%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU232+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:27:19 AM UTC 2025
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU232+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:24:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(in_type, type, (
% 0.12/0.39 in: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_B_16_type, type, (
% 0.12/0.39 tptp_fun_B_16: $i)).
% 0.12/0.39 tff(tptp_fun_B_2_type, type, (
% 0.12/0.39 tptp_fun_B_2: $i > $i)).
% 0.12/0.39 tff(tptp_fun_A_17_type, type, (
% 0.12/0.39 tptp_fun_A_17: $i)).
% 0.12/0.39 tff(tptp_fun_C_1_type, type, (
% 0.12/0.39 tptp_fun_C_1: $i > $i)).
% 0.12/0.39 tff(epsilon_connected_type, type, (
% 0.12/0.39 epsilon_connected: $i > $o)).
% 0.12/0.39 tff(epsilon_transitive_type, type, (
% 0.12/0.39 epsilon_transitive: $i > $o)).
% 0.12/0.39 tff(subset_type, type, (
% 0.12/0.39 subset: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_B_0_type, type, (
% 0.12/0.39 tptp_fun_B_0: $i > $i)).
% 0.12/0.39 tff(tptp_fun_C_3_type, type, (
% 0.12/0.39 tptp_fun_C_3: ( $i * $i ) > $i)).
% 0.12/0.39 tff(ordinal_type, type, (
% 0.12/0.39 ordinal: $i > $o)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (^[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)))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (![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))))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (^[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)))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (![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))))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (![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))))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[4, 2])).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 (^[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))))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (![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))))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (^[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))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[9])).
% 0.12/0.39 tff(11,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/sandbox2/benchmark/theBenchmark.p','d3_ordinal1')).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.12/0.39 tff(14,plain,(
% 0.12/0.39 ![A: $i] : (((~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))))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[13])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (![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))))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (![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))))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (((~![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!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!17)) | (~in(B, A!17))))) | (~(epsilon_connected(A!17) | (~((~in(tptp_fun_C_1(A!17), A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!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(A!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!17)) | (~in(B, A!17))))) | (~(epsilon_connected(A!17) | (~((~in(tptp_fun_C_1(A!17), A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17)))))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 ((~((~((~epsilon_connected(A!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!17)) | (~in(B, A!17))))) | (~(epsilon_connected(A!17) | (~(in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | (~in(tptp_fun_C_1(A!17), A!17)))))))) <=> (~((~((~epsilon_connected(A!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!17)) | (~in(B, A!17))))) | (~(epsilon_connected(A!17) | (~((~in(tptp_fun_C_1(A!17), A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (((~![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!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!17)) | (~in(B, A!17))))) | (~(epsilon_connected(A!17) | (~(in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | (~in(tptp_fun_C_1(A!17), A!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(A!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!17)) | (~in(B, A!17))))) | (~(epsilon_connected(A!17) | (~((~in(tptp_fun_C_1(A!17), A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17)))))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[18])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (((~![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!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!17)) | (~in(B, A!17))))) | (~(epsilon_connected(A!17) | (~(in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | (~in(tptp_fun_C_1(A!17), A!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(A!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!17)) | (~in(B, A!17))))) | (~(epsilon_connected(A!17) | (~((~in(tptp_fun_C_1(A!17), A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17)))))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[19, 17])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 ((~![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!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!17)) | (~in(B, A!17))))) | (~(epsilon_connected(A!17) | (~(in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | (~in(tptp_fun_C_1(A!17), A!17))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 ((~![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!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!17)) | (~in(B, A!17))))) | (~(epsilon_connected(A!17) | (~((~in(tptp_fun_C_1(A!17), A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (~((~((~epsilon_connected(A!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!17)) | (~in(B, A!17))))) | (~(epsilon_connected(A!17) | (~((~in(tptp_fun_C_1(A!17), A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17)))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (((~((~epsilon_connected(A!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!17)) | (~in(B, A!17))))) | (~(epsilon_connected(A!17) | (~((~in(tptp_fun_C_1(A!17), A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17))))))) | (epsilon_connected(A!17) | (~((~in(tptp_fun_C_1(A!17), A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17)))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (epsilon_connected(A!17) | (~((~in(tptp_fun_C_1(A!17), A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.19/0.40 tff(26,assumption,((~((~epsilon_transitive(A!17)) | ![B: $i] : ((~in(B, A!17)) | subset(B, A!17)))) | (~(epsilon_transitive(A!17) | (~((~in(tptp_fun_B_0(A!17), A!17)) | subset(tptp_fun_B_0(A!17), A!17)))))), introduced(assumption)).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (^[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))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 (^[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))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[30, 28])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (^[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)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (^[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))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[35])).
% 0.19/0.40 tff(37,axiom,(![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_ordinal1')).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.19/0.40 tff(40,plain,(
% 0.19/0.40 ![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)))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[39])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[41, 31])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 ((~![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!17)) | ![B: $i] : ((~in(B, A!17)) | subset(B, A!17)))) | (~(epsilon_transitive(A!17) | (~((~in(tptp_fun_B_0(A!17), A!17)) | subset(tptp_fun_B_0(A!17), A!17)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[43, 42, 26])).
% 0.19/0.40 tff(45,plain,(~((~((~epsilon_transitive(A!17)) | ![B: $i] : ((~in(B, A!17)) | subset(B, A!17)))) | (~(epsilon_transitive(A!17) | (~((~in(tptp_fun_B_0(A!17), A!17)) | subset(tptp_fun_B_0(A!17), A!17))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (((~((~epsilon_transitive(A!17)) | ![B: $i] : ((~in(B, A!17)) | subset(B, A!17)))) | (~(epsilon_transitive(A!17) | (~((~in(tptp_fun_B_0(A!17), A!17)) | subset(tptp_fun_B_0(A!17), A!17)))))) | (epsilon_transitive(A!17) | (~((~in(tptp_fun_B_0(A!17), A!17)) | subset(tptp_fun_B_0(A!17), A!17))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (epsilon_transitive(A!17) | (~((~in(tptp_fun_B_0(A!17), A!17)) | subset(tptp_fun_B_0(A!17), A!17)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_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))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[48])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_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))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[51, 49])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_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)))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (![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)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[56])).
