%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU232+3 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:27:20 AM UTC 2025
% Result : Theorem 0.22s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU232+3 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n001.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 06:30:50 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.22/0.41 % SZS status Theorem
% 0.22/0.41 % SZS output start Proof
% 0.22/0.41 tff(in_type, type, (
% 0.22/0.41 in: ( $i * $i ) > $o)).
% 0.22/0.41 tff(tptp_fun_A_18_type, type, (
% 0.22/0.41 tptp_fun_A_18: $i)).
% 0.22/0.41 tff(tptp_fun_B_0_type, type, (
% 0.22/0.41 tptp_fun_B_0: $i > $i)).
% 0.22/0.41 tff(tptp_fun_C_3_type, type, (
% 0.22/0.41 tptp_fun_C_3: ( $i * $i ) > $i)).
% 0.22/0.41 tff(subset_type, type, (
% 0.22/0.41 subset: ( $i * $i ) > $o)).
% 0.22/0.41 tff(epsilon_transitive_type, type, (
% 0.22/0.41 epsilon_transitive: $i > $o)).
% 0.22/0.41 tff(epsilon_connected_type, type, (
% 0.22/0.41 epsilon_connected: $i > $o)).
% 0.22/0.41 tff(tptp_fun_C_1_type, type, (
% 0.22/0.41 tptp_fun_C_1: $i > $i)).
% 0.22/0.41 tff(tptp_fun_B_2_type, type, (
% 0.22/0.41 tptp_fun_B_2: $i > $i)).
% 0.22/0.41 tff(tptp_fun_B_17_type, type, (
% 0.22/0.41 tptp_fun_B_17: $i)).
% 0.22/0.41 tff(ordinal_type, type, (
% 0.22/0.41 ordinal: $i > $o)).
% 0.22/0.41 tff(1,plain,
% 0.22/0.41 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(2,plain,
% 0.22/0.41 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(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_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.41 tff(3,plain,
% 0.22/0.41 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(4,plain,
% 0.22/0.41 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(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_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.22/0.41 tff(5,plain,
% 0.22/0.41 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(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_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))),
% 0.22/0.41 inference(transitivity,[status(thm)],[4, 2])).
% 0.22/0.41 tff(6,plain,
% 0.22/0.41 (^[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_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(7,plain,
% 0.22/0.41 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(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_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.22/0.41 tff(8,plain,
% 0.22/0.41 (![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)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(9,plain,
% 0.22/0.41 (^[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))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(10,plain,
% 0.22/0.41 (![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)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[9])).
% 0.22/0.41 tff(11,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')).
% 0.22/0.41 tff(12,plain,
% 0.22/0.41 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.22/0.41 tff(13,plain,
% 0.22/0.41 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.22/0.41 tff(14,plain,(
% 0.22/0.41 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))),
% 0.22/0.41 inference(skolemize,[status(sab)],[13])).
% 0.22/0.41 tff(15,plain,
% 0.22/0.41 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.22/0.41 tff(16,plain,
% 0.22/0.41 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.22/0.41 tff(17,plain,
% 0.22/0.41 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))) | (~((~((~subset(tptp_fun_B_0(A!18), A!18)) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!18))) | in(C, A!18)))) | (~(subset(tptp_fun_B_0(A!18), A!18) | (~((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18)))))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(18,plain,
% 0.22/0.41 (~((~((~subset(tptp_fun_B_0(A!18), A!18)) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!18))) | in(C, A!18)))) | (~(subset(tptp_fun_B_0(A!18), A!18) | (~((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18))))))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.22/0.41 tff(19,plain,
% 0.22/0.41 (((~((~subset(tptp_fun_B_0(A!18), A!18)) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!18))) | in(C, A!18)))) | (~(subset(tptp_fun_B_0(A!18), A!18) | (~((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18)))))) | (subset(tptp_fun_B_0(A!18), A!18) | (~((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18))))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(20,plain,
% 0.22/0.41 (subset(tptp_fun_B_0(A!18), A!18) | (~((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18)))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.22/0.41 tff(21,plain,
% 0.22/0.41 (^[A: $i] : refl((~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(22,plain,
% 0.22/0.41 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[21])).
% 0.22/0.41 tff(23,plain,
% 0.22/0.41 (^[A: $i] : rewrite((~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(24,plain,
% 0.22/0.41 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[23])).
% 0.22/0.41 tff(25,plain,
% 0.22/0.41 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 0.22/0.41 inference(transitivity,[status(thm)],[24, 22])).
% 0.22/0.41 tff(26,plain,
% 0.22/0.41 (^[A: $i] : trans(monotonicity(rewrite(((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) <=> ((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))), ((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))), rewrite((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))), ((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(27,plain,
% 0.22/0.41 (![A: $i] : (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[26])).
% 0.22/0.41 tff(28,plain,
% 0.22/0.41 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A))) <=> ![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(29,plain,
% 0.22/0.41 (^[A: $i] : rewrite((epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A))) <=> (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(30,plain,
% 0.22/0.41 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A))) <=> ![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[29])).
% 0.22/0.41 tff(31,axiom,(![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_ordinal1')).
% 0.22/0.41 tff(32,plain,
% 0.22/0.41 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.22/0.41 tff(33,plain,
% 0.22/0.41 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.22/0.41 tff(34,plain,(
% 0.22/0.41 ![A: $i] : (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))),
% 0.22/0.41 inference(skolemize,[status(sab)],[33])).
% 0.22/0.41 tff(35,plain,
% 0.22/0.41 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.22/0.41 tff(36,plain,
% 0.22/0.41 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.22/0.41 tff(37,plain,
% 0.22/0.41 ((~![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))) | (~((~((~epsilon_transitive(A!18)) | ![B: $i] : ((~in(B, A!18)) | subset(B, A!18)))) | (~(epsilon_transitive(A!18) | (~((~in(tptp_fun_B_0(A!18), A!18)) | subset(tptp_fun_B_0(A!18), A!18)))))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(38,plain,
% 0.22/0.41 (~((~((~epsilon_transitive(A!18)) | ![B: $i] : ((~in(B, A!18)) | subset(B, A!18)))) | (~(epsilon_transitive(A!18) | (~((~in(tptp_fun_B_0(A!18), A!18)) | subset(tptp_fun_B_0(A!18), A!18))))))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.22/0.41 tff(39,plain,
% 0.22/0.41 (((~((~epsilon_transitive(A!18)) | ![B: $i] : ((~in(B, A!18)) | subset(B, A!18)))) | (~(epsilon_transitive(A!18) | (~((~in(tptp_fun_B_0(A!18), A!18)) | subset(tptp_fun_B_0(A!18), A!18)))))) | (epsilon_transitive(A!18) | (~((~in(tptp_fun_B_0(A!18), A!18)) | subset(tptp_fun_B_0(A!18), A!18))))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(40,plain,
% 0.22/0.41 (epsilon_transitive(A!18) | (~((~in(tptp_fun_B_0(A!18), A!18)) | subset(tptp_fun_B_0(A!18), A!18)))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.22/0.41 tff(41,assumption,((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!18)) | (~in(B, A!18))))) | (~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))))))), introduced(assumption)).
