%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU234+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 05:27:20 AM UTC 2025
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU234+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 06:25:18 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(tptp_fun_C_1_type, type, (
% 0.20/0.38 tptp_fun_C_1: $i > $i)).
% 0.20/0.38 tff(tptp_fun_A_16_type, type, (
% 0.20/0.38 tptp_fun_A_16: $i)).
% 0.20/0.38 tff(in_type, type, (
% 0.20/0.38 in: ( $i * $i ) > $o)).
% 0.20/0.38 tff(ordinal_type, type, (
% 0.20/0.38 ordinal: $i > $o)).
% 0.20/0.38 tff(subset_type, type, (
% 0.20/0.38 subset: ( $i * $i ) > $o)).
% 0.20/0.38 tff(tptp_fun_B_2_type, type, (
% 0.20/0.38 tptp_fun_B_2: $i > $i)).
% 0.20/0.38 tff(epsilon_connected_type, type, (
% 0.20/0.38 epsilon_connected: $i > $o)).
% 0.20/0.38 tff(epsilon_transitive_type, type, (
% 0.20/0.38 epsilon_transitive: $i > $o)).
% 0.20/0.38 tff(tptp_fun_B_0_type, type, (
% 0.20/0.38 tptp_fun_B_0: $i > $i)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 (^[A: $i] : refl((~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, 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(B, A)) | (~in(C, 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)))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, 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(B, A)) | (~in(C, 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))))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (^[A: $i] : rewrite((~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, 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(B, A)) | (~in(C, 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)))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, 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(B, A)) | (~in(C, 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))))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, 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(B, A)) | (~in(C, 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))))))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (^[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(B, A)) | (~in(C, 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(B, A)) | (~in(C, 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(B, A)) | (~in(C, 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(B, A)) | (~in(C, 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(B, A)) | (~in(C, 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))))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (![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(B, A)) | (~in(C, 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))))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (![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)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (^[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))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (![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)))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.38 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/sandbox/benchmark/theBenchmark.p','d3_ordinal1')).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.38 tff(14,plain,(
% 0.20/0.38 ![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))))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[13])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, 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))))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, 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))))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, 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!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!16)) | (~in(B, A!16))))) | (~(epsilon_connected(A!16) | (~((~in(tptp_fun_C_1(A!16), A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16))))))))) <=> ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, 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!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!16)) | (~in(B, A!16))))) | (~(epsilon_connected(A!16) | (~((~in(tptp_fun_C_1(A!16), A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)))))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 ((~((~((~epsilon_connected(A!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!16)) | (~in(C, A!16))))) | (~(epsilon_connected(A!16) | (~(in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | (~in(tptp_fun_C_1(A!16), A!16)))))))) <=> (~((~((~epsilon_connected(A!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!16)) | (~in(B, A!16))))) | (~(epsilon_connected(A!16) | (~((~in(tptp_fun_C_1(A!16), A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16))))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 (((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, 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!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!16)) | (~in(C, A!16))))) | (~(epsilon_connected(A!16) | (~(in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | (~in(tptp_fun_C_1(A!16), A!16))))))))) <=> ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, 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!