%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU133+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:26:58 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU133+2 : TPTP v9.0.0. Released v3.3.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.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 06:06:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(in_type, type, (
% 0.12/0.38 in: ( $i * $i ) > $o)).
% 0.12/0.38 tff(set_difference_type, type, (
% 0.12/0.38 set_difference: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_B_8_type, type, (
% 0.12/0.38 tptp_fun_B_8: $i)).
% 0.12/0.38 tff(tptp_fun_A_9_type, type, (
% 0.12/0.38 tptp_fun_A_9: $i)).
% 0.12/0.38 tff(tptp_fun_C_2_type, type, (
% 0.12/0.38 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.12/0.38 tff(subset_type, type, (
% 0.12/0.38 subset: ( $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_D_4_type, type, (
% 0.12/0.38 tptp_fun_D_4: ( $i * $i * $i ) > $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[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))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,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)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (^[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))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(4,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)],[3])).
% 0.12/0.38 tff(5,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)],[4, 2])).
% 0.12/0.38 tff(6,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(7,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)],[6])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (^[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))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[9])).
% 0.12/0.39 tff(11,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')).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.12/0.39 tff(14,plain,(
% 0.12/0.39 ![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)))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[13])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 ((~![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_difference(A!9, B!8), A!9)) | ![C: $i] : ((~in(C, set_difference(A!9, B!8))) | in(C, A!9)))) | (~(subset(set_difference(A!9, B!8), A!9) | (~((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (~((~((~subset(set_difference(A!9, B!8), A!9)) | ![C: $i] : ((~in(C, set_difference(A!9, B!8))) | in(C, A!9)))) | (~(subset(set_difference(A!9, B!8), A!9) | (~((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9))))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (((~((~subset(set_difference(A!9, B!8), A!9)) | ![C: $i] : ((~in(C, set_difference(A!9, B!8))) | in(C, A!9)))) | (~(subset(set_difference(A!9, B!8), A!9) | (~((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)))))) | (subset(set_difference(A!9, B!8), A!9) | (~((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9))))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (subset(set_difference(A!9, B!8), A!9) | (~((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 ((~![A: $i, B: $i] : subset(set_difference(A, B), A)) <=> (~![A: $i, B: $i] : subset(set_difference(A, B), A))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(22,axiom,(~![A: $i, B: $i] : subset(set_difference(A, B), A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t36_xboole_1')).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (~![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (~![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[23, 21])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (~![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (~![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.12/0.39 tff(27,plain,(
% 0.12/0.39 ~subset(set_difference(A!9, B!8), A!9)),
% 0.12/0.39 inference(skolemize,[status(sab)],[26])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 ((~(subset(set_difference(A!9, B!8), A!9) | (~((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9))))) | subset(set_difference(A!9, B!8), A!9) | (~((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 ((~(subset(set_difference(A!9, B!8), A!9) | (~((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9))))) | (~((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (~((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[29, 20])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | (~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 (((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 ((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[35, 30])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 ((((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))) | (~((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8))) | (~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[37, 36, 34])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[39])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 0.12/0.39 inference(pull_quant,[status(thm)],[])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) <=> ![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> (~![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))))), pull_quant((~![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))) <=> (?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))), pull_quant((?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> (~?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))))), pull_quant((~?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[42])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[43, 41])).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[44, 40])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[46])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[47, 45])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.40 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))), rewrite(((C = set_difference(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B)))))) <=> ((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B))))))) <=> (((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) & ((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))), rewrite((((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) & ((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B))))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(52,axiom,(![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_xboole_0')).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.12/0.40 tff(54,plain,(
% 0.12/0.40 ![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B)))))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[53])).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~(((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~(((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 ((~(((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8)))) <=> (~(((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 (((((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))) | $false) <=> (((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(60,plain,
% 0.12/0.40 ((~$true) <=> $false),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 (($true | (((~in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), A!9)) | in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), B!8)) <=> in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), set_difference(A!9, B!8)))) <=> $true),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 ((set_difference(A!9, B!8) = set_difference(A!9, B!8)) <=> $true),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(63,plain,
% 0.12/0.40 (((set_difference(A!9, B!8) = set_difference(A!9, B!8)) | (((~in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), A!9)) | in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), B!8)) <=> in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), set_difference(A!9, B!8)))) <=> ($true | (((~in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), A!9)) | in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), B!8)) <=> in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), set_difference(A!9, B!8))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[62])).
% 0.12/0.40 tff(64,plain,
% 0.12/0.40 (((set_difference(A!9, B!8) = set_difference(A!9, B!8)) | (((~in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), A!9)) | in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), B!8)) <=> in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), set_difference(A!9, B!8)))) <=> $true),
% 0.12/0.40 inference(transitivity,[status(thm)],[63, 61])).
