TSTP Solution File: SEU235+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU235+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Tue Sep 20 07:28:23 EDT 2022
% Result : Theorem 112.60s 72.32s
% Output : Proof 112.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU235+3 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 10:49:50 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 112.60/72.32 % SZS status Theorem
% 112.60/72.32 % SZS output start Proof
% 112.60/72.32 tff(ordinal_subset_type, type, (
% 112.60/72.32 ordinal_subset: ( $i * $i ) > $o)).
% 112.60/72.32 tff(tptp_fun_D_17_type, type, (
% 112.60/72.32 tptp_fun_D_17: $i > $i)).
% 112.60/72.32 tff(tptp_fun_C_18_type, type, (
% 112.60/72.32 tptp_fun_C_18: $i > $i)).
% 112.60/72.32 tff(tptp_fun_A_16_type, type, (
% 112.60/72.32 tptp_fun_A_16: $i)).
% 112.60/72.32 tff(in_type, type, (
% 112.60/72.32 in: ( $i * $i ) > $o)).
% 112.60/72.32 tff(subset_type, type, (
% 112.60/72.32 subset: ( $i * $i ) > $o)).
% 112.60/72.32 tff(epsilon_transitive_type, type, (
% 112.60/72.32 epsilon_transitive: $i > $o)).
% 112.60/72.32 tff(tptp_fun_B_0_type, type, (
% 112.60/72.32 tptp_fun_B_0: $i > $i)).
% 112.60/72.32 tff(epsilon_connected_type, type, (
% 112.60/72.32 epsilon_connected: $i > $o)).
% 112.60/72.32 tff(ordinal_type, type, (
% 112.60/72.32 ordinal: $i > $o)).
% 112.60/72.32 tff(tptp_fun_B_15_type, type, (
% 112.60/72.32 tptp_fun_B_15: $i)).
% 112.60/72.32 tff(element_type, type, (
% 112.60/72.32 element: ( $i * $i ) > $o)).
% 112.60/72.32 tff(tptp_fun_B_1_type, type, (
% 112.60/72.32 tptp_fun_B_1: $i > $i)).
% 112.60/72.32 tff(empty_type, type, (
% 112.60/72.32 empty: $i > $o)).
% 112.60/72.32 tff(empty_set_type, type, (
% 112.60/72.32 empty_set: $i)).
% 112.60/72.32 tff(relation_type, type, (
% 112.60/72.32 relation: $i > $o)).
% 112.60/72.32 tff(relation_empty_yielding_type, type, (
% 112.60/72.32 relation_empty_yielding: $i > $o)).
% 112.60/72.32 tff(powerset_type, type, (
% 112.60/72.32 powerset: $i > $i)).
% 112.60/72.32 tff(1,plain,
% 112.60/72.32 (^[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))))))))),
% 112.60/72.32 inference(bind,[status(th)],[])).
% 112.60/72.32 tff(2,plain,
% 112.60/72.32 (![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)))))))),
% 112.60/72.32 inference(quant_intro,[status(thm)],[1])).
% 112.60/72.32 tff(3,plain,
% 112.60/72.32 (^[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))))))))),
% 112.60/72.32 inference(bind,[status(th)],[])).
% 112.60/72.32 tff(4,plain,
% 112.60/72.32 (![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)))))))),
% 112.60/72.32 inference(quant_intro,[status(thm)],[3])).
% 112.60/72.32 tff(5,plain,
% 112.60/72.32 (![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)))))))),
% 112.60/72.32 inference(transitivity,[status(thm)],[4, 2])).
% 112.60/72.32 tff(6,plain,
% 112.60/72.32 (^[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)))))))))),
% 112.60/72.32 inference(bind,[status(th)],[])).
% 112.60/72.32 tff(7,plain,
% 112.60/72.32 (![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)))))))),
% 112.60/72.32 inference(quant_intro,[status(thm)],[6])).
% 112.60/72.32 tff(8,plain,
% 112.60/72.32 (![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)))),
% 112.60/72.32 inference(rewrite,[status(thm)],[])).
% 112.60/72.32 tff(9,plain,
% 112.60/72.32 (^[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))))),
% 112.60/72.32 inference(bind,[status(th)],[])).
% 112.60/72.32 tff(10,plain,
% 112.60/72.32 (![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)))),
% 112.60/72.32 inference(quant_intro,[status(thm)],[9])).
% 112.60/72.32 tff(11,axiom,(![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_ordinal1')).
% 112.60/72.32 tff(12,plain,
% 112.60/72.32 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 112.60/72.32 inference(modus_ponens,[status(thm)],[11, 10])).
% 112.60/72.32 tff(13,plain,
% 112.60/72.32 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 112.60/72.32 inference(modus_ponens,[status(thm)],[12, 8])).
% 112.60/72.32 tff(14,plain,(
% 112.60/72.32 ![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)))))),
% 112.60/72.32 inference(skolemize,[status(sab)],[13])).
% 112.60/72.32 tff(15,plain,
% 112.60/72.32 (![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)))))))),
% 112.60/72.32 inference(modus_ponens,[status(thm)],[14, 7])).
% 112.60/72.32 tff(16,plain,
% 112.60/72.32 (![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)))))))),
% 112.60/72.32 inference(modus_ponens,[status(thm)],[15, 5])).
% 112.60/72.32 tff(17,plain,
% 112.60/72.32 ((~![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(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | ![B: $i] : ((~in(B, tptp_fun_D_17(tptp_fun_C_18(A!16)))) | subset(B, tptp_fun_D_17(tptp_fun_C_18(A!16)))))) | (~(epsilon_transitive(tptp_fun_D_17(tptp_fun_C_18(A!16))) | (~((~in(tptp_fun_B_0(tptp_fun_D_17(tptp_fun_C_18(A!16))), tptp_fun_D_17(tptp_fun_C_18(A!16)))) | subset(tptp_fun_B_0(tptp_fun_D_17(tptp_fun_C_18(A!16))), tptp_fun_D_17(tptp_fun_C_18(A!16)))))))))),
% 112.60/72.32 inference(quant_inst,[status(thm)],[])).
% 112.60/72.32 tff(18,plain,
% 112.60/72.32 (~((~((~epsilon_transitive(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | ![B: $i] : ((~in(B, tptp_fun_D_17(tptp_fun_C_18(A!16)))) | subset(B, tptp_fun_D_17(tptp_fun_C_18(A!16)))))) | (~(epsilon_transitive(tptp_fun_D_17(tptp_fun_C_18(A!16))) | (~((~in(tptp_fun_B_0(tptp_fun_D_17(tptp_fun_C_18(A!16))), tptp_fun_D_17(tptp_fun_C_18(A!16)))) | subset(tptp_fun_B_0(tptp_fun_D_17(tptp_fun_C_18(A!16))), tptp_fun_D_17(tptp_fun_C_18(A!16))))))))),
% 112.60/72.32 inference(unit_resolution,[status(thm)],[17, 16])).
% 112.60/72.32 tff(19,plain,
% 112.60/72.32 (((~((~epsilon_transitive(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | ![B: $i] : ((~in(B, tptp_fun_D_17(tptp_fun_C_18(A!16)))) | subset(B, tptp_fun_D_17(tptp_fun_C_18(A!16)))))) | (~(epsilon_transitive(tptp_fun_D_17(tptp_fun_C_18(A!16))) | (~((~in(tptp_fun_B_0(tptp_fun_D_17(tptp_fun_C_18(A!16))), tptp_fun_D_17(tptp_fun_C_18(A!16)))) | subset(tptp_fun_B_0(tptp_fun_D_17(tptp_fun_C_18(A!16))), tptp_fun_D_17(tptp_fun_C_18(A!16)))))))) | ((~epsilon_transitive(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | ![B: $i] : ((~in(B, tptp_fun_D_17(tptp_fun_C_18(A!16)))) | subset(B, tptp_fun_D_17(tptp_fun_C_18(A!16)))))),
% 112.60/72.32 inference(tautology,[status(thm)],[])).
% 112.60/72.32 tff(20,plain,
% 112.60/72.32 ((~epsilon_transitive(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | ![B: $i] : ((~in(B, tptp_fun_D_17(tptp_fun_C_18(A!16)))) | subset(B, tptp_fun_D_17(tptp_fun_C_18(A!16))))),
% 112.60/72.32 inference(unit_resolution,[status(thm)],[19, 18])).
% 112.60/72.32 tff(21,assumption,(empty(A!16)), introduced(assumption)).
% 112.60/72.32 tff(22,plain,
% 112.60/72.32 (^[A: $i, B: $i] : refl(((A = B) | (~empty(B)) | (~empty(A))) <=> ((A = B) | (~empty(B)) | (~empty(A))))),
% 112.60/72.32 inference(bind,[status(th)],[])).
% 112.60/72.32 tff(23,plain,
% 112.60/72.32 (![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A))) <=> ![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))),
% 112.60/72.32 inference(quant_intro,[status(thm)],[22])).
% 112.60/72.32 tff(24,plain,
% 112.60/72.32 (^[A: $i, B: $i] : trans(monotonicity(rewrite((empty(A) & (~(A = B)) & empty(B)) <=> (~((A = B) | (~empty(B)) | (~empty(A))))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> (~(~((A = B) | (~empty(B)) | (~empty(A))))))), rewrite((~(~((A = B) | (~empty(B)) | (~empty(A))))) <=> ((A = B) | (~empty(B)) | (~empty(A)))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> ((A = B) | (~empty(B)) | (~empty(A)))))),
% 112.60/72.32 inference(bind,[status(th)],[])).
% 112.60/72.32 tff(25,plain,
% 112.60/72.32 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))),
% 112.60/72.32 inference(quant_intro,[status(thm)],[24])).
% 112.60/72.32 tff(26,plain,
% 112.60/72.32 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 112.60/72.32 inference(rewrite,[status(thm)],[])).
% 112.60/72.32 tff(27,plain,
% 112.60/72.32 (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 112.60/72.32 inference(bind,[status(th)],[])).
% 112.60/72.32 tff(28,plain,
% 112.60/72.32 (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 112.60/72.32 inference(quant_intro,[status(thm)],[27])).
% 112.60/72.32 tff(29,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_boole')).
% 112.60/72.32 tff(30,plain,
% 112.60/72.32 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 112.60/72.32 inference(modus_ponens,[status(thm)],[29, 28])).
% 112.60/72.32 tff(31,plain,
% 112.60/72.32 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 112.60/72.32 inference(modus_ponens,[status(thm)],[30, 26])).
% 112.60/72.32 tff(32,plain,(
% 112.60/72.32 ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 112.60/72.32 inference(skolemize,[status(sab)],[31])).
% 112.60/72.32 tff(33,plain,
% 112.60/72.32 (![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))),
% 112.60/72.32 inference(modus_ponens,[status(thm)],[32, 25])).
% 112.60/72.32 tff(34,plain,
% 112.60/72.32 (![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))),
% 112.60/72.32 inference(modus_ponens,[status(thm)],[33, 23])).
% 112.60/72.32 tff(35,plain,
% 112.60/72.32 ((ordinal(B!15) & (subset(A!16, B!15) & (~(A!16 = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~in(C, A!16)) | (~(ordinal_subset(C, tptp_fun_D_17(C)) | (~ordinal(tptp_fun_D_17(C))) | (~in(tptp_fun_D_17(C), A!16))))))) <=> (ordinal(B!15) & subset(A!16, B!15) & (~(A!16 = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~in(C, A!16)) | (~(ordinal_subset(C, tptp_fun_D_17(C)) | (~ordinal(tptp_fun_D_17(C))) | (~in(tptp_fun_D_17(C), A!16))))))),
% 112.60/72.32 inference(rewrite,[status(thm)],[])).