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!16)) | (~in(B, A!16))))) | (~(epsilon_connected(A!16) | (~((~in(tptp_fun_C_1(A!16), A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)))))))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[18])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 (((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, 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!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!16)) | (~in(C, A!16))))) | (~(epsilon_connected(A!16) | (~(in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | (~in(tptp_fun_C_1(A!16), A!16))))))))) <=> ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, 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!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!16)) | (~in(B, A!16))))) | (~(epsilon_connected(A!16) | (~((~in(tptp_fun_C_1(A!16), A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)))))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[19, 17])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, 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!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!16)) | (~in(C, A!16))))) | (~(epsilon_connected(A!16) | (~(in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | (~in(tptp_fun_C_1(A!16), A!16))))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, 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!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!16)) | (~in(B, A!16))))) | (~(epsilon_connected(A!16) | (~((~in(tptp_fun_C_1(A!16), A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 (~((~((~epsilon_connected(A!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!16)) | (~in(B, A!16))))) | (~(epsilon_connected(A!16) | (~((~in(tptp_fun_C_1(A!16), A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)))))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 (((~((~epsilon_connected(A!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!16)) | (~in(B, A!16))))) | (~(epsilon_connected(A!16) | (~((~in(tptp_fun_C_1(A!16), A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16))))))) | (epsilon_connected(A!16) | (~((~in(tptp_fun_C_1(A!16), A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (epsilon_connected(A!16) | (~((~in(tptp_fun_C_1(A!16), A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.20/0.39 tff(26,assumption,((~((~epsilon_transitive(A!16)) | ![B: $i] : ((~in(B, A!16)) | subset(B, A!16)))) | (~(epsilon_transitive(A!16) | (~((~in(tptp_fun_B_0(A!16), A!16)) | subset(tptp_fun_B_0(A!16), A!16)))))), introduced(assumption)).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 (^[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))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (![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)))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 (^[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))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 (![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)))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 (![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)))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[30, 28])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 (^[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)))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 (![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)))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 (![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)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 (^[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))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 (![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)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.39 tff(37,axiom,(![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_ordinal1')).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.20/0.39 tff(40,plain,(
% 0.20/0.39 ![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)))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[39])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (![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)))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 (![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)))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[41, 31])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 ((~![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!16)) | ![B: $i] : ((~in(B, A!16)) | subset(B, A!16)))) | (~(epsilon_transitive(A!16) | (~((~in(tptp_fun_B_0(A!16), A!16)) | subset(tptp_fun_B_0(A!16), A!16)))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[43, 42, 26])).
