%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU234+3 : TPTP v9.0.0. Released v3.2.0.
% 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 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU234+3 : TPTP v9.0.0. Released v3.2.0.
% 0.11/0.12 % 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 06:25:03 EDT 2025
% 0.18/0.33 % CPUTime :
% 0.18/0.38 % SZS status Theorem
% 0.18/0.38 % SZS output start Proof
% 0.18/0.38 tff(subset_type, type, (
% 0.18/0.38 subset: ( $i * $i ) > $o)).
% 0.18/0.38 tff(tptp_fun_A_17_type, type, (
% 0.18/0.38 tptp_fun_A_17: $i)).
% 0.18/0.38 tff(tptp_fun_B_0_type, type, (
% 0.18/0.38 tptp_fun_B_0: $i > $i)).
% 0.18/0.38 tff(ordinal_type, type, (
% 0.18/0.38 ordinal: $i > $o)).
% 0.18/0.38 tff(in_type, type, (
% 0.18/0.38 in: ( $i * $i ) > $o)).
% 0.18/0.38 tff(epsilon_transitive_type, type, (
% 0.18/0.38 epsilon_transitive: $i > $o)).
% 0.18/0.38 tff(epsilon_connected_type, type, (
% 0.18/0.38 epsilon_connected: $i > $o)).
% 0.18/0.38 tff(tptp_fun_C_1_type, type, (
% 0.18/0.38 tptp_fun_C_1: $i > $i)).
% 0.18/0.38 tff(tptp_fun_B_2_type, type, (
% 0.18/0.38 tptp_fun_B_2: $i > $i)).
% 0.18/0.38 tff(1,plain,
% 0.18/0.38 (^[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))))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(2,plain,
% 0.18/0.38 (![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)))))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.38 tff(3,plain,
% 0.18/0.38 (^[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))))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(4,plain,
% 0.18/0.38 (![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)))))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.39 tff(5,plain,
% 0.18/0.39 (![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)))))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[4, 2])).
% 0.18/0.39 tff(6,plain,
% 0.18/0.39 (^[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)))))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(7,plain,
% 0.18/0.39 (![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)))))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.18/0.39 tff(8,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(9,plain,
% 0.18/0.39 (^[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))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(10,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[9])).
% 0.18/0.39 tff(11,axiom,(![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_ordinal1')).
% 0.18/0.39 tff(12,plain,
% 0.18/0.39 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.18/0.39 tff(13,plain,
% 0.18/0.39 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.18/0.39 tff(14,plain,(
% 0.18/0.39 ![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)))))),
% 0.18/0.39 inference(skolemize,[status(sab)],[13])).
% 0.18/0.39 tff(15,plain,
% 0.18/0.39 (![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)))))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.18/0.39 tff(16,plain,
% 0.18/0.39 (![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)))))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.18/0.39 tff(17,plain,
% 0.18/0.39 ((~![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!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)))))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(18,plain,
% 0.18/0.39 (~((~((~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))))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.18/0.39 tff(19,plain,
% 0.18/0.39 (((~((~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))))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(20,plain,
% 0.18/0.39 (epsilon_transitive(A!17) | (~((~in(tptp_fun_B_0(A!17), A!17)) | subset(tptp_fun_B_0(A!17), A!17)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.18/0.39 tff(21,assumption,((~((~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)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | (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))))))), introduced(assumption)).
% 0.18/0.39 tff(22,plain,
% 0.18/0.39 (^[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)))))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(23,plain,
% 0.18/0.39 (![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)))))))) <=> ![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))))))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.18/0.39 tff(24,plain,
% 0.18/0.39 (^[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)))))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(25,plain,
% 0.18/0.39 (![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)))))))) <=> ![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))))))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.18/0.39 tff(26,plain,
% 0.18/0.39 (![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)))))))) <=> ![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))))))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[25, 23])).
