%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM394+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:20:53 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM394+1 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n016.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 01:02:32 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(ordinal_subset_type, type, (
% 0.11/0.37 ordinal_subset: ( $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_B_14_type, type, (
% 0.11/0.37 tptp_fun_B_14: $i)).
% 0.11/0.37 tff(tptp_fun_A_13_type, type, (
% 0.11/0.37 tptp_fun_A_13: $i)).
% 0.11/0.37 tff(in_type, type, (
% 0.11/0.37 in: ( $i * $i ) > $o)).
% 0.11/0.37 tff(subset_type, type, (
% 0.11/0.37 subset: ( $i * $i ) > $o)).
% 0.11/0.37 tff(epsilon_transitive_type, type, (
% 0.11/0.37 epsilon_transitive: $i > $o)).
% 0.11/0.37 tff(tptp_fun_B_0_type, type, (
% 0.11/0.37 tptp_fun_B_0: $i > $i)).
% 0.11/0.37 tff(epsilon_connected_type, type, (
% 0.11/0.37 epsilon_connected: $i > $o)).
% 0.11/0.37 tff(ordinal_type, type, (
% 0.11/0.37 ordinal: $i > $o)).
% 0.11/0.37 tff(tptp_fun_A_3_type, type, (
% 0.11/0.37 tptp_fun_A_3: $i)).
% 0.11/0.37 tff(1,plain,
% 0.11/0.37 (^[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))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (![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)))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (^[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))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 (![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)))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 (![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)))))))),
% 0.11/0.37 inference(transitivity,[status(thm)],[4, 2])).
% 0.11/0.37 tff(6,plain,
% 0.11/0.37 (^[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)))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 (![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)))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[6])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 (![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)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 (^[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))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 (![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)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[9])).
% 0.11/0.37 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')).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.11/0.37 tff(14,plain,(
% 0.11/0.37 ![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)))))),
% 0.11/0.37 inference(skolemize,[status(sab)],[13])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 (![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)))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (![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)))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 ((~![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))) | (~((~((~epsilon_transitive(B!14)) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14)))) | (~(epsilon_transitive(B!14) | (~((~in(tptp_fun_B_0(B!14), B!14)) | subset(tptp_fun_B_0(B!14), B!14)))))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (~((~((~epsilon_transitive(B!14)) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14)))) | (~(epsilon_transitive(B!14) | (~((~in(tptp_fun_B_0(B!14), B!14)) | subset(tptp_fun_B_0(B!14), B!14))))))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (((~((~epsilon_transitive(B!14)) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14)))) | (~(epsilon_transitive(B!14) | (~((~in(tptp_fun_B_0(B!14), B!14)) | subset(tptp_fun_B_0(B!14), B!14)))))) | ((~epsilon_transitive(B!14)) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14)))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 ((~epsilon_transitive(B!14)) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 ((~(in(B!14, A!13) | ordinal_subset(A!13, B!14) | (~ordinal(B!14)))) <=> (~(in(B!14, A!13) | ordinal_subset(A!13, B!14) | (~ordinal(B!14))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 ((ordinal(A!13) & (~(in(B!14, A!13) | ordinal_subset(A!13, B!14) | (~ordinal(B!14))))) <=> (ordinal(A!13) & (~(in(B!14, A!13) | ordinal_subset(A!13, B!14) | (~ordinal(B!14)))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[21])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | ordinal_subset(A, B) | (~ordinal(B))))) <=> (~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | ordinal_subset(A, B) | (~ordinal(B)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 ((~![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (ordinal_subset(A, B) | in(B, A))))) <=> (~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | ordinal_subset(A, B) | (~ordinal(B)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(25,axiom,(~![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (ordinal_subset(A, B) | in(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t26_ordinal1')).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | ordinal_subset(A, B) | (~ordinal(B))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | ordinal_subset(A, B) | (~ordinal(B))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | ordinal_subset(A, B) | (~ordinal(B))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | ordinal_subset(A, B) | (~ordinal(B))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[28, 23])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 (ordinal(A!13) & (~(in(B!14, A!13) | ordinal_subset(A!13, B!14) | (~ordinal(B!14))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 (~(in(B!14, A!13) | ordinal_subset(A!13, B!14) | (~ordinal(B!14)))),
% 0.11/0.37 inference(and_elim,[status(thm)],[30])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 (ordinal(B!14)),
% 0.11/0.37 inference(or_elim,[status(thm)],[31])).