% 0.20/0.39 tff(45,plain,(~((~((~epsilon_transitive(A!16)) | ![B: $i] : ((~in(B, A!16)) | subset(B, A!16)))) | (~(epsilon_transitive(A!16) | (~((~in(tptp_fun_B_0(A!16), A!16)) | subset(tptp_fun_B_0(A!16), A!16))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 (((~((~epsilon_transitive(A!16)) | ![B: $i] : ((~in(B, A!16)) | subset(B, A!16)))) | (~(epsilon_transitive(A!16) | (~((~in(tptp_fun_B_0(A!16), A!16)) | subset(tptp_fun_B_0(A!16), A!16)))))) | (epsilon_transitive(A!16) | (~((~in(tptp_fun_B_0(A!16), A!16)) | subset(tptp_fun_B_0(A!16), A!16))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 (epsilon_transitive(A!16) | (~((~in(tptp_fun_B_0(A!16), A!16)) | subset(tptp_fun_B_0(A!16), A!16)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.20/0.39 tff(48,assumption,(~((~in(tptp_fun_B_0(A!16), A!16)) | subset(tptp_fun_B_0(A!16), A!16))), introduced(assumption)).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 (((~in(tptp_fun_B_0(A!16), A!16)) | subset(tptp_fun_B_0(A!16), A!16)) | (~subset(tptp_fun_B_0(A!16), A!16))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 (~subset(tptp_fun_B_0(A!16), A!16)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (((~ordinal(tptp_fun_B_0(A!16))) | (~subset(tptp_fun_B_0(A!16), A!16))) | subset(tptp_fun_B_0(A!16), A!16)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 ((~ordinal(tptp_fun_B_0(A!16))) | (~subset(tptp_fun_B_0(A!16), A!16))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 (((~in(tptp_fun_B_0(A!16), A!16)) | subset(tptp_fun_B_0(A!16), A!16)) | in(tptp_fun_B_0(A!16), A!16)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (in(tptp_fun_B_0(A!16), A!16)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[53, 48])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 (^[B: $i] : refl(((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16))))) <=> ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16))))) <=> ![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (^[B: $i] : rewrite(((~in(B, A!16)) | (ordinal(B) & subset(B, A!16))) <=> ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 (![B: $i] : ((~in(B, A!16)) | (ordinal(B) & subset(B, A!16))) <=> ![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 (((~ordinal(A!16)) & ![B: $i] : ((~in(B, A!16)) | (ordinal(B) & subset(B, A!16)))) <=> ((~ordinal(A!16)) & ![B: $i] : ((~in(B, A!16)) | (ordinal(B) & subset(B, A!16))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 ((~![A: $i] : (ordinal(A) | (~![B: $i] : ((~in(B, A)) | (ordinal(B) & subset(B, A)))))) <=> (~![A: $i] : (ordinal(A) | (~![B: $i] : ((~in(B, A)) | (ordinal(B) & subset(B, A))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 ((~![A: $i] : (![B: $i] : (in(B, A) => (ordinal(B) & subset(B, A))) => ordinal(A))) <=> (~![A: $i] : (ordinal(A) | (~![B: $i] : ((~in(B, A)) | (ordinal(B) & subset(B, A))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(62,axiom,(~![A: $i] : (![B: $i] : (in(B, A) => (ordinal(B) & subset(B, A))) => ordinal(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t31_ordinal1')).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 (~![A: $i] : (ordinal(A) | (~![B: $i] : ((~in(B, A)) | (ordinal(B) & subset(B, A)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 (~![A: $i] : (ordinal(A) | (~![B: $i] : ((~in(B, A)) | (ordinal(B) & subset(B, A)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[63, 60])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 (~![A: $i] : (ordinal(A) | (~![B: $i] : ((~in(B, A)) | (ordinal(B) & subset(B, A)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 (~![A: $i] : (ordinal(A) | (~![B: $i] : ((~in(B, A)) | (ordinal(B) & subset(B, A)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[65, 60])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 ((~ordinal(A!16)) & ![B: $i] : ((~in(B, A!16)) | (ordinal(B) & subset(B, A!16)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 (![B: $i] : ((~in(B, A!16)) | (ordinal(B) & subset(B, A!16)))),
% 0.20/0.39 inference(and_elim,[status(thm)],[67])).
% 0.20/0.39 tff(69,plain,
% 0.20/0.39 (![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[68, 58])).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 (![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[69, 56])).
% 0.20/0.39 tff(71,plain,
% 0.20/0.39 (((~![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))) | ((~in(tptp_fun_B_0(A!16), A!16)) | (~((~ordinal(tptp_fun_B_0(A!16))) | (~subset(tptp_fun_B_0(A!16), A!16)))))) <=> ((~![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))) | (~in(tptp_fun_B_0(A!16), A!16)) | (~((~ordinal(tptp_fun_B_0(A!16))) | (~subset(tptp_fun_B_0(A!16), A!16)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 ((~![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))) | ((~in(tptp_fun_B_0(A!16), A!16)) | (~((~ordinal(tptp_fun_B_0(A!16))) | (~subset(tptp_fun_B_0(A!16), A!16)))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(73,plain,
% 0.20/0.39 ((~![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))) | (~in(tptp_fun_B_0(A!16), A!16)) | (~((~ordinal(tptp_fun_B_0(A!16))) | (~subset(tptp_fun_B_0(A!16), A!16))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.39 tff(74,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[73, 70, 54, 52])).
% 0.20/0.39 tff(75,plain,((~in(tptp_fun_B_0(A!16), A!16)) | subset(tptp_fun_B_0(A!16), A!16)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(76,plain,
% 0.20/0.39 ((~(epsilon_transitive(A!16) | (~((~in(tptp_fun_B_0(A!16), A!16)) | subset(tptp_fun_B_0(A!16), A!16))))) | epsilon_transitive(A!16) | (~((~in(tptp_fun_B_0(A!16), A!16)) | subset(tptp_fun_B_0(A!16), A!16)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(77,plain,
% 0.20/0.39 ((~(epsilon_transitive(A!16) | (~((~in(tptp_fun_B_0(A!16), A!16)) | subset(tptp_fun_B_0(A!16), A!16))))) | epsilon_transitive(A!16)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.20/0.39 tff(78,plain,
% 0.20/0.39 (epsilon_transitive(A!16)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[77, 47])).