% 0.22/0.41 tff(42,plain,
% 0.22/0.41 (^[A: $i] : refl((~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))))) <=> (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(43,plain,
% 0.22/0.41 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))))) <=> ![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[42])).
% 0.22/0.42 tff(44,plain,
% 0.22/0.42 (^[A: $i] : rewrite((~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))))) <=> (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(45,plain,
% 0.22/0.42 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))))) <=> ![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[44])).
% 0.22/0.42 tff(46,plain,
% 0.22/0.42 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))))) <=> ![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))),
% 0.22/0.42 inference(transitivity,[status(thm)],[45, 43])).
% 0.22/0.42 tff(47,plain,
% 0.22/0.42 (^[A: $i] : trans(monotonicity(rewrite(((~epsilon_connected(A)) | ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) <=> ((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))), rewrite((epsilon_connected(A) | (in(tptp_fun_B_2(A), A) & in(tptp_fun_C_1(A), A) & (~in(tptp_fun_B_2(A), tptp_fun_C_1(A))) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(tptp_fun_C_1(A), tptp_fun_B_2(A))))) <=> (epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))), ((((~epsilon_connected(A)) | ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) & (epsilon_connected(A) | (in(tptp_fun_B_2(A), A) & in(tptp_fun_C_1(A), A) & (~in(tptp_fun_B_2(A), tptp_fun_C_1(A))) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(tptp_fun_C_1(A), tptp_fun_B_2(A)))))) <=> (((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A)))) & (epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))))), rewrite((((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A)))) & (epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))) <=> (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))), ((((~epsilon_connected(A)) | ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) & (epsilon_connected(A) | (in(tptp_fun_B_2(A), A) & in(tptp_fun_C_1(A), A) & (~in(tptp_fun_B_2(A), tptp_fun_C_1(A))) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(tptp_fun_C_1(A), tptp_fun_B_2(A)))))) <=> (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(48,plain,
% 0.22/0.42 (![A: $i] : (((~epsilon_connected(A)) | ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) & (epsilon_connected(A) | (in(tptp_fun_B_2(A), A) & in(tptp_fun_C_1(A), A) & (~in(tptp_fun_B_2(A), tptp_fun_C_1(A))) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(tptp_fun_C_1(A), tptp_fun_B_2(A)))))) <=> ![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[47])).
% 0.22/0.42 tff(49,plain,
% 0.22/0.42 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) <=> ![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(50,plain,
% 0.22/0.42 (^[A: $i] : rewrite((epsilon_connected(A) <=> ![B: $i, C: $i] : (~((((in(B, A) & in(C, A)) & (~in(B, C))) & (~(B = C))) & (~in(C, B))))) <=> (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(51,plain,
% 0.22/0.42 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~((((in(B, A) & in(C, A)) & (~in(B, C))) & (~(B = C))) & (~in(C, B))))) <=> ![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[50])).
% 0.22/0.42 tff(52,axiom,(![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~((((in(B, A) & in(C, A)) & (~in(B, C))) & (~(B = C))) & (~in(C, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_ordinal1')).
% 0.22/0.42 tff(53,plain,
% 0.22/0.42 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.22/0.42 tff(54,plain,
% 0.22/0.42 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.22/0.42 tff(55,plain,(
% 0.22/0.42 ![A: $i] : (((~epsilon_connected(A)) | ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) & (epsilon_connected(A) | (in(tptp_fun_B_2(A), A) & in(tptp_fun_C_1(A), A) & (~in(tptp_fun_B_2(A), tptp_fun_C_1(A))) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(tptp_fun_C_1(A), tptp_fun_B_2(A))))))),
% 0.22/0.42 inference(skolemize,[status(sab)],[54])).
% 0.22/0.42 tff(56,plain,
% 0.22/0.42 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.22/0.42 tff(57,plain,
% 0.22/0.42 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[56, 46])).
% 0.22/0.42 tff(58,plain,
% 0.22/0.42 (((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!18)) | (~in(B, A!18))))) | (~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))))))))) <=> ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!18)) | (~in(B, A!18))))) | (~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)))))))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(59,plain,
% 0.22/0.42 ((~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!18)) | (~in(B, A!18))))) | (~(epsilon_connected(A!18) | (~(in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | (~in(tptp_fun_C_1(A!18), A!18)))))))) <=> (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!18)) | (~in(B, A!18))))) | (~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))))))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(60,plain,
% 0.22/0.42 (((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!18)) | (~in(B, A!18))))) | (~(epsilon_connected(A!18) | (~(in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | (~in(tptp_fun_C_1(A!18), A!18))))))))) <=> ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!18)) | (~in(B, A!18))))) | (~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)))))))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[59])).
% 0.22/0.42 tff(61,plain,
% 0.22/0.42 (((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!18)) | (~in(B, A!18))))) | (~(epsilon_connected(A!18) | (~(in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | (~in(tptp_fun_C_1(A!18), A!18))))))))) <=> ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!18)) | (~in(B, A!18))))) | (~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)))))))))),
% 0.22/0.42 inference(transitivity,[status(thm)],[60, 58])).
% 0.22/0.42 tff(62,plain,
% 0.22/0.42 ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!18)) | (~in(B, A!18))))) | (~(epsilon_connected(A!18) | (~(in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | (~in(tptp_fun_C_1(A!18), A!18))))))))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(63,plain,
% 0.22/0.42 ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!18)) | (~in(B, A!18))))) | (~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))))))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.22/0.42 tff(64,plain,
% 0.22/0.42 ($false),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[63, 57, 41])).
% 0.22/0.42 tff(65,plain,(~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!18)) | (~in(B, A!18))))) | (~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)))))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.42 tff(66,plain,
% 0.22/0.42 (((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!18)) | (~in(B, A!18))))) | (~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))))))) | (epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)))))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(67,plain,
% 0.22/0.42 (epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.22/0.43 tff(68,assumption,(~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)))), introduced(assumption)).
% 0.22/0.43 tff(69,plain,
% 0.22/0.43 (((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))) | in(tptp_fun_B_2(A!18), A!18)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(70,plain,
% 0.22/0.43 (in(tptp_fun_B_2(A!18), A!18)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.22/0.43 tff(71,plain,
% 0.22/0.43 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))) | (~((~((~subset(A!18, B!17)) | ![C: $i] : ((~in(C, A!18)) | in(C, B!17)))) | (~(subset(A!18, B!17) | (~((~in(tptp_fun_C_3(B!17, A!18), A!18)) | in(tptp_fun_C_3(B!17, A!18), B!17)))))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(72,plain,
% 0.22/0.43 (~((~((~subset(A!18, B!17)) | ![C: $i] : ((~in(C, A!18)) | in(C, B!17)))) | (~(subset(A!18, B!17) | (~((~in(tptp_fun_C_3(B!17, A!18), A!18)) | in(tptp_fun_C_3(B!17, A!18), B!17))))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[71, 16])).
