%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM390+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:20:52 AM UTC 2025
% Result : Theorem 0.18s 0.36s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM390+1 : TPTP v9.0.0. Released v3.2.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 01:01:54 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.36 % SZS status Theorem
% 0.18/0.36 % SZS output start Proof
% 0.18/0.36 tff(subset_type, type, (
% 0.18/0.36 subset: ( $i * $i ) > $o)).
% 0.18/0.36 tff(tptp_fun_B_14_type, type, (
% 0.18/0.36 tptp_fun_B_14: $i)).
% 0.18/0.36 tff(tptp_fun_A_13_type, type, (
% 0.18/0.36 tptp_fun_A_13: $i)).
% 0.18/0.36 tff(tptp_fun_C_15_type, type, (
% 0.18/0.36 tptp_fun_C_15: $i)).
% 0.18/0.36 tff(proper_subset_type, type, (
% 0.18/0.36 proper_subset: ( $i * $i ) > $o)).
% 0.18/0.36 tff(in_type, type, (
% 0.18/0.36 in: ( $i * $i ) > $o)).
% 0.18/0.36 tff(ordinal_type, type, (
% 0.18/0.36 ordinal: $i > $o)).
% 0.18/0.36 tff(epsilon_transitive_type, type, (
% 0.18/0.36 epsilon_transitive: $i > $o)).
% 0.18/0.36 tff(tptp_fun_B_0_type, type, (
% 0.18/0.36 tptp_fun_B_0: $i > $i)).
% 0.18/0.36 tff(epsilon_connected_type, type, (
% 0.18/0.36 epsilon_connected: $i > $o)).
% 0.18/0.36 tff(1,plain,
% 0.18/0.36 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B))) <=> (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(2,plain,
% 0.18/0.36 (![A: $i, B: $i] : (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B)))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.36 tff(3,plain,
% 0.18/0.36 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & (~(A = B))) <=> (~((~subset(A, B)) | (A = B)))), ((proper_subset(A, B) <=> (subset(A, B) & (~(A = B)))) <=> (proper_subset(A, B) <=> (~((~subset(A, B)) | (A = B)))))), rewrite((proper_subset(A, B) <=> (~((~subset(A, B)) | (A = B)))) <=> (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B)))), ((proper_subset(A, B) <=> (subset(A, B) & (~(A = B)))) <=> (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B))))), rewrite((~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B))) <=> (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B)))), ((proper_subset(A, B) <=> (subset(A, B) & (~(A = B)))) <=> (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B)))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(4,plain,
% 0.18/0.36 (![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B)))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B)))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.36 tff(5,plain,
% 0.18/0.36 (![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B)))) <=> ![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B))))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(6,axiom,(![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d8_xboole_0')).
% 0.18/0.36 tff(7,plain,
% 0.18/0.36 (![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.18/0.36 tff(8,plain,(
% 0.18/0.36 ![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B))))),
% 0.18/0.36 inference(skolemize,[status(sab)],[7])).
% 0.18/0.36 tff(9,plain,
% 0.18/0.36 (![A: $i, B: $i] : (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.18/0.36 tff(10,plain,
% 0.18/0.36 (![A: $i, B: $i] : (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.18/0.36 tff(11,plain,
% 0.18/0.36 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B)))) | (~(((~subset(A!13, C!15)) | (A!13 = C!15)) <=> proper_subset(A!13, C!15)))),
% 0.18/0.36 inference(quant_inst,[status(thm)],[])).
