%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU125+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:26:57 AM UTC 2025
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU125+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 06:06:26 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(in_type, type, (
% 0.13/0.39 in: ( $i * $i ) > $o)).
% 0.13/0.39 tff(set_union2_type, type, (
% 0.13/0.39 set_union2: ( $i * $i ) > $i)).
% 0.13/0.39 tff(tptp_fun_A_10_type, type, (
% 0.13/0.39 tptp_fun_A_10: $i)).
% 0.13/0.39 tff(tptp_fun_C_8_type, type, (
% 0.13/0.39 tptp_fun_C_8: $i)).
% 0.13/0.39 tff(tptp_fun_C_2_type, type, (
% 0.13/0.39 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.13/0.39 tff(tptp_fun_B_9_type, type, (
% 0.13/0.39 tptp_fun_B_9: $i)).
% 0.13/0.39 tff(subset_type, type, (
% 0.13/0.39 subset: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_D_1_type, type, (
% 0.13/0.39 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(4,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.39 tff(6,plain,(
% 0.13/0.39 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.13/0.39 inference(skolemize,[status(sab)],[5])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(A!10, C!8) = set_union2(C!8, A!10))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (set_union2(A!10, C!8) = set_union2(C!8, A!10)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (set_union2(C!8, A!10) = set_union2(A!10, C!8)),
% 0.13/0.39 inference(symmetry,[status(thm)],[9])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(A!10, C!8))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[10])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(A!10, C!8)) <=> in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10))),
% 0.13/0.39 inference(symmetry,[status(thm)],[11])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (^[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))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (![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)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (^[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))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (![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)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (![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)))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[16, 14])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (^[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)))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (![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)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[18])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (^[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))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[21])).
% 0.13/0.39 tff(23,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.13/0.39 tff(26,plain,(
% 0.13/0.39 ![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)))))),
% 0.13/0.39 inference(skolemize,[status(sab)],[25])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (![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)))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (![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)))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 ((~![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(set_union2(A!10, C!8), B!9)) | ![C: $i] : ((~in(C, set_union2(A!10, C!8))) | in(C, B!9)))) | (~(subset(set_union2(A!10, C!8), B!9) | (~((~in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(A!10, C!8))) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), B!9)))))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (~((~((~subset(set_union2(A!10, C!8), B!9)) | ![C: $i] : ((~in(C, set_union2(A!10, C!8))) | in(C, B!9)))) | (~(subset(set_union2(A!10, C!8), B!9) | (~((~in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(A!10, C!8))) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), B!9))))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (((~((~subset(set_union2(A!10, C!8), B!9)) | ![C: $i] : ((~in(C, set_union2(A!10, C!8))) | in(C, B!9)))) | (~(subset(set_union2(A!10, C!8), B!9) | (~((~in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(A!10, C!8))) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), B!9)))))) | (subset(set_union2(A!10, C!8), B!9) | (~((~in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(A!10, C!8))) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), B!9))))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (subset(set_union2(A!10, C!8), B!9) | (~((~in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(A!10, C!8))) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), B!9)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 ((~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B))) <=> (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 ((~![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(C, B)) => subset(set_union2(A, C), B))) <=> (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(35,axiom,(~![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(C, B)) => subset(set_union2(A, C), B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t8_xboole_1')).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[36, 33])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.13/0.39 tff(40,plain,(
% 0.13/0.39 ~((~(subset(A!10, B!9) & subset(C!8, B!9))) | subset(set_union2(A!10, C!8), B!9))),
% 0.13/0.39 inference(skolemize,[status(sab)],[39])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 (~subset(set_union2(A!10, C!8), B!9)),
% 0.13/0.39 inference(or_elim,[status(thm)],[40])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 ((~(subset(set_union2(A!10, C!8), B!9) | (~((~in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(A!10, C!8))) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), B!9))))) | subset(set_union2(A!10, C!8), B!9) | (~((~in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(A!10, C!8))) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), B!9)))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 ((~(subset(set_union2(A!10, C!8), B!9) | (~((~in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(A!10, C!8))) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), B!9))))) | (~((~in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(A!10, C!8))) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), B!9)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 (~((~in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(A!10, C!8))) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), B!9))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[43, 32])).