% 0.12/0.40 tff(65,plain,
% 0.12/0.40 ((~((set_difference(A!9, B!8) = set_difference(A!9, B!8)) | (((~in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), A!9)) | in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), B!8)) <=> in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), set_difference(A!9, B!8))))) <=> (~$true)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[64])).
% 0.12/0.40 tff(66,plain,
% 0.12/0.40 ((~((set_difference(A!9, B!8) = set_difference(A!9, B!8)) | (((~in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), A!9)) | in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), B!8)) <=> in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), set_difference(A!9, B!8))))) <=> $false),
% 0.12/0.40 inference(transitivity,[status(thm)],[65, 60])).
% 0.12/0.40 tff(67,plain,
% 0.12/0.40 ((~(~(((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))))) <=> (((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 (($false | (~(((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))))) <=> (~(((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 ((~(set_difference(A!9, B!8) = set_difference(A!9, B!8))) <=> (~$true)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[62])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 ((~(set_difference(A!9, B!8) = set_difference(A!9, B!8))) <=> $false),
% 0.20/0.40 inference(transitivity,[status(thm)],[69, 60])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 (((~(set_difference(A!9, B!8) = set_difference(A!9, B!8))) | (~(((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))))) <=> ($false | (~(((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8)))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[70, 58])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 (((~(set_difference(A!9, B!8) = set_difference(A!9, B!8))) | (~(((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))))) <=> (~(((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[71, 68])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 ((~((~(set_difference(A!9, B!8) = set_difference(A!9, B!8))) | (~(((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8)))))) <=> (~(~(((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8)))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[72])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 ((~((~(set_difference(A!9, B!8) = set_difference(A!9, B!8))) | (~(((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8)))))) <=> (((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8)))),
% 0.20/0.40 inference(transitivity,[status(thm)],[73, 67])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 (((~((~(set_difference(A!9, B!8) = set_difference(A!9, B!8))) | (~(((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8)))))) | (~((set_difference(A!9, B!8) = set_difference(A!9, B!8)) | (((~in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), A!9)) | in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), B!8)) <=> in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), set_difference(A!9, B!8)))))) <=> ((((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))) | $false)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[74, 66])).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 (((~((~(set_difference(A!9, B!8) = set_difference(A!9, B!8))) | (~(((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8)))))) | (~((set_difference(A!9, B!8) = set_difference(A!9, B!8)) | (((~in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), A!9)) | in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), B!8)) <=> in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), set_difference(A!9, B!8)))))) <=> (((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[75, 59])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 ((~((~((~(set_difference(A!9, B!8) = set_difference(A!9, B!8))) | (~(((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8)))))) | (~((set_difference(A!9, B!8) = set_difference(A!9, B!8)) | (((~in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), A!9)) | in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), B!8)) <=> in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), set_difference(A!9, B!8))))))) <=> (~(((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[76])).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 ((~((~((~(set_difference(A!9, B!8) = set_difference(A!9, B!8))) | (~(((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8)))))) | (~((set_difference(A!9, B!8) = set_difference(A!9, B!8)) | (((~in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), A!9)) | in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), B!8)) <=> in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), set_difference(A!9, B!8))))))) <=> (~(((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[77, 58])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~((~((~(set_difference(A!9, B!8) = set_difference(A!9, B!8))) | (~(((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8)))))) | (~((set_difference(A!9, B!8) = set_difference(A!9, B!8)) | (((~in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), A!9)) | in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), B!8)) <=> in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), set_difference(A!9, B!8)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~(((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8)))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[78])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~((~((~(set_difference(A!9, B!8) = set_difference(A!9, B!8))) | (~(((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8)))))) | (~((set_difference(A!9, B!8) = set_difference(A!9, B!8)) | (((~in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), A!9)) | in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), B!8)) <=> in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), set_difference(A!9, B!8)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~(((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8)))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[79, 57])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~((~((~(set_difference(A!9, B!8) = set_difference(A!9, B!8))) | (~(((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8)))))) | (~((set_difference(A!9, B!8) = set_difference(A!9, B!8)) | (((~in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), A!9)) | in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), B!8)) <=> in(tptp_fun_D_4(set_difference(A!9, B!8), B!8, A!9), set_difference(A!9, B!8)))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~(((~in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), A!9)) | in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), B!8)) <=> in(tptp_fun_C_2(A!9, set_difference(A!9, B!8)), set_difference(A!9, B!8))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[82, 56, 38])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------