%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU140+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:00 AM UTC 2025
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU140+2 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 06:08:47 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(in_type, type, (
% 0.12/0.39 in: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_B_11_type, type, (
% 0.12/0.39 tptp_fun_B_11: $i)).
% 0.12/0.39 tff(tptp_fun_C_8_type, type, (
% 0.12/0.39 tptp_fun_C_8: ( $i * $i ) > $i)).
% 0.12/0.39 tff(tptp_fun_A_12_type, type, (
% 0.12/0.39 tptp_fun_A_12: $i)).
% 0.12/0.39 tff(tptp_fun_C_10_type, type, (
% 0.12/0.39 tptp_fun_C_10: $i)).
% 0.12/0.39 tff(disjoint_type, type, (
% 0.12/0.39 disjoint: ( $i * $i ) > $o)).
% 0.12/0.39 tff(subset_type, type, (
% 0.12/0.39 subset: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_C_2_type, type, (
% 0.12/0.39 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (^[A: $i, B: $i] : refl((~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))) <=> (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (^[A: $i, B: $i] : rewrite((~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))) <=> (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[4, 2])).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_C_8(B, A), A) & in(tptp_fun_C_8(B, A), B)) <=> (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B))))), ((disjoint(A, B) | (in(tptp_fun_C_8(B, A), A) & in(tptp_fun_C_8(B, A), B))) <=> (disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B))))))), rewrite((disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B))))) <=> (disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))), ((disjoint(A, B) | (in(tptp_fun_C_8(B, A), A) & in(tptp_fun_C_8(B, A), B))) <=> (disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B))))))), trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((in(C, A) & in(C, B)) <=> (~((~in(C, B)) | (~in(C, A))))), ((~(in(C, A) & in(C, B))) <=> (~(~((~in(C, B)) | (~in(C, A))))))), rewrite((~(~((~in(C, B)) | (~in(C, A))))) <=> ((~in(C, B)) | (~in(C, A)))), ((~(in(C, A) & in(C, B))) <=> ((~in(C, B)) | (~in(C, A)))))), (![C: $i] : (~(in(C, A) & in(C, B))) <=> ![C: $i] : ((~in(C, B)) | (~in(C, A))))), ((![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B))) <=> (![C: $i] : ((~in(C, B)) | (~in(C, A))) | (~disjoint(A, B))))), rewrite((![C: $i] : ((~in(C, B)) | (~in(C, A))) | (~disjoint(A, B))) <=> ((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))), ((![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B))) <=> ((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))), (((disjoint(A, B) | (in(tptp_fun_C_8(B, A), A) & in(tptp_fun_C_8(B, A), B))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B)))) <=> ((disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B))))) & ((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))), rewrite(((disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B))))) & ((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))) <=> (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))), (((disjoint(A, B) | (in(tptp_fun_C_8(B, A), A) & in(tptp_fun_C_8(B, A), B))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B)))) <=> (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (![A: $i, B: $i] : ((disjoint(A, B) | (in(tptp_fun_C_8(B, A), A) & in(tptp_fun_C_8(B, A), B))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B)))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~(in(C, A) & in(C, B))))) & (~(?[C: $i] : (in(C, A) & in(C, B)) & disjoint(A, B)))) <=> ![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~(in(C, A) & in(C, B))))) & (~(?[C: $i] : (in(C, A) & in(C, B)) & disjoint(A, B))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(9,axiom,(![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~(in(C, A) & in(C, B))))) & (~(?[C: $i] : (in(C, A) & in(C, B)) & disjoint(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_xboole_0')).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~(in(C, A) & in(C, B))))) & (~(?[C: $i] : (in(C, A) & in(C, B)) & disjoint(A, B))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.12/0.39 tff(11,plain,(