% 0.13/0.39 tff(45,plain,
% 0.13/0.39 (((~in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(A!10, C!8))) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), B!9)) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(A!10, C!8))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(46,plain,
% 0.13/0.39 (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(A!10, C!8))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[46, 12])).
% 0.13/0.39 tff(48,plain,
% 0.13/0.39 (^[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)))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(49,plain,
% 0.13/0.39 (![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)))))))) <=> ![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))))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[48])).
% 0.13/0.39 tff(50,plain,
% 0.13/0.39 (![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)))))))) <=> ![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))))))))),
% 0.13/0.39 inference(pull_quant,[status(thm)],[])).
% 0.13/0.39 tff(51,plain,
% 0.13/0.39 (^[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))))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(52,plain,
% 0.13/0.40 (![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))))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[51])).
% 0.13/0.40 tff(53,plain,
% 0.13/0.40 (![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))))))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[52, 50])).
% 0.13/0.40 tff(54,plain,
% 0.13/0.40 (![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))))))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[53, 49])).
% 0.13/0.40 tff(55,plain,
% 0.13/0.40 (^[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)))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(56,plain,
% 0.13/0.40 (![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))))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[55])).
% 0.13/0.40 tff(57,plain,
% 0.13/0.40 (![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))))))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[56, 54])).
% 0.13/0.40 tff(58,plain,
% 0.13/0.40 (^[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))))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(59,plain,
% 0.13/0.40 (![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))))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[58])).
% 0.13/0.40 tff(60,plain,
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(61,plain,
% 0.13/0.40 (^[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)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(62,plain,
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[61])).
% 0.13/0.40 tff(63,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/sandbox/benchmark/theBenchmark.p','d2_xboole_0')).
% 0.13/0.40 tff(64,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.13/0.40 tff(65,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.13/0.40 tff(66,plain,(
% 0.13/0.40 ![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))))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[65])).
% 0.13/0.40 tff(67,plain,
% 0.13/0.40 (![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))))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.13/0.40 tff(68,plain,
% 0.13/0.40 (![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))))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[67, 57])).
% 0.13/0.40 tff(69,plain,
% 0.13/0.40 (((~![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(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!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(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(70,plain,
% 0.13/0.40 ((~(~(in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8))))) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(71,plain,
% 0.13/0.40 (((~(in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8)))) | $false) <=> (~(in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(72,plain,
% 0.13/0.40 ((~$true) <=> $false),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(73,plain,
% 0.13/0.40 (($true | (~(in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), set_union2(C!8, A!10)) <=> (in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), A!10) | in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), C!8))))) <=> $true),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(74,plain,
% 0.13/0.40 ((~(in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), set_union2(C!8, A!10)) <=> (in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), A!10) | in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), C!8)))) <=> (~(in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), set_union2(C!8, A!10)) <=> (in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), A!10) | in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), C!8))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(75,plain,
% 0.21/0.40 ((set_union2(C!8, A!10) = set_union2(C!8, A!10)) <=> $true),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(76,plain,
% 0.21/0.40 (((set_union2(C!8, A!10) = set_union2(C!8, A!10)) | (~(in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), set_union2(C!8, A!10)) <=> (in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), A!10) | in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), C!8))))) <=> ($true | (~(in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), set_union2(C!8, A!10)) <=> (in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), A!10) | in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), C!8)))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[75, 74])).
% 0.21/0.40 tff(77,plain,
% 0.21/0.40 (((set_union2(C!8, A!10) = set_union2(C!8, A!10)) | (~(in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), set_union2(C!8, A!10)) <=> (in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), A!10) | in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), C!8))))) <=> $true),
% 0.21/0.40 inference(transitivity,[status(thm)],[76, 73])).