% 0.18/0.36 tff(12,plain,
% 0.18/0.36 (~(((~subset(A!13, C!15)) | (A!13 = C!15)) <=> proper_subset(A!13, C!15))),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.18/0.36 tff(13,plain,
% 0.18/0.36 ((epsilon_transitive(A!13) & (ordinal(B!14) & (~(in(A!13, C!15) | (~ordinal(C!15)) | (~(subset(A!13, B!14) & in(B!14, C!15))))))) <=> (epsilon_transitive(A!13) & ordinal(B!14) & (~(in(A!13, C!15) | (~ordinal(C!15)) | (~(subset(A!13, B!14) & in(B!14, C!15))))))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(14,plain,
% 0.18/0.36 ((~(in(A!13, C!15) | (~ordinal(C!15)) | (~(subset(A!13, B!14) & in(B!14, C!15))))) <=> (~(in(A!13, C!15) | (~ordinal(C!15)) | (~(subset(A!13, B!14) & in(B!14, C!15)))))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(15,plain,
% 0.18/0.36 ((ordinal(B!14) & (~(in(A!13, C!15) | (~ordinal(C!15)) | (~(subset(A!13, B!14) & in(B!14, C!15)))))) <=> (ordinal(B!14) & (~(in(A!13, C!15) | (~ordinal(C!15)) | (~(subset(A!13, B!14) & in(B!14, C!15))))))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[14])).
% 0.18/0.37 tff(16,plain,
% 0.18/0.37 ((epsilon_transitive(A!13) & (ordinal(B!14) & (~(in(A!13, C!15) | (~ordinal(C!15)) | (~(subset(A!13, B!14) & in(B!14, C!15))))))) <=> (epsilon_transitive(A!13) & (ordinal(B!14) & (~(in(A!13, C!15) | (~ordinal(C!15)) | (~(subset(A!13, B!14) & in(B!14, C!15)))))))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[15])).
% 0.18/0.37 tff(17,plain,
% 0.18/0.37 ((epsilon_transitive(A!13) & (ordinal(B!14) & (~(in(A!13, C!15) | (~ordinal(C!15)) | (~(subset(A!13, B!14) & in(B!14, C!15))))))) <=> (epsilon_transitive(A!13) & ordinal(B!14) & (~(in(A!13, C!15) | (~ordinal(C!15)) | (~(subset(A!13, B!14) & in(B!14, C!15))))))),
% 0.18/0.37 inference(transitivity,[status(thm)],[16, 13])).
% 0.18/0.37 tff(18,plain,
% 0.18/0.37 ((~![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : ((~ordinal(B)) | ![C: $i] : (in(A, C) | (~ordinal(C)) | (~(subset(A, B) & in(B, C))))))) <=> (~![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : ((~ordinal(B)) | ![C: $i] : (in(A, C) | (~ordinal(C)) | (~(subset(A, B) & in(B, C)))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(19,plain,
% 0.18/0.37 ((~![A: $i] : (epsilon_transitive(A) => ![B: $i] : (ordinal(B) => ![C: $i] : (ordinal(C) => ((subset(A, B) & in(B, C)) => in(A, C)))))) <=> (~![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : ((~ordinal(B)) | ![C: $i] : (in(A, C) | (~ordinal(C)) | (~(subset(A, B) & in(B, C)))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(20,axiom,(~![A: $i] : (epsilon_transitive(A) => ![B: $i] : (ordinal(B) => ![C: $i] : (ordinal(C) => ((subset(A, B) & in(B, C)) => in(A, C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t22_ordinal1')).
% 0.18/0.37 tff(21,plain,
% 0.18/0.37 (~![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : ((~ordinal(B)) | ![C: $i] : (in(A, C) | (~ordinal(C)) | (~(subset(A, B) & in(B, C))))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.18/0.37 tff(22,plain,
% 0.18/0.37 (~![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : ((~ordinal(B)) | ![C: $i] : (in(A, C) | (~ordinal(C)) | (~(subset(A, B) & in(B, C))))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.18/0.37 tff(23,plain,
% 0.18/0.37 (~![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : ((~ordinal(B)) | ![C: $i] : (in(A, C) | (~ordinal(C)) | (~(subset(A, B) & in(B, C))))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.18/0.37 tff(24,plain,
% 0.18/0.37 (~![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : ((~ordinal(B)) | ![C: $i] : (in(A, C) | (~ordinal(C)) | (~(subset(A, B) & in(B, C))))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.18/0.37 tff(25,plain,
% 0.18/0.37 (epsilon_transitive(A!13) & ordinal(B!14) & (~(in(A!13, C!15) | (~ordinal(C!15)) | (~(subset(A!13, B!14) & in(B!14, C!15)))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.18/0.37 tff(26,plain,
% 0.18/0.37 (epsilon_transitive(A!13)),
% 0.18/0.37 inference(and_elim,[status(thm)],[25])).