% 0.12/0.39 ![A: $i, B: $i] : ((disjoint(A, B) | (in(tptp_fun_C_8(B, A), A) & in(tptp_fun_C_8(B, A), B))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[10])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(A!12, C!10) | (~((~in(tptp_fun_C_8(C!10, A!12), A!12)) | (~in(tptp_fun_C_8(C!10, A!12), C!10)))))) | (~((~disjoint(A!12, C!10)) | ![C: $i] : ((~in(C, A!12)) | (~in(C, C!10)))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(A!12, C!10) | (~((~in(tptp_fun_C_8(C!10, A!12), A!12)) | (~in(tptp_fun_C_8(C!10, A!12), C!10)))))) | (~((~disjoint(A!12, C!10)) | ![C: $i] : ((~in(C, A!12)) | (~in(C, C!10))))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 ((~((~(disjoint(A!12, C!10) | (~((~in(tptp_fun_C_8(C!10, A!12), A!12)) | (~in(tptp_fun_C_8(C!10, A!12), C!10)))))) | (~((~disjoint(A!12, C!10)) | ![C: $i] : ((~in(C, C!10)) | (~in(C, A!12))))))) <=> (~((~(disjoint(A!12, C!10) | (~((~in(tptp_fun_C_8(C!10, A!12), A!12)) | (~in(tptp_fun_C_8(C!10, A!12), C!10)))))) | (~((~disjoint(A!12, C!10)) | ![C: $i] : ((~in(C, A!12)) | (~in(C, C!10)))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(A!12, C!10) | (~((~in(tptp_fun_C_8(C!10, A!12), A!12)) | (~in(tptp_fun_C_8(C!10, A!12), C!10)))))) | (~((~disjoint(A!12, C!10)) | ![C: $i] : ((~in(C, C!10)) | (~in(C, A!12)))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(A!12, C!10) | (~((~in(tptp_fun_C_8(C!10, A!12), A!12)) | (~in(tptp_fun_C_8(C!10, A!12), C!10)))))) | (~((~disjoint(A!12, C!10)) | ![C: $i] : ((~in(C, A!12)) | (~in(C, C!10))))))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[15])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(A!12, C!10) | (~((~in(tptp_fun_C_8(C!10, A!12), A!12)) | (~in(tptp_fun_C_8(C!10, A!12), C!10)))))) | (~((~disjoint(A!12, C!10)) | ![C: $i] : ((~in(C, C!10)) | (~in(C, A!12)))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(A!12, C!10) | (~((~in(tptp_fun_C_8(C!10, A!12), A!12)) | (~in(tptp_fun_C_8(C!10, A!12), C!10)))))) | (~((~disjoint(A!12, C!10)) | ![C: $i] : ((~in(C, A!12)) | (~in(C, C!10))))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[16, 14])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(A!12, C!10) | (~((~in(tptp_fun_C_8(C!10, A!12), A!12)) | (~in(tptp_fun_C_8(C!10, A!12), C!10)))))) | (~((~disjoint(A!12, C!10)) | ![C: $i] : ((~in(C, C!10)) | (~in(C, A!12)))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(A!12, C!10) | (~((~in(tptp_fun_C_8(C!10, A!12), A!12)) | (~in(tptp_fun_C_8(C!10, A!12), C!10)))))) | (~((~disjoint(A!12, C!10)) | ![C: $i] : ((~in(C, A!12)) | (~in(C, C!10)))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (~((~(disjoint(A!12, C!10) | (~((~in(tptp_fun_C_8(C!10, A!12), A!12)) | (~in(tptp_fun_C_8(C!10, A!12), C!10)))))) | (~((~disjoint(A!12, C!10)) | ![C: $i] : ((~in(C, A!12)) | (~in(C, C!10))))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[19, 13])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (((~(disjoint(A!12, C!10) | (~((~in(tptp_fun_C_8(C!10, A!12), A!12)) | (~in(tptp_fun_C_8(C!10, A!12), C!10)))))) | (~((~disjoint(A!12, C!10)) | ![C: $i] : ((~in(C, A!12)) | (~in(C, C!10)))))) | (disjoint(A!12, C!10) | (~((~in(tptp_fun_C_8(C!10, A!12), A!12)) | (~in(tptp_fun_C_8(C!10, A!12), C!10)))))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (disjoint(A!12, C!10) | (~((~in(tptp_fun_C_8(C!10, A!12), A!12)) | (~in(tptp_fun_C_8(C!10, A!12), C!10))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 ((~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C))) <=> (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 ((~![A: $i, B: $i, C: $i] : ((subset(A, B) & disjoint(B, C)) => disjoint(A, C))) <=> (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(25,axiom,(~![A: $i, B: $i, C: $i] : ((subset(A, B) & disjoint(B, C)) => disjoint(A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t63_xboole_1')).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.12/0.40 tff(27,plain,
% 0.12/0.40 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[28, 23])).