% 0.18/0.39 tff(27,plain,
% 0.18/0.39 (^[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(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))))))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(28,plain,
% 0.18/0.39 (![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(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))))))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.18/0.39 tff(29,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(30,plain,
% 0.18/0.39 (^[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))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(31,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[30])).
% 0.18/0.39 tff(32,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')).
% 0.18/0.39 tff(33,plain,
% 0.18/0.39 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.18/0.39 tff(34,plain,
% 0.18/0.39 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.18/0.39 tff(35,plain,(
% 0.18/0.39 ![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))))))),
% 0.18/0.39 inference(skolemize,[status(sab)],[34])).
% 0.18/0.39 tff(36,plain,
% 0.18/0.39 (![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))))))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.18/0.39 tff(37,plain,
% 0.18/0.39 (![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))))))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[36, 26])).
% 0.18/0.39 tff(38,plain,
% 0.18/0.39 (((~![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!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)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | (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))))))))) <=> ((~![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!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)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | (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)))))))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(39,plain,
% 0.18/0.39 ((~((~((~epsilon_connected(A!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!17)) | (~in(C, 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)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | (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))))))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(40,plain,
% 0.18/0.39 (((~![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!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!17)) | (~in(C, 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(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!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)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | (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)))))))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[39])).
% 0.18/0.40 tff(41,plain,
% 0.18/0.40 (((~![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!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!17)) | (~in(C, 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(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!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)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | (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)))))))))),
% 0.18/0.40 inference(transitivity,[status(thm)],[40, 38])).
% 0.18/0.40 tff(42,plain,
% 0.18/0.40 ((~![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!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!17)) | (~in(C, 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))))))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(43,plain,
% 0.18/0.40 ((~![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!17)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!17)) | (~in(B, A!17))))) | (~(epsilon_connected(A!17) | (~((~in(tptp_fun_C_1(A!17), A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17))))))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.18/0.40 tff(44,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[43, 37, 21])).
% 0.18/0.40 tff(45,plain,(~((~((~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)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | (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)))))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(46,plain,
% 0.18/0.40 (((~((~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)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | (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))))))) | (epsilon_connected(A!17) | (~((~in(tptp_fun_C_1(A!17), A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | (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)))))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(47,plain,
% 0.18/0.40 (epsilon_connected(A!17) | (~((~in(tptp_fun_C_1(A!17), A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | (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))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.18/0.40 tff(48,assumption,(~((~in(tptp_fun_C_1(A!17), A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | (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)))), introduced(assumption)).
% 0.18/0.40 tff(49,plain,
% 0.18/0.40 (((~in(tptp_fun_C_1(A!17), A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | (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))) | in(tptp_fun_C_1(A!17), A!17)),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(50,plain,
% 0.18/0.40 (in(tptp_fun_C_1(A!17), A!17)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.18/0.40 tff(51,plain,
% 0.18/0.40 (^[B: $i] : refl(((~in(B, A!17)) | (~((~ordinal(B)) | (~subset(B, A!17))))) <=> ((~in(B, A!17)) | (~((~ordinal(B)) | (~subset(B, A!17))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(52,plain,
% 0.18/0.40 (![B: $i] : ((~in(B, A!17)) | (~((~ordinal(B)) | (~subset(B, A!17))))) <=> ![B: $i] : ((~in(B, A!17)) | (~((~ordinal(B)) | (~subset(B, A!17)))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[51])).
% 0.18/0.40 tff(53,plain,
% 0.18/0.40 (^[B: $i] : rewrite(((~in(B, A!17)) | (ordinal(B) & subset(B, A!17))) <=> ((~in(B, A!17)) | (~((~ordinal(B)) | (~subset(B, A!17))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(54,plain,
% 0.18/0.40 (![B: $i] : ((~in(B, A!17)) | (ordinal(B) & subset(B, A!17))) <=> ![B: $i] : ((~in(B, A!17)) | (~((~ordinal(B)) | (~subset(B, A!17)))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[53])).