% 0.22/0.43 tff(73,plain,
% 0.22/0.43 (((~((~subset(A!18, B!17)) | ![C: $i] : ((~in(C, A!18)) | in(C, B!17)))) | (~(subset(A!18, B!17) | (~((~in(tptp_fun_C_3(B!17, A!18), A!18)) | in(tptp_fun_C_3(B!17, A!18), B!17)))))) | ((~subset(A!18, B!17)) | ![C: $i] : ((~in(C, A!18)) | in(C, B!17)))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(74,plain,
% 0.22/0.43 ((~subset(A!18, B!17)) | ![C: $i] : ((~in(C, A!18)) | in(C, B!17))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.22/0.43 tff(75,plain,
% 0.22/0.43 ((~![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))) | (~((~((~epsilon_transitive(B!17)) | ![B: $i] : ((~in(B, B!17)) | subset(B, B!17)))) | (~(epsilon_transitive(B!17) | (~((~in(tptp_fun_B_0(B!17), B!17)) | subset(tptp_fun_B_0(B!17), B!17)))))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(76,plain,
% 0.22/0.43 (~((~((~epsilon_transitive(B!17)) | ![B: $i] : ((~in(B, B!17)) | subset(B, B!17)))) | (~(epsilon_transitive(B!17) | (~((~in(tptp_fun_B_0(B!17), B!17)) | subset(tptp_fun_B_0(B!17), B!17))))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[75, 36])).
% 0.22/0.43 tff(77,plain,
% 0.22/0.43 (((~((~epsilon_transitive(B!17)) | ![B: $i] : ((~in(B, B!17)) | subset(B, B!17)))) | (~(epsilon_transitive(B!17) | (~((~in(tptp_fun_B_0(B!17), B!17)) | subset(tptp_fun_B_0(B!17), B!17)))))) | ((~epsilon_transitive(B!17)) | ![B: $i] : ((~in(B, B!17)) | subset(B, B!17)))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(78,plain,
% 0.22/0.43 ((~epsilon_transitive(B!17)) | ![B: $i] : ((~in(B, B!17)) | subset(B, B!17))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.22/0.43 tff(79,plain,
% 0.22/0.43 ((~((~in(A!18, B!17)) | ordinal(A!18) | (~ordinal(B!17)))) <=> (~((~in(A!18, B!17)) | ordinal(A!18) | (~ordinal(B!17))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(80,plain,
% 0.22/0.43 ((~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))) <=> (~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(81,plain,
% 0.22/0.43 ((~![A: $i, B: $i] : (ordinal(B) => (in(A, B) => ordinal(A)))) <=> (~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(82,axiom,(~![A: $i, B: $i] : (ordinal(B) => (in(A, B) => ordinal(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t23_ordinal1')).
% 0.22/0.43 tff(83,plain,
% 0.22/0.43 (~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.22/0.43 tff(84,plain,
% 0.22/0.43 (~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[83, 80])).
% 0.22/0.43 tff(85,plain,
% 0.22/0.43 (~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.22/0.43 tff(86,plain,
% 0.22/0.43 (~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[85, 80])).
% 0.22/0.43 tff(87,plain,(
% 0.22/0.43 ~((~in(A!18, B!17)) | ordinal(A!18) | (~ordinal(B!17)))),
% 0.22/0.43 inference(skolemize,[status(sab)],[86])).
% 0.22/0.43 tff(88,plain,
% 0.22/0.43 (~((~in(A!18, B!17)) | ordinal(A!18) | (~ordinal(B!17)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[87, 79])).
% 0.22/0.43 tff(89,plain,
% 0.22/0.43 (ordinal(B!17)),
% 0.22/0.43 inference(or_elim,[status(thm)],[88])).
% 0.22/0.43 tff(90,plain,
% 0.22/0.43 (^[A: $i] : refl(((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(91,plain,
% 0.22/0.43 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[90])).
% 0.22/0.43 tff(92,plain,
% 0.22/0.43 (^[A: $i] : rewrite(((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(93,plain,
% 0.22/0.43 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[92])).
% 0.22/0.43 tff(94,plain,
% 0.22/0.43 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(95,plain,
% 0.22/0.43 (^[A: $i] : rewrite((ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(96,plain,
% 0.22/0.43 (![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[95])).
% 0.22/0.43 tff(97,axiom,(![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_ordinal1')).
% 0.22/0.43 tff(98,plain,
% 0.22/0.43 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.22/0.43 tff(99,plain,
% 0.22/0.43 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.22/0.43 tff(100,plain,(
% 0.22/0.43 ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.22/0.43 inference(skolemize,[status(sab)],[99])).
% 0.22/0.43 tff(101,plain,
% 0.22/0.43 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.22/0.43 tff(102,plain,
% 0.22/0.43 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[101, 91])).
% 0.22/0.43 tff(103,plain,
% 0.22/0.43 (((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(B!17)) | (~((~epsilon_transitive(B!17)) | (~epsilon_connected(B!17)))))) <=> ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(B!17)) | (~((~epsilon_transitive(B!17)) | (~epsilon_connected(B!17)))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(104,plain,
% 0.22/0.43 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(B!17)) | (~((~epsilon_transitive(B!17)) | (~epsilon_connected(B!17)))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(105,plain,
% 0.22/0.43 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(B!17)) | (~((~epsilon_transitive(B!17)) | (~epsilon_connected(B!17))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.22/0.43 tff(106,plain,
% 0.22/0.43 (~((~epsilon_transitive(B!17)) | (~epsilon_connected(B!17)))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[105, 102, 89])).
% 0.22/0.43 tff(107,plain,
% 0.22/0.43 (((~epsilon_transitive(B!17)) | (~epsilon_connected(B!17))) | epsilon_transitive(B!17)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(108,plain,
% 0.22/0.43 (epsilon_transitive(B!17)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.22/0.43 tff(109,plain,
% 0.22/0.43 ((~((~epsilon_transitive(B!17)) | ![B: $i] : ((~in(B, B!17)) | subset(B, B!17)))) | (~epsilon_transitive(B!17)) | ![B: $i] : ((~in(B, B!17)) | subset(B, B!17))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(110,plain,
% 0.22/0.43 ((~((~epsilon_transitive(B!17)) | ![B: $i] : ((~in(B, B!17)) | subset(B, B!17)))) | ![B: $i] : ((~in(B, B!17)) | subset(B, B!17))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.22/0.43 tff(111,plain,
% 0.22/0.43 (![B: $i] : ((~in(B, B!17)) | subset(B, B!17))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[110, 78])).
% 0.22/0.43 tff(112,plain,
% 0.22/0.43 (in(A!18, B!17)),
% 0.22/0.43 inference(or_elim,[status(thm)],[88])).