% 0.11/0.37 tff(33,plain,
% 0.11/0.37 (^[A: $i] : refl(((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[33])).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 (^[A: $i] : rewrite(((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[35])).
% 0.11/0.37 tff(37,plain,
% 0.11/0.37 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 (^[A: $i] : rewrite((ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(39,plain,
% 0.11/0.37 (![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[38])).
% 0.11/0.37 tff(40,axiom,(![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_ordinal1')).
% 0.11/0.38 tff(41,plain,
% 0.11/0.38 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.11/0.38 tff(42,plain,
% 0.11/0.38 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.11/0.38 tff(43,plain,(
% 0.11/0.38 ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[42])).
% 0.11/0.38 tff(44,plain,
% 0.11/0.38 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.11/0.38 tff(45,plain,
% 0.11/0.38 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[44, 34])).
% 0.11/0.38 tff(46,plain,
% 0.11/0.38 (((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(B!14)) | (~((~epsilon_transitive(B!14)) | (~epsilon_connected(B!14)))))) <=> ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(B!14)) | (~((~epsilon_transitive(B!14)) | (~epsilon_connected(B!14)))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(47,plain,
% 0.11/0.38 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(B!14)) | (~((~epsilon_transitive(B!14)) | (~epsilon_connected(B!14)))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(48,plain,
% 0.11/0.38 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(B!14)) | (~((~epsilon_transitive(B!14)) | (~epsilon_connected(B!14))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.11/0.38 tff(49,plain,
% 0.11/0.38 (~((~epsilon_transitive(B!14)) | (~epsilon_connected(B!14)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[48, 45, 32])).
% 0.11/0.38 tff(50,plain,
% 0.11/0.38 (((~epsilon_transitive(B!14)) | (~epsilon_connected(B!14))) | epsilon_transitive(B!14)),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(51,plain,
% 0.11/0.38 (epsilon_transitive(B!14)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.11/0.38 tff(52,plain,
% 0.11/0.38 ((~((~epsilon_transitive(B!14)) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14)))) | (~epsilon_transitive(B!14)) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(53,plain,
% 0.11/0.38 ((~((~epsilon_transitive(B!14)) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14)))) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.11/0.38 tff(54,plain,
% 0.11/0.38 (![B: $i] : ((~in(B, B!14)) | subset(B, B!14))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[53, 20])).
% 0.11/0.38 tff(55,plain,
% 0.11/0.38 (ordinal(A!13)),
% 0.11/0.38 inference(and_elim,[status(thm)],[30])).
% 0.11/0.38 tff(56,plain,
% 0.11/0.38 (^[A: $i, B: $i] : refl(((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A))) <=> ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(57,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A))) <=> ![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[56])).
% 0.11/0.38 tff(58,plain,
% 0.11/0.38 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((ordinal(A) & ordinal(B)) <=> (~((~ordinal(B)) | (~ordinal(A))))), ((~(ordinal(A) & ordinal(B))) <=> (~(~((~ordinal(B)) | (~ordinal(A))))))), rewrite((~(~((~ordinal(B)) | (~ordinal(A))))) <=> ((~ordinal(B)) | (~ordinal(A)))), ((~(ordinal(A) & ordinal(B))) <=> ((~ordinal(B)) | (~ordinal(A))))), (((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> (((~ordinal(B)) | (~ordinal(A))) | (ordinal_subset(A, B) <=> subset(A, B))))), rewrite((((~ordinal(B)) | (~ordinal(A))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))), (((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(59,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[58])).