% 0.18/0.40 tff(55,plain,
% 0.18/0.40 (((~ordinal(A!17)) & ![B: $i] : ((~in(B, A!17)) | (ordinal(B) & subset(B, A!17)))) <=> ((~ordinal(A!17)) & ![B: $i] : ((~in(B, A!17)) | (ordinal(B) & subset(B, A!17))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(56,plain,
% 0.18/0.40 ((~![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))))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(57,plain,
% 0.18/0.40 ((~![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))))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(58,axiom,(~![A: $i] : (![B: $i] : (in(B, A) => (ordinal(B) & subset(B, A))) => ordinal(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t31_ordinal1')).
% 0.18/0.40 tff(59,plain,
% 0.18/0.40 (~![A: $i] : (ordinal(A) | (~![B: $i] : ((~in(B, A)) | (ordinal(B) & subset(B, A)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.18/0.40 tff(60,plain,
% 0.18/0.40 (~![A: $i] : (ordinal(A) | (~![B: $i] : ((~in(B, A)) | (ordinal(B) & subset(B, A)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[59, 56])).
% 0.18/0.40 tff(61,plain,
% 0.18/0.40 (~![A: $i] : (ordinal(A) | (~![B: $i] : ((~in(B, A)) | (ordinal(B) & subset(B, A)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.18/0.40 tff(62,plain,
% 0.18/0.40 (~![A: $i] : (ordinal(A) | (~![B: $i] : ((~in(B, A)) | (ordinal(B) & subset(B, A)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[61, 56])).
% 0.18/0.40 tff(63,plain,
% 0.18/0.40 ((~ordinal(A!17)) & ![B: $i] : ((~in(B, A!17)) | (ordinal(B) & subset(B, A!17)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.18/0.40 tff(64,plain,
% 0.18/0.40 (![B: $i] : ((~in(B, A!17)) | (ordinal(B) & subset(B, A!17)))),
% 0.18/0.40 inference(and_elim,[status(thm)],[63])).
% 0.18/0.40 tff(65,plain,
% 0.18/0.40 (![B: $i] : ((~in(B, A!17)) | (~((~ordinal(B)) | (~subset(B, A!17)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[64, 54])).
% 0.18/0.40 tff(66,plain,
% 0.18/0.40 (![B: $i] : ((~in(B, A!17)) | (~((~ordinal(B)) | (~subset(B, A!17)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[65, 52])).
% 0.18/0.40 tff(67,plain,
% 0.18/0.40 (((~![B: $i] : ((~in(B, A!17)) | (~((~ordinal(B)) | (~subset(B, A!17)))))) | ((~in(tptp_fun_C_1(A!17), A!17)) | (~((~ordinal(tptp_fun_C_1(A!17))) | (~subset(tptp_fun_C_1(A!17), A!17)))))) <=> ((~![B: $i] : ((~in(B, A!17)) | (~((~ordinal(B)) | (~subset(B, A!17)))))) | (~in(tptp_fun_C_1(A!17), A!17)) | (~((~ordinal(tptp_fun_C_1(A!17))) | (~subset(tptp_fun_C_1(A!17), A!17)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(68,plain,
% 0.18/0.40 ((~![B: $i] : ((~in(B, A!17)) | (~((~ordinal(B)) | (~subset(B, A!17)))))) | ((~in(tptp_fun_C_1(A!17), A!17)) | (~((~ordinal(tptp_fun_C_1(A!17))) | (~subset(tptp_fun_C_1(A!17), A!17)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(69,plain,
% 0.18/0.40 ((~![B: $i] : ((~in(B, A!17)) | (~((~ordinal(B)) | (~subset(B, A!17)))))) | (~in(tptp_fun_C_1(A!17), A!17)) | (~((~ordinal(tptp_fun_C_1(A!17))) | (~subset(tptp_fun_C_1(A!17), A!17))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.18/0.40 tff(70,plain,
% 0.18/0.40 (~((~ordinal(tptp_fun_C_1(A!17))) | (~subset(tptp_fun_C_1(A!17), A!17)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[69, 66, 50])).
