: $i, C: $i] : refl((~in(ordered_pair(B, C), A!46)) <=> (~in(ordered_pair(B, C), A!46)))),
% 6.54/6.75 inference(bind,[status(th)],[])).
% 6.54/6.75 tff(75,plain,
% 6.54/6.75 (![B: $i, C: $i] : (~in(ordered_pair(B, C), A!46)) <=> ![B: $i, C: $i] : (~in(ordered_pair(B, C), A!46))),
% 6.54/6.75 inference(quant_intro,[status(thm)],[74])).
% 6.54/6.75 tff(76,plain,
% 6.54/6.75 (![B: $i, C: $i] : (~in(ordered_pair(B, C), A!46))),
% 6.54/6.75 inference(and_elim,[status(thm)],[9])).
% 6.54/6.75 tff(77,plain,
% 6.54/6.75 (![B: $i, C: $i] : (~in(ordered_pair(B, C), A!46))),
% 6.54/6.75 inference(modus_ponens,[status(thm)],[76, 75])).
% 6.54/6.75 tff(78,plain,
% 6.54/6.75 ((~![B: $i, C: $i] : (~in(ordered_pair(B, C), A!46))) | (~in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!46))),
% 6.54/6.75 inference(quant_inst,[status(thm)],[])).
% 6.54/6.75 tff(79,plain,
% 6.54/6.75 (~in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!46)),
% 6.54/6.75 inference(unit_resolution,[status(thm)],[78, 77])).
% 6.54/6.75 tff(80,plain,
% 6.54/6.75 (?[A: $i] : (empty(A) & relation(A)) <=> ?[A: $i] : (empty(A) & relation(A))),
% 6.54/6.75 inference(rewrite,[status(thm)],[])).
% 6.54/6.75 tff(81,axiom,(?[A: $i] : (empty(A) & relation(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rc1_relat_1')).
% 6.54/6.75 tff(82,plain,
% 6.54/6.75 (?[A: $i] : (empty(A) & relation(A))),
% 6.54/6.75 inference(modus_ponens,[status(thm)],[81, 80])).
% 6.54/6.75 tff(83,plain,(
% 6.54/6.75 empty(A!36) & relation(A!36)),
% 6.54/6.75 inference(skolemize,[status(sab)],[82])).
% 6.54/6.75 tff(84,plain,
% 6.54/6.75 (relation(A!36)),
% 6.54/6.75 inference(and_elim,[status(thm)],[83])).
% 6.54/6.75 tff(85,plain,
% 6.54/6.75 (((~![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46)))) | (B = relation_inverse(relation_inverse(A!46))))))))) | ((~relation(A!36)) | (~((~((~(A!36 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!36) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46)))) | (A!36 = relation_inverse(relation_inverse(A!46))))))))) <=> ((~![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46)))) | (B = relation_inverse(relation_inverse(A!46))))))))) | (~relation(A!36)) | (~((~((~(A!36 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!36) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46)))) | (A!36 = relation_inverse(relation_inverse(A!46))))))))),
% 6.54/6.75 inference(rewrite,[status(thm)],[])).
% 6.54/6.75 tff(86,plain,
% 6.54/6.75 ((~![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46)))) | (B = relation_inverse(relation_inverse(A!46))))))))) | ((~relation(A!36)) | (~((~((~(A!36 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!36) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46)))) | (A!36 = relation_inverse(relation_inverse(A!46))))))))),
% 6.54/6.75 inference(quant_inst,[status(thm)],[])).
% 6.54/6.75 tff(87,plain,
% 6.54/6.75 ((~![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46)))) | (B = relation_inverse(relation_inverse(A!46))))))))) | (~relation(A!36)) | (~((~((~(A!36 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!36) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46)))) | (A!36 = relation_inverse(relation_inverse(A!46)))))))),
% 6.54/6.75 inference(modus_ponens,[status(thm)],[86, 85])).
% 6.54/6.75 tff(88,plain,
% 6.54/6.75 (~((~((~(A!36 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!36) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46)))) | (A!36 = relation_inverse(relation_inverse(A!46))))))),
% 6.54/6.75 inference(unit_resolution,[status(thm)],[87, 84, 47])).
% 6.54/6.75 tff(89,plain,
% 6.54/6.75 (((~((~(A!36 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!36) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((~(in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46)))) | (A!36 = relation_inverse(relation_inverse(A!46)))))) | ((~(in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46)))) | (A!36 = relation_inverse(relation_inverse(A!46))))),
% 6.54/6.76 inference(tautology,[status(thm)],[])).
% 6.54/6.76 tff(90,plain,
% 6.54/6.76 ((~(in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46)))) | (A!36 = relation_inverse(relation_inverse(A!46)))),
% 6.54/6.76 inference(unit_resolution,[status(thm)],[89, 88])).
% 6.54/6.76 tff(91,plain,
% 6.54/6.76 ((empty_set = A!46) <=> (A!46 = empty_set)),
% 6.54/6.76 inference(commutativity,[status(thm)],[])).