% 0.11/0.38 tff(60,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(61,plain,
% 0.11/0.38 (^[A: $i, B: $i] : rewrite(((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B))) <=> ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(62,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B))) <=> ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[61])).
% 0.11/0.38 tff(63,axiom,(![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_r1_ordinal1')).
% 0.11/0.38 tff(64,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.11/0.38 tff(65,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.11/0.38 tff(66,plain,(
% 0.11/0.38 ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[65])).
% 0.11/0.38 tff(67,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.11/0.38 tff(68,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[67, 57])).
% 0.11/0.38 tff(69,plain,
% 0.11/0.38 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(A!13)) | (~ordinal(B!14)) | (ordinal_subset(A!13, B!14) <=> subset(A!13, B!14)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!13)) | (~ordinal(B!14)) | (ordinal_subset(A!13, B!14) <=> subset(A!13, B!14)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(70,plain,
% 0.11/0.38 (((ordinal_subset(A!13, B!14) <=> subset(A!13, B!14)) | (~ordinal(B!14)) | (~ordinal(A!13))) <=> ((~ordinal(A!13)) | (~ordinal(B!14)) | (ordinal_subset(A!13, B!14) <=> subset(A!13, B!14)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(71,plain,
% 0.11/0.38 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(A!13, B!14) <=> subset(A!13, B!14)) | (~ordinal(B!14)) | (~ordinal(A!13)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(A!13)) | (~ordinal(B!14)) | (ordinal_subset(A!13, B!14) <=> subset(A!13, B!14))))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[70])).
% 0.11/0.38 tff(72,plain,
% 0.11/0.38 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(A!13, B!14) <=> subset(A!13, B!14)) | (~ordinal(B!14)) | (~ordinal(A!13)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!13)) | (~ordinal(B!14)) | (ordinal_subset(A!13, B!14) <=> subset(A!13, B!14)))),
% 0.11/0.38 inference(transitivity,[status(thm)],[71, 69])).
% 0.11/0.38 tff(73,plain,
% 0.11/0.38 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(A!13, B!14) <=> subset(A!13, B!14)) | (~ordinal(B!14)) | (~ordinal(A!13)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(74,plain,
% 0.11/0.38 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!13)) | (~ordinal(B!14)) | (ordinal_subset(A!13, B!14) <=> subset(A!13, B!14))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.11/0.38 tff(75,plain,
% 0.11/0.38 (ordinal_subset(A!13, B!14) <=> subset(A!13, B!14)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[74, 68, 55, 32])).
% 0.11/0.38 tff(76,plain,
% 0.11/0.38 (~ordinal_subset(A!13, B!14)),
% 0.11/0.38 inference(or_elim,[status(thm)],[31])).
% 0.11/0.38 tff(77,plain,
% 0.11/0.38 ((~(ordinal_subset(A!13, B!14) <=> subset(A!13, B!14))) | ordinal_subset(A!13, B!14) | (~subset(A!13, B!14))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(78,plain,
% 0.11/0.38 ((~(ordinal_subset(A!13, B!14) <=> subset(A!13, B!14))) | (~subset(A!13, B!14))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.11/0.38 tff(79,plain,
% 0.11/0.38 (~subset(A!13, B!14)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[78, 75])).
% 0.11/0.38 tff(80,plain,
% 0.11/0.38 (((~![B: $i] : ((~in(B, B!14)) | subset(B, B!14))) | ((~in(A!13, B!14)) | subset(A!13, B!14))) <=> ((~![B: $i] : ((~in(B, B!14)) | subset(B, B!14))) | (~in(A!13, B!14)) | subset(A!13, B!14))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(81,plain,
% 0.11/0.38 ((~![B: $i] : ((~in(B, B!14)) | subset(B, B!14))) | ((~in(A!13, B!14)) | subset(A!13, B!14))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(82,plain,
% 0.11/0.38 ((~![B: $i] : ((~in(B, B!14)) | subset(B, B!14))) | (~in(A!13, B!14)) | subset(A!13, B!14)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.11/0.38 tff(83,plain,
% 0.11/0.38 (~in(A!13, B!14)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[82, 79, 54])).
