%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU124+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:26:56 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU124+2 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.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 06:07:57 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(in_type, type, (
% 0.12/0.37 in: ( $i * $i ) > $o)).
% 0.12/0.37 tff(set_union2_type, type, (
% 0.12/0.37 set_union2: ( $i * $i ) > $i)).
% 0.12/0.37 tff(tptp_fun_A_9_type, type, (
% 0.12/0.37 tptp_fun_A_9: $i)).
% 0.12/0.37 tff(tptp_fun_B_8_type, type, (
% 0.12/0.37 tptp_fun_B_8: $i)).
% 0.12/0.37 tff(tptp_fun_C_2_type, type, (
% 0.12/0.37 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.12/0.37 tff(subset_type, type, (
% 0.12/0.37 subset: ( $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_D_1_type, type, (
% 0.12/0.37 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(4,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.37 tff(6,plain,(
% 0.12/0.37 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.12/0.37 inference(skolemize,[status(sab)],[5])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(A!9, B!8) = set_union2(B!8, A!9))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (set_union2(A!9, B!8) = set_union2(B!8, A!9)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (set_union2(B!8, A!9) = set_union2(A!9, B!8)),
% 0.12/0.37 inference(symmetry,[status(thm)],[9])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(A!9, B!8))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[10])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(A!9, B!8)) <=> in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9))),
% 0.12/0.37 inference(symmetry,[status(thm)],[11])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 ((~in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(A!9, B!8))) <=> (~in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[12])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[14])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[16])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[17, 15])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[19])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[22])).
% 0.12/0.38 tff(24,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.12/0.38 tff(27,plain,(
% 0.12/0.38 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[26])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | (~((~((~subset(A!9, set_union2(A!9, B!8))) | ![C: $i] : ((~in(C, A!9)) | in(C, set_union2(A!9, B!8))))) | (~(subset(A!9, set_union2(A!9, B!8)) | (~((~in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9)) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(A!9, B!8))))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (~((~((~subset(A!9, set_union2(A!9, B!8))) | ![C: $i] : ((~in(C, A!9)) | in(C, set_union2(A!9, B!8))))) | (~(subset(A!9, set_union2(A!9, B!8)) | (~((~in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9)) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(A!9, B!8)))))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (((~((~subset(A!9, set_union2(A!9, B!8))) | ![C: $i] : ((~in(C, A!9)) | in(C, set_union2(A!9, B!8))))) | (~(subset(A!9, set_union2(A!9, B!8)) | (~((~in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9)) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(A!9, B!8))))))) | (subset(A!9, set_union2(A!9, B!8)) | (~((~in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9)) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(A!9, B!8)))))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (subset(A!9, set_union2(A!9, B!8)) | (~((~in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9)) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(A!9, B!8))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : subset(A, set_union2(A, B))) <=> (~![A: $i, B: $i] : subset(A, set_union2(A, B)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(35,axiom,(~![A: $i, B: $i] : subset(A, set_union2(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t7_xboole_1')).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (~![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (~![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[36, 34])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (~![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (~![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.12/0.38 tff(40,plain,(
% 0.12/0.38 ~subset(A!9, set_union2(A!9, B!8))),
% 0.12/0.38 inference(skolemize,[status(sab)],[39])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 ((~(subset(A!9, set_union2(A!9, B!8)) | (~((~in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9)) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(A!9, B!8)))))) | subset(A!9, set_union2(A!9, B!8)) | (~((~in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9)) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(A!9, B!8))))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 ((~(subset(A!9, set_union2(A!9, B!8)) | (~((~in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9)) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(A!9, B!8)))))) | (~((~in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9)) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(A!9, B!8))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (~((~in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9)) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(A!9, B!8)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[42, 33])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (((~in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9)) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(A!9, B!8))) | (~in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(A!9, B!8)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (~in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(A!9, B!8))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (~in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[45, 13])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))))))) <=> (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[47])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))),
% 0.12/0.38 inference(pull_quant,[status(thm)],[])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> (~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), pull_quant((~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A)))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))) <=> (?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))), pull_quant((?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))))))) <=> (~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[50])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[51, 49])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[52, 48])).