% 0.22/0.43 tff(113,plain,
% 0.22/0.43 (((~![B: $i] : ((~in(B, B!17)) | subset(B, B!17))) | ((~in(A!18, B!17)) | subset(A!18, B!17))) <=> ((~![B: $i] : ((~in(B, B!17)) | subset(B, B!17))) | (~in(A!18, B!17)) | subset(A!18, B!17))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(114,plain,
% 0.22/0.43 ((~![B: $i] : ((~in(B, B!17)) | subset(B, B!17))) | ((~in(A!18, B!17)) | subset(A!18, B!17))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(115,plain,
% 0.22/0.43 ((~![B: $i] : ((~in(B, B!17)) | subset(B, B!17))) | (~in(A!18, B!17)) | subset(A!18, B!17)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.22/0.43 tff(116,plain,
% 0.22/0.43 (subset(A!18, B!17)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[115, 112, 111])).
% 0.22/0.43 tff(117,plain,
% 0.22/0.43 ((~((~subset(A!18, B!17)) | ![C: $i] : ((~in(C, A!18)) | in(C, B!17)))) | (~subset(A!18, B!17)) | ![C: $i] : ((~in(C, A!18)) | in(C, B!17))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(118,plain,
% 0.22/0.43 ((~((~subset(A!18, B!17)) | ![C: $i] : ((~in(C, A!18)) | in(C, B!17)))) | ![C: $i] : ((~in(C, A!18)) | in(C, B!17))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.22/0.43 tff(119,plain,
% 0.22/0.43 (![C: $i] : ((~in(C, A!18)) | in(C, B!17))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[118, 74])).
% 0.22/0.43 tff(120,plain,
% 0.22/0.43 (((~![C: $i] : ((~in(C, A!18)) | in(C, B!17))) | ((~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_B_2(A!18), B!17))) <=> ((~![C: $i] : ((~in(C, A!18)) | in(C, B!17))) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_B_2(A!18), B!17))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(121,plain,
% 0.22/0.43 ((~![C: $i] : ((~in(C, A!18)) | in(C, B!17))) | ((~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_B_2(A!18), B!17))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(122,plain,
% 0.22/0.43 ((~![C: $i] : ((~in(C, A!18)) | in(C, B!17))) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_B_2(A!18), B!17)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.22/0.43 tff(123,plain,
% 0.22/0.43 (in(tptp_fun_B_2(A!18), B!17)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[122, 119, 70])).
% 0.22/0.43 tff(124,plain,
% 0.22/0.43 (((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))) | in(tptp_fun_C_1(A!18), A!18)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(125,plain,
% 0.22/0.43 (in(tptp_fun_C_1(A!18), A!18)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[124, 68])).
% 0.22/0.43 tff(126,plain,
% 0.22/0.43 (((~![C: $i] : ((~in(C, A!18)) | in(C, B!17))) | ((~in(tptp_fun_C_1(A!18), A!18)) | in(tptp_fun_C_1(A!18), B!17))) <=> ((~![C: $i] : ((~in(C, A!18)) | in(C, B!17))) | (~in(tptp_fun_C_1(A!18), A!18)) | in(tptp_fun_C_1(A!18), B!17))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(127,plain,
% 0.22/0.43 ((~![C: $i] : ((~in(C, A!18)) | in(C, B!17))) | ((~in(tptp_fun_C_1(A!18), A!18)) | in(tptp_fun_C_1(A!18), B!17))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(128,plain,
% 0.22/0.43 ((~![C: $i] : ((~in(C, A!18)) | in(C, B!17))) | (~in(tptp_fun_C_1(A!18), A!18)) | in(tptp_fun_C_1(A!18), B!17)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.22/0.43 tff(129,plain,
% 0.22/0.43 (in(tptp_fun_C_1(A!18), B!17)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[128, 119, 125])).
% 0.22/0.43 tff(130,plain,
% 0.22/0.43 (((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))) | (~in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(131,plain,
% 0.22/0.43 (~in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[130, 68])).
% 0.22/0.43 tff(132,plain,
% 0.22/0.43 (((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))) | (~(tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(133,plain,
% 0.22/0.43 (~(tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[132, 68])).
% 0.22/0.43 tff(134,plain,
% 0.22/0.43 (((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))) | (~in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(135,plain,
% 0.22/0.43 (~in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[134, 68])).
% 0.22/0.43 tff(136,plain,
% 0.22/0.43 (((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(B!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17))))) | (~(epsilon_connected(B!17) | (~((~in(tptp_fun_C_1(B!17), B!17)) | (~in(tptp_fun_B_2(B!17), B!17)) | in(tptp_fun_C_1(B!17), tptp_fun_B_2(B!17)) | (tptp_fun_B_2(B!17) = tptp_fun_C_1(B!17)) | in(tptp_fun_B_2(B!17), tptp_fun_C_1(B!17))))))))) <=> ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(B!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17))))) | (~(epsilon_connected(B!17) | (~((~in(tptp_fun_C_1(B!17), B!17)) | (~in(tptp_fun_B_2(B!17), B!17)) | in(tptp_fun_C_1(B!17), tptp_fun_B_2(B!17)) | (tptp_fun_B_2(B!17) = tptp_fun_C_1(B!17)) | in(tptp_fun_B_2(B!17), tptp_fun_C_1(B!17)))))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(137,plain,
% 0.22/0.43 ((~((~((~epsilon_connected(B!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17))))) | (~(epsilon_connected(B!17) | (~(in(tptp_fun_B_2(B!17), tptp_fun_C_1(B!17)) | (tptp_fun_B_2(B!17) = tptp_fun_C_1(B!17)) | in(tptp_fun_C_1(B!17), tptp_fun_B_2(B!17)) | (~in(tptp_fun_B_2(B!17), B!17)) | (~in(tptp_fun_C_1(B!17), B!17)))))))) <=> (~((~((~epsilon_connected(B!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17))))) | (~(epsilon_connected(B!17) | (~((~in(tptp_fun_C_1(B!17), B!17)) | (~in(tptp_fun_B_2(B!17), B!17)) | in(tptp_fun_C_1(B!17), tptp_fun_B_2(B!17)) | (tptp_fun_B_2(B!17) = tptp_fun_C_1(B!17)) | in(tptp_fun_B_2(B!17), tptp_fun_C_1(B!17))))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(138,plain,
% 0.22/0.43 (((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(B!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17))))) | (~(epsilon_connected(B!17) | (~(in(tptp_fun_B_2(B!17), tptp_fun_C_1(B!17)) | (tptp_fun_B_2(B!17) = tptp_fun_C_1(B!17)) | in(tptp_fun_C_1(B!17), tptp_fun_B_2(B!17)) | (~in(tptp_fun_B_2(B!17), B!17)) | (~in(tptp_fun_C_1(B!17), B!17))))))))) <=> ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(B!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17))))) | (~(epsilon_connected(B!17) | (~((~in(tptp_fun_C_1(B!17), B!17)) | (~in(tptp_fun_B_2(B!17), B!17)) | in(tptp_fun_C_1(B!17), tptp_fun_B_2(B!17)) | (tptp_fun_B_2(B!17) = tptp_fun_C_1(B!17)) | in(tptp_fun_B_2(B!17), tptp_fun_C_1(B!17)))))))))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[137])).