% 0.18/0.40 tff(71,plain,
% 0.18/0.40 (((~ordinal(tptp_fun_C_1(A!17))) | (~subset(tptp_fun_C_1(A!17), A!17))) | ordinal(tptp_fun_C_1(A!17))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(72,plain,
% 0.18/0.40 (ordinal(tptp_fun_C_1(A!17))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.18/0.40 tff(73,plain,
% 0.18/0.40 (^[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)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(74,plain,
% 0.18/0.40 (![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))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[73])).
% 0.18/0.40 tff(75,plain,
% 0.18/0.40 (^[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)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(76,plain,
% 0.18/0.40 (![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))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[75])).
% 0.18/0.40 tff(77,plain,
% 0.18/0.40 (![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))))),
% 0.18/0.40 inference(transitivity,[status(thm)],[76, 74])).
% 0.18/0.40 tff(78,plain,
% 0.18/0.40 (^[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)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(79,plain,
% 0.18/0.40 (![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))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[78])).
% 0.18/0.40 tff(80,plain,
% 0.18/0.40 (![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))))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(81,plain,
% 0.18/0.40 (^[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))))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(82,plain,
% 0.18/0.40 (![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))))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[81])).
% 0.18/0.40 tff(83,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')).
% 0.18/0.40 tff(84,plain,
% 0.18/0.40 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.18/0.40 tff(85,plain,
% 0.18/0.40 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.18/0.40 tff(86,plain,(
% 0.18/0.40 ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[85])).
% 0.18/0.40 tff(87,plain,
% 0.18/0.40 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.18/0.40 tff(88,plain,
% 0.18/0.40 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[87, 77])).
% 0.18/0.40 tff(89,plain,
% 0.18/0.40 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(A!17))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), B) | (tptp_fun_C_1(A!17) = B)))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_1(A!17))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), B) | (tptp_fun_C_1(A!17) = B)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(90,plain,
% 0.18/0.40 (((~ordinal(tptp_fun_C_1(A!17))) | ![B: $i] : (in(B, tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), B) | (tptp_fun_C_1(A!17) = B) | (~ordinal(B)))) <=> ((~ordinal(tptp_fun_C_1(A!17))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), B) | (tptp_fun_C_1(A!17) = B)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(91,plain,
% 0.18/0.40 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(A!17))) | ![B: $i] : (in(B, tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), B) | (tptp_fun_C_1(A!17) = 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!17))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), B) | (tptp_fun_C_1(A!17) = B))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[90])).
% 0.18/0.41 tff(92,plain,
% 0.18/0.41 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(A!17))) | ![B: $i] : (in(B, tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), B) | (tptp_fun_C_1(A!17) = 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!17))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), B) | (tptp_fun_C_1(A!17) = B)))),
% 0.18/0.41 inference(transitivity,[status(thm)],[91, 89])).
% 0.18/0.41 tff(93,plain,
% 0.18/0.41 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(A!17))) | ![B: $i] : (in(B, tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), B) | (tptp_fun_C_1(A!17) = B) | (~ordinal(B))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(94,plain,
% 0.18/0.41 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_1(A!17))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), B) | (tptp_fun_C_1(A!17) = B))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.18/0.41 tff(95,plain,
% 0.18/0.41 (![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), B) | (tptp_fun_C_1(A!17) = B))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[94, 88, 72])).
% 0.18/0.41 tff(96,plain,
% 0.18/0.41 (((~in(tptp_fun_C_1(A!17), A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | (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))) | in(tptp_fun_B_2(A!17), A!17)),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(97,plain,
% 0.18/0.41 (in(tptp_fun_B_2(A!17), A!17)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[96, 48])).