% 0.19/0.41 tff(58,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.19/0.41 tff(61,plain,(
% 0.19/0.41 ![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)))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[60])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (![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)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (![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)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[62, 52])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 ((~![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!17), A!17)) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!17))) | in(C, A!17)))) | (~(subset(tptp_fun_B_0(A!17), A!17) | (~((~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), A!17)))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (~((~((~subset(tptp_fun_B_0(A!17), A!17)) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!17))) | in(C, A!17)))) | (~(subset(tptp_fun_B_0(A!17), A!17) | (~((~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), A!17))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (((~((~subset(tptp_fun_B_0(A!17), A!17)) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!17))) | in(C, A!17)))) | (~(subset(tptp_fun_B_0(A!17), A!17) | (~((~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), A!17)))))) | (subset(tptp_fun_B_0(A!17), A!17) | (~((~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), A!17))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (subset(tptp_fun_B_0(A!17), A!17) | (~((~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), A!17)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.19/0.41 tff(68,assumption,(~((~in(tptp_fun_B_0(A!17), A!17)) | subset(tptp_fun_B_0(A!17), A!17))), introduced(assumption)).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (((~in(tptp_fun_B_0(A!17), A!17)) | subset(tptp_fun_B_0(A!17), A!17)) | (~subset(tptp_fun_B_0(A!17), A!17))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (~subset(tptp_fun_B_0(A!17), A!17)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 ((~(subset(tptp_fun_B_0(A!17), A!17) | (~((~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), A!17))))) | subset(tptp_fun_B_0(A!17), A!17) | (~((~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), A!17)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 ((~(subset(tptp_fun_B_0(A!17), A!17) | (~((~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), A!17))))) | (~((~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), A!17)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 (~((~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), A!17))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[72, 67])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (((~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), A!17)) | in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (((~in(tptp_fun_B_0(A!17), A!17)) | subset(tptp_fun_B_0(A!17), A!17)) | in(tptp_fun_B_0(A!17), A!17)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (in(tptp_fun_B_0(A!17), A!17)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[76, 68])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[78])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.41 tff(85,axiom,(![A: $i, B: $i, C: $i] : (~((in(A, B) & in(B, C)) & in(C, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_ordinal1')).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (~(in(A, B) & in(B, C) & in(C, A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (~(in(A, B) & in(B, C) & in(C, A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.19/0.41 tff(88,plain,(
% 0.19/0.41 ![A: $i, B: $i, C: $i] : (~(in(A, B) & in(B, C) & in(C, A)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[87])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~in(C, A)) | (~in(A, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~in(C, A)) | (~in(A, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[89, 79])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~in(C, A)) | (~in(A, B)))) | ((~in(tptp_fun_B_0(A!17), A!17)) | (~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | (~in(A!17, tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~in(C, A)) | (~in(A, B)))) | (~in(tptp_fun_B_0(A!17), A!17)) | (~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | (~in(A!17, tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (((~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | (~in(tptp_fun_B_0(A!17), A!17)) | (~in(A!17, tptp_fun_C_3(A!17, tptp_fun_B_0(A!17))))) <=> ((~in(tptp_fun_B_0(A!17), A!17)) | (~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | (~in(A!17, tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~in(C, A)) | (~in(A, B)))) | ((~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | (~in(tptp_fun_B_0(A!17), A!17)) | (~in(A!17, tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~in(C, A)) | (~in(A, B)))) | ((~in(tptp_fun_B_0(A!17), A!17)) | (~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | (~in(A!17, tptp_fun_C_3(A!17, tptp_fun_B_0(A!17))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[92])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 (((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~in(C, A)) | (~in(A, B)))) | ((~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | (~in(tptp_fun_B_0(A!17), A!17)) | (~in(A!17, tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~in(C, A)) | (~in(A, B)))) | (~in(tptp_fun_B_0(A!17), A!17)) | (~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | (~in(A!17, tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[93, 91])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~in(C, A)) | (~in(A, B)))) | ((~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | (~in(tptp_fun_B_0(A!17), A!17)) | (~in(A!17, tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~in(C, A)) | (~in(A, B)))) | (~in(tptp_fun_B_0(A!17), A!17)) | (~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | (~in(A!17, tptp_fun_C_3(A!17, tptp_fun_B_0(A!17))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 (~in(A!17, tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[96, 90, 77, 75])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 ((~![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!17), B!16)) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!17))) | in(C, B!16)))) | (~(subset(tptp_fun_B_0(A!17), B!16) | (~((~in(tptp_fun_C_3(B!16, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | in(tptp_fun_C_3(B!16, tptp_fun_B_0(A!17)), B!16)))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 (~((~((~subset(tptp_fun_B_0(A!17), B!16)) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!17))) | in(C, B!16)))) | (~(subset(tptp_fun_B_0(A!17), B!16) | (~((~in(tptp_fun_C_3(B!16, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | in(tptp_fun_C_3(B!16, tptp_fun_B_0(A!17)), B!16))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[98, 63])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 (((~((~subset(tptp_fun_B_0(A!17), B!16)) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!17))) | in(C, B!16)))) | (~(subset(tptp_fun_B_0(A!17), B!16) | (~((~in(tptp_fun_C_3(B!16, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | in(tptp_fun_C_3(B!16, tptp_fun_B_0(A!17)), B!16)))))) | ((~subset(tptp_fun_B_0(A!17), B!16)) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!17))) | in(C, B!16)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 ((~subset(tptp_fun_B_0(A!17), B!16)) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!17))) | in(C, B!16))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 ((~![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(A!17, B!16)) | ![C: $i] : ((~in(C, A!17)) | in(C, B!16)))) | (~(subset(A!17, B!16) | (~((~in(tptp_fun_C_3(B!16, A!17), A!17)) | in(tptp_fun_C_3(B!16, A!17), B!16)))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 (~((~((~subset(A!17, B!16)) | ![C: $i] : ((~in(C, A!17)) | in(C, B!16)))) | (~(subset(A!17, B!16) | (~((~in(tptp_fun_C_3(B!16, A!17), A!17)) | in(tptp_fun_C_3(B!16, A!17), B!16))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[102, 63])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 (((~((~subset(A!17, B!16)) | ![C: $i] : ((~in(C, A!17)) | in(C, B!16)))) | (~(subset(A!17, B!16) | (~((~in(tptp_fun_C_3(B!16, A!17), A!17)) | in(tptp_fun_C_3(B!16, A!17), B!16)))))) | ((~subset(A!17, B!16)) | ![C: $i] : ((~in(C, A!17)) | in(C, B!16)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 ((~subset(A!17, B!16)) | ![C: $i] : ((~in(C, A!17)) | in(C, B!16))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 ((~![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(B!16)) | ![B: $i] : ((~in(B, B!16)) | subset(B, B!16)))) | (~(epsilon_transitive(B!16) | (~((~in(tptp_fun_B_0(B!16), B!16)) | subset(tptp_fun_B_0(B!16), B!16)))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 (~((~((~epsilon_transitive(B!16)) | ![B: $i] : ((~in(B, B!16)) | subset(B, B!16)))) | (~(epsilon_transitive(B!16) | (~((~in(tptp_fun_B_0(B!16), B!16)) | subset(tptp_fun_B_0(B!16), B!16))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[106, 42])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (((~((~epsilon_transitive(B!16)) | ![B: $i] : ((~in(B, B!16)) | subset(B, B!16)))) | (~(epsilon_transitive(B!16) | (~((~in(tptp_fun_B_0(B!16), B!16)) | subset(tptp_fun_B_0(B!16), B!16)))))) | ((~epsilon_transitive(B!16)) | ![B: $i] : ((~in(B, B!16)) | subset(B, B!16)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 ((~epsilon_transitive(B!16)) | ![B: $i] : ((~in(B, B!16)) | subset(B, B!16))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 ((~((~in(A!17, B!16)) | ordinal(A!17) | (~ordinal(B!16)))) <=> (~((~in(A!17, B!16)) | ordinal(A!17) | (~ordinal(B!16))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))) <=> (~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : (ordinal(B) => (in(A, B) => ordinal(A)))) <=> (~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(113,axiom,(~![A: $i, B: $i] : (ordinal(B) => (in(A, B) => ordinal(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t23_ordinal1')).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 (~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[114, 111])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 (~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 (~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[116, 111])).
% 0.19/0.42 tff(118,plain,(
% 0.19/0.42 ~((~in(A!17, B!16)) | ordinal(A!17) | (~ordinal(B!16)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[117])).
% 0.19/0.42 tff(119,plain,
% 0.19/0.42 (~((~in(A!17, B!16)) | ordinal(A!17) | (~ordinal(B!16)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[118, 110])).
% 0.19/0.42 tff(120,plain,
% 0.19/0.42 (ordinal(B!16)),
% 0.19/0.42 inference(or_elim,[status(thm)],[119])).
% 0.19/0.42 tff(121,plain,
% 0.19/0.42 (^[A: $i] : refl(((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(122,plain,
% 0.19/0.42 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[121])).
% 0.19/0.42 tff(123,plain,
% 0.19/0.42 (^[A: $i] : rewrite(((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(124,plain,
% 0.19/0.42 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[123])).
% 0.19/0.42 tff(125,plain,
% 0.19/0.42 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(126,plain,
% 0.19/0.42 (^[A: $i] : rewrite((ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(127,plain,
% 0.19/0.42 (![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[126])).
% 0.19/0.42 tff(128,axiom,(![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc1_ordinal1')).
% 0.19/0.42 tff(129,plain,
% 0.19/0.42 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.19/0.42 tff(130,plain,
% 0.19/0.42 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.19/0.42 tff(131,plain,(
% 0.19/0.42 ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[130])).
% 0.19/0.42 tff(132,plain,
% 0.19/0.42 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.19/0.42 tff(133,plain,
% 0.19/0.42 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[132, 122])).
% 0.19/0.42 tff(134,plain,
% 0.19/0.42 (((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(B!16)) | (~((~epsilon_transitive(B!16)) | (~epsilon_connected(B!16)))))) <=> ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(B!16)) | (~((~epsilon_transitive(B!16)) | (~epsilon_connected(B!16)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(B!16)) | (~((~epsilon_transitive(B!16)) | (~epsilon_connected(B!16)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(136,plain,
% 0.19/0.42 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(B!16)) | (~((~epsilon_transitive(B!16)) | (~epsilon_connected(B!16))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.19/0.42 tff(137,plain,
% 0.19/0.42 (~((~epsilon_transitive(B!16)) | (~epsilon_connected(B!16)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[136, 133, 120])).