% 0.18/0.37 tff(27,plain,
% 0.18/0.37 (^[A: $i] : refl(((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B)))) <=> ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B)))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(28,plain,
% 0.18/0.37 (![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B)))) <=> ![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[27])).
% 0.18/0.37 tff(29,plain,
% 0.18/0.37 (^[A: $i] : rewrite(((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B)))) <=> ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B)))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(30,plain,
% 0.18/0.37 (![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B)))) <=> ![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[29])).
% 0.18/0.37 tff(31,plain,
% 0.18/0.37 (![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B)))) <=> ![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))),
% 0.18/0.37 inference(transitivity,[status(thm)],[30, 28])).
% 0.18/0.37 tff(32,plain,
% 0.18/0.37 (![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B)))) <=> ![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(33,plain,
% 0.18/0.37 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((proper_subset(A, B) => in(A, B)) <=> ((~proper_subset(A, B)) | in(A, B))), ((ordinal(B) => (proper_subset(A, B) => in(A, B))) <=> (ordinal(B) => ((~proper_subset(A, B)) | in(A, B))))), rewrite((ordinal(B) => ((~proper_subset(A, B)) | in(A, B))) <=> (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B)))), ((ordinal(B) => (proper_subset(A, B) => in(A, B))) <=> (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B)))))), (![B: $i] : (ordinal(B) => (proper_subset(A, B) => in(A, B))) <=> ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))), ((epsilon_transitive(A) => ![B: $i] : (ordinal(B) => (proper_subset(A, B) => in(A, B)))) <=> (epsilon_transitive(A) => ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B)))))), rewrite((epsilon_transitive(A) => ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B)))) <=> ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))), ((epsilon_transitive(A) => ![B: $i] : (ordinal(B) => (proper_subset(A, B) => in(A, B)))) <=> ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(34,plain,
% 0.18/0.37 (![A: $i] : (epsilon_transitive(A) => ![B: $i] : (ordinal(B) => (proper_subset(A, B) => in(A, B)))) <=> ![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[33])).
% 0.18/0.37 tff(35,axiom,(![A: $i] : (epsilon_transitive(A) => ![B: $i] : (ordinal(B) => (proper_subset(A, B) => in(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t21_ordinal1')).
% 0.18/0.37 tff(36,plain,
% 0.18/0.37 (![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.18/0.37 tff(37,plain,
% 0.18/0.37 (![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.18/0.37 tff(38,plain,(
% 0.18/0.37 ![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))),
% 0.18/0.37 inference(skolemize,[status(sab)],[37])).
% 0.18/0.37 tff(39,plain,
% 0.18/0.37 (![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.18/0.37 tff(40,plain,
% 0.18/0.37 (((~![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))) | ((~epsilon_transitive(A!13)) | ![B: $i] : ((~ordinal(B)) | in(A!13, B) | (~proper_subset(A!13, B))))) <=> ((~![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))) | (~epsilon_transitive(A!13)) | ![B: $i] : ((~ordinal(B)) | in(A!13, B) | (~proper_subset(A!13, B))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(41,plain,
% 0.18/0.37 (((~epsilon_transitive(A!13)) | ![B: $i] : (in(A!13, B) | (~proper_subset(A!13, B)) | (~ordinal(B)))) <=> ((~epsilon_transitive(A!13)) | ![B: $i] : ((~ordinal(B)) | in(A!13, B) | (~proper_subset(A!13, B))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(42,plain,
% 0.18/0.37 (((~![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))) | ((~epsilon_transitive(A!13)) | ![B: $i] : (in(A!13, B) | (~proper_subset(A!13, B)) | (~ordinal(B))))) <=> ((~![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))) | ((~epsilon_transitive(A!13)) | ![B: $i] : ((~ordinal(B)) | in(A!13, B) | (~proper_subset(A!13, B)))))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[41])).