% 112.60/72.32 tff(36,plain,
% 112.60/72.32 ((subset(A!16, B!15) & (~(A!16 = empty_set)) & ![C: $i] : ((~ordinal(C)) | ((~in(C, A!16)) | (~(ordinal_subset(C, tptp_fun_D_17(C)) | (~ordinal(tptp_fun_D_17(C))) | (~in(tptp_fun_D_17(C), A!16))))))) <=> (subset(A!16, B!15) & (~(A!16 = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~in(C, A!16)) | (~(ordinal_subset(C, tptp_fun_D_17(C)) | (~ordinal(tptp_fun_D_17(C))) | (~in(tptp_fun_D_17(C), A!16))))))),
% 112.60/72.32 inference(rewrite,[status(thm)],[])).
% 112.60/72.32 tff(37,plain,
% 112.60/72.32 ((~(~ordinal(B!15))) <=> ordinal(B!15)),
% 112.60/72.32 inference(rewrite,[status(thm)],[])).
% 112.60/72.32 tff(38,plain,
% 112.60/72.32 (((~(~ordinal(B!15))) & (subset(A!16, B!15) & (~(A!16 = empty_set)) & ![C: $i] : ((~ordinal(C)) | ((~in(C, A!16)) | (~(ordinal_subset(C, tptp_fun_D_17(C)) | (~ordinal(tptp_fun_D_17(C))) | (~in(tptp_fun_D_17(C), A!16)))))))) <=> (ordinal(B!15) & (subset(A!16, B!15) & (~(A!16 = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~in(C, A!16)) | (~(ordinal_subset(C, tptp_fun_D_17(C)) | (~ordinal(tptp_fun_D_17(C))) | (~in(tptp_fun_D_17(C), A!16)))))))),
% 112.60/72.32 inference(monotonicity,[status(thm)],[37, 36])).
% 112.60/72.32 tff(39,plain,
% 112.60/72.32 (((~(~ordinal(B!15))) & (subset(A!16, B!15) & (~(A!16 = empty_set)) & ![C: $i] : ((~ordinal(C)) | ((~in(C, A!16)) | (~(ordinal_subset(C, tptp_fun_D_17(C)) | (~ordinal(tptp_fun_D_17(C))) | (~in(tptp_fun_D_17(C), A!16)))))))) <=> (ordinal(B!15) & subset(A!16, B!15) & (~(A!16 = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~in(C, A!16)) | (~(ordinal_subset(C, tptp_fun_D_17(C)) | (~ordinal(tptp_fun_D_17(C))) | (~in(tptp_fun_D_17(C), A!16))))))),
% 112.60/72.32 inference(transitivity,[status(thm)],[38, 35])).
% 112.60/72.32 tff(40,plain,
% 112.60/72.32 ((~![A: $i, B: $i] : ((~ordinal(B)) | (~(subset(A, B) & (~(A = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~(in(C, A) & ![D: $i] : (ordinal_subset(C, D) | (~ordinal(D)) | (~in(D, A)))))))))) <=> (~![A: $i, B: $i] : ((~ordinal(B)) | (~(subset(A, B) & (~(A = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~(in(C, A) & ![D: $i] : (ordinal_subset(C, D) | (~ordinal(D)) | (~in(D, A))))))))))),
% 112.60/72.32 inference(rewrite,[status(thm)],[])).
% 112.60/72.32 tff(41,plain,
% 112.60/72.32 ((~![A: $i, B: $i] : (ordinal(B) => (~((subset(A, B) & (~(A = empty_set))) & ![C: $i] : (ordinal(C) => (~(in(C, A) & ![D: $i] : (ordinal(D) => (in(D, A) => ordinal_subset(C, D)))))))))) <=> (~![A: $i, B: $i] : ((~ordinal(B)) | (~(subset(A, B) & (~(A = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~(in(C, A) & ![D: $i] : (ordinal_subset(C, D) | (~ordinal(D)) | (~in(D, A))))))))))),
% 112.60/72.32 inference(rewrite,[status(thm)],[])).
% 112.60/72.32 tff(42,axiom,(~![A: $i, B: $i] : (ordinal(B) => (~((subset(A, B) & (~(A = empty_set))) & ![C: $i] : (ordinal(C) => (~(in(C, A) & ![D: $i] : (ordinal(D) => (in(D, A) => ordinal_subset(C, D)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t32_ordinal1')).
% 112.60/72.32 tff(43,plain,
% 112.60/72.32 (~![A: $i, B: $i] : ((~ordinal(B)) | (~(subset(A, B) & (~(A = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~(in(C, A) & ![D: $i] : (ordinal_subset(C, D) | (~ordinal(D)) | (~in(D, A)))))))))),
% 112.60/72.32 inference(modus_ponens,[status(thm)],[42, 41])).
% 112.60/72.32 tff(44,plain,
% 112.60/72.32 (~![A: $i, B: $i] : ((~ordinal(B)) | (~(subset(A, B) & (~(A = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~(in(C, A) & ![D: $i] : (ordinal_subset(C, D) | (~ordinal(D)) | (~in(D, A)))))))))),
% 112.60/72.32 inference(modus_ponens,[status(thm)],[43, 40])).
% 112.60/72.32 tff(45,plain,
% 112.60/72.32 (~![A: $i, B: $i] : ((~ordinal(B)) | (~(subset(A, B) & (~(A = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~(in(C, A) & ![D: $i] : (ordinal_subset(C, D) | (~ordinal(D)) | (~in(D, A)))))))))),
% 112.60/72.32 inference(modus_ponens,[status(thm)],[44, 40])).
% 112.60/72.32 tff(46,plain,
% 112.60/72.32 (~![A: $i, B: $i] : ((~ordinal(B)) | (~(subset(A, B) & (~(A = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~(in(C, A) & ![D: $i] : (ordinal_subset(C, D) | (~ordinal(D)) | (~in(D, A)))))))))),
% 112.60/72.32 inference(modus_ponens,[status(thm)],[45, 40])).
% 112.60/72.32 tff(47,plain,
% 112.60/72.32 (~![A: $i, B: $i] : ((~ordinal(B)) | (~(subset(A, B) & (~(A = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~(in(C, A) & ![D: $i] : (ordinal_subset(C, D) | (~ordinal(D)) | (~in(D, A)))))))))),
% 112.60/72.32 inference(modus_ponens,[status(thm)],[46, 40])).
% 112.60/72.32 tff(48,plain,
% 112.60/72.32 (~![A: $i, B: $i] : ((~ordinal(B)) | (~(subset(A, B) & (~(A = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~(in(C, A) & ![D: $i] : (ordinal_subset(C, D) | (~ordinal(D)) | (~in(D, A)))))))))),
% 112.60/72.32 inference(modus_ponens,[status(thm)],[47, 40])).
% 112.60/72.32 tff(49,plain,
% 112.60/72.32 (~![A: $i, B: $i] : ((~ordinal(B)) | (~(subset(A, B) & (~(A = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~(in(C, A) & ![D: $i] : (ordinal_subset(C, D) | (~ordinal(D)) | (~in(D, A)))))))))),
% 112.60/72.32 inference(modus_ponens,[status(thm)],[48, 40])).
% 112.60/72.32 tff(50,plain,
% 112.60/72.32 (ordinal(B!15) & subset(A!16, B!15) & (~(A!16 = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~in(C, A!16)) | (~(ordinal_subset(C, tptp_fun_D_17(C)) | (~ordinal(tptp_fun_D_17(C))) | (~in(tptp_fun_D_17(C), A!16)))))),
% 112.60/72.32 inference(modus_ponens,[status(thm)],[49, 39])).
% 112.60/72.32 tff(51,plain,
% 112.60/72.32 (~(A!16 = empty_set)),
% 112.60/72.32 inference(and_elim,[status(thm)],[50])).
% 112.60/72.32 tff(52,plain,
% 112.60/72.32 (empty(empty_set) <=> empty(empty_set)),
% 112.60/72.32 inference(rewrite,[status(thm)],[])).
% 112.60/72.32 tff(53,axiom,((empty(empty_set) & relation(empty_set)) & relation_empty_yielding(empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc12_relat_1')).
% 112.60/72.32 tff(54,plain,
% 112.60/72.32 (empty(empty_set) & relation(empty_set)),
% 112.60/72.32 inference(and_elim,[status(thm)],[53])).
% 112.60/72.32 tff(55,plain,
% 112.60/72.32 (empty(empty_set)),
% 112.60/72.32 inference(and_elim,[status(thm)],[54])).
% 112.60/72.32 tff(56,plain,
% 112.60/72.32 (empty(empty_set)),
% 112.60/72.32 inference(modus_ponens,[status(thm)],[55, 52])).
% 112.60/72.32 tff(57,plain,
% 112.60/72.32 (((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | ((A!16 = empty_set) | (~empty(empty_set)) | (~empty(A!16)))) <=> ((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | (A!16 = empty_set) | (~empty(empty_set)) | (~empty(A!16)))),
% 112.60/72.32 inference(rewrite,[status(thm)],[])).
% 112.60/72.32 tff(58,plain,
% 112.60/72.32 ((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | ((A!16 = empty_set) | (~empty(empty_set)) | (~empty(A!16)))),
% 112.60/72.32 inference(quant_inst,[status(thm)],[])).
% 112.60/72.32 tff(59,plain,
% 112.60/72.32 ((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | (A!16 = empty_set) | (~empty(empty_set)) | (~empty(A!16))),
% 112.60/72.32 inference(modus_ponens,[status(thm)],[58, 57])).
% 112.60/72.32 tff(60,plain,
% 112.60/72.32 ($false),
% 112.60/72.32 inference(unit_resolution,[status(thm)],[59, 56, 51, 34, 21])).
% 112.60/72.32 tff(61,plain,(~empty(A!16)), inference(lemma,lemma(discharge,[]))).
% 112.60/72.32 tff(62,plain,
% 112.60/72.32 (![A: $i] : ?[B: $i] : element(B, A) <=> ![A: $i] : ?[B: $i] : element(B, A)),
% 112.60/72.32 inference(rewrite,[status(thm)],[])).
% 112.60/72.32 tff(63,axiom,(![A: $i] : ?[B: $i] : element(B, A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','existence_m1_subset_1')).
% 112.60/72.32 tff(64,plain,
% 112.60/72.32 (![A: $i] : ?[B: $i] : element(B, A)),
% 112.60/72.32 inference(modus_ponens,[status(thm)],[63, 62])).
% 112.60/72.32 tff(65,plain,(
% 112.60/72.32 ![A: $i] : element(tptp_fun_B_1(A), A)),
% 112.60/72.32 inference(skolemize,[status(sab)],[64])).
% 112.60/72.32 tff(66,plain,
% 112.60/72.32 ((~![A: $i] : element(tptp_fun_B_1(A), A)) | element(tptp_fun_B_1(A!16), A!16)),
% 112.60/72.32 inference(quant_inst,[status(thm)],[])).
% 112.60/72.32 tff(67,plain,
% 112.60/72.32 (element(tptp_fun_B_1(A!16), A!16)),
% 112.60/72.32 inference(unit_resolution,[status(thm)],[66, 65])).
% 112.60/72.32 tff(68,plain,
% 112.60/72.32 (^[A: $i, B: $i] : refl((empty(B) | in(A, B) | (~element(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 112.60/72.32 inference(bind,[status(th)],[])).