% 0.19/0.42 tff(138,plain,
% 0.19/0.42 (((~epsilon_transitive(B!16)) | (~epsilon_connected(B!16))) | epsilon_transitive(B!16)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(139,plain,
% 0.19/0.42 (epsilon_transitive(B!16)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.19/0.42 tff(140,plain,
% 0.19/0.42 ((~((~epsilon_transitive(B!16)) | ![B: $i] : ((~in(B, B!16)) | subset(B, B!16)))) | (~epsilon_transitive(B!16)) | ![B: $i] : ((~in(B, B!16)) | subset(B, B!16))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(141,plain,
% 0.19/0.42 ((~((~epsilon_transitive(B!16)) | ![B: $i] : ((~in(B, B!16)) | subset(B, B!16)))) | ![B: $i] : ((~in(B, B!16)) | subset(B, B!16))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.19/0.42 tff(142,plain,
% 0.19/0.42 (![B: $i] : ((~in(B, B!16)) | subset(B, B!16))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[141, 109])).
% 0.19/0.42 tff(143,plain,
% 0.19/0.42 (in(A!17, B!16)),
% 0.19/0.42 inference(or_elim,[status(thm)],[119])).
% 0.19/0.42 tff(144,plain,
% 0.19/0.42 (((~![B: $i] : ((~in(B, B!16)) | subset(B, B!16))) | ((~in(A!17, B!16)) | subset(A!17, B!16))) <=> ((~![B: $i] : ((~in(B, B!16)) | subset(B, B!16))) | (~in(A!17, B!16)) | subset(A!17, B!16))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(145,plain,
% 0.19/0.42 ((~![B: $i] : ((~in(B, B!16)) | subset(B, B!16))) | ((~in(A!17, B!16)) | subset(A!17, B!16))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(146,plain,
% 0.19/0.42 ((~![B: $i] : ((~in(B, B!16)) | subset(B, B!16))) | (~in(A!17, B!16)) | subset(A!17, B!16)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.19/0.42 tff(147,plain,
% 0.19/0.42 (subset(A!17, B!16)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[146, 143, 142])).
% 0.19/0.42 tff(148,plain,
% 0.19/0.42 ((~((~subset(A!17, B!16)) | ![C: $i] : ((~in(C, A!17)) | in(C, B!16)))) | (~subset(A!17, B!16)) | ![C: $i] : ((~in(C, A!17)) | in(C, B!16))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(149,plain,
% 0.19/0.42 ((~((~subset(A!17, B!16)) | ![C: $i] : ((~in(C, A!17)) | in(C, B!16)))) | ![C: $i] : ((~in(C, A!17)) | in(C, B!16))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.19/0.42 tff(150,plain,
% 0.19/0.42 (![C: $i] : ((~in(C, A!17)) | in(C, B!16))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[149, 105])).
% 0.19/0.42 tff(151,plain,
% 0.19/0.42 (((~![C: $i] : ((~in(C, A!17)) | in(C, B!16))) | ((~in(tptp_fun_B_0(A!17), A!17)) | in(tptp_fun_B_0(A!17), B!16))) <=> ((~![C: $i] : ((~in(C, A!17)) | in(C, B!16))) | (~in(tptp_fun_B_0(A!17), A!17)) | in(tptp_fun_B_0(A!17), B!16))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(152,plain,
% 0.19/0.42 ((~![C: $i] : ((~in(C, A!17)) | in(C, B!16))) | ((~in(tptp_fun_B_0(A!17), A!17)) | in(tptp_fun_B_0(A!17), B!16))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(153,plain,
% 0.19/0.42 ((~![C: $i] : ((~in(C, A!17)) | in(C, B!16))) | (~in(tptp_fun_B_0(A!17), A!17)) | in(tptp_fun_B_0(A!17), B!16)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.19/0.42 tff(154,plain,
% 0.19/0.42 (in(tptp_fun_B_0(A!17), B!16)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[153, 150, 77])).
% 0.19/0.42 tff(155,plain,
% 0.19/0.42 (((~![B: $i] : ((~in(B, B!16)) | subset(B, B!16))) | ((~in(tptp_fun_B_0(A!17), B!16)) | subset(tptp_fun_B_0(A!17), B!16))) <=> ((~![B: $i] : ((~in(B, B!16)) | subset(B, B!16))) | (~in(tptp_fun_B_0(A!17), B!16)) | subset(tptp_fun_B_0(A!17), B!16))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(156,plain,
% 0.19/0.42 ((~![B: $i] : ((~in(B, B!16)) | subset(B, B!16))) | ((~in(tptp_fun_B_0(A!17), B!16)) | subset(tptp_fun_B_0(A!17), B!16))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(157,plain,
% 0.19/0.42 ((~![B: $i] : ((~in(B, B!16)) | subset(B, B!16))) | (~in(tptp_fun_B_0(A!17), B!16)) | subset(tptp_fun_B_0(A!17), B!16)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.19/0.42 tff(158,plain,
% 0.19/0.42 (subset(tptp_fun_B_0(A!17), B!16)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[157, 142, 154])).
% 0.19/0.42 tff(159,plain,
% 0.19/0.42 ((~((~subset(tptp_fun_B_0(A!17), B!16)) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!17))) | in(C, B!16)))) | (~subset(tptp_fun_B_0(A!17), B!16)) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!17))) | in(C, B!16))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(160,plain,
% 0.19/0.42 ((~((~subset(tptp_fun_B_0(A!17), B!16)) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!17))) | in(C, B!16)))) | ![C: $i] : ((~in(C, tptp_fun_B_0(A!17))) | in(C, B!16))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.19/0.42 tff(161,plain,
% 0.19/0.42 (![C: $i] : ((~in(C, tptp_fun_B_0(A!17))) | in(C, B!16))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[160, 101])).
% 0.19/0.42 tff(162,plain,
% 0.19/0.42 (((~![C: $i] : ((~in(C, tptp_fun_B_0(A!17))) | in(C, B!16))) | ((~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), B!16))) <=> ((~![C: $i] : ((~in(C, tptp_fun_B_0(A!17))) | in(C, B!16))) | (~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), B!16))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(163,plain,
% 0.19/0.42 ((~![C: $i] : ((~in(C, tptp_fun_B_0(A!17))) | in(C, B!16))) | ((~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), B!16))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(164,plain,
% 0.19/0.42 ((~![C: $i] : ((~in(C, tptp_fun_B_0(A!17))) | in(C, B!16))) | (~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), B!16)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.19/0.42 tff(165,plain,
% 0.19/0.42 (in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), B!16)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[164, 75, 161])).