% 0.11/0.38 tff(84,plain,
% 0.11/0.38 (^[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)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(85,plain,
% 0.11/0.38 (![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))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[84])).
% 0.11/0.38 tff(86,plain,
% 0.11/0.38 (^[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)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(87,plain,
% 0.11/0.38 (![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))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[86])).
% 0.11/0.38 tff(88,plain,
% 0.11/0.38 (![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))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[87, 85])).
% 0.11/0.38 tff(89,plain,
% 0.11/0.38 (^[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)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(90,plain,
% 0.11/0.38 (![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))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[89])).
% 0.11/0.38 tff(91,plain,
% 0.11/0.38 (![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))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(92,plain,
% 0.11/0.38 (^[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))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(93,plain,
% 0.11/0.38 (![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))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[92])).
% 0.11/0.38 tff(94,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')).
% 0.11/0.38 tff(95,plain,
% 0.11/0.38 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.11/0.38 tff(96,plain,
% 0.11/0.38 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.11/0.38 tff(97,plain,(
% 0.11/0.38 ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.11/0.38 inference(skolemize,[status(sab)],[96])).
% 0.11/0.38 tff(98,plain,
% 0.11/0.38 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.11/0.38 tff(99,plain,
% 0.11/0.38 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[98, 88])).
% 0.11/0.39 tff(100,plain,
% 0.11/0.39 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(B!14)) | ![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B)))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(B!14)) | ![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(101,plain,
% 0.11/0.39 (((~ordinal(B!14)) | ![B: $i] : (in(B, B!14) | in(B!14, B) | (B!14 = B) | (~ordinal(B)))) <=> ((~ordinal(B!14)) | ![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(102,plain,
% 0.11/0.39 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(B!14)) | ![B: $i] : (in(B, B!14) | in(B!14, B) | (B!14 = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(B!14)) | ![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[101])).
% 0.11/0.39 tff(103,plain,
% 0.11/0.39 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(B!14)) | ![B: $i] : (in(B, B!14) | in(B!14, B) | (B!14 = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(B!14)) | ![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B)))),
% 0.11/0.39 inference(transitivity,[status(thm)],[102, 100])).
% 0.11/0.39 tff(104,plain,
% 0.11/0.39 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(B!14)) | ![B: $i] : (in(B, B!14) | in(B!14, B) | (B!14 = B) | (~ordinal(B))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(105,plain,
% 0.11/0.39 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(B!14)) | ![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.11/0.39 tff(106,plain,
% 0.11/0.39 (![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[105, 99, 32])).
% 0.11/0.39 tff(107,plain,
% 0.11/0.39 (~in(B!14, A!13)),
% 0.11/0.39 inference(or_elim,[status(thm)],[31])).
% 0.11/0.39 tff(108,plain,
% 0.11/0.39 (((~![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))) | ((~ordinal(A!13)) | in(B!14, A!13) | in(A!13, B!14) | (B!14 = A!13))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))) | (~ordinal(A!13)) | in(B!14, A!13) | in(A!13, B!14) | (B!14 = A!13))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(109,plain,
% 0.11/0.39 (((~ordinal(A!13)) | in(A!13, B!14) | in(B!14, A!13) | (B!14 = A!13)) <=> ((~ordinal(A!13)) | in(B!14, A!13) | in(A!13, B!14) | (B!14 = A!13))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(110,plain,
% 0.11/0.39 (((~![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))) | ((~ordinal(A!13)) | in(A!13, B!14) | in(B!14, A!13) | (B!14 = A!13))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))) | ((~ordinal(A!13)) | in(B!14, A!13) | in(A!13, B!14) | (B!14 = A!13)))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[109])).