% 112.60/72.32 tff(69,plain,
% 112.60/72.32 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 112.60/72.32 inference(quant_intro,[status(thm)],[68])).
% 112.60/72.32 tff(70,plain,
% 112.60/72.32 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 112.60/72.32 inference(rewrite,[status(thm)],[])).
% 112.60/72.32 tff(71,plain,
% 112.60/72.32 (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 112.60/72.32 inference(bind,[status(th)],[])).
% 112.60/72.32 tff(72,plain,
% 112.60/72.32 (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 112.60/72.32 inference(quant_intro,[status(thm)],[71])).
% 112.60/72.32 tff(73,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_subset')).
% 112.60/72.32 tff(74,plain,
% 112.60/72.32 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 112.60/72.32 inference(modus_ponens,[status(thm)],[73, 72])).
% 112.60/72.32 tff(75,plain,
% 112.60/72.32 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 112.60/72.32 inference(modus_ponens,[status(thm)],[74, 70])).
% 112.60/72.32 tff(76,plain,(
% 112.60/72.32 ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 112.60/72.32 inference(skolemize,[status(sab)],[75])).
% 112.60/72.32 tff(77,plain,
% 112.60/72.32 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 112.60/72.32 inference(modus_ponens,[status(thm)],[76, 69])).
% 112.60/72.32 tff(78,plain,
% 112.60/72.32 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!16) | in(tptp_fun_B_1(A!16), A!16) | (~element(tptp_fun_B_1(A!16), A!16)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(A!16) | in(tptp_fun_B_1(A!16), A!16) | (~element(tptp_fun_B_1(A!16), A!16)))),
% 112.65/72.33 inference(rewrite,[status(thm)],[])).
% 112.65/72.33 tff(79,plain,
% 112.65/72.33 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!16) | in(tptp_fun_B_1(A!16), A!16) | (~element(tptp_fun_B_1(A!16), A!16)))),
% 112.65/72.33 inference(quant_inst,[status(thm)],[])).
% 112.65/72.33 tff(80,plain,
% 112.65/72.33 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(A!16) | in(tptp_fun_B_1(A!16), A!16) | (~element(tptp_fun_B_1(A!16), A!16))),
% 112.65/72.33 inference(modus_ponens,[status(thm)],[79, 78])).
% 112.65/72.33 tff(81,plain,
% 112.65/72.33 (empty(A!16) | in(tptp_fun_B_1(A!16), A!16)),
% 112.65/72.33 inference(unit_resolution,[status(thm)],[80, 77, 67])).
% 112.65/72.33 tff(82,plain,
% 112.65/72.33 (in(tptp_fun_B_1(A!16), A!16)),
% 112.65/72.33 inference(unit_resolution,[status(thm)],[81, 61])).
% 112.65/72.33 tff(83,plain,
% 112.65/72.33 (^[A: $i, B: $i] : refl(((~in(A, B)) | (~((~in(tptp_fun_C_18(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_18(B)))))))) <=> ((~in(A, B)) | (~((~in(tptp_fun_C_18(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_18(B)))))))))),
% 112.65/72.33 inference(bind,[status(th)],[])).
% 112.65/72.33 tff(84,plain,
% 112.65/72.33 (![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_18(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_18(B)))))))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_18(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_18(B))))))))),
% 112.65/72.33 inference(quant_intro,[status(thm)],[83])).
% 112.65/72.33 tff(85,plain,
% 112.65/72.33 (^[A: $i, B: $i] : rewrite(((~in(A, B)) | (~((~in(tptp_fun_C_18(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_18(B)))))))) <=> ((~in(A, B)) | (~((~in(tptp_fun_C_18(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_18(B)))))))))),
% 112.65/72.33 inference(bind,[status(th)],[])).
% 112.65/72.33 tff(86,plain,
% 112.65/72.33 (![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_18(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_18(B)))))))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_18(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_18(B))))))))),
% 112.65/72.33 inference(quant_intro,[status(thm)],[85])).
% 112.65/72.33 tff(87,plain,
% 112.65/72.33 (![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_18(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_18(B)))))))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_18(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_18(B))))))))),
% 112.65/72.33 inference(transitivity,[status(thm)],[86, 84])).
% 112.65/72.33 tff(88,plain,
% 112.65/72.33 (^[A: $i, B: $i] : rewrite(((~in(A, B)) | (in(tptp_fun_C_18(B), B) & ![D: $i] : (~(in(D, B) & in(D, tptp_fun_C_18(B)))))) <=> ((~in(A, B)) | (~((~in(tptp_fun_C_18(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_18(B)))))))))),
% 112.65/72.33 inference(bind,[status(th)],[])).
% 112.65/72.33 tff(89,plain,
% 112.65/72.33 (![A: $i, B: $i] : ((~in(A, B)) | (in(tptp_fun_C_18(B), B) & ![D: $i] : (~(in(D, B) & in(D, tptp_fun_C_18(B)))))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_18(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_18(B))))))))),
% 112.65/72.33 inference(quant_intro,[status(thm)],[88])).
% 112.65/72.33 tff(90,plain,
% 112.65/72.33 (![A: $i, B: $i] : (~(in(A, B) & ![C: $i] : (~(in(C, B) & ![D: $i] : (~(in(D, B) & in(D, C))))))) <=> ![A: $i, B: $i] : (~(in(A, B) & ![C: $i] : (~(in(C, B) & ![D: $i] : (~(in(D, B) & in(D, C)))))))),
% 112.65/72.33 inference(rewrite,[status(thm)],[])).
% 112.65/72.33 tff(91,axiom,(![A: $i, B: $i] : (~(in(A, B) & ![C: $i] : (~(in(C, B) & ![D: $i] : (~(in(D, B) & in(D, C)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t7_tarski')).
% 112.65/72.33 tff(92,plain,
% 112.65/72.33 (![A: $i, B: $i] : (~(in(A, B) & ![C: $i] : (~(in(C, B) & ![D: $i] : (~(in(D, B) & in(D, C)))))))),
% 112.65/72.33 inference(modus_ponens,[status(thm)],[91, 90])).
% 112.65/72.33 tff(93,plain,(
% 112.65/72.33 ![A: $i, B: $i] : ((~in(A, B)) | (in(tptp_fun_C_18(B), B) & ![D: $i] : (~(in(D, B) & in(D, tptp_fun_C_18(B))))))),
% 112.65/72.33 inference(skolemize,[status(sab)],[92])).
% 112.65/72.33 tff(94,plain,
% 112.65/72.33 (![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_18(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_18(B))))))))),
% 112.65/72.33 inference(modus_ponens,[status(thm)],[93, 89])).
% 112.65/72.33 tff(95,plain,
% 112.65/72.33 (![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_18(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_18(B))))))))),
% 112.65/72.33 inference(modus_ponens,[status(thm)],[94, 87])).
% 112.65/72.33 tff(96,plain,
% 112.65/72.33 (((~![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_18(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_18(B))))))))) | ((~in(tptp_fun_B_1(A!16), A!16)) | (~((~in(tptp_fun_C_18(A!16), A!16)) | (~![D: $i] : ((~in(D, A!16)) | (~in(D, tptp_fun_C_18(A!16))))))))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_18(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_18(B))))))))) | (~in(tptp_fun_B_1(A!16), A!16)) | (~((~in(tptp_fun_C_18(A!16), A!16)) | (~![D: $i] : ((~in(D, A!16)) | (~in(D, tptp_fun_C_18(A!16))))))))),
% 112.65/72.33 inference(rewrite,[status(thm)],[])).
% 112.65/72.33 tff(97,plain,
% 112.65/72.33 ((~![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_18(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_18(B))))))))) | ((~in(tptp_fun_B_1(A!16), A!16)) | (~((~in(tptp_fun_C_18(A!16), A!16)) | (~![D: $i] : ((~in(D, A!16)) | (~in(D, tptp_fun_C_18(A!16))))))))),
% 112.65/72.33 inference(quant_inst,[status(thm)],[])).
% 112.65/72.33 tff(98,plain,
% 112.65/72.33 ((~![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_18(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_18(B))))))))) | (~in(tptp_fun_B_1(A!16), A!16)) | (~((~in(tptp_fun_C_18(A!16), A!16)) | (~![D: $i] : ((~in(D, A!16)) | (~in(D, tptp_fun_C_18(A!16)))))))),
% 112.65/72.33 inference(modus_ponens,[status(thm)],[97, 96])).
% 112.65/72.33 tff(99,plain,
% 112.65/72.33 (~((~in(tptp_fun_C_18(A!16), A!16)) | (~![D: $i] : ((~in(D, A!16)) | (~in(D, tptp_fun_C_18(A!16))))))),
% 112.65/72.33 inference(unit_resolution,[status(thm)],[98, 95, 82])).
% 112.65/72.33 tff(100,plain,
% 112.65/72.33 (((~in(tptp_fun_C_18(A!16), A!16)) | (~![D: $i] : ((~in(D, A!16)) | (~in(D, tptp_fun_C_18(A!16)))))) | in(tptp_fun_C_18(A!16), A!16)),
% 112.65/72.33 inference(tautology,[status(thm)],[])).
% 112.65/72.33 tff(101,plain,
% 112.65/72.33 (in(tptp_fun_C_18(A!16), A!16)),
% 112.65/72.33 inference(unit_resolution,[status(thm)],[100, 99])).
% 112.65/72.33 tff(102,plain,
% 112.65/72.33 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 112.65/72.33 inference(bind,[status(th)],[])).
% 112.65/72.33 tff(103,plain,
% 112.65/72.33 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 112.65/72.33 inference(quant_intro,[status(thm)],[102])).
% 112.65/72.33 tff(104,plain,
% 112.65/72.33 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 112.65/72.33 inference(rewrite,[status(thm)],[])).
% 112.65/72.33 tff(105,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_subset')).
% 112.65/72.33 tff(106,plain,
% 112.65/72.33 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 112.65/72.33 inference(modus_ponens,[status(thm)],[105, 104])).
% 112.65/72.33 tff(107,plain,(
% 112.65/72.33 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 112.65/72.33 inference(skolemize,[status(sab)],[106])).
% 112.65/72.33 tff(108,plain,
% 112.65/72.33 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 112.65/72.33 inference(modus_ponens,[status(thm)],[107, 103])).
% 112.65/72.33 tff(109,plain,
% 112.65/72.33 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(A!16, powerset(B!15)) <=> subset(A!16, B!15))),
% 112.65/72.33 inference(quant_inst,[status(thm)],[])).
% 112.65/72.33 tff(110,plain,
% 112.65/72.33 (element(A!16, powerset(B!15)) <=> subset(A!16, B!15)),
% 112.65/72.33 inference(unit_resolution,[status(thm)],[109, 108])).
% 112.65/72.33 tff(111,plain,
% 112.65/72.33 (subset(A!16, B!15)),
% 112.65/72.33 inference(and_elim,[status(thm)],[50])).
% 112.65/72.33 tff(112,plain,
% 112.65/72.33 ((~(element(A!16, powerset(B!15)) <=> subset(A!16, B!15))) | element(A!16, powerset(B!15)) | (~subset(A!16, B!15))),
% 112.65/72.33 inference(tautology,[status(thm)],[])).
% 112.65/72.33 tff(113,plain,
% 112.65/72.33 ((~(element(A!16, powerset(B!15)) <=> subset(A!16, B!15))) | element(A!16, powerset(B!15))),
% 112.65/72.33 inference(unit_resolution,[status(thm)],[112, 111])).