% 0.20/0.39 tff(79,plain,
% 0.20/0.39 (^[A: $i] : refl((~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))) <=> (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(80,plain,
% 0.20/0.39 (![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))) <=> ![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.39 tff(81,plain,
% 0.20/0.39 (^[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)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(82,plain,
% 0.20/0.39 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.40 tff(83,plain,
% 0.20/0.40 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(84,axiom,(![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_ordinal1')).
% 0.20/0.40 tff(85,plain,
% 0.20/0.40 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.40 tff(86,plain,(
% 0.20/0.40 ![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[85])).
% 0.20/0.40 tff(87,plain,
% 0.20/0.40 (![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.20/0.40 tff(88,plain,
% 0.20/0.40 (![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.20/0.40 tff(89,plain,
% 0.20/0.40 ((~![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))) | (~(((~epsilon_transitive(A!16)) | (~epsilon_connected(A!16))) <=> ordinal(A!16)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(90,plain,
% 0.20/0.40 (~(((~epsilon_transitive(A!16)) | (~epsilon_connected(A!16))) <=> ordinal(A!16))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.20/0.40 tff(91,plain,
% 0.20/0.40 (~ordinal(A!16)),
% 0.20/0.40 inference(and_elim,[status(thm)],[67])).
% 0.20/0.40 tff(92,plain,
% 0.20/0.40 ((((~epsilon_transitive(A!16)) | (~epsilon_connected(A!16))) <=> ordinal(A!16)) | ((~epsilon_transitive(A!16)) | (~epsilon_connected(A!16))) | ordinal(A!16)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(93,plain,
% 0.20/0.40 ((((~epsilon_transitive(A!16)) | (~epsilon_connected(A!16))) <=> ordinal(A!16)) | ((~epsilon_transitive(A!16)) | (~epsilon_connected(A!16)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.20/0.40 tff(94,plain,
% 0.20/0.40 ((~epsilon_transitive(A!16)) | (~epsilon_connected(A!16))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[93, 90])).
% 0.20/0.40 tff(95,plain,
% 0.20/0.40 ((~((~epsilon_transitive(A!16)) | (~epsilon_connected(A!16)))) | (~epsilon_transitive(A!16)) | (~epsilon_connected(A!16))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(96,plain,
% 0.20/0.40 ((~epsilon_transitive(A!16)) | (~epsilon_connected(A!16))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.20/0.40 tff(97,plain,
% 0.20/0.40 (~epsilon_connected(A!16)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[96, 78])).
% 0.20/0.40 tff(98,plain,
% 0.20/0.40 ((~(epsilon_connected(A!16) | (~((~in(tptp_fun_C_1(A!16), A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)))))) | epsilon_connected(A!16) | (~((~in(tptp_fun_C_1(A!16), A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(99,plain,
% 0.20/0.40 ((~(epsilon_connected(A!16) | (~((~in(tptp_fun_C_1(A!16), A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)))))) | (~((~in(tptp_fun_C_1(A!16), A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.20/0.40 tff(100,plain,
% 0.20/0.40 (~((~in(tptp_fun_C_1(A!16), A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[99, 25])).
% 0.20/0.40 tff(101,plain,
% 0.20/0.40 (((~in(tptp_fun_C_1(A!16), A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16))) | in(tptp_fun_C_1(A!16), A!16)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(102,plain,
% 0.20/0.40 (in(tptp_fun_C_1(A!16), A!16)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.20/0.40 tff(103,plain,
% 0.20/0.40 (((~![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))) | ((~in(tptp_fun_C_1(A!16), A!16)) | (~((~ordinal(tptp_fun_C_1(A!16))) | (~subset(tptp_fun_C_1(A!16), A!16)))))) <=> ((~![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))) | (~in(tptp_fun_C_1(A!16), A!16)) | (~((~ordinal(tptp_fun_C_1(A!16))) | (~subset(tptp_fun_C_1(A!16), A!16)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(104,plain,
% 0.20/0.40 ((~![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))) | ((~in(tptp_fun_C_1(A!16), A!16)) | (~((~ordinal(tptp_fun_C_1(A!16))) | (~subset(tptp_fun_C_1(A!16), A!16)))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(105,plain,
% 0.20/0.40 ((~![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))) | (~in(tptp_fun_C_1(A!16), A!16)) | (~((~ordinal(tptp_fun_C_1(A!16))) | (~subset(tptp_fun_C_1(A!16), A!16))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.40 tff(106,plain,
% 0.20/0.40 (~((~ordinal(tptp_fun_C_1(A!16))) | (~subset(tptp_fun_C_1(A!16), A!16)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[105, 70, 102])).