% 0.11/0.39 tff(111,plain,
% 0.11/0.39 (((~![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))) | ((~ordinal(A!13)) | in(A!13, B!14) | in(B!14, A!13) | (B!14 = A!13))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))) | (~ordinal(A!13)) | in(B!14, A!13) | in(A!13, B!14) | (B!14 = A!13))),
% 0.11/0.39 inference(transitivity,[status(thm)],[110, 108])).
% 0.11/0.39 tff(112,plain,
% 0.11/0.39 ((~![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))) | ((~ordinal(A!13)) | in(A!13, B!14) | in(B!14, A!13) | (B!14 = A!13))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(113,plain,
% 0.11/0.39 ((~![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))) | (~ordinal(A!13)) | in(B!14, A!13) | in(A!13, B!14) | (B!14 = A!13)),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.11/0.39 tff(114,plain,
% 0.11/0.39 (in(A!13, B!14) | (B!14 = A!13)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[113, 55, 107, 106])).
% 0.11/0.39 tff(115,plain,
% 0.11/0.39 (B!14 = A!13),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[114, 83])).
% 0.11/0.39 tff(116,plain,
% 0.11/0.39 (ordinal_subset(A!13, B!14) <=> ordinal_subset(A!13, A!13)),
% 0.11/0.39 inference(monotonicity,[status(thm)],[115])).
% 0.11/0.39 tff(117,plain,
% 0.11/0.39 (ordinal_subset(A!13, A!13) <=> ordinal_subset(A!13, B!14)),
% 0.11/0.39 inference(symmetry,[status(thm)],[116])).
% 0.11/0.39 tff(118,plain,
% 0.11/0.39 (^[A: $i, B: $i] : refl((ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A))) <=> (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(119,plain,
% 0.11/0.39 (![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A))) <=> ![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[118])).
% 0.11/0.39 tff(120,plain,
% 0.11/0.39 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((ordinal(A) & ordinal(B)) <=> (~((~ordinal(B)) | (~ordinal(A))))), ((~(ordinal(A) & ordinal(B))) <=> (~(~((~ordinal(B)) | (~ordinal(A))))))), rewrite((~(~((~ordinal(B)) | (~ordinal(A))))) <=> ((~ordinal(B)) | (~ordinal(A)))), ((~(ordinal(A) & ordinal(B))) <=> ((~ordinal(B)) | (~ordinal(A))))), (((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A)) <=> (((~ordinal(B)) | (~ordinal(A))) | ordinal_subset(A, A)))), rewrite((((~ordinal(B)) | (~ordinal(A))) | ordinal_subset(A, A)) <=> (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))), (((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A)) <=> (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(121,plain,
% 0.11/0.39 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A)) <=> ![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[120])).
% 0.11/0.39 tff(122,plain,
% 0.11/0.39 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A)) <=> ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(123,plain,
% 0.11/0.39 (^[A: $i, B: $i] : rewrite(((ordinal(A) & ordinal(B)) => ordinal_subset(A, A)) <=> ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A)))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(124,plain,
% 0.11/0.39 (![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => ordinal_subset(A, A)) <=> ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[123])).
% 0.11/0.39 tff(125,axiom,(![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => ordinal_subset(A, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity_r1_ordinal1')).
% 0.11/0.39 tff(126,plain,
% 0.11/0.39 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.11/0.39 tff(127,plain,
% 0.11/0.39 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.11/0.39 tff(128,plain,(
% 0.11/0.39 ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A))),
% 0.11/0.39 inference(skolemize,[status(sab)],[127])).
% 0.11/0.39 tff(129,plain,
% 0.11/0.39 (![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[128, 121])).