% 0.18/0.37 tff(43,plain,
% 0.18/0.37 (((~![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))) | ((~epsilon_transitive(A!13)) | ![B: $i] : (in(A!13, B) | (~proper_subset(A!13, B)) | (~ordinal(B))))) <=> ((~![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))) | (~epsilon_transitive(A!13)) | ![B: $i] : ((~ordinal(B)) | in(A!13, B) | (~proper_subset(A!13, B))))),
% 0.18/0.37 inference(transitivity,[status(thm)],[42, 40])).
% 0.18/0.37 tff(44,plain,
% 0.18/0.37 ((~![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))) | ((~epsilon_transitive(A!13)) | ![B: $i] : (in(A!13, B) | (~proper_subset(A!13, B)) | (~ordinal(B))))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(45,plain,
% 0.18/0.37 ((~![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))) | (~epsilon_transitive(A!13)) | ![B: $i] : ((~ordinal(B)) | in(A!13, B) | (~proper_subset(A!13, B)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.18/0.37 tff(46,plain,
% 0.18/0.37 (![B: $i] : ((~ordinal(B)) | in(A!13, B) | (~proper_subset(A!13, B)))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[45, 39, 26])).
% 0.18/0.37 tff(47,plain,
% 0.18/0.37 (~(in(A!13, C!15) | (~ordinal(C!15)) | (~(subset(A!13, B!14) & in(B!14, C!15))))),
% 0.18/0.37 inference(and_elim,[status(thm)],[25])).
% 0.18/0.37 tff(48,plain,
% 0.18/0.37 (ordinal(C!15)),
% 0.18/0.37 inference(or_elim,[status(thm)],[47])).
% 0.18/0.37 tff(49,plain,
% 0.18/0.37 (~in(A!13, C!15)),
% 0.18/0.37 inference(or_elim,[status(thm)],[47])).
% 0.18/0.37 tff(50,plain,
% 0.18/0.37 (((~![B: $i] : ((~ordinal(B)) | in(A!13, B) | (~proper_subset(A!13, B)))) | (in(A!13, C!15) | (~ordinal(C!15)) | (~proper_subset(A!13, C!15)))) <=> ((~![B: $i] : ((~ordinal(B)) | in(A!13, B) | (~proper_subset(A!13, B)))) | in(A!13, C!15) | (~ordinal(C!15)) | (~proper_subset(A!13, C!15)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(51,plain,
% 0.18/0.37 (((~ordinal(C!15)) | in(A!13, C!15) | (~proper_subset(A!13, C!15))) <=> (in(A!13, C!15) | (~ordinal(C!15)) | (~proper_subset(A!13, C!15)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(52,plain,
% 0.18/0.37 (((~![B: $i] : ((~ordinal(B)) | in(A!13, B) | (~proper_subset(A!13, B)))) | ((~ordinal(C!15)) | in(A!13, C!15) | (~proper_subset(A!13, C!15)))) <=> ((~![B: $i] : ((~ordinal(B)) | in(A!13, B) | (~proper_subset(A!13, B)))) | (in(A!13, C!15) | (~ordinal(C!15)) | (~proper_subset(A!13, C!15))))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[51])).
% 0.18/0.37 tff(53,plain,
% 0.18/0.37 (((~![B: $i] : ((~ordinal(B)) | in(A!13, B) | (~proper_subset(A!13, B)))) | ((~ordinal(C!15)) | in(A!13, C!15) | (~proper_subset(A!13, C!15)))) <=> ((~![B: $i] : ((~ordinal(B)) | in(A!13, B) | (~proper_subset(A!13, B)))) | in(A!13, C!15) | (~ordinal(C!15)) | (~proper_subset(A!13, C!15)))),
% 0.18/0.37 inference(transitivity,[status(thm)],[52, 50])).