% 0.12/0.38 tff(54,plain,
% 0.12/0.38 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(55,plain,
% 0.12/0.38 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[54])).
% 0.12/0.38 tff(56,plain,
% 0.12/0.38 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[55, 53])).
% 0.12/0.38 tff(57,plain,
% 0.12/0.38 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))), trans(monotonicity(rewrite((~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))) <=> (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))), rewrite(((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))))))), rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(58,plain,
% 0.12/0.38 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[57])).
% 0.12/0.38 tff(59,plain,
% 0.12/0.38 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(60,plain,
% 0.12/0.38 (^[A: $i, B: $i, C: $i] : rewrite(((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(61,plain,
% 0.12/0.38 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[60])).
% 0.12/0.38 tff(62,axiom,(![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_xboole_0')).
% 0.12/0.38 tff(63,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.12/0.39 tff(65,plain,(
% 0.12/0.39 ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[64])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[66, 56])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))) | (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))) | (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 ((~(~(in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8))))) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 (((~(in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8)))) | $false) <=> (~(in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(71,plain,
% 0.12/0.39 ((~$true) <=> $false),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 (($true | (~(in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), set_union2(B!8, A!9)) <=> (in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), A!9) | in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), B!8))))) <=> $true),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(73,plain,
% 0.12/0.39 ((~(in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), set_union2(B!8, A!9)) <=> (in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), A!9) | in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), B!8)))) <=> (~(in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), set_union2(B!8, A!9)) <=> (in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), A!9) | in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), B!8))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 ((set_union2(B!8, A!9) = set_union2(B!8, A!9)) <=> $true),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 (((set_union2(B!8, A!9) = set_union2(B!8, A!9)) | (~(in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), set_union2(B!8, A!9)) <=> (in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), A!9) | in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), B!8))))) <=> ($true | (~(in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), set_union2(B!8, A!9)) <=> (in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), A!9) | in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), B!8)))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[74, 73])).
% 0.12/0.39 tff(76,plain,
% 0.12/0.39 (((set_union2(B!8, A!9) = set_union2(B!8, A!9)) | (~(in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), set_union2(B!8, A!9)) <=> (in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), A!9) | in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), B!8))))) <=> $true),
% 0.12/0.39 inference(transitivity,[status(thm)],[75, 72])).
% 0.12/0.39 tff(77,plain,
% 0.12/0.39 ((~((set_union2(B!8, A!9) = set_union2(B!8, A!9)) | (~(in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), set_union2(B!8, A!9)) <=> (in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), A!9) | in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), B!8)))))) <=> (~$true)),
% 0.12/0.39 inference(monotonicity,[status(thm)],[76])).
% 0.12/0.39 tff(78,plain,
% 0.12/0.39 ((~((set_union2(B!8, A!9) = set_union2(B!8, A!9)) | (~(in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), set_union2(B!8, A!9)) <=> (in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), A!9) | in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), B!8)))))) <=> $false),
% 0.12/0.39 inference(transitivity,[status(thm)],[77, 71])).
% 0.12/0.39 tff(79,plain,
% 0.12/0.39 ((~(in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8)))) <=> (~(in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(80,plain,
% 0.12/0.39 (($false | (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8)))) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(81,plain,
% 0.12/0.39 ((~(set_union2(B!8, A!9) = set_union2(B!8, A!9))) <=> (~$true)),
% 0.12/0.39 inference(monotonicity,[status(thm)],[74])).
% 0.12/0.39 tff(82,plain,
% 0.12/0.39 ((~(set_union2(B!8, A!9) = set_union2(B!8, A!9))) <=> $false),
% 0.12/0.39 inference(transitivity,[status(thm)],[81, 71])).
% 0.12/0.39 tff(83,plain,
% 0.12/0.39 (((~(set_union2(B!8, A!9) = set_union2(B!8, A!9))) | (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8)))) <=> ($false | (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[82])).
% 0.12/0.39 tff(84,plain,
% 0.12/0.39 (((~(set_union2(B!8, A!9) = set_union2(B!8, A!9))) | (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8)))) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8)))),
% 0.12/0.39 inference(transitivity,[status(thm)],[83, 80])).