% 112.65/72.33 tff(114,plain,
% 112.65/72.33 (element(A!16, powerset(B!15))),
% 112.65/72.33 inference(unit_resolution,[status(thm)],[113, 110])).
% 112.65/72.33 tff(115,plain,
% 112.65/72.33 (^[A: $i, B: $i, C: $i] : refl((element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))))),
% 112.65/72.33 inference(bind,[status(th)],[])).
% 112.65/72.33 tff(116,plain,
% 112.65/72.33 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 112.65/72.33 inference(quant_intro,[status(thm)],[115])).
% 112.65/72.33 tff(117,plain,
% 112.65/72.33 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((in(A, B) & element(B, powerset(C))) <=> (~((~in(A, B)) | (~element(B, powerset(C)))))), ((~(in(A, B) & element(B, powerset(C)))) <=> (~(~((~in(A, B)) | (~element(B, powerset(C)))))))), rewrite((~(~((~in(A, B)) | (~element(B, powerset(C)))))) <=> ((~in(A, B)) | (~element(B, powerset(C))))), ((~(in(A, B) & element(B, powerset(C)))) <=> ((~in(A, B)) | (~element(B, powerset(C)))))), (((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> (((~in(A, B)) | (~element(B, powerset(C)))) | element(A, C)))), rewrite((((~in(A, B)) | (~element(B, powerset(C)))) | element(A, C)) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))), (((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))))),
% 112.65/72.33 inference(bind,[status(th)],[])).
% 112.65/72.33 tff(118,plain,
% 112.65/72.33 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> ![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 112.65/72.33 inference(quant_intro,[status(thm)],[117])).
% 112.65/72.33 tff(119,plain,
% 112.65/72.33 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 112.65/72.33 inference(rewrite,[status(thm)],[])).
% 112.65/72.33 tff(120,plain,
% 112.65/72.33 (^[A: $i, B: $i, C: $i] : rewrite(((in(A, B) & element(B, powerset(C))) => element(A, C)) <=> ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)))),
% 112.65/72.33 inference(bind,[status(th)],[])).
% 112.65/72.33 tff(121,plain,
% 112.65/72.33 (![A: $i, B: $i, C: $i] : ((in(A, B) & element(B, powerset(C))) => element(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 112.65/72.33 inference(quant_intro,[status(thm)],[120])).
% 112.65/72.33 tff(122,axiom,(![A: $i, B: $i, C: $i] : ((in(A, B) & element(B, powerset(C))) => element(A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t4_subset')).
% 112.65/72.33 tff(123,plain,
% 112.65/72.33 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 112.65/72.33 inference(modus_ponens,[status(thm)],[122, 121])).
% 112.65/72.33 tff(124,plain,
% 112.65/72.33 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 112.65/72.33 inference(modus_ponens,[status(thm)],[123, 119])).
% 112.65/72.33 tff(125,plain,(
% 112.65/72.33 ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 112.65/72.33 inference(skolemize,[status(sab)],[124])).
% 112.65/72.33 tff(126,plain,
% 112.65/72.33 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 112.65/72.33 inference(modus_ponens,[status(thm)],[125, 118])).
% 112.65/72.33 tff(127,plain,
% 112.65/72.33 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 112.65/72.33 inference(modus_ponens,[status(thm)],[126, 116])).
% 112.65/72.33 tff(128,plain,
% 112.65/72.33 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(A!16, powerset(B!15))) | (~in(tptp_fun_C_18(A!16), A!16)) | element(tptp_fun_C_18(A!16), B!15))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(A!16, powerset(B!15))) | (~in(tptp_fun_C_18(A!16), A!16)) | element(tptp_fun_C_18(A!16), B!15))),
% 112.65/72.33 inference(rewrite,[status(thm)],[])).
% 112.65/72.33 tff(129,plain,
% 112.65/72.33 ((element(tptp_fun_C_18(A!16), B!15) | (~in(tptp_fun_C_18(A!16), A!16)) | (~element(A!16, powerset(B!15)))) <=> ((~element(A!16, powerset(B!15))) | (~in(tptp_fun_C_18(A!16), A!16)) | element(tptp_fun_C_18(A!16), B!15))),
% 112.65/72.33 inference(rewrite,[status(thm)],[])).
% 112.65/72.33 tff(130,plain,
% 112.65/72.33 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_C_18(A!16), B!15) | (~in(tptp_fun_C_18(A!16), A!16)) | (~element(A!16, powerset(B!15))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(A!16, powerset(B!15))) | (~in(tptp_fun_C_18(A!16), A!16)) | element(tptp_fun_C_18(A!16), B!15)))),
% 112.65/72.33 inference(monotonicity,[status(thm)],[129])).
% 112.65/72.33 tff(131,plain,
% 112.65/72.33 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_C_18(A!16), B!15) | (~in(tptp_fun_C_18(A!16), A!16)) | (~element(A!16, powerset(B!15))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(A!16, powerset(B!15))) | (~in(tptp_fun_C_18(A!16), A!16)) | element(tptp_fun_C_18(A!16), B!15))),
% 112.65/72.33 inference(transitivity,[status(thm)],[130, 128])).
% 112.65/72.33 tff(132,plain,
% 112.65/72.33 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_C_18(A!16), B!15) | (~in(tptp_fun_C_18(A!16), A!16)) | (~element(A!16, powerset(B!15))))),
% 112.65/72.33 inference(quant_inst,[status(thm)],[])).
% 112.65/72.33 tff(133,plain,
% 112.65/72.33 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(A!16, powerset(B!15))) | (~in(tptp_fun_C_18(A!16), A!16)) | element(tptp_fun_C_18(A!16), B!15)),
% 112.65/72.33 inference(modus_ponens,[status(thm)],[132, 131])).
% 112.65/72.33 tff(134,plain,
% 112.65/72.33 (element(tptp_fun_C_18(A!16), B!15)),
% 112.65/72.33 inference(unit_resolution,[status(thm)],[133, 127, 114, 101])).
% 112.65/72.33 tff(135,plain,
% 112.65/72.33 (^[A: $i, B: $i, C: $i] : refl(((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))),
% 112.65/72.33 inference(bind,[status(th)],[])).
% 112.65/72.33 tff(136,plain,
% 112.65/72.33 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 112.65/72.33 inference(quant_intro,[status(thm)],[135])).
% 112.65/72.33 tff(137,plain,
% 112.65/72.33 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, B) & element(B, powerset(C)) & empty(C)) <=> (~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))), ((~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> (~(~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))))), rewrite((~(~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))), ((~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))))),
% 112.65/72.33 inference(bind,[status(th)],[])).
% 112.65/72.33 tff(138,plain,
% 112.65/72.33 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 112.65/72.33 inference(quant_intro,[status(thm)],[137])).
% 112.65/72.33 tff(139,plain,
% 112.65/72.33 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 112.65/72.33 inference(rewrite,[status(thm)],[])).
% 112.65/72.33 tff(140,plain,
% 112.65/72.33 (^[A: $i, B: $i, C: $i] : rewrite((~((in(A, B) & element(B, powerset(C))) & empty(C))) <=> (~(in(A, B) & element(B, powerset(C)) & empty(C))))),
% 112.65/72.33 inference(bind,[status(th)],[])).
% 112.65/72.33 tff(141,plain,
% 112.65/72.33 (![A: $i, B: $i, C: $i] : (~((in(A, B) & element(B, powerset(C))) & empty(C))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 112.65/72.33 inference(quant_intro,[status(thm)],[140])).
% 112.65/72.33 tff(142,axiom,(![A: $i, B: $i, C: $i] : (~((in(A, B) & element(B, powerset(C))) & empty(C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t5_subset')).
% 112.65/72.33 tff(143,plain,
% 112.65/72.33 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 112.65/72.33 inference(modus_ponens,[status(thm)],[142, 141])).
% 112.65/72.33 tff(144,plain,
% 112.65/72.33 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 112.65/72.33 inference(modus_ponens,[status(thm)],[143, 139])).
% 112.65/72.33 tff(145,plain,(
% 112.65/72.33 ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 112.65/72.33 inference(skolemize,[status(sab)],[144])).
% 112.65/72.33 tff(146,plain,
% 112.65/72.33 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 112.65/72.33 inference(modus_ponens,[status(thm)],[145, 138])).
% 112.65/72.34 tff(147,plain,
% 112.65/72.34 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 112.65/72.34 inference(modus_ponens,[status(thm)],[146, 136])).
% 112.65/72.34 tff(148,plain,
% 112.65/72.34 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(B!15)) | (~element(A!16, powerset(B!15))) | (~in(tptp_fun_B_1(A!16), A!16)))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~empty(B!15)) | (~element(A!16, powerset(B!15))) | (~in(tptp_fun_B_1(A!16), A!16)))),
% 112.65/72.34 inference(rewrite,[status(thm)],[])).
% 112.65/72.34 tff(149,plain,
% 112.65/72.34 (((~empty(B!15)) | (~in(tptp_fun_B_1(A!16), A!16)) | (~element(A!16, powerset(B!15)))) <=> ((~empty(B!15)) | (~element(A!16, powerset(B!15))) | (~in(tptp_fun_B_1(A!16), A!16)))),
% 112.65/72.34 inference(rewrite,[status(thm)],[])).
% 112.65/72.34 tff(150,plain,
% 112.65/72.34 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(B!15)) | (~in(tptp_fun_B_1(A!16), A!16)) | (~element(A!16, powerset(B!15))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(B!15)) | (~element(A!16, powerset(B!15))) | (~in(tptp_fun_B_1(A!16), A!16))))),
% 112.65/72.34 inference(monotonicity,[status(thm)],[149])).
% 112.65/72.34 tff(151,plain,
% 112.65/72.34 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(B!15)) | (~in(tptp_fun_B_1(A!16), A!16)) | (~element(A!16, powerset(B!15))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~empty(B!15)) | (~element(A!16, powerset(B!15))) | (~in(tptp_fun_B_1(A!16), A!16)))),
% 112.65/72.34 inference(transitivity,[status(thm)],[150, 148])).
% 112.65/72.34 tff(152,plain,
% 112.65/72.34 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(B!15)) | (~in(tptp_fun_B_1(A!16), A!16)) | (~element(A!16, powerset(B!15))))),
% 112.65/72.34 inference(quant_inst,[status(thm)],[])).
% 112.65/72.34 tff(153,plain,
% 112.65/72.34 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~empty(B!15)) | (~element(A!16, powerset(B!15))) | (~in(tptp_fun_B_1(A!16), A!16))),
% 112.65/72.34 inference(modus_ponens,[status(thm)],[152, 151])).
% 112.65/72.34 tff(154,plain,
% 112.65/72.34 (~empty(B!15)),
% 112.65/72.34 inference(unit_resolution,[status(thm)],[153, 147, 114, 82])).
% 112.65/72.34 tff(155,plain,
% 112.65/72.34 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(B!15) | in(tptp_fun_C_18(A!16), B!15) | (~element(tptp_fun_C_18(A!16), B!15)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(B!15) | in(tptp_fun_C_18(A!16), B!15) | (~element(tptp_fun_C_18(A!16), B!15)))),
% 112.65/72.34 inference(rewrite,[status(thm)],[])).
% 112.65/72.34 tff(156,plain,
% 112.65/72.34 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(B!15) | in(tptp_fun_C_18(A!16), B!15) | (~element(tptp_fun_C_18(A!16), B!15)))),
% 112.65/72.34 inference(quant_inst,[status(thm)],[])).