% 0.12/0.40 tff(30,plain,(
% 0.12/0.40 ~((~(subset(A!12, B!11) & disjoint(B!11, C!10))) | disjoint(A!12, C!10))),
% 0.12/0.40 inference(skolemize,[status(sab)],[29])).
% 0.12/0.40 tff(31,plain,
% 0.12/0.40 (~disjoint(A!12, C!10)),
% 0.12/0.40 inference(or_elim,[status(thm)],[30])).
% 0.12/0.40 tff(32,plain,
% 0.12/0.40 ((~(disjoint(A!12, C!10) | (~((~in(tptp_fun_C_8(C!10, A!12), A!12)) | (~in(tptp_fun_C_8(C!10, A!12), C!10)))))) | disjoint(A!12, C!10) | (~((~in(tptp_fun_C_8(C!10, A!12), A!12)) | (~in(tptp_fun_C_8(C!10, A!12), C!10))))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(33,plain,
% 0.12/0.40 ((~(disjoint(A!12, C!10) | (~((~in(tptp_fun_C_8(C!10, A!12), A!12)) | (~in(tptp_fun_C_8(C!10, A!12), C!10)))))) | (~((~in(tptp_fun_C_8(C!10, A!12), A!12)) | (~in(tptp_fun_C_8(C!10, A!12), C!10))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.12/0.40 tff(34,plain,
% 0.12/0.40 (~((~in(tptp_fun_C_8(C!10, A!12), A!12)) | (~in(tptp_fun_C_8(C!10, A!12), C!10)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[33, 22])).
% 0.12/0.40 tff(35,plain,
% 0.12/0.40 (((~in(tptp_fun_C_8(C!10, A!12), A!12)) | (~in(tptp_fun_C_8(C!10, A!12), C!10))) | in(tptp_fun_C_8(C!10, A!12), C!10)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(36,plain,
% 0.12/0.40 (in(tptp_fun_C_8(C!10, A!12), C!10)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.12/0.40 tff(37,plain,
% 0.12/0.40 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~((~disjoint(B!11, C!10)) | ![C: $i] : ((~in(C, C!10)) | (~in(C, B!11))))) | (~(disjoint(B!11, C!10) | (~((~in(tptp_fun_C_8(C!10, B!11), B!11)) | (~in(tptp_fun_C_8(C!10, B!11), C!10))))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~((~disjoint(B!11, C!10)) | ![C: $i] : ((~in(C, C!10)) | (~in(C, B!11))))) | (~(disjoint(B!11, C!10) | (~((~in(tptp_fun_C_8(C!10, B!11), B!11)) | (~in(tptp_fun_C_8(C!10, B!11), C!10)))))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(38,plain,
% 0.12/0.40 ((~((~(disjoint(B!11, C!10) | (~((~in(tptp_fun_C_8(C!10, B!11), B!11)) | (~in(tptp_fun_C_8(C!10, B!11), C!10)))))) | (~((~disjoint(B!11, C!10)) | ![C: $i] : ((~in(C, C!10)) | (~in(C, B!11))))))) <=> (~((~((~disjoint(B!11, C!10)) | ![C: $i] : ((~in(C, C!10)) | (~in(C, B!11))))) | (~(disjoint(B!11, C!10) | (~((~in(tptp_fun_C_8(C!10, B!11), B!11)) | (~in(tptp_fun_C_8(C!10, B!11), C!10))))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(39,plain,
% 0.12/0.40 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(B!11, C!10) | (~((~in(tptp_fun_C_8(C!10, B!11), B!11)) | (~in(tptp_fun_C_8(C!10, B!11), C!10)))))) | (~((~disjoint(B!11, C!10)) | ![C: $i] : ((~in(C, C!10)) | (~in(C, B!11)))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~((~disjoint(B!11, C!10)) | ![C: $i] : ((~in(C, C!10)) | (~in(C, B!11))))) | (~(disjoint(B!11, C!10) | (~((~in(tptp_fun_C_8(C!10, B!11), B!11)) | (~in(tptp_fun_C_8(C!10, B!11), C!10)))))))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[38])).