% 0.20/0.40 tff(107,plain,
% 0.20/0.40 (((~ordinal(tptp_fun_C_1(A!16))) | (~subset(tptp_fun_C_1(A!16), A!16))) | ordinal(tptp_fun_C_1(A!16))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(108,plain,
% 0.20/0.40 (ordinal(tptp_fun_C_1(A!16))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.20/0.40 tff(109,plain,
% 0.20/0.40 (^[A: $i] : refl(((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(110,plain,
% 0.20/0.40 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[109])).
% 0.20/0.40 tff(111,plain,
% 0.20/0.40 (^[A: $i] : rewrite(((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(112,plain,
% 0.20/0.40 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[111])).
% 0.20/0.40 tff(113,plain,
% 0.20/0.40 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[112, 110])).
% 0.20/0.40 tff(114,plain,
% 0.20/0.40 (^[A: $i] : rewrite(((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(115,plain,
% 0.20/0.40 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[114])).
% 0.20/0.40 tff(116,plain,
% 0.20/0.40 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(117,plain,
% 0.20/0.40 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))) <=> (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))), ((ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))) <=> (ordinal(B) => (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))), rewrite((ordinal(B) => (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))) <=> ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))), ((ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))) <=> ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))))), (![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))) <=> ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))), ((ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))))) <=> (ordinal(A) => ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))))), rewrite((ordinal(A) => ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))), ((ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))))) <=> ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(118,plain,
% 0.20/0.40 (![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[117])).
% 0.20/0.40 tff(119,axiom,(![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t24_ordinal1')).
% 0.20/0.40 tff(120,plain,
% 0.20/0.40 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.40 tff(121,plain,
% 0.20/0.40 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.20/0.40 tff(122,plain,(
% 0.20/0.40 ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[121])).
% 0.20/0.40 tff(123,plain,
% 0.20/0.40 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[122, 115])).
% 0.20/0.40 tff(124,plain,
% 0.20/0.40 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[123, 113])).
% 0.20/0.40 tff(125,plain,
% 0.20/0.40 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(A!16))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B)))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_1(A!16))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(126,plain,
% 0.20/0.40 (((~ordinal(tptp_fun_C_1(A!16))) | ![B: $i] : (in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B) | (~ordinal(B)))) <=> ((~ordinal(tptp_fun_C_1(A!16))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(127,plain,
% 0.20/0.40 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(A!16))) | ![B: $i] : (in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(A!16))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[126])).
% 0.20/0.40 tff(128,plain,
% 0.20/0.40 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(A!16))) | ![B: $i] : (in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_1(A!16))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B)))),
% 0.20/0.40 inference(transitivity,[status(thm)],[127, 125])).
% 0.20/0.40 tff(129,plain,
% 0.20/0.40 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(A!16))) | ![B: $i] : (in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B) | (~ordinal(B))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(130,plain,
% 0.20/0.40 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_1(A!16))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.20/0.40 tff(131,plain,
% 0.20/0.40 (![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[130, 124, 108])).
% 0.20/0.40 tff(132,plain,
% 0.20/0.40 (((~in(tptp_fun_C_1(A!16), A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16))) | in(tptp_fun_B_2(A!16), A!16)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(133,plain,
% 0.20/0.40 (in(tptp_fun_B_2(A!16), A!16)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[132, 100])).