% 112.65/72.34 tff(157,plain,
% 112.65/72.34 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(B!15) | in(tptp_fun_C_18(A!16), B!15) | (~element(tptp_fun_C_18(A!16), B!15))),
% 112.65/72.34 inference(modus_ponens,[status(thm)],[156, 155])).
% 112.65/72.34 tff(158,plain,
% 112.65/72.34 (in(tptp_fun_C_18(A!16), B!15)),
% 112.65/72.34 inference(unit_resolution,[status(thm)],[157, 77, 154, 134])).
% 112.65/72.34 tff(159,plain,
% 112.65/72.34 (ordinal(B!15)),
% 112.65/72.34 inference(and_elim,[status(thm)],[50])).
% 112.65/72.34 tff(160,plain,
% 112.65/72.34 (^[A: $i, B: $i] : refl((ordinal(A) | (~in(A, B)) | (~ordinal(B))) <=> (ordinal(A) | (~in(A, B)) | (~ordinal(B))))),
% 112.65/72.34 inference(bind,[status(th)],[])).
% 112.65/72.34 tff(161,plain,
% 112.65/72.34 (![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B))) <=> ![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 112.65/72.34 inference(quant_intro,[status(thm)],[160])).
% 112.65/72.34 tff(162,plain,
% 112.65/72.34 (![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B))) <=> ![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 112.65/72.34 inference(rewrite,[status(thm)],[])).
% 112.65/72.34 tff(163,plain,
% 112.65/72.34 (^[A: $i, B: $i] : trans(monotonicity(rewrite((in(A, B) => ordinal(A)) <=> (ordinal(A) | (~in(A, B)))), ((ordinal(B) => (in(A, B) => ordinal(A))) <=> (ordinal(B) => (ordinal(A) | (~in(A, B)))))), rewrite((ordinal(B) => (ordinal(A) | (~in(A, B)))) <=> (ordinal(A) | (~in(A, B)) | (~ordinal(B)))), ((ordinal(B) => (in(A, B) => ordinal(A))) <=> (ordinal(A) | (~in(A, B)) | (~ordinal(B)))))),
% 112.65/72.34 inference(bind,[status(th)],[])).
% 112.65/72.34 tff(164,plain,
% 112.65/72.34 (![A: $i, B: $i] : (ordinal(B) => (in(A, B) => ordinal(A))) <=> ![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 112.65/72.34 inference(quant_intro,[status(thm)],[163])).
% 112.65/72.34 tff(165,axiom,(![A: $i, B: $i] : (ordinal(B) => (in(A, B) => ordinal(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t23_ordinal1')).
% 112.65/72.34 tff(166,plain,
% 112.65/72.34 (![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 112.65/72.34 inference(modus_ponens,[status(thm)],[165, 164])).
% 112.65/72.34 tff(167,plain,
% 112.65/72.34 (![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 112.65/72.34 inference(modus_ponens,[status(thm)],[166, 162])).
% 112.65/72.34 tff(168,plain,(
% 112.65/72.34 ![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 112.65/72.34 inference(skolemize,[status(sab)],[167])).
% 112.65/72.34 tff(169,plain,
% 112.65/72.34 (![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 112.65/72.34 inference(modus_ponens,[status(thm)],[168, 161])).
% 112.65/72.34 tff(170,plain,
% 112.65/72.34 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ((~ordinal(B!15)) | ordinal(tptp_fun_C_18(A!16)) | (~in(tptp_fun_C_18(A!16), B!15)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(B!15)) | ordinal(tptp_fun_C_18(A!16)) | (~in(tptp_fun_C_18(A!16), B!15)))),
% 112.65/72.34 inference(rewrite,[status(thm)],[])).
% 112.65/72.34 tff(171,plain,
% 112.65/72.34 ((ordinal(tptp_fun_C_18(A!16)) | (~in(tptp_fun_C_18(A!16), B!15)) | (~ordinal(B!15))) <=> ((~ordinal(B!15)) | ordinal(tptp_fun_C_18(A!16)) | (~in(tptp_fun_C_18(A!16), B!15)))),
% 112.65/72.34 inference(rewrite,[status(thm)],[])).
% 112.65/72.34 tff(172,plain,
% 112.65/72.34 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_C_18(A!16)) | (~in(tptp_fun_C_18(A!16), B!15)) | (~ordinal(B!15)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ((~ordinal(B!15)) | ordinal(tptp_fun_C_18(A!16)) | (~in(tptp_fun_C_18(A!16), B!15))))),
% 112.65/72.34 inference(monotonicity,[status(thm)],[171])).
% 112.65/72.34 tff(173,plain,
% 112.65/72.34 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_C_18(A!16)) | (~in(tptp_fun_C_18(A!16), B!15)) | (~ordinal(B!15)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(B!15)) | ordinal(tptp_fun_C_18(A!16)) | (~in(tptp_fun_C_18(A!16), B!15)))),
% 112.65/72.34 inference(transitivity,[status(thm)],[172, 170])).
% 112.65/72.34 tff(174,plain,
% 112.65/72.34 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_C_18(A!16)) | (~in(tptp_fun_C_18(A!16), B!15)) | (~ordinal(B!15)))),
% 112.65/72.34 inference(quant_inst,[status(thm)],[])).
% 112.65/72.34 tff(175,plain,
% 112.65/72.34 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(B!15)) | ordinal(tptp_fun_C_18(A!16)) | (~in(tptp_fun_C_18(A!16), B!15))),
% 112.65/72.34 inference(modus_ponens,[status(thm)],[174, 173])).
% 112.65/72.34 tff(176,plain,
% 112.65/72.34 (ordinal(tptp_fun_C_18(A!16))),
% 112.65/72.34 inference(unit_resolution,[status(thm)],[175, 169, 159, 158])).
% 112.65/72.34 tff(177,plain,
% 112.65/72.34 (^[C: $i] : refl(((~ordinal(C)) | (~in(C, A!16)) | (~(ordinal_subset(C, tptp_fun_D_17(C)) | (~ordinal(tptp_fun_D_17(C))) | (~in(tptp_fun_D_17(C), A!16))))) <=> ((~ordinal(C)) | (~in(C, A!16)) | (~(ordinal_subset(C, tptp_fun_D_17(C)) | (~ordinal(tptp_fun_D_17(C))) | (~in(tptp_fun_D_17(C), A!16))))))),
% 112.65/72.34 inference(bind,[status(th)],[])).
% 112.65/72.34 tff(178,plain,
% 112.65/72.34 (![C: $i] : ((~ordinal(C)) | (~in(C, A!16)) | (~(ordinal_subset(C, tptp_fun_D_17(C)) | (~ordinal(tptp_fun_D_17(C))) | (~in(tptp_fun_D_17(C), A!16))))) <=> ![C: $i] : ((~ordinal(C)) | (~in(C, A!16)) | (~(ordinal_subset(C, tptp_fun_D_17(C)) | (~ordinal(tptp_fun_D_17(C))) | (~in(tptp_fun_D_17(C), A!16)))))),
% 112.65/72.34 inference(quant_intro,[status(thm)],[177])).
% 112.65/72.34 tff(179,plain,
% 112.65/72.34 (![C: $i] : ((~ordinal(C)) | (~in(C, A!16)) | (~(ordinal_subset(C, tptp_fun_D_17(C)) | (~ordinal(tptp_fun_D_17(C))) | (~in(tptp_fun_D_17(C), A!16)))))),
% 112.65/72.34 inference(and_elim,[status(thm)],[50])).
% 112.65/72.34 tff(180,plain,
% 112.65/72.34 (![C: $i] : ((~ordinal(C)) | (~in(C, A!16)) | (~(ordinal_subset(C, tptp_fun_D_17(C)) | (~ordinal(tptp_fun_D_17(C))) | (~in(tptp_fun_D_17(C), A!16)))))),
% 112.65/72.34 inference(modus_ponens,[status(thm)],[179, 178])).
% 112.65/72.34 tff(181,plain,
% 112.65/72.34 (((~![C: $i] : ((~ordinal(C)) | (~in(C, A!16)) | (~(ordinal_subset(C, tptp_fun_D_17(C)) | (~ordinal(tptp_fun_D_17(C))) | (~in(tptp_fun_D_17(C), A!16)))))) | ((~ordinal(tptp_fun_C_18(A!16))) | (~in(tptp_fun_C_18(A!16), A!16)) | (~(ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) | (~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~in(tptp_fun_D_17(tptp_fun_C_18(A!16)), A!16)))))) <=> ((~![C: $i] : ((~ordinal(C)) | (~in(C, A!16)) | (~(ordinal_subset(C, tptp_fun_D_17(C)) | (~ordinal(tptp_fun_D_17(C))) | (~in(tptp_fun_D_17(C), A!16)))))) | (~ordinal(tptp_fun_C_18(A!16))) | (~in(tptp_fun_C_18(A!16), A!16)) | (~(ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) | (~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~in(tptp_fun_D_17(tptp_fun_C_18(A!16)), A!16)))))),
% 112.65/72.34 inference(rewrite,[status(thm)],[])).
% 112.65/72.34 tff(182,plain,
% 112.65/72.34 ((~![C: $i] : ((~ordinal(C)) | (~in(C, A!16)) | (~(ordinal_subset(C, tptp_fun_D_17(C)) | (~ordinal(tptp_fun_D_17(C))) | (~in(tptp_fun_D_17(C), A!16)))))) | ((~ordinal(tptp_fun_C_18(A!16))) | (~in(tptp_fun_C_18(A!16), A!16)) | (~(ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) | (~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~in(tptp_fun_D_17(tptp_fun_C_18(A!16)), A!16)))))),
% 112.65/72.34 inference(quant_inst,[status(thm)],[])).
% 112.65/72.34 tff(183,plain,
% 112.65/72.34 ((~![C: $i] : ((~ordinal(C)) | (~in(C, A!16)) | (~(ordinal_subset(C, tptp_fun_D_17(C)) | (~ordinal(tptp_fun_D_17(C))) | (~in(tptp_fun_D_17(C), A!16)))))) | (~ordinal(tptp_fun_C_18(A!16))) | (~in(tptp_fun_C_18(A!16), A!16)) | (~(ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) | (~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~in(tptp_fun_D_17(tptp_fun_C_18(A!16)), A!16))))),
% 112.65/72.34 inference(modus_ponens,[status(thm)],[182, 181])).
% 112.65/72.34 tff(184,plain,
% 112.65/72.34 ((~ordinal(tptp_fun_C_18(A!16))) | (~(ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) | (~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~in(tptp_fun_D_17(tptp_fun_C_18(A!16)), A!16))))),
% 112.65/72.34 inference(unit_resolution,[status(thm)],[183, 180, 101])).
% 112.65/72.34 tff(185,plain,
% 112.65/72.34 (~(ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) | (~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~in(tptp_fun_D_17(tptp_fun_C_18(A!16)), A!16)))),
% 112.65/72.34 inference(unit_resolution,[status(thm)],[184, 176])).
% 112.65/72.34 tff(186,plain,
% 112.65/72.34 ((ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) | (~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~in(tptp_fun_D_17(tptp_fun_C_18(A!16)), A!16))) | ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))),
% 112.65/72.34 inference(tautology,[status(thm)],[])).
% 112.65/72.34 tff(187,plain,
% 112.65/72.34 (ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))),
% 112.65/72.34 inference(unit_resolution,[status(thm)],[186, 185])).
% 112.65/72.34 tff(188,plain,
% 112.65/72.34 (^[A: $i] : refl(((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 112.65/72.34 inference(bind,[status(th)],[])).
% 112.65/72.34 tff(189,plain,
% 112.65/72.34 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 112.65/72.34 inference(quant_intro,[status(thm)],[188])).