% 0.19/0.42 tff(166,plain,
% 0.19/0.42 (((~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), A!17)) | (~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), A!17))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(167,plain,
% 0.19/0.42 (~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), A!17)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[166, 73])).
% 0.19/0.42 tff(168,plain,
% 0.19/0.42 (((~![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(B!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16))))) | (~(epsilon_connected(B!16) | (~((~in(tptp_fun_C_1(B!16), B!16)) | (~in(tptp_fun_B_2(B!16), B!16)) | in(tptp_fun_C_1(B!16), tptp_fun_B_2(B!16)) | (tptp_fun_B_2(B!16) = tptp_fun_C_1(B!16)) | in(tptp_fun_B_2(B!16), tptp_fun_C_1(B!16))))))))) <=> ((~![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!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16))))) | (~(epsilon_connected(B!16) | (~((~in(tptp_fun_C_1(B!16), B!16)) | (~in(tptp_fun_B_2(B!16), B!16)) | in(tptp_fun_C_1(B!16), tptp_fun_B_2(B!16)) | (tptp_fun_B_2(B!16) = tptp_fun_C_1(B!16)) | in(tptp_fun_B_2(B!16), tptp_fun_C_1(B!16)))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(169,plain,
% 0.19/0.42 ((~((~((~epsilon_connected(B!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16))))) | (~(epsilon_connected(B!16) | (~(in(tptp_fun_B_2(B!16), tptp_fun_C_1(B!16)) | (tptp_fun_B_2(B!16) = tptp_fun_C_1(B!16)) | in(tptp_fun_C_1(B!16), tptp_fun_B_2(B!16)) | (~in(tptp_fun_B_2(B!16), B!16)) | (~in(tptp_fun_C_1(B!16), B!16)))))))) <=> (~((~((~epsilon_connected(B!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16))))) | (~(epsilon_connected(B!16) | (~((~in(tptp_fun_C_1(B!16), B!16)) | (~in(tptp_fun_B_2(B!16), B!16)) | in(tptp_fun_C_1(B!16), tptp_fun_B_2(B!16)) | (tptp_fun_B_2(B!16) = tptp_fun_C_1(B!16)) | in(tptp_fun_B_2(B!16), tptp_fun_C_1(B!16))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(170,plain,
% 0.19/0.42 (((~![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(B!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16))))) | (~(epsilon_connected(B!16) | (~(in(tptp_fun_B_2(B!16), tptp_fun_C_1(B!16)) | (tptp_fun_B_2(B!16) = tptp_fun_C_1(B!16)) | in(tptp_fun_C_1(B!16), tptp_fun_B_2(B!16)) | (~in(tptp_fun_B_2(B!16), B!16)) | (~in(tptp_fun_C_1(B!16), B!16))))))))) <=> ((~![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!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16))))) | (~(epsilon_connected(B!16) | (~((~in(tptp_fun_C_1(B!16), B!16)) | (~in(tptp_fun_B_2(B!16), B!16)) | in(tptp_fun_C_1(B!16), tptp_fun_B_2(B!16)) | (tptp_fun_B_2(B!16) = tptp_fun_C_1(B!16)) | in(tptp_fun_B_2(B!16), tptp_fun_C_1(B!16)))))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[169])).
% 0.19/0.42 tff(171,plain,
% 0.19/0.42 (((~![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(B!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16))))) | (~(epsilon_connected(B!16) | (~(in(tptp_fun_B_2(B!16), tptp_fun_C_1(B!16)) | (tptp_fun_B_2(B!16) = tptp_fun_C_1(B!16)) | in(tptp_fun_C_1(B!16), tptp_fun_B_2(B!16)) | (~in(tptp_fun_B_2(B!16), B!16)) | (~in(tptp_fun_C_1(B!16), B!16))))))))) <=> ((~![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!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16))))) | (~(epsilon_connected(B!16) | (~((~in(tptp_fun_C_1(B!16), B!16)) | (~in(tptp_fun_B_2(B!16), B!16)) | in(tptp_fun_C_1(B!16), tptp_fun_B_2(B!16)) | (tptp_fun_B_2(B!16) = tptp_fun_C_1(B!16)) | in(tptp_fun_B_2(B!16), tptp_fun_C_1(B!16)))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[170, 168])).
% 0.19/0.42 tff(172,plain,
% 0.19/0.42 ((~![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(B!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16))))) | (~(epsilon_connected(B!16) | (~(in(tptp_fun_B_2(B!16), tptp_fun_C_1(B!16)) | (tptp_fun_B_2(B!16) = tptp_fun_C_1(B!16)) | in(tptp_fun_C_1(B!16), tptp_fun_B_2(B!16)) | (~in(tptp_fun_B_2(B!16), B!16)) | (~in(tptp_fun_C_1(B!16), B!16))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(173,plain,
% 0.19/0.42 ((~![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(B!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16))))) | (~(epsilon_connected(B!16) | (~((~in(tptp_fun_C_1(B!16), B!16)) | (~in(tptp_fun_B_2(B!16), B!16)) | in(tptp_fun_C_1(B!16), tptp_fun_B_2(B!16)) | (tptp_fun_B_2(B!16) = tptp_fun_C_1(B!16)) | in(tptp_fun_B_2(B!16), tptp_fun_C_1(B!16))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.19/0.43 tff(174,plain,
% 0.19/0.43 (~((~((~epsilon_connected(B!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16))))) | (~(epsilon_connected(B!16) | (~((~in(tptp_fun_C_1(B!16), B!16)) | (~in(tptp_fun_B_2(B!16), B!16)) | in(tptp_fun_C_1(B!16), tptp_fun_B_2(B!16)) | (tptp_fun_B_2(B!16) = tptp_fun_C_1(B!16)) | in(tptp_fun_B_2(B!16), tptp_fun_C_1(B!16)))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[173, 16])).