% 0.20/0.40 tff(134,plain,
% 0.20/0.40 (((~![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))) | ((~in(tptp_fun_B_2(A!16), A!16)) | (~((~ordinal(tptp_fun_B_2(A!16))) | (~subset(tptp_fun_B_2(A!16), A!16)))))) <=> ((~![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))) | (~in(tptp_fun_B_2(A!16), A!16)) | (~((~ordinal(tptp_fun_B_2(A!16))) | (~subset(tptp_fun_B_2(A!16), A!16)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(135,plain,
% 0.20/0.40 ((~![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))) | ((~in(tptp_fun_B_2(A!16), A!16)) | (~((~ordinal(tptp_fun_B_2(A!16))) | (~subset(tptp_fun_B_2(A!16), A!16)))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(136,plain,
% 0.20/0.40 ((~![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))) | (~in(tptp_fun_B_2(A!16), A!16)) | (~((~ordinal(tptp_fun_B_2(A!16))) | (~subset(tptp_fun_B_2(A!16), A!16))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.20/0.40 tff(137,plain,
% 0.20/0.40 (~((~ordinal(tptp_fun_B_2(A!16))) | (~subset(tptp_fun_B_2(A!16), A!16)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[136, 70, 133])).
% 0.20/0.40 tff(138,plain,
% 0.20/0.40 (((~ordinal(tptp_fun_B_2(A!16))) | (~subset(tptp_fun_B_2(A!16), A!16))) | ordinal(tptp_fun_B_2(A!16))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(139,plain,
% 0.20/0.40 (ordinal(tptp_fun_B_2(A!16))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.20/0.40 tff(140,plain,
% 0.20/0.40 ((tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16)) <=> (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16))),
% 0.20/0.40 inference(commutativity,[status(thm)],[])).
% 0.20/0.40 tff(141,plain,
% 0.20/0.40 ((tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) <=> (tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16))),
% 0.20/0.40 inference(symmetry,[status(thm)],[140])).
% 0.20/0.40 tff(142,plain,
% 0.20/0.40 ((~(tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16))) <=> (~(tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[141])).
% 0.20/0.40 tff(143,plain,
% 0.20/0.40 (((~in(tptp_fun_C_1(A!16), A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16))) | (~(tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(144,plain,
% 0.20/0.40 (~(tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[143, 100])).
% 0.20/0.40 tff(145,plain,
% 0.20/0.40 (~(tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[144, 142])).
% 0.20/0.40 tff(146,plain,
% 0.20/0.40 (((~in(tptp_fun_C_1(A!16), A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16))) | (~in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(147,plain,
% 0.20/0.41 (~in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[146, 100])).
% 0.20/0.41 tff(148,plain,
% 0.20/0.41 (((~in(tptp_fun_C_1(A!16), A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16))) | (~in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(149,plain,
% 0.20/0.41 (~in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[148, 100])).
% 0.20/0.41 tff(150,plain,
% 0.20/0.41 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B))) | (in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16)) | (~ordinal(tptp_fun_B_2(A!16))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B))) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16)) | (~ordinal(tptp_fun_B_2(A!16))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(151,plain,
% 0.20/0.41 (((~ordinal(tptp_fun_B_2(A!16))) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | (tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16))) <=> (in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16)) | (~ordinal(tptp_fun_B_2(A!16))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(152,plain,
% 0.20/0.41 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B))) | ((~ordinal(tptp_fun_B_2(A!16))) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | (tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16)))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B))) | (in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16)) | (~ordinal(tptp_fun_B_2(A!16)))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[151])).
% 0.20/0.41 tff(153,plain,
% 0.20/0.41 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B))) | ((~ordinal(tptp_fun_B_2(A!16))) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | (tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16)))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B))) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16)) | (~ordinal(tptp_fun_B_2(A!16))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[152, 150])).
% 0.20/0.41 tff(154,plain,
% 0.20/0.41 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B))) | ((~ordinal(tptp_fun_B_2(A!16))) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | (tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(155,plain,
% 0.20/0.41 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B))) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16)) | (~ordinal(tptp_fun_B_2(A!16)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.20/0.41 tff(156,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[155, 149, 147, 145, 139, 131])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------