% 112.65/72.34 tff(190,plain,
% 112.65/72.34 (^[A: $i] : rewrite(((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 112.65/72.34 inference(bind,[status(th)],[])).
% 112.65/72.34 tff(191,plain,
% 112.65/72.34 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 112.65/72.34 inference(quant_intro,[status(thm)],[190])).
% 112.65/72.34 tff(192,plain,
% 112.65/72.34 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 112.65/72.34 inference(rewrite,[status(thm)],[])).
% 112.65/72.34 tff(193,plain,
% 112.65/72.34 (^[A: $i] : rewrite((ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))))),
% 112.65/72.34 inference(bind,[status(th)],[])).
% 112.65/72.34 tff(194,plain,
% 112.65/72.34 (![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 112.65/72.34 inference(quant_intro,[status(thm)],[193])).
% 112.65/72.34 tff(195,axiom,(![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc1_ordinal1')).
% 112.65/72.34 tff(196,plain,
% 112.65/72.34 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 112.65/72.34 inference(modus_ponens,[status(thm)],[195, 194])).
% 112.65/72.34 tff(197,plain,
% 112.65/72.34 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 112.65/72.34 inference(modus_ponens,[status(thm)],[196, 192])).
% 112.65/72.34 tff(198,plain,(
% 112.65/72.34 ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 112.65/72.34 inference(skolemize,[status(sab)],[197])).
% 112.65/72.34 tff(199,plain,
% 112.65/72.34 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 112.65/72.34 inference(modus_ponens,[status(thm)],[198, 191])).
% 112.65/72.34 tff(200,plain,
% 112.65/72.34 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 112.65/72.34 inference(modus_ponens,[status(thm)],[199, 189])).
% 112.65/72.34 tff(201,plain,
% 112.65/72.34 (((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~((~epsilon_transitive(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~epsilon_connected(tptp_fun_D_17(tptp_fun_C_18(A!16)))))))) <=> ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~((~epsilon_transitive(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~epsilon_connected(tptp_fun_D_17(tptp_fun_C_18(A!16)))))))),
% 112.65/72.34 inference(rewrite,[status(thm)],[])).
% 112.65/72.34 tff(202,plain,
% 112.65/72.34 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~((~epsilon_transitive(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~epsilon_connected(tptp_fun_D_17(tptp_fun_C_18(A!16)))))))),
% 112.65/72.34 inference(quant_inst,[status(thm)],[])).
% 112.65/72.34 tff(203,plain,
% 112.65/72.34 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~((~epsilon_transitive(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~epsilon_connected(tptp_fun_D_17(tptp_fun_C_18(A!16))))))),
% 112.65/72.34 inference(modus_ponens,[status(thm)],[202, 201])).
% 112.65/72.34 tff(204,plain,
% 112.65/72.34 (~((~epsilon_transitive(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~epsilon_connected(tptp_fun_D_17(tptp_fun_C_18(A!16)))))),
% 112.65/72.34 inference(unit_resolution,[status(thm)],[203, 200, 187])).
% 112.65/72.34 tff(205,plain,
% 112.65/72.34 (((~epsilon_transitive(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~epsilon_connected(tptp_fun_D_17(tptp_fun_C_18(A!16))))) | epsilon_transitive(tptp_fun_D_17(tptp_fun_C_18(A!16)))),
% 112.65/72.34 inference(tautology,[status(thm)],[])).
% 112.65/72.34 tff(206,plain,
% 112.65/72.34 (epsilon_transitive(tptp_fun_D_17(tptp_fun_C_18(A!16)))),
% 112.65/72.34 inference(unit_resolution,[status(thm)],[205, 204])).
% 112.65/72.34 tff(207,plain,
% 112.65/72.34 ((~((~epsilon_transitive(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | ![B: $i] : ((~in(B, tptp_fun_D_17(tptp_fun_C_18(A!16)))) | subset(B, tptp_fun_D_17(tptp_fun_C_18(A!16)))))) | (~epsilon_transitive(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | ![B: $i] : ((~in(B, tptp_fun_D_17(tptp_fun_C_18(A!16)))) | subset(B, tptp_fun_D_17(tptp_fun_C_18(A!16))))),
% 112.65/72.34 inference(tautology,[status(thm)],[])).
% 112.65/72.34 tff(208,plain,
% 112.65/72.34 ((~((~epsilon_transitive(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | ![B: $i] : ((~in(B, tptp_fun_D_17(tptp_fun_C_18(A!16)))) | subset(B, tptp_fun_D_17(tptp_fun_C_18(A!16)))))) | ![B: $i] : ((~in(B, tptp_fun_D_17(tptp_fun_C_18(A!16)))) | subset(B, tptp_fun_D_17(tptp_fun_C_18(A!16))))),
% 112.65/72.34 inference(unit_resolution,[status(thm)],[207, 206])).
% 112.65/72.34 tff(209,plain,
% 112.65/72.34 (![B: $i] : ((~in(B, tptp_fun_D_17(tptp_fun_C_18(A!16)))) | subset(B, tptp_fun_D_17(tptp_fun_C_18(A!16))))),
% 112.65/72.34 inference(unit_resolution,[status(thm)],[208, 20])).
% 112.65/72.34 tff(210,plain,
% 112.65/72.34 (^[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))))),
% 112.65/72.34 inference(bind,[status(th)],[])).
% 112.65/72.34 tff(211,plain,
% 112.65/72.34 (![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)))),
% 112.65/72.34 inference(quant_intro,[status(thm)],[210])).
% 112.65/72.34 tff(212,plain,
% 112.65/72.34 (^[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)))))),
% 112.65/72.34 inference(bind,[status(th)],[])).
% 112.65/72.34 tff(213,plain,
% 112.65/72.34 (![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)))),
% 112.65/72.34 inference(quant_intro,[status(thm)],[212])).
% 112.65/72.34 tff(214,plain,
% 112.65/72.34 (![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)))),
% 112.65/72.34 inference(rewrite,[status(thm)],[])).
% 112.65/72.34 tff(215,plain,
% 112.65/72.34 (^[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))))),
% 112.65/72.34 inference(bind,[status(th)],[])).
% 112.65/72.34 tff(216,plain,
% 112.65/72.34 (![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)))),
% 112.65/72.34 inference(quant_intro,[status(thm)],[215])).
% 112.65/72.34 tff(217,axiom,(![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_r1_ordinal1')).
% 112.65/72.34 tff(218,plain,
% 112.65/72.34 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 112.65/72.34 inference(modus_ponens,[status(thm)],[217, 216])).
% 112.65/72.34 tff(219,plain,
% 112.65/72.34 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 112.65/72.34 inference(modus_ponens,[status(thm)],[218, 214])).
% 112.65/72.34 tff(220,plain,(
% 112.65/72.34 ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 112.65/72.34 inference(skolemize,[status(sab)],[219])).
% 112.65/72.34 tff(221,plain,
% 112.65/72.34 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 112.65/72.34 inference(modus_ponens,[status(thm)],[220, 213])).
% 112.65/72.34 tff(222,plain,
% 112.65/72.34 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 112.65/72.34 inference(modus_ponens,[status(thm)],[221, 211])).
% 112.65/72.34 tff(223,plain,
% 112.65/72.34 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_C_18(A!16))) | (~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) <=> subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16)))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_C_18(A!16))) | (~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) <=> subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16)))))),
% 112.65/72.35 inference(rewrite,[status(thm)],[])).
% 112.65/72.35 tff(224,plain,
% 112.65/72.35 (((ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) <=> subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~ordinal(tptp_fun_C_18(A!16)))) <=> ((~ordinal(tptp_fun_C_18(A!16))) | (~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) <=> subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16)))))),
% 112.65/72.35 inference(rewrite,[status(thm)],[])).
% 112.65/72.35 tff(225,plain,
% 112.65/72.35 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) <=> subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~ordinal(tptp_fun_C_18(A!16))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_C_18(A!16))) | (~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) <=> subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))))))),
% 112.65/72.35 inference(monotonicity,[status(thm)],[224])).
% 112.65/72.35 tff(226,plain,
% 112.65/72.35 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) <=> subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~ordinal(tptp_fun_C_18(A!16))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_C_18(A!16))) | (~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) <=> subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16)))))),
% 112.65/72.35 inference(transitivity,[status(thm)],[225, 223])).
% 112.65/72.35 tff(227,plain,
% 112.65/72.35 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) <=> subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~ordinal(tptp_fun_C_18(A!16))))),
% 112.65/72.35 inference(quant_inst,[status(thm)],[])).
% 112.65/72.35 tff(228,plain,
% 112.65/72.35 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_C_18(A!16))) | (~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) <=> subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))))),
% 112.65/72.35 inference(modus_ponens,[status(thm)],[227, 226])).
% 112.65/72.35 tff(229,plain,
% 112.65/72.35 (ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) <=> subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16)))),
% 112.65/72.35 inference(unit_resolution,[status(thm)],[228, 222, 176, 187])).
% 112.65/72.35 tff(230,plain,
% 112.65/72.35 ((ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) | (~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~in(tptp_fun_D_17(tptp_fun_C_18(A!16)), A!16))) | (~ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))))),
% 112.65/72.35 inference(tautology,[status(thm)],[])).
% 112.65/72.35 tff(231,plain,
% 112.65/72.35 (~ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16)))),
% 112.65/72.35 inference(unit_resolution,[status(thm)],[230, 185])).
% 112.65/72.35 tff(232,plain,
% 112.65/72.35 ((~(ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) <=> subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))))) | ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) | (~subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))))),
% 112.65/72.35 inference(tautology,[status(thm)],[])).
% 112.65/72.35 tff(233,plain,
% 112.65/72.35 ((~(ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) <=> subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))))) | (~subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))))),
% 112.65/72.35 inference(unit_resolution,[status(thm)],[232, 231])).
% 112.65/72.35 tff(234,plain,
% 112.65/72.35 (~subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16)))),
% 112.65/72.35 inference(unit_resolution,[status(thm)],[233, 229])).
% 112.65/72.35 tff(235,plain,
% 112.65/72.35 (((~![B: $i] : ((~in(B, tptp_fun_D_17(tptp_fun_C_18(A!16)))) | subset(B, tptp_fun_D_17(tptp_fun_C_18(A!16))))) | ((~in(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16)))) | subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))))) <=> ((~![B: $i] : ((~in(B, tptp_fun_D_17(tptp_fun_C_18(A!16)))) | subset(B, tptp_fun_D_17(tptp_fun_C_18(A!16))))) | (~in(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16)))) | subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))))),
% 112.65/72.35 inference(rewrite,[status(thm)],[])).
% 112.65/72.35 tff(236,plain,
% 112.65/72.35 ((~![B: $i] : ((~in(B, tptp_fun_D_17(tptp_fun_C_18(A!16)))) | subset(B, tptp_fun_D_17(tptp_fun_C_18(A!16))))) | ((~in(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16)))) | subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))))),
% 112.65/72.35 inference(quant_inst,[status(thm)],[])).
% 112.65/72.35 tff(237,plain,
% 112.65/72.35 ((~![B: $i] : ((~in(B, tptp_fun_D_17(tptp_fun_C_18(A!16)))) | subset(B, tptp_fun_D_17(tptp_fun_C_18(A!16))))) | (~in(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16)))) | subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16)))),
% 112.65/72.35 inference(modus_ponens,[status(thm)],[236, 235])).