% 0.12/0.40 tff(40,plain,
% 0.12/0.40 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(B!11, C!10) | (~((~in(tptp_fun_C_8(C!10, B!11), B!11)) | (~in(tptp_fun_C_8(C!10, B!11), C!10)))))) | (~((~disjoint(B!11, C!10)) | ![C: $i] : ((~in(C, C!10)) | (~in(C, B!11)))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~((~disjoint(B!11, C!10)) | ![C: $i] : ((~in(C, C!10)) | (~in(C, B!11))))) | (~(disjoint(B!11, C!10) | (~((~in(tptp_fun_C_8(C!10, B!11), B!11)) | (~in(tptp_fun_C_8(C!10, B!11), C!10)))))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[39, 37])).
% 0.12/0.40 tff(41,plain,
% 0.12/0.40 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(B!11, C!10) | (~((~in(tptp_fun_C_8(C!10, B!11), B!11)) | (~in(tptp_fun_C_8(C!10, B!11), C!10)))))) | (~((~disjoint(B!11, C!10)) | ![C: $i] : ((~in(C, C!10)) | (~in(C, B!11)))))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(42,plain,
% 0.12/0.40 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_8(B, A), A)) | (~in(tptp_fun_C_8(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~((~disjoint(B!11, C!10)) | ![C: $i] : ((~in(C, C!10)) | (~in(C, B!11))))) | (~(disjoint(B!11, C!10) | (~((~in(tptp_fun_C_8(C!10, B!11), B!11)) | (~in(tptp_fun_C_8(C!10, B!11), C!10))))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.12/0.40 tff(43,plain,
% 0.12/0.40 (~((~((~disjoint(B!11, C!10)) | ![C: $i] : ((~in(C, C!10)) | (~in(C, B!11))))) | (~(disjoint(B!11, C!10) | (~((~in(tptp_fun_C_8(C!10, B!11), B!11)) | (~in(tptp_fun_C_8(C!10, B!11), C!10)))))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[42, 13])).
% 0.12/0.40 tff(44,plain,
% 0.12/0.40 (((~((~disjoint(B!11, C!10)) | ![C: $i] : ((~in(C, C!10)) | (~in(C, B!11))))) | (~(disjoint(B!11, C!10) | (~((~in(tptp_fun_C_8(C!10, B!11), B!11)) | (~in(tptp_fun_C_8(C!10, B!11), C!10))))))) | ((~disjoint(B!11, C!10)) | ![C: $i] : ((~in(C, C!10)) | (~in(C, B!11))))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 ((~disjoint(B!11, C!10)) | ![C: $i] : ((~in(C, C!10)) | (~in(C, B!11)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.12/0.40 tff(46,plain,
% 0.12/0.40 (subset(A!12, B!11) & disjoint(B!11, C!10)),
% 0.12/0.40 inference(or_elim,[status(thm)],[30])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 (disjoint(B!11, C!10)),
% 0.12/0.40 inference(and_elim,[status(thm)],[46])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 ((~((~disjoint(B!11, C!10)) | ![C: $i] : ((~in(C, C!10)) | (~in(C, B!11))))) | (~disjoint(B!11, C!10)) | ![C: $i] : ((~in(C, C!10)) | (~in(C, B!11)))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 ((~((~disjoint(B!11, C!10)) | ![C: $i] : ((~in(C, C!10)) | (~in(C, B!11))))) | ![C: $i] : ((~in(C, C!10)) | (~in(C, B!11)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (![C: $i] : ((~in(C, C!10)) | (~in(C, B!11)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[49, 45])).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 (((~![C: $i] : ((~in(C, C!10)) | (~in(C, B!11)))) | ((~in(tptp_fun_C_8(C!10, A!12), C!10)) | (~in(tptp_fun_C_8(C!10, A!12), B!11)))) <=> ((~![C: $i] : ((~in(C, C!10)) | (~in(C, B!11)))) | (~in(tptp_fun_C_8(C!10, A!12), C!10)) | (~in(tptp_fun_C_8(C!10, A!12), B!11)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 ((~![C: $i] : ((~in(C, C!10)) | (~in(C, B!11)))) | ((~in(tptp_fun_C_8(C!10, A!12), C!10)) | (~in(tptp_fun_C_8(C!10, A!12), B!11)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 ((~![C: $i] : ((~in(C, C!10)) | (~in(C, B!11)))) | (~in(tptp_fun_C_8(C!10, A!12), C!10)) | (~in(tptp_fun_C_8(C!10, A!12), B!11))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.12/0.40 tff(54,plain,
% 0.12/0.40 (~in(tptp_fun_C_8(C!10, A!12), B!11)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[53, 50, 36])).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 (((~in(tptp_fun_C_8(C!10, A!12), A!12)) | (~in(tptp_fun_C_8(C!10, A!12), C!10))) | in(tptp_fun_C_8(C!10, A!12), A!12)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 (in(tptp_fun_C_8(C!10, A!12), A!12)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[55, 34])).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 (^[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))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 (![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)))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[57])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 (^[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))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(60,plain,
% 0.12/0.40 (![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)))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[59])).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 (![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)))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[60, 58])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 (^[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)))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(63,plain,
% 0.12/0.40 (![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)))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[62])).