% 0.22/0.44 tff(139,plain,
% 0.22/0.44 (((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(B!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17))))) | (~(epsilon_connected(B!17) | (~(in(tptp_fun_B_2(B!17), tptp_fun_C_1(B!17)) | (tptp_fun_B_2(B!17) = tptp_fun_C_1(B!17)) | in(tptp_fun_C_1(B!17), tptp_fun_B_2(B!17)) | (~in(tptp_fun_B_2(B!17), B!17)) | (~in(tptp_fun_C_1(B!17), B!17))))))))) <=> ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(B!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17))))) | (~(epsilon_connected(B!17) | (~((~in(tptp_fun_C_1(B!17), B!17)) | (~in(tptp_fun_B_2(B!17), B!17)) | in(tptp_fun_C_1(B!17), tptp_fun_B_2(B!17)) | (tptp_fun_B_2(B!17) = tptp_fun_C_1(B!17)) | in(tptp_fun_B_2(B!17), tptp_fun_C_1(B!17)))))))))),
% 0.22/0.44 inference(transitivity,[status(thm)],[138, 136])).
% 0.22/0.44 tff(140,plain,
% 0.22/0.44 ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(B!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17))))) | (~(epsilon_connected(B!17) | (~(in(tptp_fun_B_2(B!17), tptp_fun_C_1(B!17)) | (tptp_fun_B_2(B!17) = tptp_fun_C_1(B!17)) | in(tptp_fun_C_1(B!17), tptp_fun_B_2(B!17)) | (~in(tptp_fun_B_2(B!17), B!17)) | (~in(tptp_fun_C_1(B!17), B!17))))))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(141,plain,
% 0.22/0.44 ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(B!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17))))) | (~(epsilon_connected(B!17) | (~((~in(tptp_fun_C_1(B!17), B!17)) | (~in(tptp_fun_B_2(B!17), B!17)) | in(tptp_fun_C_1(B!17), tptp_fun_B_2(B!17)) | (tptp_fun_B_2(B!17) = tptp_fun_C_1(B!17)) | in(tptp_fun_B_2(B!17), tptp_fun_C_1(B!17))))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.22/0.44 tff(142,plain,
% 0.22/0.44 (~((~((~epsilon_connected(B!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17))))) | (~(epsilon_connected(B!17) | (~((~in(tptp_fun_C_1(B!17), B!17)) | (~in(tptp_fun_B_2(B!17), B!17)) | in(tptp_fun_C_1(B!17), tptp_fun_B_2(B!17)) | (tptp_fun_B_2(B!17) = tptp_fun_C_1(B!17)) | in(tptp_fun_B_2(B!17), tptp_fun_C_1(B!17)))))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[141, 57])).
% 0.22/0.44 tff(143,plain,
% 0.22/0.44 (((~((~epsilon_connected(B!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17))))) | (~(epsilon_connected(B!17) | (~((~in(tptp_fun_C_1(B!17), B!17)) | (~in(tptp_fun_B_2(B!17), B!17)) | in(tptp_fun_C_1(B!17), tptp_fun_B_2(B!17)) | (tptp_fun_B_2(B!17) = tptp_fun_C_1(B!17)) | in(tptp_fun_B_2(B!17), tptp_fun_C_1(B!17))))))) | ((~epsilon_connected(B!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17))))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(144,plain,
% 0.22/0.44 ((~epsilon_connected(B!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17)))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.22/0.44 tff(145,plain,
% 0.22/0.44 (((~epsilon_transitive(B!17)) | (~epsilon_connected(B!17))) | epsilon_connected(B!17)),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(146,plain,
% 0.22/0.44 (epsilon_connected(B!17)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[145, 106])).
% 0.22/0.44 tff(147,plain,
% 0.22/0.44 ((~((~epsilon_connected(B!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17))))) | (~epsilon_connected(B!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17)))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(148,plain,
% 0.22/0.44 ((~((~epsilon_connected(B!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17))))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17)))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.22/0.44 tff(149,plain,
% 0.22/0.44 (![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17)))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[148, 144])).
% 0.22/0.44 tff(150,plain,
% 0.22/0.44 (((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17)))) | (in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | (~in(tptp_fun_C_1(A!18), B!17)) | (~in(tptp_fun_B_2(A!18), B!17)))) <=> ((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17)))) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | (~in(tptp_fun_C_1(A!18), B!17)) | (~in(tptp_fun_B_2(A!18), B!17)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(151,plain,
% 0.22/0.44 ((in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | (~in(tptp_fun_C_1(A!18), B!17)) | (~in(tptp_fun_B_2(A!18), B!17))) <=> (in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | (~in(tptp_fun_C_1(A!18), B!17)) | (~in(tptp_fun_B_2(A!18), B!17)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(152,plain,
% 0.22/0.44 (((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17)))) | (in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | (~in(tptp_fun_C_1(A!18), B!17)) | (~in(tptp_fun_B_2(A!18), B!17)))) <=> ((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17)))) | (in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | (~in(tptp_fun_C_1(A!18), B!17)) | (~in(tptp_fun_B_2(A!18), B!17))))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[151])).
% 0.22/0.44 tff(153,plain,
% 0.22/0.44 (((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17)))) | (in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | (~in(tptp_fun_C_1(A!18), B!17)) | (~in(tptp_fun_B_2(A!18), B!17)))) <=> ((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17)))) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | (~in(tptp_fun_C_1(A!18), B!17)) | (~in(tptp_fun_B_2(A!18), B!17)))),
% 0.22/0.44 inference(transitivity,[status(thm)],[152, 150])).
% 0.22/0.44 tff(154,plain,
% 0.22/0.44 ((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17)))) | (in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | (~in(tptp_fun_C_1(A!18), B!17)) | (~in(tptp_fun_B_2(A!18), B!17)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(155,plain,
% 0.22/0.44 ((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17)))) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)) | (~in(tptp_fun_C_1(A!18), B!17)) | (~in(tptp_fun_B_2(A!18), B!17))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.22/0.44 tff(156,plain,
% 0.22/0.44 ((~in(tptp_fun_C_1(A!18), B!17)) | (~in(tptp_fun_B_2(A!18), B!17))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[155, 149, 135, 133, 131])).
% 0.22/0.44 tff(157,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[156, 129, 123])).
% 0.22/0.44 tff(158,plain,((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.44 tff(159,plain,
% 0.22/0.44 ((~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)))))) | epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18))))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(160,plain,
% 0.22/0.44 ((~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_1(A!18), A!18)) | (~in(tptp_fun_B_2(A!18), A!18)) | in(tptp_fun_C_1(A!18), tptp_fun_B_2(A!18)) | (tptp_fun_B_2(A!18) = tptp_fun_C_1(A!18)) | in(tptp_fun_B_2(A!18), tptp_fun_C_1(A!18)))))) | epsilon_connected(A!18)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.22/0.44 tff(161,plain,
% 0.22/0.44 (epsilon_connected(A!18)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[160, 67])).