% 112.65/72.35 tff(238,plain,
% 112.65/72.35 (~in(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16)))),
% 112.65/72.35 inference(unit_resolution,[status(thm)],[237, 234, 209])).
% 112.65/72.35 tff(239,plain,
% 112.65/72.35 (^[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)))))),
% 112.65/72.35 inference(bind,[status(th)],[])).
% 112.65/72.35 tff(240,plain,
% 112.65/72.35 (![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))))),
% 112.65/72.35 inference(quant_intro,[status(thm)],[239])).
% 112.65/72.35 tff(241,plain,
% 112.65/72.35 (^[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)))))),
% 112.65/72.35 inference(bind,[status(th)],[])).
% 112.65/72.35 tff(242,plain,
% 112.65/72.35 (![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))))),
% 112.65/72.35 inference(quant_intro,[status(thm)],[241])).
% 112.65/72.35 tff(243,plain,
% 112.65/72.35 (![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))))),
% 112.65/72.35 inference(transitivity,[status(thm)],[242, 240])).
% 112.65/72.35 tff(244,plain,
% 112.65/72.35 (^[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)))))),
% 112.65/72.35 inference(bind,[status(th)],[])).
% 112.65/72.35 tff(245,plain,
% 112.65/72.35 (![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))))),
% 112.65/72.35 inference(quant_intro,[status(thm)],[244])).
% 112.65/72.35 tff(246,plain,
% 112.65/72.35 (![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))))))),
% 112.65/72.35 inference(rewrite,[status(thm)],[])).
% 112.65/72.35 tff(247,plain,
% 112.65/72.35 (^[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))))))))),
% 112.65/72.35 inference(bind,[status(th)],[])).
% 112.65/72.35 tff(248,plain,
% 112.65/72.35 (![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))))))),
% 112.65/72.35 inference(quant_intro,[status(thm)],[247])).
% 112.65/72.35 tff(249,axiom,(![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t24_ordinal1')).
% 112.65/72.35 tff(250,plain,
% 112.65/72.35 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 112.65/72.35 inference(modus_ponens,[status(thm)],[249, 248])).
% 112.65/72.35 tff(251,plain,
% 112.65/72.35 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 112.65/72.35 inference(modus_ponens,[status(thm)],[250, 246])).
% 112.65/72.35 tff(252,plain,(
% 112.65/72.35 ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 112.65/72.35 inference(skolemize,[status(sab)],[251])).
% 112.65/72.35 tff(253,plain,
% 112.65/72.35 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 112.65/72.35 inference(modus_ponens,[status(thm)],[252, 245])).
% 112.65/72.35 tff(254,plain,
% 112.65/72.35 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 112.65/72.35 inference(modus_ponens,[status(thm)],[253, 243])).
% 112.65/72.35 tff(255,plain,
% 112.65/72.35 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_17(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), B) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = B)))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_17(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), B) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = B)))),
% 112.65/72.35 inference(rewrite,[status(thm)],[])).
% 112.65/72.35 tff(256,plain,
% 112.65/72.35 (((~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | ![B: $i] : (in(B, tptp_fun_D_17(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), B) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = B) | (~ordinal(B)))) <=> ((~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_17(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), B) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = B)))),
% 112.65/72.35 inference(rewrite,[status(thm)],[])).
% 112.65/72.35 tff(257,plain,
% 112.65/72.35 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | ![B: $i] : (in(B, tptp_fun_D_17(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), B) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_17(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), B) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = B))))),
% 112.65/72.35 inference(monotonicity,[status(thm)],[256])).
% 112.65/72.35 tff(258,plain,
% 112.65/72.35 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | ![B: $i] : (in(B, tptp_fun_D_17(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), B) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_17(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), B) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = B)))),
% 112.65/72.35 inference(transitivity,[status(thm)],[257, 255])).
% 112.65/72.35 tff(259,plain,
% 112.65/72.35 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | ![B: $i] : (in(B, tptp_fun_D_17(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), B) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = B) | (~ordinal(B))))),
% 112.65/72.35 inference(quant_inst,[status(thm)],[])).
% 112.65/72.35 tff(260,plain,
% 112.65/72.35 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_17(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), B) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = B))),
% 112.65/72.35 inference(modus_ponens,[status(thm)],[259, 258])).
% 112.65/72.35 tff(261,plain,
% 112.65/72.35 (![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_17(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), B) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = B))),
% 112.65/72.35 inference(unit_resolution,[status(thm)],[260, 254, 187])).
% 112.65/72.35 tff(262,plain,
% 112.65/72.35 ((ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) | (~ordinal(tptp_fun_D_17(tptp_fun_C_18(A!16)))) | (~in(tptp_fun_D_17(tptp_fun_C_18(A!16)), A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), A!16)),
% 112.65/72.35 inference(tautology,[status(thm)],[])).
% 112.65/72.35 tff(263,plain,
% 112.65/72.35 (in(tptp_fun_D_17(tptp_fun_C_18(A!16)), A!16)),
% 112.65/72.35 inference(unit_resolution,[status(thm)],[262, 185])).
% 112.65/72.35 tff(264,plain,
% 112.65/72.35 (((~in(tptp_fun_C_18(A!16), A!16)) | (~![D: $i] : ((~in(D, A!16)) | (~in(D, tptp_fun_C_18(A!16)))))) | ![D: $i] : ((~in(D, A!16)) | (~in(D, tptp_fun_C_18(A!16))))),
% 112.65/72.35 inference(tautology,[status(thm)],[])).
% 112.65/72.35 tff(265,plain,
% 112.65/72.35 (![D: $i] : ((~in(D, A!16)) | (~in(D, tptp_fun_C_18(A!16))))),
% 112.65/72.35 inference(unit_resolution,[status(thm)],[264, 99])).
% 112.65/72.35 tff(266,plain,
% 112.65/72.35 (((~![D: $i] : ((~in(D, A!16)) | (~in(D, tptp_fun_C_18(A!16))))) | ((~in(tptp_fun_D_17(tptp_fun_C_18(A!16)), A!16)) | (~in(tptp_fun_D_17(tptp_fun_C_18(A!16)), tptp_fun_C_18(A!16))))) <=> ((~![D: $i] : ((~in(D, A!16)) | (~in(D, tptp_fun_C_18(A!16))))) | (~in(tptp_fun_D_17(tptp_fun_C_18(A!16)), A!16)) | (~in(tptp_fun_D_17(tptp_fun_C_18(A!16)), tptp_fun_C_18(A!16))))),
% 112.65/72.35 inference(rewrite,[status(thm)],[])).
% 112.65/72.35 tff(267,plain,
% 112.65/72.35 ((~![D: $i] : ((~in(D, A!16)) | (~in(D, tptp_fun_C_18(A!16))))) | ((~in(tptp_fun_D_17(tptp_fun_C_18(A!16)), A!16)) | (~in(tptp_fun_D_17(tptp_fun_C_18(A!16)), tptp_fun_C_18(A!16))))),
% 112.65/72.35 inference(quant_inst,[status(thm)],[])).
% 112.65/72.35 tff(268,plain,
% 112.65/72.35 ((~![D: $i] : ((~in(D, A!16)) | (~in(D, tptp_fun_C_18(A!16))))) | (~in(tptp_fun_D_17(tptp_fun_C_18(A!16)), A!16)) | (~in(tptp_fun_D_17(tptp_fun_C_18(A!16)), tptp_fun_C_18(A!16)))),
% 112.65/72.35 inference(modus_ponens,[status(thm)],[267, 266])).
% 112.65/72.35 tff(269,plain,
% 112.65/72.35 (~in(tptp_fun_D_17(tptp_fun_C_18(A!16)), tptp_fun_C_18(A!16))),
% 112.65/72.35 inference(unit_resolution,[status(thm)],[268, 265, 263])).
% 112.65/72.35 tff(270,plain,
% 112.65/72.35 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_17(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), B) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = B))) | ((~ordinal(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), tptp_fun_C_18(A!16)) | in(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = tptp_fun_C_18(A!16)))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_17(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), B) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = B))) | (~ordinal(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), tptp_fun_C_18(A!16)) | in(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = tptp_fun_C_18(A!16)))),
% 112.65/72.35 inference(rewrite,[status(thm)],[])).
% 112.65/72.35 tff(271,plain,
% 112.65/72.35 (((~ordinal(tptp_fun_C_18(A!16))) | in(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), tptp_fun_C_18(A!16)) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = tptp_fun_C_18(A!16))) <=> ((~ordinal(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), tptp_fun_C_18(A!16)) | in(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = tptp_fun_C_18(A!16)))),
% 112.65/72.35 inference(rewrite,[status(thm)],[])).
% 112.65/72.35 tff(272,plain,
% 112.65/72.35 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_17(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), B) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = B))) | ((~ordinal(tptp_fun_C_18(A!16))) | in(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), tptp_fun_C_18(A!16)) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = tptp_fun_C_18(A!16)))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_17(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), B) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = B))) | ((~ordinal(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), tptp_fun_C_18(A!16)) | in(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = tptp_fun_C_18(A!16))))),
% 112.65/72.35 inference(monotonicity,[status(thm)],[271])).
% 112.65/72.35 tff(273,plain,
% 112.65/72.35 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_17(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), B) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = B))) | ((~ordinal(tptp_fun_C_18(A!16))) | in(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), tptp_fun_C_18(A!16)) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = tptp_fun_C_18(A!16)))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_17(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), B) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = B))) | (~ordinal(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), tptp_fun_C_18(A!16)) | in(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = tptp_fun_C_18(A!16)))),
% 112.65/72.35 inference(transitivity,[status(thm)],[272, 270])).
% 112.65/72.35 tff(274,plain,
% 112.65/72.35 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_17(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), B) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = B))) | ((~ordinal(tptp_fun_C_18(A!16))) | in(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), tptp_fun_C_18(A!16)) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = tptp_fun_C_18(A!16)))),
% 112.65/72.35 inference(quant_inst,[status(thm)],[])).
% 112.65/72.35 tff(275,plain,
% 112.65/72.35 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_17(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), B) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = B))) | (~ordinal(tptp_fun_C_18(A!16))) | in(tptp_fun_D_17(tptp_fun_C_18(A!16)), tptp_fun_C_18(A!16)) | in(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = tptp_fun_C_18(A!16))),
% 112.65/72.35 inference(modus_ponens,[status(thm)],[274, 273])).
% 112.65/72.35 tff(276,plain,
% 112.65/72.35 (in(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) | (tptp_fun_D_17(tptp_fun_C_18(A!16)) = tptp_fun_C_18(A!16))),
% 112.65/72.35 inference(unit_resolution,[status(thm)],[275, 176, 269, 261])).
% 112.65/72.35 tff(277,plain,
% 112.65/72.35 (tptp_fun_D_17(tptp_fun_C_18(A!16)) = tptp_fun_C_18(A!16)),
% 112.65/72.35 inference(unit_resolution,[status(thm)],[276, 238])).
% 112.65/72.35 tff(278,plain,
% 112.65/72.35 (ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16))) <=> ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_C_18(A!16))),
% 112.65/72.35 inference(monotonicity,[status(thm)],[277])).
% 112.65/72.35 tff(279,plain,
% 112.65/72.35 (ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_C_18(A!16)) <=> ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16)))),
% 112.65/72.35 inference(symmetry,[status(thm)],[278])).
% 112.65/72.35 tff(280,plain,
% 112.65/72.35 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(A!16, powerset(B!15))) | (~in(tptp_fun_B_1(A!16), A!16)) | element(tptp_fun_B_1(A!16), B!15))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(A!16, powerset(B!15))) | (~in(tptp_fun_B_1(A!16), A!16)) | element(tptp_fun_B_1(A!16), B!15))),
% 112.65/72.36 inference(rewrite,[status(thm)],[])).