% 0.18/0.41 tff(98,plain,
% 0.18/0.41 (((~![B: $i] : ((~in(B, A!17)) | (~((~ordinal(B)) | (~subset(B, A!17)))))) | ((~in(tptp_fun_B_2(A!17), A!17)) | (~((~ordinal(tptp_fun_B_2(A!17))) | (~subset(tptp_fun_B_2(A!17), A!17)))))) <=> ((~![B: $i] : ((~in(B, A!17)) | (~((~ordinal(B)) | (~subset(B, A!17)))))) | (~in(tptp_fun_B_2(A!17), A!17)) | (~((~ordinal(tptp_fun_B_2(A!17))) | (~subset(tptp_fun_B_2(A!17), A!17)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(99,plain,
% 0.18/0.41 ((~![B: $i] : ((~in(B, A!17)) | (~((~ordinal(B)) | (~subset(B, A!17)))))) | ((~in(tptp_fun_B_2(A!17), A!17)) | (~((~ordinal(tptp_fun_B_2(A!17))) | (~subset(tptp_fun_B_2(A!17), A!17)))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(100,plain,
% 0.18/0.41 ((~![B: $i] : ((~in(B, A!17)) | (~((~ordinal(B)) | (~subset(B, A!17)))))) | (~in(tptp_fun_B_2(A!17), A!17)) | (~((~ordinal(tptp_fun_B_2(A!17))) | (~subset(tptp_fun_B_2(A!17), A!17))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.18/0.41 tff(101,plain,
% 0.18/0.41 (~((~ordinal(tptp_fun_B_2(A!17))) | (~subset(tptp_fun_B_2(A!17), A!17)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[100, 66, 97])).
% 0.18/0.41 tff(102,plain,
% 0.18/0.41 (((~ordinal(tptp_fun_B_2(A!17))) | (~subset(tptp_fun_B_2(A!17), A!17))) | ordinal(tptp_fun_B_2(A!17))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(103,plain,
% 0.18/0.41 (ordinal(tptp_fun_B_2(A!17))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.18/0.41 tff(104,plain,
% 0.18/0.41 ((tptp_fun_C_1(A!17) = tptp_fun_B_2(A!17)) <=> (tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17))),
% 0.18/0.41 inference(commutativity,[status(thm)],[])).
% 0.18/0.41 tff(105,plain,
% 0.18/0.41 ((tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)) <=> (tptp_fun_C_1(A!17) = tptp_fun_B_2(A!17))),
% 0.18/0.41 inference(symmetry,[status(thm)],[104])).
% 0.18/0.41 tff(106,plain,
% 0.18/0.41 ((~(tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17))) <=> (~(tptp_fun_C_1(A!17) = tptp_fun_B_2(A!17)))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[105])).
% 0.18/0.41 tff(107,plain,
% 0.18/0.41 (((~in(tptp_fun_C_1(A!17), A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | (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))) | (~(tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17)))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(108,plain,
% 0.18/0.41 (~(tptp_fun_B_2(A!17) = tptp_fun_C_1(A!17))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[107, 48])).
% 0.18/0.41 tff(109,plain,
% 0.18/0.41 (~(tptp_fun_C_1(A!17) = tptp_fun_B_2(A!17))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[108, 106])).
% 0.18/0.41 tff(110,plain,
% 0.18/0.41 (((~in(tptp_fun_C_1(A!17), A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | (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))) | (~in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17)))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(111,plain,
% 0.18/0.41 (~in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[110, 48])).
% 0.18/0.41 tff(112,plain,
% 0.18/0.41 (((~in(tptp_fun_C_1(A!17), A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | (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))) | (~in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(113,plain,
% 0.18/0.41 (~in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[112, 48])).