% 0.22/0.44 tff(162,plain,
% 0.22/0.44 (^[A: $i] : refl((~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))) <=> (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(163,plain,
% 0.22/0.44 (![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))) <=> ![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[162])).
% 0.22/0.44 tff(164,plain,
% 0.22/0.44 (^[A: $i] : trans(trans(monotonicity(rewrite((epsilon_transitive(A) & epsilon_connected(A)) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))), ((ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))), rewrite((ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))), ((ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))))), rewrite((~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))) <=> (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))), ((ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(165,plain,
% 0.22/0.44 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[164])).
% 0.22/0.44 tff(166,plain,
% 0.22/0.44 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(167,axiom,(![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_ordinal1')).
% 0.22/0.44 tff(168,plain,
% 0.22/0.44 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.22/0.44 tff(169,plain,(
% 0.22/0.44 ![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.22/0.44 inference(skolemize,[status(sab)],[168])).
% 0.22/0.44 tff(170,plain,
% 0.22/0.44 (![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[169, 165])).
% 0.22/0.44 tff(171,plain,
% 0.22/0.44 (![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[170, 163])).
% 0.22/0.44 tff(172,plain,
% 0.22/0.44 ((~![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))) | (~(((~epsilon_transitive(A!18)) | (~epsilon_connected(A!18))) <=> ordinal(A!18)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(173,plain,
% 0.22/0.44 (~(((~epsilon_transitive(A!18)) | (~epsilon_connected(A!18))) <=> ordinal(A!18))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[172, 171])).
% 0.22/0.44 tff(174,plain,
% 0.22/0.44 (~ordinal(A!18)),
% 0.22/0.44 inference(or_elim,[status(thm)],[88])).
% 0.22/0.44 tff(175,plain,
% 0.22/0.44 ((((~epsilon_transitive(A!18)) | (~epsilon_connected(A!18))) <=> ordinal(A!18)) | ((~epsilon_transitive(A!18)) | (~epsilon_connected(A!18))) | ordinal(A!18)),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(176,plain,
% 0.22/0.44 ((((~epsilon_transitive(A!18)) | (~epsilon_connected(A!18))) <=> ordinal(A!18)) | ((~epsilon_transitive(A!18)) | (~epsilon_connected(A!18)))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.22/0.44 tff(177,plain,
% 0.22/0.44 ((~epsilon_transitive(A!18)) | (~epsilon_connected(A!18))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[176, 173])).
% 0.22/0.44 tff(178,plain,
% 0.22/0.44 ((~((~epsilon_transitive(A!18)) | (~epsilon_connected(A!18)))) | (~epsilon_transitive(A!18)) | (~epsilon_connected(A!18))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(179,plain,
% 0.22/0.44 ((~epsilon_transitive(A!18)) | (~epsilon_connected(A!18))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.22/0.44 tff(180,plain,
% 0.22/0.44 (~epsilon_transitive(A!18)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[179, 161])).
% 0.22/0.44 tff(181,plain,
% 0.22/0.44 ((~(epsilon_transitive(A!18) | (~((~in(tptp_fun_B_0(A!18), A!18)) | subset(tptp_fun_B_0(A!18), A!18))))) | epsilon_transitive(A!18) | (~((~in(tptp_fun_B_0(A!18), A!18)) | subset(tptp_fun_B_0(A!18), A!18)))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(182,plain,
% 0.22/0.44 ((~(epsilon_transitive(A!18) | (~((~in(tptp_fun_B_0(A!18), A!18)) | subset(tptp_fun_B_0(A!18), A!18))))) | (~((~in(tptp_fun_B_0(A!18), A!18)) | subset(tptp_fun_B_0(A!18), A!18)))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[181, 180])).
% 0.22/0.44 tff(183,plain,
% 0.22/0.44 (~((~in(tptp_fun_B_0(A!18), A!18)) | subset(tptp_fun_B_0(A!18), A!18))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[182, 40])).
% 0.22/0.44 tff(184,plain,
% 0.22/0.44 (((~in(tptp_fun_B_0(A!18), A!18)) | subset(tptp_fun_B_0(A!18), A!18)) | (~subset(tptp_fun_B_0(A!18), A!18))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(185,plain,
% 0.22/0.44 (~subset(tptp_fun_B_0(A!18), A!18)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.22/0.44 tff(186,plain,
% 0.22/0.44 ((~(subset(tptp_fun_B_0(A!18), A!18) | (~((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18))))) | subset(tptp_fun_B_0(A!18), A!18) | (~((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18)))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(187,plain,
% 0.22/0.45 ((~(subset(tptp_fun_B_0(A!18), A!18) | (~((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18))))) | (~((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18)))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.22/0.45 tff(188,plain,
% 0.22/0.45 (~((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[187, 20])).
% 0.22/0.45 tff(189,plain,
% 0.22/0.45 (((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18)) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(190,plain,
% 0.22/0.45 (in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.22/0.45 tff(191,plain,
% 0.22/0.45 (((~in(tptp_fun_B_0(A!18), A!18)) | subset(tptp_fun_B_0(A!18), A!18)) | in(tptp_fun_B_0(A!18), A!18)),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(192,plain,
% 0.22/0.45 (in(tptp_fun_B_0(A!18), A!18)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[191, 183])).
% 0.22/0.45 tff(193,plain,
% 0.22/0.45 (^[A: $i, B: $i, C: $i] : refl(((~in(B, C)) | (~in(C, A)) | (~in(A, B))) <=> ((~in(B, C)) | (~in(C, A)) | (~in(A, B))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(194,plain,
% 0.22/0.45 (![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~in(C, A)) | (~in(A, B))) <=> ![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~in(C, A)) | (~in(A, B)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[193])).
% 0.22/0.45 tff(195,plain,
% 0.22/0.45 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, B) & in(B, C) & in(C, A)) <=> (~((~in(B, C)) | (~in(C, A)) | (~in(A, B))))), ((~(in(A, B) & in(B, C) & in(C, A))) <=> (~(~((~in(B, C)) | (~in(C, A)) | (~in(A, B))))))), rewrite((~(~((~in(B, C)) | (~in(C, A)) | (~in(A, B))))) <=> ((~in(B, C)) | (~in(C, A)) | (~in(A, B)))), ((~(in(A, B) & in(B, C) & in(C, A))) <=> ((~in(B, C)) | (~in(C, A)) | (~in(A, B)))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(196,plain,
% 0.22/0.45 (![A: $i, B: $i, C: $i] : (~(in(A, B) & in(B, C) & in(C, A))) <=> ![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~in(C, A)) | (~in(A, B)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[195])).