% 0.19/0.43 tff(175,plain,
% 0.19/0.43 (((~((~epsilon_connected(B!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16))))) | (~(epsilon_connected(B!16) | (~((~in(tptp_fun_C_1(B!16), B!16)) | (~in(tptp_fun_B_2(B!16), B!16)) | in(tptp_fun_C_1(B!16), tptp_fun_B_2(B!16)) | (tptp_fun_B_2(B!16) = tptp_fun_C_1(B!16)) | in(tptp_fun_B_2(B!16), tptp_fun_C_1(B!16))))))) | ((~epsilon_connected(B!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(176,plain,
% 0.19/0.43 ((~epsilon_connected(B!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.19/0.43 tff(177,plain,
% 0.19/0.43 (((~epsilon_transitive(B!16)) | (~epsilon_connected(B!16))) | epsilon_connected(B!16)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(178,plain,
% 0.19/0.43 (epsilon_connected(B!16)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[177, 137])).
% 0.19/0.43 tff(179,plain,
% 0.19/0.43 ((~((~epsilon_connected(B!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16))))) | (~epsilon_connected(B!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(180,plain,
% 0.19/0.43 ((~((~epsilon_connected(B!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16))))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.19/0.43 tff(181,plain,
% 0.19/0.43 (![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[180, 176])).
% 0.19/0.43 tff(182,plain,
% 0.19/0.43 (((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16)))) | ((~in(A!17, B!16)) | in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), A!17) | in(A!17, tptp_fun_C_3(A!17, tptp_fun_B_0(A!17))) | (~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), B!16)) | (A!17 = tptp_fun_C_3(A!17, tptp_fun_B_0(A!17))))) <=> ((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16)))) | (~in(A!17, B!16)) | in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), A!17) | in(A!17, tptp_fun_C_3(A!17, tptp_fun_B_0(A!17))) | (~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), B!16)) | (A!17 = tptp_fun_C_3(A!17, tptp_fun_B_0(A!17))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(183,plain,
% 0.19/0.43 ((in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), A!17) | in(A!17, tptp_fun_C_3(A!17, tptp_fun_B_0(A!17))) | (A!17 = tptp_fun_C_3(A!17, tptp_fun_B_0(A!17))) | (~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), B!16)) | (~in(A!17, B!16))) <=> ((~in(A!17, B!16)) | in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), A!17) | in(A!17, tptp_fun_C_3(A!17, tptp_fun_B_0(A!17))) | (~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), B!16)) | (A!17 = tptp_fun_C_3(A!17, tptp_fun_B_0(A!17))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(184,plain,
% 0.19/0.43 (((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16)))) | (in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), A!17) | in(A!17, tptp_fun_C_3(A!17, tptp_fun_B_0(A!17))) | (A!17 = tptp_fun_C_3(A!17, tptp_fun_B_0(A!17))) | (~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), B!16)) | (~in(A!17, B!16)))) <=> ((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16)))) | ((~in(A!17, B!16)) | in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), A!17) | in(A!17, tptp_fun_C_3(A!17, tptp_fun_B_0(A!17))) | (~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), B!16)) | (A!17 = tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[183])).
% 0.19/0.43 tff(185,plain,
% 0.19/0.43 (((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16)))) | (in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), A!17) | in(A!17, tptp_fun_C_3(A!17, tptp_fun_B_0(A!17))) | (A!17 = tptp_fun_C_3(A!17, tptp_fun_B_0(A!17))) | (~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), B!16)) | (~in(A!17, B!16)))) <=> ((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16)))) | (~in(A!17, B!16)) | in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), A!17) | in(A!17, tptp_fun_C_3(A!17, tptp_fun_B_0(A!17))) | (~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), B!16)) | (A!17 = tptp_fun_C_3(A!17, tptp_fun_B_0(A!17))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[184, 182])).
% 0.19/0.43 tff(186,plain,
% 0.19/0.43 ((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16)))) | (in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), A!17) | in(A!17, tptp_fun_C_3(A!17, tptp_fun_B_0(A!17))) | (A!17 = tptp_fun_C_3(A!17, tptp_fun_B_0(A!17))) | (~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), B!16)) | (~in(A!17, B!16)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(187,plain,
% 0.19/0.43 ((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16)))) | (~in(A!17, B!16)) | in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), A!17) | in(A!17, tptp_fun_C_3(A!17, tptp_fun_B_0(A!17))) | (~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), B!16)) | (A!17 = tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.19/0.43 tff(188,plain,
% 0.19/0.43 (in(A!17, tptp_fun_C_3(A!17, tptp_fun_B_0(A!17))) | (~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), B!16)) | (A!17 = tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[187, 143, 181, 167])).
% 0.19/0.43 tff(189,plain,
% 0.19/0.43 (A!17 = tptp_fun_C_3(A!17, tptp_fun_B_0(A!17))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[188, 165, 97])).
% 0.19/0.43 tff(190,plain,
% 0.19/0.43 (in(tptp_fun_B_0(A!17), A!17) <=> in(tptp_fun_B_0(A!17), tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[189])).
% 0.19/0.43 tff(191,plain,
% 0.19/0.43 (in(tptp_fun_B_0(A!17), tptp_fun_C_3(A!17, tptp_fun_B_0(A!17))) <=> in(tptp_fun_B_0(A!17), A!17)),
% 0.19/0.43 inference(symmetry,[status(thm)],[190])).