% 0.11/0.39 tff(130,plain,
% 0.11/0.39 (![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[129, 119])).
% 0.11/0.39 tff(131,plain,
% 0.11/0.39 (?[A: $i] : (epsilon_transitive(A) & epsilon_connected(A) & ordinal(A)) <=> ?[A: $i] : (epsilon_transitive(A) & epsilon_connected(A) & ordinal(A))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(132,plain,
% 0.11/0.39 (^[A: $i] : rewrite(((epsilon_transitive(A) & epsilon_connected(A)) & ordinal(A)) <=> (epsilon_transitive(A) & epsilon_connected(A) & ordinal(A)))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(133,plain,
% 0.11/0.39 (?[A: $i] : ((epsilon_transitive(A) & epsilon_connected(A)) & ordinal(A)) <=> ?[A: $i] : (epsilon_transitive(A) & epsilon_connected(A) & ordinal(A))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[132])).
% 0.11/0.39 tff(134,axiom,(?[A: $i] : ((epsilon_transitive(A) & epsilon_connected(A)) & ordinal(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rc1_ordinal1')).
% 0.11/0.39 tff(135,plain,
% 0.11/0.39 (?[A: $i] : (epsilon_transitive(A) & epsilon_connected(A) & ordinal(A))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.11/0.39 tff(136,plain,
% 0.11/0.39 (?[A: $i] : (epsilon_transitive(A) & epsilon_connected(A) & ordinal(A))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[135, 131])).
% 0.11/0.39 tff(137,plain,(
% 0.11/0.39 epsilon_transitive(A!3) & epsilon_connected(A!3) & ordinal(A!3)),
% 0.11/0.39 inference(skolemize,[status(sab)],[136])).
% 0.11/0.39 tff(138,plain,
% 0.11/0.39 (ordinal(A!3)),
% 0.11/0.39 inference(and_elim,[status(thm)],[137])).
% 0.11/0.39 tff(139,plain,
% 0.11/0.39 (((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(A!13)) | (~ordinal(A!3)) | ordinal_subset(A!13, A!13))) <=> ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!13)) | (~ordinal(A!3)) | ordinal_subset(A!13, A!13))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(140,plain,
% 0.11/0.39 ((ordinal_subset(A!13, A!13) | (~ordinal(A!3)) | (~ordinal(A!13))) <=> ((~ordinal(A!13)) | (~ordinal(A!3)) | ordinal_subset(A!13, A!13))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(141,plain,
% 0.11/0.39 (((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(A!13, A!13) | (~ordinal(A!3)) | (~ordinal(A!13)))) <=> ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(A!13)) | (~ordinal(A!3)) | ordinal_subset(A!13, A!13)))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[140])).
% 0.11/0.39 tff(142,plain,
% 0.11/0.39 (((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(A!13, A!13) | (~ordinal(A!3)) | (~ordinal(A!13)))) <=> ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!13)) | (~ordinal(A!3)) | ordinal_subset(A!13, A!13))),
% 0.11/0.39 inference(transitivity,[status(thm)],[141, 139])).
% 0.11/0.39 tff(143,plain,
% 0.11/0.39 ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(A!13, A!13) | (~ordinal(A!3)) | (~ordinal(A!13)))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(144,plain,
% 0.11/0.39 ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!13)) | (~ordinal(A!3)) | ordinal_subset(A!13, A!13)),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.11/0.39 tff(145,plain,
% 0.11/0.39 (ordinal_subset(A!13, A!13)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[144, 138, 130, 55])).
% 0.11/0.39 tff(146,plain,
% 0.11/0.39 (ordinal_subset(A!13, B!14)),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[145, 117])).
% 0.11/0.39 tff(147,plain,
% 0.11/0.39 ($false),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[76, 146])).
% 0.11/0.39 % SZS output end Proof
% 0.11/0.39 % E exiting
%------------------------------------------------------------------------------