% 0.21/0.40 tff(78,plain,
% 0.21/0.40 ((~((set_union2(C!8, A!10) = set_union2(C!8, A!10)) | (~(in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), set_union2(C!8, A!10)) <=> (in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), A!10) | in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), C!8)))))) <=> (~$true)),
% 0.21/0.40 inference(monotonicity,[status(thm)],[77])).
% 0.21/0.40 tff(79,plain,
% 0.21/0.40 ((~((set_union2(C!8, A!10) = set_union2(C!8, A!10)) | (~(in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), set_union2(C!8, A!10)) <=> (in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), A!10) | in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), C!8)))))) <=> $false),
% 0.21/0.40 inference(transitivity,[status(thm)],[78, 72])).
% 0.21/0.40 tff(80,plain,
% 0.21/0.40 ((~(in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8)))) <=> (~(in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(81,plain,
% 0.21/0.40 (($false | (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8)))) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(82,plain,
% 0.21/0.40 ((~(set_union2(C!8, A!10) = set_union2(C!8, A!10))) <=> (~$true)),
% 0.21/0.40 inference(monotonicity,[status(thm)],[75])).
% 0.21/0.40 tff(83,plain,
% 0.21/0.40 ((~(set_union2(C!8, A!10) = set_union2(C!8, A!10))) <=> $false),
% 0.21/0.40 inference(transitivity,[status(thm)],[82, 72])).
% 0.21/0.40 tff(84,plain,
% 0.21/0.40 (((~(set_union2(C!8, A!10) = set_union2(C!8, A!10))) | (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8)))) <=> ($false | (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[83])).
% 0.21/0.40 tff(85,plain,
% 0.21/0.40 (((~(set_union2(C!8, A!10) = set_union2(C!8, A!10))) | (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8)))) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[84, 81])).
% 0.21/0.41 tff(86,plain,
% 0.21/0.41 ((~((~(set_union2(C!8, A!10) = set_union2(C!8, A!10))) | (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8))))) <=> (~(in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[85])).
% 0.21/0.41 tff(87,plain,
% 0.21/0.41 ((~((~(set_union2(C!8, A!10) = set_union2(C!8, A!10))) | (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8))))) <=> (~(in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[86, 80])).
% 0.21/0.41 tff(88,plain,
% 0.21/0.41 (((~((~(set_union2(C!8, A!10) = set_union2(C!8, A!10))) | (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8))))) | (~((set_union2(C!8, A!10) = set_union2(C!8, A!10)) | (~(in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), set_union2(C!8, A!10)) <=> (in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), A!10) | in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), C!8))))))) <=> ((~(in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8)))) | $false)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[87, 79])).
% 0.21/0.41 tff(89,plain,
% 0.21/0.41 (((~((~(set_union2(C!8, A!10) = set_union2(C!8, A!10))) | (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8))))) | (~((set_union2(C!8, A!10) = set_union2(C!8, A!10)) | (~(in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), set_union2(C!8, A!10)) <=> (in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), A!10) | in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), C!8))))))) <=> (~(in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[88, 71])).
% 0.21/0.41 tff(90,plain,
% 0.21/0.41 ((~((~((~(set_union2(C!8, A!10) = set_union2(C!8, A!10))) | (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8))))) | (~((set_union2(C!8, A!10) = set_union2(C!8, A!10)) | (~(in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), set_union2(C!8, A!10)) <=> (in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), A!10) | in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), C!8)))))))) <=> (~(~(in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8)))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[89])).
% 0.21/0.41 tff(91,plain,
% 0.21/0.41 ((~((~((~(set_union2(C!8, A!10) = set_union2(C!8, A!10))) | (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8))))) | (~((set_union2(C!8, A!10) = set_union2(C!8, A!10)) | (~(in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), set_union2(C!8, A!10)) <=> (in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), A!10) | in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), C!8)))))))) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[90, 70])).