% 0.22/0.45 tff(197,plain,
% 0.22/0.45 (![A: $i, B: $i, C: $i] : (~(in(A, B) & in(B, C) & in(C, A))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, B) & in(B, C) & in(C, A)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(198,plain,
% 0.22/0.45 (^[A: $i, B: $i, C: $i] : rewrite((~((in(A, B) & in(B, C)) & in(C, A))) <=> (~(in(A, B) & in(B, C) & in(C, A))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(199,plain,
% 0.22/0.45 (![A: $i, B: $i, C: $i] : (~((in(A, B) & in(B, C)) & in(C, A))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, B) & in(B, C) & in(C, A)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[198])).
% 0.22/0.45 tff(200,axiom,(![A: $i, B: $i, C: $i] : (~((in(A, B) & in(B, C)) & in(C, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_ordinal1')).
% 0.22/0.45 tff(201,plain,
% 0.22/0.45 (![A: $i, B: $i, C: $i] : (~(in(A, B) & in(B, C) & in(C, A)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.22/0.45 tff(202,plain,
% 0.22/0.45 (![A: $i, B: $i, C: $i] : (~(in(A, B) & in(B, C) & in(C, A)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[201, 197])).
% 0.22/0.45 tff(203,plain,(
% 0.22/0.45 ![A: $i, B: $i, C: $i] : (~(in(A, B) & in(B, C) & in(C, A)))),
% 0.22/0.45 inference(skolemize,[status(sab)],[202])).
% 0.22/0.45 tff(204,plain,
% 0.22/0.45 (![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~in(C, A)) | (~in(A, B)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[203, 196])).
% 0.22/0.45 tff(205,plain,
% 0.22/0.45 (![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~in(C, A)) | (~in(A, B)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[204, 194])).
% 0.22/0.45 tff(206,plain,
% 0.22/0.45 (((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~in(C, A)) | (~in(A, B)))) | ((~in(tptp_fun_B_0(A!18), A!18)) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | (~in(A!18, tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~in(C, A)) | (~in(A, B)))) | (~in(tptp_fun_B_0(A!18), A!18)) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | (~in(A!18, tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(207,plain,
% 0.22/0.45 (((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | (~in(tptp_fun_B_0(A!18), A!18)) | (~in(A!18, tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))))) <=> ((~in(tptp_fun_B_0(A!18), A!18)) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | (~in(A!18, tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(208,plain,
% 0.22/0.45 (((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~in(C, A)) | (~in(A, B)))) | ((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | (~in(tptp_fun_B_0(A!18), A!18)) | (~in(A!18, tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~in(C, A)) | (~in(A, B)))) | ((~in(tptp_fun_B_0(A!18), A!18)) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | (~in(A!18, tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))))))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[207])).
% 0.22/0.45 tff(209,plain,
% 0.22/0.45 (((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~in(C, A)) | (~in(A, B)))) | ((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | (~in(tptp_fun_B_0(A!18), A!18)) | (~in(A!18, tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~in(C, A)) | (~in(A, B)))) | (~in(tptp_fun_B_0(A!18), A!18)) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | (~in(A!18, tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)))))),
% 0.22/0.45 inference(transitivity,[status(thm)],[208, 206])).
% 0.22/0.45 tff(210,plain,
% 0.22/0.45 ((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~in(C, A)) | (~in(A, B)))) | ((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | (~in(tptp_fun_B_0(A!18), A!18)) | (~in(A!18, tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(211,plain,
% 0.22/0.45 ((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~in(C, A)) | (~in(A, B)))) | (~in(tptp_fun_B_0(A!18), A!18)) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | (~in(A!18, tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.22/0.45 tff(212,plain,
% 0.22/0.45 (~in(A!18, tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[211, 205, 192, 190])).
% 0.22/0.45 tff(213,plain,
% 0.22/0.45 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))) | (~((~((~subset(tptp_fun_B_0(A!18), B!17)) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!18))) | in(C, B!17)))) | (~(subset(tptp_fun_B_0(A!18), B!17) | (~((~in(tptp_fun_C_3(B!17, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(B!17, tptp_fun_B_0(A!18)), B!17)))))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(214,plain,
% 0.22/0.45 (~((~((~subset(tptp_fun_B_0(A!18), B!17)) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!18))) | in(C, B!17)))) | (~(subset(tptp_fun_B_0(A!18), B!17) | (~((~in(tptp_fun_C_3(B!17, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(B!17, tptp_fun_B_0(A!18)), B!17))))))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[213, 16])).
% 0.22/0.45 tff(215,plain,
% 0.22/0.45 (((~((~subset(tptp_fun_B_0(A!18), B!17)) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!18))) | in(C, B!17)))) | (~(subset(tptp_fun_B_0(A!18), B!17) | (~((~in(tptp_fun_C_3(B!17, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(B!17, tptp_fun_B_0(A!18)), B!17)))))) | ((~subset(tptp_fun_B_0(A!18), B!17)) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!18))) | in(C, B!17)))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(216,plain,
% 0.22/0.45 ((~subset(tptp_fun_B_0(A!18), B!17)) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!18))) | in(C, B!17))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.22/0.45 tff(217,plain,
% 0.22/0.45 (((~![C: $i] : ((~in(C, A!18)) | in(C, B!17))) | ((~in(tptp_fun_B_0(A!18), A!18)) | in(tptp_fun_B_0(A!18), B!17))) <=> ((~![C: $i] : ((~in(C, A!18)) | in(C, B!17))) | (~in(tptp_fun_B_0(A!18), A!18)) | in(tptp_fun_B_0(A!18), B!17))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(218,plain,
% 0.22/0.45 ((~![C: $i] : ((~in(C, A!18)) | in(C, B!17))) | ((~in(tptp_fun_B_0(A!18), A!18)) | in(tptp_fun_B_0(A!18), B!17))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(219,plain,
% 0.22/0.45 ((~![C: $i] : ((~in(C, A!18)) | in(C, B!17))) | (~in(tptp_fun_B_0(A!18), A!18)) | in(tptp_fun_B_0(A!18), B!17)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.22/0.45 tff(220,plain,
% 0.22/0.45 (in(tptp_fun_B_0(A!18), B!17)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[219, 119, 192])).
% 0.22/0.45 tff(221,plain,
% 0.22/0.45 (((~![B: $i] : ((~in(B, B!17)) | subset(B, B!17))) | ((~in(tptp_fun_B_0(A!18), B!17)) | subset(tptp_fun_B_0(A!18), B!17))) <=> ((~![B: $i] : ((~in(B, B!17)) | subset(B, B!17))) | (~in(tptp_fun_B_0(A!18), B!17)) | subset(tptp_fun_B_0(A!18), B!17))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(222,plain,
% 0.22/0.45 ((~![B: $i] : ((~in(B, B!17)) | subset(B, B!17))) | ((~in(tptp_fun_B_0(A!18), B!17)) | subset(tptp_fun_B_0(A!18), B!17))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(223,plain,
% 0.22/0.45 ((~![B: $i] : ((~in(B, B!17)) | subset(B, B!17))) | (~in(tptp_fun_B_0(A!18), B!17)) | subset(tptp_fun_B_0(A!18), B!17)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.22/0.45 tff(224,plain,
% 0.22/0.45 (subset(tptp_fun_B_0(A!18), B!17)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[223, 111, 220])).