% 0.18/0.41 tff(114,plain,
% 0.18/0.41 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), B) | (tptp_fun_C_1(A!17) = B))) | (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_C_1(A!17) = tptp_fun_B_2(A!17)) | (~ordinal(tptp_fun_B_2(A!17))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), B) | (tptp_fun_C_1(A!17) = B))) | 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_C_1(A!17) = tptp_fun_B_2(A!17)) | (~ordinal(tptp_fun_B_2(A!17))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(115,plain,
% 0.18/0.41 (((~ordinal(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)) | (tptp_fun_C_1(A!17) = tptp_fun_B_2(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_C_1(A!17) = tptp_fun_B_2(A!17)) | (~ordinal(tptp_fun_B_2(A!17))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(116,plain,
% 0.18/0.41 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), B) | (tptp_fun_C_1(A!17) = B))) | ((~ordinal(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)) | (tptp_fun_C_1(A!17) = tptp_fun_B_2(A!17)))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), B) | (tptp_fun_C_1(A!17) = B))) | (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_C_1(A!17) = tptp_fun_B_2(A!17)) | (~ordinal(tptp_fun_B_2(A!17)))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[115])).
% 0.18/0.41 tff(117,plain,
% 0.18/0.41 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), B) | (tptp_fun_C_1(A!17) = B))) | ((~ordinal(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)) | (tptp_fun_C_1(A!17) = tptp_fun_B_2(A!17)))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), B) | (tptp_fun_C_1(A!17) = B))) | 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_C_1(A!17) = tptp_fun_B_2(A!17)) | (~ordinal(tptp_fun_B_2(A!17))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[116, 114])).
% 0.18/0.41 tff(118,plain,
% 0.18/0.41 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), B) | (tptp_fun_C_1(A!17) = B))) | ((~ordinal(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)) | (tptp_fun_C_1(A!17) = tptp_fun_B_2(A!17)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(119,plain,
% 0.18/0.41 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!17)) | in(tptp_fun_C_1(A!17), B) | (tptp_fun_C_1(A!17) = B))) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | in(tptp_fun_B_2(A!17), tptp_fun_C_1(A!17)) | (tptp_fun_C_1(A!17) = tptp_fun_B_2(A!17)) | (~ordinal(tptp_fun_B_2(A!17)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.18/0.41 tff(120,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[119, 113, 111, 109, 103, 95])).
% 0.18/0.41 tff(121,plain,((~in(tptp_fun_C_1(A!17), A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | (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))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.41 tff(122,plain,
% 0.18/0.41 ((~(epsilon_connected(A!17) | (~((~in(tptp_fun_C_1(A!17), A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | (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)))))) | epsilon_connected(A!17) | (~((~in(tptp_fun_C_1(A!17), A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | (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))))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(123,plain,
% 0.18/0.41 ((~(epsilon_connected(A!17) | (~((~in(tptp_fun_C_1(A!17), A!17)) | (~in(tptp_fun_B_2(A!17), A!17)) | in(tptp_fun_C_1(A!17), tptp_fun_B_2(A!17)) | (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)))))) | epsilon_connected(A!17)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.18/0.41 tff(124,plain,
% 0.18/0.41 (epsilon_connected(A!17)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[123, 47])).
% 0.18/0.41 tff(125,plain,
% 0.18/0.41 (^[A: $i] : refl((~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))) <=> (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(126,plain,
% 0.18/0.41 (![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))) <=> ![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[125])).
% 0.18/0.41 tff(127,plain,
% 0.18/0.41 (^[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)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(128,plain,
% 0.18/0.41 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[127])).
% 0.18/0.41 tff(129,plain,
% 0.18/0.41 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(130,axiom,(![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_ordinal1')).
% 0.18/0.41 tff(131,plain,
% 0.18/0.41 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.18/0.41 tff(132,plain,(
% 0.18/0.41 ![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.18/0.41 inference(skolemize,[status(sab)],[131])).
% 0.18/0.41 tff(133,plain,
% 0.18/0.41 (![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.18/0.41 tff(134,plain,
% 0.18/0.41 (![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.18/0.41 tff(135,plain,
% 0.18/0.41 ((~![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))) | (~(((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17))) <=> ordinal(A!17)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(136,plain,
% 0.18/0.41 (~(((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17))) <=> ordinal(A!17))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.18/0.41 tff(137,plain,
% 0.18/0.41 (~ordinal(A!17)),
% 0.18/0.41 inference(and_elim,[status(thm)],[63])).