% 0.21/0.41 tff(92,plain,
% 0.21/0.41 (((~![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(C!8, A!10) = set_union2(C!8, A!10))) | (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8))))) | (~((set_union2(C!8, A!10) = set_union2(C!8, A!10)) | (~(in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), set_union2(C!8, A!10)) <=> (in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), A!10) | in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), C!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(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[91])).
% 0.21/0.41 tff(93,plain,
% 0.21/0.41 (((~![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(C!8, A!10) = set_union2(C!8, A!10))) | (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8))))) | (~((set_union2(C!8, A!10) = set_union2(C!8, A!10)) | (~(in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), set_union2(C!8, A!10)) <=> (in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), A!10) | in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), C!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(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[92, 69])).
% 0.21/0.41 tff(94,plain,
% 0.21/0.41 ((~![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(C!8, A!10) = set_union2(C!8, A!10))) | (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8))))) | (~((set_union2(C!8, A!10) = set_union2(C!8, A!10)) | (~(in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), set_union2(C!8, A!10)) <=> (in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), A!10) | in(tptp_fun_D_1(set_union2(C!8, A!10), A!10, C!8), C!8))))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(95,plain,
% 0.21/0.41 ((~![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(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.21/0.41 tff(96,plain,
% 0.21/0.41 (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[95, 68])).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 (((~in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(A!10, C!8))) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), B!9)) | (~in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), B!9))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 (~in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), B!9)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[97, 44])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 ((~![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!10, B!9)) | ![C: $i] : ((~in(C, A!10)) | in(C, B!9)))) | (~(subset(A!10, B!9) | (~((~in(tptp_fun_C_2(B!9, A!10), A!10)) | in(tptp_fun_C_2(B!9, A!10), B!9)))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 (~((~((~subset(A!10, B!9)) | ![C: $i] : ((~in(C, A!10)) | in(C, B!9)))) | (~(subset(A!10, B!9) | (~((~in(tptp_fun_C_2(B!9, A!10), A!10)) | in(tptp_fun_C_2(B!9, A!10), B!9))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[99, 28])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 (((~((~subset(A!10, B!9)) | ![C: $i] : ((~in(C, A!10)) | in(C, B!9)))) | (~(subset(A!10, B!9) | (~((~in(tptp_fun_C_2(B!9, A!10), A!10)) | in(tptp_fun_C_2(B!9, A!10), B!9)))))) | ((~subset(A!10, B!9)) | ![C: $i] : ((~in(C, A!10)) | in(C, B!9)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 ((~subset(A!10, B!9)) | ![C: $i] : ((~in(C, A!10)) | in(C, B!9))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 (subset(A!10, B!9) & subset(C!8, B!9)),
% 0.21/0.42 inference(or_elim,[status(thm)],[40])).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 (subset(A!10, B!9)),
% 0.21/0.42 inference(and_elim,[status(thm)],[103])).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 ((~((~subset(A!10, B!9)) | ![C: $i] : ((~in(C, A!10)) | in(C, B!9)))) | (~subset(A!10, B!9)) | ![C: $i] : ((~in(C, A!10)) | in(C, B!9))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 ((~((~subset(A!10, B!9)) | ![C: $i] : ((~in(C, A!10)) | in(C, B!9)))) | ![C: $i] : ((~in(C, A!10)) | in(C, B!9))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.21/0.42 tff(107,plain,
% 0.21/0.42 (![C: $i] : ((~in(C, A!10)) | in(C, B!9))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[106, 102])).
% 0.21/0.42 tff(108,plain,
% 0.21/0.42 (((~![C: $i] : ((~in(C, A!10)) | in(C, B!9))) | ((~in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10)) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), B!9))) <=> ((~![C: $i] : ((~in(C, A!10)) | in(C, B!9))) | (~in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10)) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), B!9))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(109,plain,
% 0.21/0.42 ((~![C: $i] : ((~in(C, A!10)) | in(C, B!9))) | ((~in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10)) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), B!9))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(110,plain,
% 0.21/0.42 ((~![C: $i] : ((~in(C, A!10)) | in(C, B!9))) | (~in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10)) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), B!9)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.21/0.42 tff(111,plain,
% 0.21/0.42 (~in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[110, 107, 98])).