% 0.22/0.45 tff(225,plain,
% 0.22/0.45 ((~((~subset(tptp_fun_B_0(A!18), B!17)) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!18))) | in(C, B!17)))) | (~subset(tptp_fun_B_0(A!18), B!17)) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!18))) | in(C, B!17))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(226,plain,
% 0.22/0.45 ((~((~subset(tptp_fun_B_0(A!18), B!17)) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!18))) | in(C, B!17)))) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!18))) | in(C, B!17))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[225, 224])).
% 0.22/0.45 tff(227,plain,
% 0.22/0.45 (![C: $i] : ((~in(C, tptp_fun_B_0(A!18))) | in(C, B!17))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[226, 216])).
% 0.22/0.45 tff(228,plain,
% 0.22/0.45 (((~![C: $i] : ((~in(C, tptp_fun_B_0(A!18))) | in(C, B!17))) | ((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), B!17))) <=> ((~![C: $i] : ((~in(C, tptp_fun_B_0(A!18))) | in(C, B!17))) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), B!17))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(229,plain,
% 0.22/0.45 ((~![C: $i] : ((~in(C, tptp_fun_B_0(A!18))) | in(C, B!17))) | ((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), B!17))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(230,plain,
% 0.22/0.45 ((~![C: $i] : ((~in(C, tptp_fun_B_0(A!18))) | in(C, B!17))) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), B!17)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.22/0.45 tff(231,plain,
% 0.22/0.45 (in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), B!17)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[230, 190, 227])).
% 0.22/0.45 tff(232,plain,
% 0.22/0.45 (((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18)) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(233,plain,
% 0.22/0.45 (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[232, 188])).
% 0.22/0.45 tff(234,plain,
% 0.22/0.45 (((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17)))) | ((~in(A!18, B!17)) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18) | in(A!18, tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), B!17)) | (A!18 = tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))))) <=> ((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17)))) | (~in(A!18, B!17)) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18) | in(A!18, tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), B!17)) | (A!18 = tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(235,plain,
% 0.22/0.46 ((in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18) | in(A!18, tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))) | (A!18 = tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), B!17)) | (~in(A!18, B!17))) <=> ((~in(A!18, B!17)) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18) | in(A!18, tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), B!17)) | (A!18 = tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(236,plain,
% 0.22/0.46 (((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17)))) | (in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18) | in(A!18, tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))) | (A!18 = tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), B!17)) | (~in(A!18, B!17)))) <=> ((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17)))) | ((~in(A!18, B!17)) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18) | in(A!18, tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), B!17)) | (A!18 = tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[235])).
% 0.22/0.46 tff(237,plain,
% 0.22/0.46 (((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17)))) | (in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18) | in(A!18, tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))) | (A!18 = tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), B!17)) | (~in(A!18, B!17)))) <=> ((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17)))) | (~in(A!18, B!17)) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18) | in(A!18, tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), B!17)) | (A!18 = tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))))),
% 0.22/0.46 inference(transitivity,[status(thm)],[236, 234])).
% 0.22/0.46 tff(238,plain,
% 0.22/0.46 ((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17)))) | (in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18) | in(A!18, tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))) | (A!18 = tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), B!17)) | (~in(A!18, B!17)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(239,plain,
% 0.22/0.46 ((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!17)) | (~in(B, B!17)))) | (~in(A!18, B!17)) | in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), A!18) | in(A!18, tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), B!17)) | (A!18 = tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.22/0.46 tff(240,plain,
% 0.22/0.46 (in(A!18, tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), B!17)) | (A!18 = tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[239, 112, 149, 233])).
% 0.22/0.46 tff(241,plain,
% 0.22/0.46 (A!18 = tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[240, 231, 212])).
% 0.22/0.46 tff(242,plain,
% 0.22/0.46 (in(tptp_fun_B_0(A!18), A!18) <=> in(tptp_fun_B_0(A!18), tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[241])).
% 0.22/0.46 tff(243,plain,
% 0.22/0.46 (in(tptp_fun_B_0(A!18), tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))) <=> in(tptp_fun_B_0(A!18), A!18)),
% 0.22/0.46 inference(symmetry,[status(thm)],[242])).
% 0.22/0.46 tff(244,plain,
% 0.22/0.46 ((~in(tptp_fun_B_0(A!18), tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)))) <=> (~in(tptp_fun_B_0(A!18), A!18))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[243])).
% 0.22/0.46 tff(245,plain,
% 0.22/0.46 (^[A: $i, B: $i] : refl(((~in(B, A)) | (~in(A, B))) <=> ((~in(B, A)) | (~in(A, B))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(246,plain,
% 0.22/0.46 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[245])).
% 0.22/0.46 tff(247,plain,
% 0.22/0.46 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(248,plain,
% 0.22/0.46 (^[A: $i, B: $i] : rewrite((in(A, B) => (~in(B, A))) <=> ((~in(B, A)) | (~in(A, B))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(249,plain,
% 0.22/0.46 (![A: $i, B: $i] : (in(A, B) => (~in(B, A))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[248])).
% 0.22/0.46 tff(250,axiom,(![A: $i, B: $i] : (in(A, B) => (~in(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','antisymmetry_r2_hidden')).
% 0.22/0.46 tff(251,plain,
% 0.22/0.46 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.22/0.46 tff(252,plain,
% 0.22/0.46 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[251, 247])).
% 0.22/0.46 tff(253,plain,(
% 0.22/0.46 ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.22/0.46 inference(skolemize,[status(sab)],[252])).
% 0.22/0.46 tff(254,plain,
% 0.22/0.46 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[253, 246])).
% 0.22/0.46 tff(255,plain,
% 0.22/0.46 (((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | (~in(tptp_fun_B_0(A!18), tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)))))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | (~in(tptp_fun_B_0(A!18), tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(256,plain,
% 0.22/0.46 ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | (~in(tptp_fun_B_0(A!18), tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(257,plain,
% 0.22/0.46 ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)), tptp_fun_B_0(A!18))) | (~in(tptp_fun_B_0(A!18), tptp_fun_C_3(A!18, tptp_fun_B_0(A!18))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.22/0.46 tff(258,plain,
% 0.22/0.46 (~in(tptp_fun_B_0(A!18), tptp_fun_C_3(A!18, tptp_fun_B_0(A!18)))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[257, 254, 190])).
% 0.22/0.46 tff(259,plain,
% 0.22/0.46 (~in(tptp_fun_B_0(A!18), A!18)),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[258, 244])).
% 0.22/0.46 tff(260,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[192, 259])).
% 0.22/0.46 % SZS output end Proof
% 0.22/0.46 % E exiting
%------------------------------------------------------------------------------