% 0.18/0.37 tff(54,plain,
% 0.18/0.37 ((~![B: $i] : ((~ordinal(B)) | in(A!13, B) | (~proper_subset(A!13, B)))) | ((~ordinal(C!15)) | in(A!13, C!15) | (~proper_subset(A!13, C!15)))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(55,plain,
% 0.18/0.37 ((~![B: $i] : ((~ordinal(B)) | in(A!13, B) | (~proper_subset(A!13, B)))) | in(A!13, C!15) | (~ordinal(C!15)) | (~proper_subset(A!13, C!15))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.18/0.37 tff(56,plain,
% 0.18/0.37 (~proper_subset(A!13, C!15)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[55, 49, 48, 46])).
% 0.18/0.37 tff(57,plain,
% 0.18/0.37 ((((~subset(A!13, C!15)) | (A!13 = C!15)) <=> proper_subset(A!13, C!15)) | ((~subset(A!13, C!15)) | (A!13 = C!15)) | proper_subset(A!13, C!15)),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(58,plain,
% 0.18/0.37 ((((~subset(A!13, C!15)) | (A!13 = C!15)) <=> proper_subset(A!13, C!15)) | ((~subset(A!13, C!15)) | (A!13 = C!15))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.18/0.37 tff(59,plain,
% 0.18/0.37 ((~subset(A!13, C!15)) | (A!13 = C!15)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[58, 12])).
% 0.18/0.37 tff(60,plain,
% 0.18/0.37 (^[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))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(61,plain,
% 0.18/0.37 (![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)))))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[60])).
% 0.18/0.37 tff(62,plain,
% 0.18/0.37 (^[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))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(63,plain,
% 0.18/0.37 (![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)))))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[62])).
% 0.18/0.37 tff(64,plain,
% 0.18/0.37 (![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)))))))),
% 0.18/0.37 inference(transitivity,[status(thm)],[63, 61])).
% 0.18/0.37 tff(65,plain,
% 0.18/0.37 (^[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)))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(66,plain,
% 0.18/0.37 (![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)))))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[65])).
% 0.18/0.37 tff(67,plain,
% 0.18/0.37 (![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)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(68,plain,
% 0.18/0.37 (^[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))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(69,plain,
% 0.18/0.37 (![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)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[68])).
% 0.18/0.37 tff(70,axiom,(![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_ordinal1')).
% 0.18/0.37 tff(71,plain,
% 0.18/0.37 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.18/0.37 tff(72,plain,
% 0.18/0.37 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.18/0.37 tff(73,plain,(
% 0.18/0.37 ![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)))))),
% 0.18/0.37 inference(skolemize,[status(sab)],[72])).
% 0.18/0.37 tff(74,plain,
% 0.18/0.37 (![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)))))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.18/0.37 tff(75,plain,
% 0.18/0.37 (![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)))))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[74, 64])).
% 0.18/0.37 tff(76,plain,
% 0.18/0.37 ((~![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(C!15)) | ![B: $i] : ((~in(B, C!15)) | subset(B, C!15)))) | (~(epsilon_transitive(C!15) | (~((~in(tptp_fun_B_0(C!15), C!15)) | subset(tptp_fun_B_0(C!15), C!15)))))))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(77,plain,
% 0.18/0.37 (~((~((~epsilon_transitive(C!15)) | ![B: $i] : ((~in(B, C!15)) | subset(B, C!15)))) | (~(epsilon_transitive(C!15) | (~((~in(tptp_fun_B_0(C!15), C!15)) | subset(tptp_fun_B_0(C!15), C!15))))))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.18/0.37 tff(78,plain,
% 0.18/0.37 (((~((~epsilon_transitive(C!15)) | ![B: $i] : ((~in(B, C!15)) | subset(B, C!15)))) | (~(epsilon_transitive(C!15) | (~((~in(tptp_fun_B_0(C!15), C!15)) | subset(tptp_fun_B_0(C!15), C!15)))))) | ((~epsilon_transitive(C!15)) | ![B: $i] : ((~in(B, C!15)) | subset(B, C!15)))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(79,plain,
% 0.18/0.37 ((~epsilon_transitive(C!15)) | ![B: $i] : ((~in(B, C!15)) | subset(B, C!15))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.18/0.37 tff(80,plain,
% 0.18/0.37 (^[A: $i] : refl(((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(81,plain,
% 0.18/0.37 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[80])).