% 0.18/0.41 tff(138,plain,
% 0.18/0.41 ((((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17))) <=> ordinal(A!17)) | ((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17))) | ordinal(A!17)),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(139,plain,
% 0.18/0.41 ((((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17))) <=> ordinal(A!17)) | ((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.18/0.41 tff(140,plain,
% 0.18/0.41 ((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[139, 136])).
% 0.18/0.41 tff(141,plain,
% 0.18/0.41 ((~((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17)))) | (~epsilon_transitive(A!17)) | (~epsilon_connected(A!17))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(142,plain,
% 0.18/0.42 ((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.18/0.42 tff(143,plain,
% 0.18/0.42 (~epsilon_transitive(A!17)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[142, 124])).
% 0.18/0.42 tff(144,plain,
% 0.18/0.42 ((~(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)))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(145,plain,
% 0.18/0.42 ((~(epsilon_transitive(A!17) | (~((~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)) | subset(tptp_fun_B_0(A!17), A!17)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.18/0.42 tff(146,plain,
% 0.18/0.42 (~((~in(tptp_fun_B_0(A!17), A!17)) | subset(tptp_fun_B_0(A!17), A!17))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[145, 20])).
% 0.18/0.42 tff(147,plain,
% 0.18/0.42 (((~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))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(148,plain,
% 0.18/0.42 (~subset(tptp_fun_B_0(A!17), A!17)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.18/0.42 tff(149,plain,
% 0.18/0.42 (((~ordinal(tptp_fun_B_0(A!17))) | (~subset(tptp_fun_B_0(A!17), A!17))) | subset(tptp_fun_B_0(A!17), A!17)),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(150,plain,
% 0.18/0.42 ((~ordinal(tptp_fun_B_0(A!17))) | (~subset(tptp_fun_B_0(A!17), A!17))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.18/0.42 tff(151,plain,
% 0.18/0.42 (((~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)),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(152,plain,
% 0.18/0.42 (in(tptp_fun_B_0(A!17), A!17)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[151, 146])).
% 0.18/0.42 tff(153,plain,
% 0.18/0.42 (((~![B: $i] : ((~in(B, A!17)) | (~((~ordinal(B)) | (~subset(B, A!17)))))) | ((~in(tptp_fun_B_0(A!17), A!17)) | (~((~ordinal(tptp_fun_B_0(A!17))) | (~subset(tptp_fun_B_0(A!17), A!17)))))) <=> ((~![B: $i] : ((~in(B, A!17)) | (~((~ordinal(B)) | (~subset(B, A!17)))))) | (~in(tptp_fun_B_0(A!17), A!17)) | (~((~ordinal(tptp_fun_B_0(A!17))) | (~subset(tptp_fun_B_0(A!17), A!17)))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(154,plain,
% 0.18/0.42 ((~![B: $i] : ((~in(B, A!17)) | (~((~ordinal(B)) | (~subset(B, A!17)))))) | ((~in(tptp_fun_B_0(A!17), A!17)) | (~((~ordinal(tptp_fun_B_0(A!17))) | (~subset(tptp_fun_B_0(A!17), A!17)))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(155,plain,
% 0.18/0.42 ((~![B: $i] : ((~in(B, A!17)) | (~((~ordinal(B)) | (~subset(B, A!17)))))) | (~in(tptp_fun_B_0(A!17), A!17)) | (~((~ordinal(tptp_fun_B_0(A!17))) | (~subset(tptp_fun_B_0(A!17), A!17))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.18/0.42 tff(156,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[155, 66, 152, 150])).
% 0.18/0.42 % SZS output end Proof
% 0.18/0.42 % E exiting
%------------------------------------------------------------------------------