% 6.54/6.76 tff(92,plain,
% 6.54/6.76 (^[A: $i, B: $i] : refl(((A = B) | (~empty(A)) | (~empty(B))) <=> ((A = B) | (~empty(A)) | (~empty(B))))),
% 6.54/6.76 inference(bind,[status(th)],[])).
% 6.54/6.76 tff(93,plain,
% 6.54/6.76 (![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B))) <=> ![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 6.54/6.76 inference(quant_intro,[status(thm)],[92])).
% 6.54/6.76 tff(94,plain,
% 6.54/6.76 (^[A: $i, B: $i] : trans(monotonicity(rewrite((empty(A) & (~(A = B)) & empty(B)) <=> (~((A = B) | (~empty(A)) | (~empty(B))))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> (~(~((A = B) | (~empty(A)) | (~empty(B))))))), rewrite((~(~((A = B) | (~empty(A)) | (~empty(B))))) <=> ((A = B) | (~empty(A)) | (~empty(B)))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> ((A = B) | (~empty(A)) | (~empty(B)))))),
% 6.54/6.76 inference(bind,[status(th)],[])).
% 6.54/6.76 tff(95,plain,
% 6.54/6.76 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 6.54/6.76 inference(quant_intro,[status(thm)],[94])).
% 6.54/6.76 tff(96,plain,
% 6.54/6.76 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 6.54/6.76 inference(rewrite,[status(thm)],[])).
% 6.54/6.76 tff(97,plain,
% 6.54/6.76 (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 6.54/6.76 inference(bind,[status(th)],[])).
% 6.54/6.76 tff(98,plain,
% 6.54/6.76 (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 6.54/6.76 inference(quant_intro,[status(thm)],[97])).
% 6.54/6.76 tff(99,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t8_boole')).
% 6.54/6.76 tff(100,plain,
% 6.54/6.76 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 6.54/6.76 inference(modus_ponens,[status(thm)],[99, 98])).
% 6.54/6.76 tff(101,plain,
% 6.54/6.76 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 6.54/6.76 inference(modus_ponens,[status(thm)],[100, 96])).
% 6.54/6.76 tff(102,plain,(
% 6.54/6.76 ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 6.54/6.76 inference(skolemize,[status(sab)],[101])).
% 6.54/6.76 tff(103,plain,
% 6.54/6.76 (![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 6.54/6.76 inference(modus_ponens,[status(thm)],[102, 95])).
% 6.54/6.76 tff(104,plain,
% 6.54/6.76 (![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 6.54/6.76 inference(modus_ponens,[status(thm)],[103, 93])).
% 6.54/6.76 tff(105,plain,
% 6.54/6.76 (empty(A!36)),
% 6.54/6.76 inference(and_elim,[status(thm)],[83])).
% 6.54/6.76 tff(106,plain,
% 6.54/6.76 (empty(empty_set) <=> empty(empty_set)),
% 6.54/6.76 inference(rewrite,[status(thm)],[])).
% 6.54/6.76 tff(107,axiom,(empty(empty_set)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_xboole_0')).
% 6.54/6.76 tff(108,plain,
% 6.54/6.76 (empty(empty_set)),
% 6.54/6.76 inference(modus_ponens,[status(thm)],[107, 106])).
% 6.54/6.76 tff(109,plain,
% 6.54/6.76 (((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | ((empty_set = A!36) | (~empty(empty_set)) | (~empty(A!36)))) <=> ((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | (empty_set = A!36) | (~empty(empty_set)) | (~empty(A!36)))),
% 6.54/6.76 inference(rewrite,[status(thm)],[])).
% 6.54/6.76 tff(110,plain,
% 6.54/6.76 ((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | ((empty_set = A!36) | (~empty(empty_set)) | (~empty(A!36)))),
% 6.54/6.76 inference(quant_inst,[status(thm)],[])).
% 6.54/6.76 tff(111,plain,
% 6.54/6.76 ((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | (empty_set = A!36) | (~empty(empty_set)) | (~empty(A!36))),
% 6.54/6.76 inference(modus_ponens,[status(thm)],[110, 109])).
% 6.54/6.76 tff(112,plain,
% 6.54/6.76 (empty_set = A!36),
% 6.54/6.76 inference(unit_resolution,[status(thm)],[111, 108, 105, 104])).
% 6.54/6.76 tff(113,plain,
% 6.54/6.76 (A!36 = empty_set),
% 6.54/6.76 inference(symmetry,[status(thm)],[112])).
% 6.54/6.76 tff(114,plain,
% 6.54/6.76 ((A!36 = relation_inverse(relation_inverse(A!46))) <=> (empty_set = A!46)),
% 6.54/6.76 inference(monotonicity,[status(thm)],[113, 67])).
% 6.54/6.76 tff(115,plain,
% 6.54/6.76 ((A!36 = relation_inverse(relation_inverse(A!46))) <=> (A!46 = empty_set)),
% 6.54/6.76 inference(transitivity,[status(thm)],[114, 91])).
% 6.54/6.76 tff(116,plain,
% 6.54/6.76 ((A!46 = empty_set) <=> (A!36 = relation_inverse(relation_inverse(A!46)))),
% 6.54/6.76 inference(symmetry,[status(thm)],[115])).