% 0.18/0.37 tff(82,plain,
% 0.18/0.37 (^[A: $i] : rewrite(((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(83,plain,
% 0.18/0.37 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[82])).
% 0.18/0.37 tff(84,plain,
% 0.18/0.37 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(85,plain,
% 0.18/0.37 (^[A: $i] : rewrite((ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(86,plain,
% 0.18/0.37 (![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[85])).
% 0.18/0.37 tff(87,axiom,(![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_ordinal1')).
% 0.18/0.38 tff(88,plain,
% 0.18/0.38 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.18/0.38 tff(89,plain,
% 0.18/0.38 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.18/0.38 tff(90,plain,(
% 0.18/0.38 ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.18/0.38 inference(skolemize,[status(sab)],[89])).
% 0.18/0.38 tff(91,plain,
% 0.18/0.38 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.18/0.38 tff(92,plain,
% 0.18/0.38 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[91, 81])).
% 0.18/0.38 tff(93,plain,
% 0.18/0.38 (((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(C!15)) | (~((~epsilon_transitive(C!15)) | (~epsilon_connected(C!15)))))) <=> ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(C!15)) | (~((~epsilon_transitive(C!15)) | (~epsilon_connected(C!15)))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(94,plain,
% 0.18/0.38 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(C!15)) | (~((~epsilon_transitive(C!15)) | (~epsilon_connected(C!15)))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(95,plain,
% 0.18/0.38 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(C!15)) | (~((~epsilon_transitive(C!15)) | (~epsilon_connected(C!15))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.18/0.38 tff(96,plain,
% 0.18/0.38 (~((~epsilon_transitive(C!15)) | (~epsilon_connected(C!15)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[95, 92, 48])).
% 0.18/0.38 tff(97,plain,
% 0.18/0.38 (((~epsilon_transitive(C!15)) | (~epsilon_connected(C!15))) | epsilon_transitive(C!15)),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(98,plain,
% 0.18/0.38 (epsilon_transitive(C!15)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.18/0.38 tff(99,plain,
% 0.18/0.38 ((~((~epsilon_transitive(C!15)) | ![B: $i] : ((~in(B, C!15)) | subset(B, C!15)))) | (~epsilon_transitive(C!15)) | ![B: $i] : ((~in(B, C!15)) | subset(B, C!15))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(100,plain,
% 0.18/0.38 ((~((~epsilon_transitive(C!15)) | ![B: $i] : ((~in(B, C!15)) | subset(B, C!15)))) | ![B: $i] : ((~in(B, C!15)) | subset(B, C!15))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.18/0.38 tff(101,plain,
% 0.18/0.38 (![B: $i] : ((~in(B, C!15)) | subset(B, C!15))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[100, 79])).
% 0.18/0.38 tff(102,plain,
% 0.18/0.38 (subset(A!13, B!14) & in(B!14, C!15)),
% 0.18/0.38 inference(or_elim,[status(thm)],[47])).
% 0.18/0.38 tff(103,plain,
% 0.18/0.38 (in(B!14, C!15)),
% 0.18/0.38 inference(and_elim,[status(thm)],[102])).
% 0.18/0.38 tff(104,plain,
% 0.18/0.38 (((~![B: $i] : ((~in(B, C!15)) | subset(B, C!15))) | ((~in(B!14, C!15)) | subset(B!14, C!15))) <=> ((~![B: $i] : ((~in(B, C!15)) | subset(B, C!15))) | (~in(B!14, C!15)) | subset(B!14, C!15))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(105,plain,
% 0.18/0.38 ((~![B: $i] : ((~in(B, C!15)) | subset(B, C!15))) | ((~in(B!14, C!15)) | subset(B!14, C!15))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(106,plain,
% 0.18/0.38 ((~![B: $i] : ((~in(B, C!15)) | subset(B, C!15))) | (~in(B!14, C!15)) | subset(B!14, C!15)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.18/0.38 tff(107,plain,
% 0.18/0.38 (subset(B!14, C!15)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[106, 103, 101])).
