%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET603+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:25:58 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET603+3 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 05:32:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(member_type, type, (
% 0.11/0.37 member: ( $i * $i ) > $o)).
% 0.11/0.37 tff(empty_set_type, type, (
% 0.11/0.37 empty_set: $i)).
% 0.11/0.37 tff(tptp_fun_D_0_type, type, (
% 0.11/0.37 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.11/0.37 tff(difference_type, type, (
% 0.11/0.37 difference: ( $i * $i ) > $i)).
% 0.11/0.37 tff(tptp_fun_B_3_type, type, (
% 0.11/0.37 tptp_fun_B_3: $i)).
% 0.11/0.37 tff(1,assumption,(~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)), introduced(assumption)).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (^[B: $i, C: $i, D: $i] : refl((~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 (![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 0.11/0.37 inference(pull_quant,[status(thm)],[])).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 (^[B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))), ((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) <=> (~![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))))), pull_quant((~![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))) <=> ?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C))))), ((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) <=> ?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))) <=> (?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))), pull_quant((?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> (~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))))), pull_quant((~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(6,plain,
% 0.11/0.38 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[5])).
% 0.11/0.38 tff(7,plain,
% 0.11/0.38 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[6, 4])).
% 0.11/0.38 tff(8,plain,
% 0.11/0.38 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[7, 3])).
% 0.11/0.38 tff(9,plain,
% 0.11/0.38 (^[B: $i, C: $i] : rewrite((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(10,plain,
% 0.11/0.38 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[9])).
% 0.11/0.38 tff(11,plain,
% 0.11/0.38 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[10, 8])).
% 0.11/0.38 tff(12,plain,
% 0.11/0.38 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))), trans(monotonicity(rewrite((~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))) <=> (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))), (((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))), rewrite(((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))), (((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))), rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(13,plain,
% 0.11/0.38 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.11/0.38 tff(14,plain,
% 0.11/0.38 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C))) <=> ![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(15,axiom,(![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','equal_member_defn')).
% 0.11/0.38 tff(16,plain,
% 0.11/0.38 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.11/0.38 tff(17,plain,(
% 0.11/0.38 ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))),
% 0.11/0.38 inference(skolemize,[status(sab)],[16])).
% 0.11/0.38 tff(18,plain,
% 0.11/0.38 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.11/0.38 tff(19,plain,
% 0.11/0.38 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.11/0.38 tff(20,plain,
% 0.11/0.38 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(difference(B!3, empty_set) = B!3)) | (member(tptp_fun_D_0(empty_set, difference(B!3, empty_set)), difference(B!3, empty_set)) <=> member(tptp_fun_D_0(empty_set, difference(B!3, empty_set)), B!3)))) | (~((difference(B!3, empty_set) = B!3) | (~(member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set)) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)))))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(21,plain,
% 0.11/0.38 (~((~((~(difference(B!3, empty_set) = B!3)) | (member(tptp_fun_D_0(empty_set, difference(B!3, empty_set)), difference(B!3, empty_set)) <=> member(tptp_fun_D_0(empty_set, difference(B!3, empty_set)), B!3)))) | (~((difference(B!3, empty_set) = B!3) | (~(member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set)) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3))))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.11/0.38 tff(22,plain,
% 0.11/0.38 (((~((~(difference(B!3, empty_set) = B!3)) | (member(tptp_fun_D_0(empty_set, difference(B!3, empty_set)), difference(B!3, empty_set)) <=> member(tptp_fun_D_0(empty_set, difference(B!3, empty_set)), B!3)))) | (~((difference(B!3, empty_set) = B!3) | (~(member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set)) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)))))) | ((difference(B!3, empty_set) = B!3) | (~(member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set)) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3))))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(23,plain,
% 0.11/0.38 ((difference(B!3, empty_set) = B!3) | (~(member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set)) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.11/0.38 tff(24,plain,
% 0.11/0.38 ((~![B: $i] : (difference(B, empty_set) = B)) <=> (~![B: $i] : (difference(B, empty_set) = B))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(25,axiom,(~![B: $i] : (difference(B, empty_set) = B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th74')).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 (~![B: $i] : (difference(B, empty_set) = B)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 (~![B: $i] : (difference(B, empty_set) = B)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[26, 24])).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 (~![B: $i] : (difference(B, empty_set) = B)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 (~![B: $i] : (difference(B, empty_set) = B)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.19/0.38 tff(30,plain,(
% 0.19/0.38 ~(difference(B!3, empty_set) = B!3)),
% 0.19/0.38 inference(skolemize,[status(sab)],[29])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 ((~((difference(B!3, empty_set) = B!3) | (~(member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set)) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3))))) | (difference(B!3, empty_set) = B!3) | (~(member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set)) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 ((~((difference(B!3, empty_set) = B!3) | (~(member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set)) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3))))) | (~(member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set)) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 (~(member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set)) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[32, 23])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 ((member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set)) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(35,plain,
% 0.19/0.38 (member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.19/0.38 tff(36,plain,
% 0.19/0.38 (member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[35, 1])).
% 0.19/0.38 tff(37,plain,
% 0.19/0.38 (((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 ((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[37, 1])).
% 0.19/0.38 tff(39,plain,
% 0.19/0.38 (^[B: $i, C: $i, D: $i] : refl((~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(40,plain,
% 0.19/0.38 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[39])).
% 0.19/0.38 tff(41,plain,
% 0.19/0.38 (^[B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((member(D, B) & (~member(D, C))) <=> (~((~member(D, B)) | member(D, C)))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))))), rewrite((member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))))), rewrite((~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(42,plain,
% 0.19/0.38 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[41])).
% 0.19/0.38 tff(43,plain,
% 0.19/0.38 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(44,axiom,(![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','difference_defn')).
% 0.19/0.38 tff(45,plain,
% 0.19/0.38 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.38 tff(46,plain,(
% 0.19/0.38 ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[45])).
% 0.19/0.38 tff(47,plain,
% 0.19/0.38 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.19/0.38 tff(49,plain,
% 0.19/0.38 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set)) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(50,plain,
% 0.19/0.38 (~(((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set)) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.19/0.38 tff(51,plain,
% 0.19/0.38 ((((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set)) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))) | (~((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set))) | (~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(52,plain,
% 0.19/0.38 ((~((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set))) | (~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.19/0.38 tff(53,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[52, 38, 36])).
% 0.19/0.38 tff(54,plain,(member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(55,plain,
% 0.19/0.38 ((member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set)) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | (~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))) | (~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(56,plain,
% 0.19/0.38 ((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))) | (~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[55, 33])).
% 0.19/0.38 tff(57,plain,
% 0.19/0.38 (~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[56, 54])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 ((((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set)) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))) | ((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[58, 50])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 ((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[59, 57])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 ((~((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set))) | (~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[61, 60, 54])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (^[B: $i] : refl((~member(B, empty_set)) <=> (~member(B, empty_set)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[63])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(66,axiom,(![B: $i] : (~member(B, empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','empty_set_defn')).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 (![B: $i] : (~member(B, empty_set))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.39 tff(68,plain,(
% 0.19/0.39 ![B: $i] : (~member(B, empty_set))),
% 0.19/0.39 inference(skolemize,[status(sab)],[67])).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 (![B: $i] : (~member(B, empty_set))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.19/0.39 tff(70,plain,
% 0.19/0.39 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[70, 69, 62])).
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------