% 0.21/0.42 tff(112,plain,
% 0.21/0.42 ((~![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(C!8, B!9)) | ![C: $i] : ((~in(C, C!8)) | in(C, B!9)))) | (~(subset(C!8, B!9) | (~((~in(tptp_fun_C_2(B!9, C!8), C!8)) | in(tptp_fun_C_2(B!9, C!8), B!9)))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 (~((~((~subset(C!8, B!9)) | ![C: $i] : ((~in(C, C!8)) | in(C, B!9)))) | (~(subset(C!8, B!9) | (~((~in(tptp_fun_C_2(B!9, C!8), C!8)) | in(tptp_fun_C_2(B!9, C!8), B!9))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[112, 28])).
% 0.21/0.42 tff(114,plain,
% 0.21/0.42 (((~((~subset(C!8, B!9)) | ![C: $i] : ((~in(C, C!8)) | in(C, B!9)))) | (~(subset(C!8, B!9) | (~((~in(tptp_fun_C_2(B!9, C!8), C!8)) | in(tptp_fun_C_2(B!9, C!8), B!9)))))) | ((~subset(C!8, B!9)) | ![C: $i] : ((~in(C, C!8)) | in(C, B!9)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(115,plain,
% 0.21/0.42 ((~subset(C!8, B!9)) | ![C: $i] : ((~in(C, C!8)) | in(C, B!9))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.21/0.42 tff(116,plain,
% 0.21/0.42 (subset(C!8, B!9)),
% 0.21/0.42 inference(and_elim,[status(thm)],[103])).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 ((~((~subset(C!8, B!9)) | ![C: $i] : ((~in(C, C!8)) | in(C, B!9)))) | (~subset(C!8, B!9)) | ![C: $i] : ((~in(C, C!8)) | in(C, B!9))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(118,plain,
% 0.21/0.42 ((~((~subset(C!8, B!9)) | ![C: $i] : ((~in(C, C!8)) | in(C, B!9)))) | ![C: $i] : ((~in(C, C!8)) | in(C, B!9))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.21/0.42 tff(119,plain,
% 0.21/0.42 (![C: $i] : ((~in(C, C!8)) | in(C, B!9))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[118, 115])).
% 0.21/0.42 tff(120,plain,
% 0.21/0.42 (((~![C: $i] : ((~in(C, C!8)) | in(C, B!9))) | ((~in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8)) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), B!9))) <=> ((~![C: $i] : ((~in(C, C!8)) | in(C, B!9))) | (~in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8)) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), B!9))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(121,plain,
% 0.21/0.42 ((~![C: $i] : ((~in(C, C!8)) | in(C, B!9))) | ((~in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8)) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), B!9))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(122,plain,
% 0.21/0.42 ((~![C: $i] : ((~in(C, C!8)) | in(C, B!9))) | (~in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8)) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), B!9)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.21/0.42 tff(123,plain,
% 0.21/0.42 (~in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[122, 119, 98])).
% 0.21/0.42 tff(124,plain,
% 0.21/0.42 ((~(in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8))) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(125,plain,
% 0.21/0.42 (~(in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[124, 123, 111])).
% 0.21/0.42 tff(126,plain,
% 0.21/0.42 ((~(in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10)) <=> (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8)))) | (~in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10))) | (in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), A!10) | in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), C!8))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(127,plain,
% 0.21/0.42 (~in(tptp_fun_C_2(B!9, set_union2(A!10, C!8)), set_union2(C!8, A!10))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[126, 125, 96])).
% 0.21/0.42 tff(128,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[127, 47])).
% 0.21/0.42 % SZS output end Proof
% 0.21/0.42 % E exiting
%------------------------------------------------------------------------------