% 0.12/0.39 tff(85,plain,
% 0.12/0.39 ((~((~(set_union2(B!8, A!9) = set_union2(B!8, A!9))) | (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8))))) <=> (~(in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[84])).
% 0.12/0.39 tff(86,plain,
% 0.12/0.39 ((~((~(set_union2(B!8, A!9) = set_union2(B!8, A!9))) | (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8))))) <=> (~(in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[85, 79])).
% 0.12/0.40 tff(87,plain,
% 0.12/0.40 (((~((~(set_union2(B!8, A!9) = set_union2(B!8, A!9))) | (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8))))) | (~((set_union2(B!8, A!9) = set_union2(B!8, A!9)) | (~(in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), set_union2(B!8, A!9)) <=> (in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), A!9) | in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), B!8))))))) <=> ((~(in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8)))) | $false)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[86, 78])).
% 0.12/0.40 tff(88,plain,
% 0.12/0.40 (((~((~(set_union2(B!8, A!9) = set_union2(B!8, A!9))) | (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8))))) | (~((set_union2(B!8, A!9) = set_union2(B!8, A!9)) | (~(in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), set_union2(B!8, A!9)) <=> (in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), A!9) | in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), B!8))))))) <=> (~(in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[87, 70])).
% 0.12/0.40 tff(89,plain,
% 0.12/0.40 ((~((~((~(set_union2(B!8, A!9) = set_union2(B!8, A!9))) | (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8))))) | (~((set_union2(B!8, A!9) = set_union2(B!8, A!9)) | (~(in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), set_union2(B!8, A!9)) <=> (in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), A!9) | in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), B!8)))))))) <=> (~(~(in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8)))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[88])).
% 0.12/0.40 tff(90,plain,
% 0.12/0.40 ((~((~((~(set_union2(B!8, A!9) = set_union2(B!8, A!9))) | (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8))))) | (~((set_union2(B!8, A!9) = set_union2(B!8, A!9)) | (~(in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), set_union2(B!8, A!9)) <=> (in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), A!9) | in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), B!8)))))))) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8)))),
% 0.12/0.40 inference(transitivity,[status(thm)],[89, 69])).
% 0.12/0.40 tff(91,plain,
% 0.12/0.40 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))) | (~((~((~(set_union2(B!8, A!9) = set_union2(B!8, A!9))) | (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8))))) | (~((set_union2(B!8, A!9) = set_union2(B!8, A!9)) | (~(in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), set_union2(B!8, A!9)) <=> (in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), A!9) | in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), B!8))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))) | (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[90])).
% 0.12/0.40 tff(92,plain,
% 0.12/0.40 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))) | (~((~((~(set_union2(B!8, A!9) = set_union2(B!8, A!9))) | (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8))))) | (~((set_union2(B!8, A!9) = set_union2(B!8, A!9)) | (~(in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), set_union2(B!8, A!9)) <=> (in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), A!9) | in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), B!8))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))) | (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[91, 68])).
% 0.12/0.40 tff(93,plain,
% 0.12/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))) | (~((~((~(set_union2(B!8, A!9) = set_union2(B!8, A!9))) | (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8))))) | (~((set_union2(B!8, A!9) = set_union2(B!8, A!9)) | (~(in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), set_union2(B!8, A!9)) <=> (in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), A!9) | in(tptp_fun_D_1(set_union2(B!8, A!9), A!9, B!8), B!8))))))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(94,plain,
% 0.12/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))) | (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.12/0.40 tff(95,plain,
% 0.12/0.40 (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[94, 67])).
% 0.12/0.40 tff(96,plain,
% 0.12/0.40 (((~in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9)) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(A!9, B!8))) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(97,plain,
% 0.12/0.40 (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[96, 43])).
% 0.12/0.40 tff(98,plain,
% 0.12/0.40 ((in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8)) | (~in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(99,plain,
% 0.12/0.40 (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.12/0.40 tff(100,plain,
% 0.12/0.40 ((~(in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8)))) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) | (~(in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 ((~(in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9)) <=> (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), A!9) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), B!8)))) | in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 (in(tptp_fun_C_2(set_union2(A!9, B!8), A!9), set_union2(B!8, A!9))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[101, 95])).
% 0.19/0.40 tff(103,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[102, 46])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------