% 0.12/0.40 tff(64,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(65,plain,
% 0.12/0.40 (^[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))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[65])).
% 0.20/0.41 tff(67,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')).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.20/0.41 tff(70,plain,(
% 0.20/0.41 ![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)))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[69])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 (![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)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 (![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)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[71, 61])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 ((~![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!12, B!11)) | ![C: $i] : ((~in(C, A!12)) | in(C, B!11)))) | (~(subset(A!12, B!11) | (~((~in(tptp_fun_C_2(B!11, A!12), A!12)) | in(tptp_fun_C_2(B!11, A!12), B!11)))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 (~((~((~subset(A!12, B!11)) | ![C: $i] : ((~in(C, A!12)) | in(C, B!11)))) | (~(subset(A!12, B!11) | (~((~in(tptp_fun_C_2(B!11, A!12), A!12)) | in(tptp_fun_C_2(B!11, A!12), B!11))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 (((~((~subset(A!12, B!11)) | ![C: $i] : ((~in(C, A!12)) | in(C, B!11)))) | (~(subset(A!12, B!11) | (~((~in(tptp_fun_C_2(B!11, A!12), A!12)) | in(tptp_fun_C_2(B!11, A!12), B!11)))))) | ((~subset(A!12, B!11)) | ![C: $i] : ((~in(C, A!12)) | in(C, B!11)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 ((~subset(A!12, B!11)) | ![C: $i] : ((~in(C, A!12)) | in(C, B!11))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 (subset(A!12, B!11)),
% 0.20/0.41 inference(and_elim,[status(thm)],[46])).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 ((~((~subset(A!12, B!11)) | ![C: $i] : ((~in(C, A!12)) | in(C, B!11)))) | (~subset(A!12, B!11)) | ![C: $i] : ((~in(C, A!12)) | in(C, B!11))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 ((~((~subset(A!12, B!11)) | ![C: $i] : ((~in(C, A!12)) | in(C, B!11)))) | ![C: $i] : ((~in(C, A!12)) | in(C, B!11))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 (![C: $i] : ((~in(C, A!12)) | in(C, B!11))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[79, 76])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (((~![C: $i] : ((~in(C, A!12)) | in(C, B!11))) | ((~in(tptp_fun_C_8(C!10, A!12), A!12)) | in(tptp_fun_C_8(C!10, A!12), B!11))) <=> ((~![C: $i] : ((~in(C, A!12)) | in(C, B!11))) | (~in(tptp_fun_C_8(C!10, A!12), A!12)) | in(tptp_fun_C_8(C!10, A!12), B!11))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 ((~![C: $i] : ((~in(C, A!12)) | in(C, B!11))) | ((~in(tptp_fun_C_8(C!10, A!12), A!12)) | in(tptp_fun_C_8(C!10, A!12), B!11))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 ((~![C: $i] : ((~in(C, A!12)) | in(C, B!11))) | (~in(tptp_fun_C_8(C!10, A!12), A!12)) | in(tptp_fun_C_8(C!10, A!12), B!11)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[83, 80, 56, 54])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------