% 0.18/0.38 tff(108,plain,
% 0.18/0.38 (subset(A!13, B!14)),
% 0.18/0.38 inference(and_elim,[status(thm)],[102])).
% 0.18/0.38 tff(109,plain,
% 0.18/0.38 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B))) <=> ![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(110,plain,
% 0.18/0.38 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(A, B) & subset(B, C)) <=> (~((~subset(B, C)) | (~subset(A, B))))), ((~(subset(A, B) & subset(B, C))) <=> (~(~((~subset(B, C)) | (~subset(A, B))))))), rewrite((~(~((~subset(B, C)) | (~subset(A, B))))) <=> ((~subset(B, C)) | (~subset(A, B)))), ((~(subset(A, B) & subset(B, C))) <=> ((~subset(B, C)) | (~subset(A, B))))), (((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> (((~subset(B, C)) | (~subset(A, B))) | subset(A, C)))), rewrite((((~subset(B, C)) | (~subset(A, B))) | subset(A, C)) <=> (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))), (((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(111,plain,
% 0.18/0.38 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> ![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[110])).
% 0.18/0.38 tff(112,plain,
% 0.18/0.38 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(113,plain,
% 0.18/0.38 (^[A: $i, B: $i, C: $i] : rewrite(((subset(A, B) & subset(B, C)) => subset(A, C)) <=> ((~(subset(A, B) & subset(B, C))) | subset(A, C)))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(114,plain,
% 0.18/0.38 (![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(B, C)) => subset(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[113])).
% 0.18/0.38 tff(115,axiom,(![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(B, C)) => subset(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_xboole_1')).
% 0.18/0.38 tff(116,plain,
% 0.18/0.38 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.18/0.38 tff(117,plain,
% 0.18/0.38 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.18/0.38 tff(118,plain,(
% 0.18/0.38 ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.18/0.38 inference(skolemize,[status(sab)],[117])).
% 0.18/0.38 tff(119,plain,
% 0.18/0.38 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[118, 111])).
% 0.18/0.38 tff(120,plain,
% 0.18/0.38 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[119, 109])).
% 0.18/0.38 tff(121,plain,
% 0.18/0.38 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | ((~subset(A!13, B!14)) | subset(A!13, C!15) | (~subset(B!14, C!15)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (~subset(A!13, B!14)) | subset(A!13, C!15) | (~subset(B!14, C!15)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(122,plain,
% 0.18/0.38 ((subset(A!13, C!15) | (~subset(B!14, C!15)) | (~subset(A!13, B!14))) <=> ((~subset(A!13, B!14)) | subset(A!13, C!15) | (~subset(B!14, C!15)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(123,plain,
% 0.18/0.38 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(A!13, C!15) | (~subset(B!14, C!15)) | (~subset(A!13, B!14)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | ((~subset(A!13, B!14)) | subset(A!13, C!15) | (~subset(B!14, C!15))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[122])).
% 0.18/0.38 tff(124,plain,
% 0.18/0.38 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(A!13, C!15) | (~subset(B!14, C!15)) | (~subset(A!13, B!14)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (~subset(A!13, B!14)) | subset(A!13, C!15) | (~subset(B!14, C!15)))),
% 0.18/0.38 inference(transitivity,[status(thm)],[123, 121])).
% 0.18/0.38 tff(125,plain,
% 0.18/0.38 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(A!13, C!15) | (~subset(B!14, C!15)) | (~subset(A!13, B!14)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(126,plain,
% 0.18/0.38 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (~subset(A!13, B!14)) | subset(A!13, C!15) | (~subset(B!14, C!15))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.18/0.38 tff(127,plain,
% 0.18/0.38 (subset(A!13, C!15)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[126, 120, 108, 107])).