% 112.65/72.36 tff(281,plain,
% 112.65/72.36 ((element(tptp_fun_B_1(A!16), B!15) | (~in(tptp_fun_B_1(A!16), A!16)) | (~element(A!16, powerset(B!15)))) <=> ((~element(A!16, powerset(B!15))) | (~in(tptp_fun_B_1(A!16), A!16)) | element(tptp_fun_B_1(A!16), B!15))),
% 112.65/72.36 inference(rewrite,[status(thm)],[])).
% 112.65/72.36 tff(282,plain,
% 112.65/72.36 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_B_1(A!16), B!15) | (~in(tptp_fun_B_1(A!16), A!16)) | (~element(A!16, powerset(B!15))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(A!16, powerset(B!15))) | (~in(tptp_fun_B_1(A!16), A!16)) | element(tptp_fun_B_1(A!16), B!15)))),
% 112.65/72.36 inference(monotonicity,[status(thm)],[281])).
% 112.65/72.36 tff(283,plain,
% 112.65/72.36 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_B_1(A!16), B!15) | (~in(tptp_fun_B_1(A!16), A!16)) | (~element(A!16, powerset(B!15))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(A!16, powerset(B!15))) | (~in(tptp_fun_B_1(A!16), A!16)) | element(tptp_fun_B_1(A!16), B!15))),
% 112.65/72.36 inference(transitivity,[status(thm)],[282, 280])).
% 112.65/72.36 tff(284,plain,
% 112.65/72.36 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_B_1(A!16), B!15) | (~in(tptp_fun_B_1(A!16), A!16)) | (~element(A!16, powerset(B!15))))),
% 112.65/72.36 inference(quant_inst,[status(thm)],[])).
% 112.65/72.36 tff(285,plain,
% 112.65/72.36 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(A!16, powerset(B!15))) | (~in(tptp_fun_B_1(A!16), A!16)) | element(tptp_fun_B_1(A!16), B!15)),
% 112.65/72.36 inference(modus_ponens,[status(thm)],[284, 283])).
% 112.65/72.36 tff(286,plain,
% 112.65/72.36 (element(tptp_fun_B_1(A!16), B!15)),
% 112.65/72.36 inference(unit_resolution,[status(thm)],[285, 127, 114, 82])).
% 112.65/72.36 tff(287,plain,
% 112.65/72.36 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(B!15) | in(tptp_fun_B_1(A!16), B!15) | (~element(tptp_fun_B_1(A!16), B!15)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(B!15) | in(tptp_fun_B_1(A!16), B!15) | (~element(tptp_fun_B_1(A!16), B!15)))),
% 112.65/72.36 inference(rewrite,[status(thm)],[])).
% 112.65/72.36 tff(288,plain,
% 112.65/72.36 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(B!15) | in(tptp_fun_B_1(A!16), B!15) | (~element(tptp_fun_B_1(A!16), B!15)))),
% 112.65/72.36 inference(quant_inst,[status(thm)],[])).
% 112.65/72.36 tff(289,plain,
% 112.65/72.36 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(B!15) | in(tptp_fun_B_1(A!16), B!15) | (~element(tptp_fun_B_1(A!16), B!15))),
% 112.65/72.36 inference(modus_ponens,[status(thm)],[288, 287])).
% 112.65/72.36 tff(290,plain,
% 112.65/72.36 (in(tptp_fun_B_1(A!16), B!15)),
% 112.65/72.36 inference(unit_resolution,[status(thm)],[289, 77, 154, 286])).
% 112.65/72.36 tff(291,plain,
% 112.65/72.36 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ((~ordinal(B!15)) | ordinal(tptp_fun_B_1(A!16)) | (~in(tptp_fun_B_1(A!16), B!15)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(B!15)) | ordinal(tptp_fun_B_1(A!16)) | (~in(tptp_fun_B_1(A!16), B!15)))),
% 112.65/72.36 inference(rewrite,[status(thm)],[])).
% 112.65/72.36 tff(292,plain,
% 112.65/72.36 ((ordinal(tptp_fun_B_1(A!16)) | (~in(tptp_fun_B_1(A!16), B!15)) | (~ordinal(B!15))) <=> ((~ordinal(B!15)) | ordinal(tptp_fun_B_1(A!16)) | (~in(tptp_fun_B_1(A!16), B!15)))),
% 112.65/72.36 inference(rewrite,[status(thm)],[])).
% 112.65/72.36 tff(293,plain,
% 112.65/72.36 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_B_1(A!16)) | (~in(tptp_fun_B_1(A!16), B!15)) | (~ordinal(B!15)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ((~ordinal(B!15)) | ordinal(tptp_fun_B_1(A!16)) | (~in(tptp_fun_B_1(A!16), B!15))))),
% 112.65/72.36 inference(monotonicity,[status(thm)],[292])).
% 112.65/72.36 tff(294,plain,
% 112.65/72.36 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_B_1(A!16)) | (~in(tptp_fun_B_1(A!16), B!15)) | (~ordinal(B!15)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(B!15)) | ordinal(tptp_fun_B_1(A!16)) | (~in(tptp_fun_B_1(A!16), B!15)))),
% 112.65/72.36 inference(transitivity,[status(thm)],[293, 291])).
% 112.65/72.36 tff(295,plain,
% 112.65/72.36 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_B_1(A!16)) | (~in(tptp_fun_B_1(A!16), B!15)) | (~ordinal(B!15)))),
% 112.65/72.36 inference(quant_inst,[status(thm)],[])).
% 112.65/72.36 tff(296,plain,
% 112.65/72.36 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(B!15)) | ordinal(tptp_fun_B_1(A!16)) | (~in(tptp_fun_B_1(A!16), B!15))),
% 112.65/72.36 inference(modus_ponens,[status(thm)],[295, 294])).
% 112.65/72.36 tff(297,plain,
% 112.65/72.36 (ordinal(tptp_fun_B_1(A!16))),
% 112.65/72.36 inference(unit_resolution,[status(thm)],[296, 169, 159, 290])).
% 112.65/72.36 tff(298,plain,
% 112.65/72.36 (^[A: $i, B: $i] : refl((ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A))) <=> (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A))))),
% 112.65/72.36 inference(bind,[status(th)],[])).
% 112.65/72.36 tff(299,plain,
% 112.65/72.36 (![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A))) <=> ![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))),
% 112.65/72.36 inference(quant_intro,[status(thm)],[298])).
% 112.65/72.36 tff(300,plain,
% 112.65/72.36 (^[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)))))),
% 112.65/72.36 inference(bind,[status(th)],[])).
% 112.65/72.36 tff(301,plain,
% 112.65/72.36 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A)) <=> ![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))),
% 112.65/72.36 inference(quant_intro,[status(thm)],[300])).
% 112.65/72.36 tff(302,plain,
% 112.65/72.36 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A)) <=> ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A))),
% 112.65/72.36 inference(rewrite,[status(thm)],[])).
% 112.65/72.36 tff(303,plain,
% 112.65/72.36 (^[A: $i, B: $i] : rewrite(((ordinal(A) & ordinal(B)) => ordinal_subset(A, A)) <=> ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A)))),
% 112.65/72.36 inference(bind,[status(th)],[])).
% 112.65/72.36 tff(304,plain,
% 112.65/72.36 (![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => ordinal_subset(A, A)) <=> ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A))),
% 112.65/72.36 inference(quant_intro,[status(thm)],[303])).
% 112.65/72.36 tff(305,axiom,(![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => ordinal_subset(A, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reflexivity_r1_ordinal1')).
% 112.65/72.36 tff(306,plain,
% 112.65/72.36 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A))),
% 112.65/72.36 inference(modus_ponens,[status(thm)],[305, 304])).
% 112.65/72.36 tff(307,plain,
% 112.65/72.36 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A))),
% 112.65/72.36 inference(modus_ponens,[status(thm)],[306, 302])).
% 112.65/72.36 tff(308,plain,(
% 112.65/72.36 ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A))),
% 112.65/72.36 inference(skolemize,[status(sab)],[307])).
% 112.65/72.36 tff(309,plain,
% 112.65/72.36 (![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))),
% 112.65/72.36 inference(modus_ponens,[status(thm)],[308, 301])).
% 112.65/72.36 tff(310,plain,
% 112.65/72.36 (![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))),
% 112.65/72.36 inference(modus_ponens,[status(thm)],[309, 299])).
% 112.65/72.36 tff(311,plain,
% 112.65/72.36 (((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_C_18(A!16))) | (~ordinal(tptp_fun_B_1(A!16))) | ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_C_18(A!16)))) <=> ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_C_18(A!16))) | (~ordinal(tptp_fun_B_1(A!16))) | ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_C_18(A!16)))),
% 112.65/72.37 inference(rewrite,[status(thm)],[])).
% 112.65/72.37 tff(312,plain,
% 112.65/72.37 ((ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_C_18(A!16)) | (~ordinal(tptp_fun_B_1(A!16))) | (~ordinal(tptp_fun_C_18(A!16)))) <=> ((~ordinal(tptp_fun_C_18(A!16))) | (~ordinal(tptp_fun_B_1(A!16))) | ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_C_18(A!16)))),
% 112.65/72.37 inference(rewrite,[status(thm)],[])).
% 112.65/72.37 tff(313,plain,
% 112.65/72.37 (((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_C_18(A!16)) | (~ordinal(tptp_fun_B_1(A!16))) | (~ordinal(tptp_fun_C_18(A!16))))) <=> ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_C_18(A!16))) | (~ordinal(tptp_fun_B_1(A!16))) | ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_C_18(A!16))))),
% 112.65/72.38 inference(monotonicity,[status(thm)],[312])).
% 112.65/72.38 tff(314,plain,
% 112.65/72.38 (((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_C_18(A!16)) | (~ordinal(tptp_fun_B_1(A!16))) | (~ordinal(tptp_fun_C_18(A!16))))) <=> ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_C_18(A!16))) | (~ordinal(tptp_fun_B_1(A!16))) | ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_C_18(A!16)))),
% 112.65/72.38 inference(transitivity,[status(thm)],[313, 311])).
% 112.65/72.38 tff(315,plain,
% 112.65/72.38 ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_C_18(A!16)) | (~ordinal(tptp_fun_B_1(A!16))) | (~ordinal(tptp_fun_C_18(A!16))))),
% 112.65/72.38 inference(quant_inst,[status(thm)],[])).
% 112.65/72.38 tff(316,plain,
% 112.65/72.38 ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_C_18(A!16))) | (~ordinal(tptp_fun_B_1(A!16))) | ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_C_18(A!16))),
% 112.65/72.38 inference(modus_ponens,[status(thm)],[315, 314])).
% 112.65/72.38 tff(317,plain,
% 112.65/72.38 (ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_C_18(A!16))),
% 112.65/72.38 inference(unit_resolution,[status(thm)],[316, 310, 297, 176])).
% 112.65/72.38 tff(318,plain,
% 112.65/72.38 (ordinal_subset(tptp_fun_C_18(A!16), tptp_fun_D_17(tptp_fun_C_18(A!16)))),
% 112.65/72.38 inference(modus_ponens,[status(thm)],[317, 279])).
% 112.65/72.38 tff(319,plain,
% 112.65/72.38 ($false),
% 112.65/72.38 inference(unit_resolution,[status(thm)],[231, 318])).
% 112.65/72.38 % SZS output end Proof
%------------------------------------------------------------------------------