% 0.19/0.43 tff(192,plain,
% 0.19/0.43 ((~in(tptp_fun_B_0(A!17), tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)))) <=> (~in(tptp_fun_B_0(A!17), A!17))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[191])).
% 0.19/0.43 tff(193,plain,
% 0.19/0.43 (^[A: $i, B: $i] : refl(((~in(B, A)) | (~in(A, B))) <=> ((~in(B, A)) | (~in(A, B))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(194,plain,
% 0.19/0.43 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[193])).
% 0.19/0.43 tff(195,plain,
% 0.19/0.43 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(196,plain,
% 0.19/0.43 (^[A: $i, B: $i] : rewrite((in(A, B) => (~in(B, A))) <=> ((~in(B, A)) | (~in(A, B))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(197,plain,
% 0.19/0.43 (![A: $i, B: $i] : (in(A, B) => (~in(B, A))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[196])).
% 0.19/0.43 tff(198,axiom,(![A: $i, B: $i] : (in(A, B) => (~in(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','antisymmetry_r2_hidden')).
% 0.19/0.43 tff(199,plain,
% 0.19/0.43 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.19/0.43 tff(200,plain,
% 0.19/0.43 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[199, 195])).
% 0.19/0.43 tff(201,plain,(
% 0.19/0.43 ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[200])).
% 0.19/0.43 tff(202,plain,
% 0.19/0.43 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[201, 194])).
% 0.19/0.43 tff(203,plain,
% 0.19/0.43 (((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | (~in(tptp_fun_B_0(A!17), tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)))))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | (~in(tptp_fun_B_0(A!17), tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(204,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | (~in(tptp_fun_B_0(A!17), tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(205,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)), tptp_fun_B_0(A!17))) | (~in(tptp_fun_B_0(A!17), tptp_fun_C_3(A!17, tptp_fun_B_0(A!17))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.19/0.43 tff(206,plain,
% 0.19/0.43 (~in(tptp_fun_B_0(A!17), tptp_fun_C_3(A!17, tptp_fun_B_0(A!17)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[205, 202, 75])).
% 0.19/0.43 tff(207,plain,
% 0.19/0.43 (~in(tptp_fun_B_0(A!17), A!17)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[206, 192])).
% 0.19/0.43 tff(208,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[77, 207])).
% 0.19/0.43 tff(209,plain,((~in(tptp_fun_B_0(A!17), A!17)) | subset(tptp_fun_B_0(A!17), A!17)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(210,plain,
% 0.19/0.43 ((~(epsilon_transitive(A!17) | (~((~in(tptp_fun_B_0(A!17), A!17)) | subset(tptp_fun_B_0(A!17), A!17))))) | epsilon_transitive(A!17) | (~((~in(tptp_fun_B_0(A!17), A!17)) | subset(tptp_fun_B_0(A!17), A!17)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(211,plain,
% 0.19/0.43 ((~(epsilon_transitive(A!17) | (~((~in(tptp_fun_B_0(A!17), A!17)) | subset(tptp_fun_B_0(A!17), A!17))))) | epsilon_transitive(A!17)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[210, 209])).
% 0.19/0.43 tff(212,plain,
% 0.19/0.43 (epsilon_transitive(A!17)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[211, 47])).
% 0.19/0.43 tff(213,plain,
% 0.19/0.43 (^[A: $i] : refl((~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))) <=> (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(214,plain,
% 0.19/0.43 (![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))) <=> ![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[213])).
% 0.19/0.43 tff(215,plain,
% 0.19/0.43 (^[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)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(216,plain,
% 0.19/0.43 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[215])).
% 0.19/0.43 tff(217,plain,
% 0.19/0.43 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(218,axiom,(![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_ordinal1')).
% 0.19/0.43 tff(219,plain,
% 0.19/0.43 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.19/0.43 tff(220,plain,(
% 0.19/0.43 ![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[219])).
% 0.19/0.44 tff(221,plain,
% 0.19/0.44 (![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[220, 216])).
% 0.19/0.44 tff(222,plain,
% 0.19/0.44 (![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[221, 214])).
% 0.19/0.44 tff(223,plain,
% 0.19/0.44 ((~![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))) | (~(((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17))) <=> ordinal(A!17)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(224,plain,
% 0.19/0.44 (~(((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17))) <=> ordinal(A!17))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[223, 222])).
% 0.19/0.44 tff(225,plain,
% 0.19/0.44 (~ordinal(A!17)),
% 0.19/0.44 inference(or_elim,[status(thm)],[119])).
% 0.19/0.44 tff(226,plain,
% 0.19/0.44 ((((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17))) <=> ordinal(A!17)) | ((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17))) | ordinal(A!17)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(227,plain,
% 0.19/0.44 ((((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17))) <=> ordinal(A!17)) | ((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[226, 225])).
% 0.19/0.44 tff(228,plain,
% 0.19/0.44 ((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[227, 224])).
% 0.19/0.44 tff(229,plain,
% 0.19/0.44 ((~((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17)))) | (~epsilon_transitive(A!17)) | (~epsilon_connected(A!17))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(230,plain,
% 0.19/0.44 ((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[229, 228])).
% 0.19/0.44 tff(231,plain,
% 0.19/0.44 (~epsilon_connected(A!17)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[230, 212])).
% 0.19/0.44 tff(232,plain,
% 0.19/0.44 ((~(epsilon_connected(A!17) | (~((~in(tptp_fun_C_1(A!17), A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17)))))) | epsilon_connected(A!17) | (~((~in(tptp_fun_C_1(A!17), A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(233,plain,
% 0.19/0.44 ((~(epsilon_connected(A!17) | (~((~in(tptp_fun_C_1(A!17), A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17)))))) | (~((~in(tptp_fun_C_1(A!17), A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[232, 231])).