% 6.54/6.76 tff(117,plain,
% 6.54/6.76 ((~(A!46 = empty_set)) <=> (~(A!36 = relation_inverse(relation_inverse(A!46))))),
% 6.54/6.76 inference(monotonicity,[status(thm)],[116])).
% 6.54/6.76 tff(118,plain,
% 6.54/6.76 (~(A!46 = empty_set)),
% 6.54/6.76 inference(and_elim,[status(thm)],[9])).
% 6.54/6.76 tff(119,plain,
% 6.54/6.76 (~(A!36 = relation_inverse(relation_inverse(A!46)))),
% 6.54/6.76 inference(modus_ponens,[status(thm)],[118, 117])).
% 6.54/6.76 tff(120,plain,
% 6.54/6.76 ((~((~(in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46)))) | (A!36 = relation_inverse(relation_inverse(A!46))))) | (~(in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46)))) | (A!36 = relation_inverse(relation_inverse(A!46)))),
% 6.54/6.76 inference(tautology,[status(thm)],[])).
% 6.54/6.76 tff(121,plain,
% 6.54/6.76 (~(in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46)))),
% 6.54/6.76 inference(unit_resolution,[status(thm)],[120, 119, 90])).
% 6.54/6.76 tff(122,plain,
% 6.54/6.76 (^[A: $i, B: $i] : refl(((~empty(B)) | (~in(A, B))) <=> ((~empty(B)) | (~in(A, B))))),
% 6.54/6.76 inference(bind,[status(th)],[])).
% 6.54/6.76 tff(123,plain,
% 6.54/6.76 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 6.54/6.76 inference(quant_intro,[status(thm)],[122])).
% 6.54/6.76 tff(124,plain,
% 6.54/6.76 (^[A: $i, B: $i] : trans(monotonicity(rewrite((in(A, B) & empty(B)) <=> (~((~empty(B)) | (~in(A, B))))), ((~(in(A, B) & empty(B))) <=> (~(~((~empty(B)) | (~in(A, B))))))), rewrite((~(~((~empty(B)) | (~in(A, B))))) <=> ((~empty(B)) | (~in(A, B)))), ((~(in(A, B) & empty(B))) <=> ((~empty(B)) | (~in(A, B)))))),
% 6.54/6.76 inference(bind,[status(th)],[])).
% 6.54/6.76 tff(125,plain,
% 6.54/6.76 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 6.54/6.76 inference(quant_intro,[status(thm)],[124])).
% 6.54/6.76 tff(126,plain,
% 6.54/6.76 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 6.54/6.76 inference(rewrite,[status(thm)],[])).
% 6.54/6.76 tff(127,axiom,(![A: $i, B: $i] : (~(in(A, B) & empty(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_boole')).
% 6.54/6.76 tff(128,plain,
% 6.54/6.76 (![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 6.54/6.76 inference(modus_ponens,[status(thm)],[127, 126])).
% 6.54/6.76 tff(129,plain,(
% 6.54/6.76 ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 6.54/6.76 inference(skolemize,[status(sab)],[128])).
% 6.54/6.76 tff(130,plain,
% 6.54/6.76 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 6.54/6.76 inference(modus_ponens,[status(thm)],[129, 125])).
% 6.54/6.76 tff(131,plain,
% 6.54/6.76 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 6.54/6.77 inference(modus_ponens,[status(thm)],[130, 123])).
% 6.54/6.77 tff(132,plain,
% 6.54/6.77 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(A!36)) | (~in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(A!36)) | (~in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36)))),
% 6.54/6.77 inference(rewrite,[status(thm)],[])).
% 6.54/6.77 tff(133,plain,
% 6.54/6.77 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(A!36)) | (~in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36)))),
% 6.54/6.77 inference(quant_inst,[status(thm)],[])).
% 6.54/6.77 tff(134,plain,
% 6.54/6.77 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(A!36)) | (~in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36))),
% 6.54/6.77 inference(modus_ponens,[status(thm)],[133, 132])).
% 6.54/6.77 tff(135,plain,
% 6.54/6.77 (~in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36)),
% 6.54/6.77 inference(unit_resolution,[status(thm)],[134, 105, 131])).
% 6.54/6.77 tff(136,plain,
% 6.54/6.77 ((in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46))) | in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36) | in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46))),
% 6.54/6.77 inference(tautology,[status(thm)],[])).
% 6.54/6.77 tff(137,plain,
% 6.54/6.77 (in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46))),
% 6.54/6.77 inference(unit_resolution,[status(thm)],[136, 135, 121])).
% 6.54/6.77 tff(138,plain,
% 6.54/6.77 ((~(in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!46) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46)))) | in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!46) | (~in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46)))),
% 6.54/6.77 inference(tautology,[status(thm)],[])).
% 6.54/6.77 tff(139,plain,
% 6.54/6.77 ($false),
% 6.54/6.77 inference(unit_resolution,[status(thm)],[138, 137, 79, 73])).
% 6.54/6.77 % SZS output end Proof
% 6.65/6.80 % E exiting
%------------------------------------------------------------------------------