% 0.18/0.38 tff(128,plain,
% 0.18/0.38 ((~((~subset(A!13, C!15)) | (A!13 = C!15))) | (~subset(A!13, C!15)) | (A!13 = C!15)),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(129,plain,
% 0.18/0.38 (A!13 = C!15),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[128, 127, 59])).
% 0.18/0.38 tff(130,plain,
% 0.18/0.38 (subset(A!13, B!14) <=> subset(C!15, B!14)),
% 0.18/0.38 inference(monotonicity,[status(thm)],[129])).
% 0.18/0.38 tff(131,plain,
% 0.18/0.38 (subset(C!15, B!14) <=> subset(A!13, B!14)),
% 0.18/0.38 inference(symmetry,[status(thm)],[130])).
% 0.18/0.38 tff(132,plain,
% 0.18/0.38 ((~subset(C!15, B!14)) <=> (~subset(A!13, B!14))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[131])).
% 0.18/0.38 tff(133,plain,
% 0.18/0.38 (^[A: $i, B: $i] : refl(((~in(A, B)) | (~subset(B, A))) <=> ((~in(A, B)) | (~subset(B, A))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(134,plain,
% 0.18/0.38 (![A: $i, B: $i] : ((~in(A, B)) | (~subset(B, A))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (~subset(B, A)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[133])).
% 0.18/0.38 tff(135,plain,
% 0.18/0.38 (^[A: $i, B: $i] : trans(monotonicity(rewrite((in(A, B) & subset(B, A)) <=> (~((~in(A, B)) | (~subset(B, A))))), ((~(in(A, B) & subset(B, A))) <=> (~(~((~in(A, B)) | (~subset(B, A))))))), rewrite((~(~((~in(A, B)) | (~subset(B, A))))) <=> ((~in(A, B)) | (~subset(B, A)))), ((~(in(A, B) & subset(B, A))) <=> ((~in(A, B)) | (~subset(B, A)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(136,plain,
% 0.18/0.38 (![A: $i, B: $i] : (~(in(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (~subset(B, A)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[135])).
% 0.18/0.38 tff(137,plain,
% 0.18/0.38 (![A: $i, B: $i] : (~(in(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(in(A, B) & subset(B, A)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(138,axiom,(![A: $i, B: $i] : (~(in(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_ordinal1')).
% 0.18/0.38 tff(139,plain,
% 0.18/0.38 (![A: $i, B: $i] : (~(in(A, B) & subset(B, A)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.18/0.38 tff(140,plain,(
% 0.18/0.38 ![A: $i, B: $i] : (~(in(A, B) & subset(B, A)))),
% 0.18/0.38 inference(skolemize,[status(sab)],[139])).
% 0.18/0.38 tff(141,plain,
% 0.18/0.38 (![A: $i, B: $i] : ((~in(A, B)) | (~subset(B, A)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.18/0.38 tff(142,plain,
% 0.18/0.38 (![A: $i, B: $i] : ((~in(A, B)) | (~subset(B, A)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.18/0.38 tff(143,plain,
% 0.18/0.38 (((~![A: $i, B: $i] : ((~in(A, B)) | (~subset(B, A)))) | ((~in(B!14, C!15)) | (~subset(C!15, B!14)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (~subset(B, A)))) | (~in(B!14, C!15)) | (~subset(C!15, B!14)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(144,plain,
% 0.18/0.38 ((~![A: $i, B: $i] : ((~in(A, B)) | (~subset(B, A)))) | ((~in(B!14, C!15)) | (~subset(C!15, B!14)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(145,plain,
% 0.18/0.38 ((~![A: $i, B: $i] : ((~in(A, B)) | (~subset(B, A)))) | (~in(B!14, C!15)) | (~subset(C!15, B!14))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.18/0.38 tff(146,plain,
% 0.18/0.38 (~subset(C!15, B!14)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[145, 103, 142])).
% 0.18/0.38 tff(147,plain,
% 0.18/0.38 (~subset(A!13, B!14)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[146, 132])).
% 0.18/0.38 tff(148,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[108, 147])).
% 0.18/0.38 % SZS output end Proof
% 0.18/0.38 % E exiting
%------------------------------------------------------------------------------