% 0.19/0.44 tff(234,plain,
% 0.19/0.44 (~((~in(tptp_fun_C_1(A!17), A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[233, 25])).
% 0.19/0.44 tff(235,plain,
% 0.19/0.44 (((~in(tptp_fun_C_1(A!17), A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17))) | in(tptp_fun_B_2(A!17), A!17)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(236,plain,
% 0.19/0.44 (in(tptp_fun_B_2(A!17), A!17)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[235, 234])).
% 0.19/0.44 tff(237,plain,
% 0.19/0.44 (((~![C: $i] : ((~in(C, A!17)) | in(C, B!16))) | ((~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_B_2(A!17), B!16))) <=> ((~![C: $i] : ((~in(C, A!17)) | in(C, B!16))) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_B_2(A!17), B!16))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(238,plain,
% 0.19/0.44 ((~![C: $i] : ((~in(C, A!17)) | in(C, B!16))) | ((~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_B_2(A!17), B!16))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(239,plain,
% 0.19/0.44 ((~![C: $i] : ((~in(C, A!17)) | in(C, B!16))) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_B_2(A!17), B!16)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.19/0.44 tff(240,plain,
% 0.19/0.44 (in(tptp_fun_B_2(A!17), B!16)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[239, 150, 236])).
% 0.19/0.44 tff(241,plain,
% 0.19/0.44 (((~in(tptp_fun_C_1(A!17), A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17))) | in(tptp_fun_C_1(A!17), A!17)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(242,plain,
% 0.19/0.44 (in(tptp_fun_C_1(A!17), A!17)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[241, 234])).
% 0.19/0.44 tff(243,plain,
% 0.19/0.44 (((~![C: $i] : ((~in(C, A!17)) | in(C, B!16))) | ((~in(tptp_fun_C_1(A!17), A!17)) | in(tptp_fun_C_1(A!17), B!16))) <=> ((~![C: $i] : ((~in(C, A!17)) | in(C, B!16))) | (~in(tptp_fun_C_1(A!17), A!17)) | in(tptp_fun_C_1(A!17), B!16))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(244,plain,
% 0.19/0.44 ((~![C: $i] : ((~in(C, A!17)) | in(C, B!16))) | ((~in(tptp_fun_C_1(A!17), A!17)) | in(tptp_fun_C_1(A!17), B!16))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(245,plain,
% 0.19/0.44 ((~![C: $i] : ((~in(C, A!17)) | in(C, B!16))) | (~in(tptp_fun_C_1(A!17), A!17)) | in(tptp_fun_C_1(A!17), B!16)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.19/0.44 tff(246,plain,
% 0.19/0.44 (in(tptp_fun_C_1(A!17), B!16)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[245, 150, 242])).
% 0.19/0.44 tff(247,plain,
% 0.19/0.44 (((~in(tptp_fun_C_1(A!17), A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17))) | (~in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(248,plain,
% 0.19/0.44 (~in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[247, 234])).
% 0.19/0.44 tff(249,plain,
% 0.19/0.44 (((~in(tptp_fun_C_1(A!17), A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17))) | (~in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(250,plain,
% 0.19/0.44 (~in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[249, 234])).
% 0.19/0.44 tff(251,plain,
% 0.19/0.44 (((~in(tptp_fun_C_1(A!17), A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17))) | (~(tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(252,plain,
% 0.19/0.44 (~(tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[251, 234])).
% 0.19/0.44 tff(253,plain,
% 0.19/0.44 (((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16)))) | ((tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17)) | (~in(tptp_fun_B_2(A!17), B!16)) | (~in(tptp_fun_C_1(A!17), B!16)))) <=> ((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16)))) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17)) | (~in(tptp_fun_B_2(A!17), B!16)) | (~in(tptp_fun_C_1(A!17), B!16)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(254,plain,
% 0.19/0.44 ((in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | (~in(tptp_fun_C_1(A!17), B!16)) | (~in(tptp_fun_B_2(A!17), B!16))) <=> ((tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17)) | (~in(tptp_fun_B_2(A!17), B!16)) | (~in(tptp_fun_C_1(A!17), B!16)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(255,plain,
% 0.19/0.44 (((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16)))) | (in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | (~in(tptp_fun_C_1(A!17), B!16)) | (~in(tptp_fun_B_2(A!17), B!16)))) <=> ((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16)))) | ((tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17)) | (~in(tptp_fun_B_2(A!17), B!16)) | (~in(tptp_fun_C_1(A!17), B!16))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[254])).
% 0.19/0.44 tff(256,plain,
% 0.19/0.44 (((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16)))) | (in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | (~in(tptp_fun_C_1(A!17), B!16)) | (~in(tptp_fun_B_2(A!17), B!16)))) <=> ((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16)))) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17)) | (~in(tptp_fun_B_2(A!17), B!16)) | (~in(tptp_fun_C_1(A!17), B!16)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[255, 253])).
% 0.19/0.44 tff(257,plain,
% 0.19/0.44 ((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16)))) | (in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | (~in(tptp_fun_C_1(A!17), B!16)) | (~in(tptp_fun_B_2(A!17), B!16)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(258,plain,
% 0.19/0.44 ((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, B!16)) | (~in(B, B!16)))) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17)) | (~in(tptp_fun_B_2(A!17), B!16)) | (~in(tptp_fun_C_1(A!17), B!16))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.19/0.44 tff(259,plain,
% 0.19/0.44 ((~in(tptp_fun_B_2(A!17), B!16)) | (~in(tptp_fun_C_1(A!17), B!16))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[258, 181, 252, 250, 248])).
% 0.19/0.44 tff(260,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[259, 246, 240])).
% 0.19/0.44 % SZS output end Proof
% 0.19/0.45 % E exiting
%------------------------------------------------------------------------------