TSTP Solution File: SEU186+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU186+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 07:28:03 EDT 2022
% Result : Theorem 29.83s 19.27s
% Output : Proof 30.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU186+2 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Sep 3 10:09:59 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 29.83/19.27 % SZS status Theorem
% 29.83/19.27 % SZS output start Proof
% 29.83/19.27 tff(in_type, type, (
% 29.83/19.27 in: ( $i * $i ) > $o)).
% 29.83/19.27 tff(relation_inverse_type, type, (
% 29.83/19.27 relation_inverse: $i > $i)).
% 29.83/19.27 tff(tptp_fun_A_46_type, type, (
% 29.83/19.27 tptp_fun_A_46: $i)).
% 29.83/19.27 tff(ordered_pair_type, type, (
% 29.83/19.27 ordered_pair: ( $i * $i ) > $i)).
% 29.83/19.27 tff(tptp_fun_C_29_type, type, (
% 29.83/19.27 tptp_fun_C_29: ( $i * $i ) > $i)).
% 29.83/19.27 tff(tptp_fun_A_36_type, type, (
% 29.83/19.27 tptp_fun_A_36: $i)).
% 29.83/19.27 tff(tptp_fun_D_28_type, type, (
% 29.83/19.27 tptp_fun_D_28: ( $i * $i ) > $i)).
% 29.83/19.27 tff(relation_type, type, (
% 29.83/19.27 relation: $i > $o)).
% 29.83/19.27 tff(empty_set_type, type, (
% 29.83/19.27 empty_set: $i)).
% 29.83/19.27 tff(empty_type, type, (
% 29.83/19.27 empty: $i > $o)).
% 29.83/19.27 tff(1,plain,
% 29.83/19.27 (((~(A!46 = empty_set)) & (~(~relation(A!46))) & ![B: $i, C: $i] : (~in(ordered_pair(B, C), A!46))) <=> ((~(A!46 = empty_set)) & relation(A!46) & ![B: $i, C: $i] : (~in(ordered_pair(B, C), A!46)))),
% 29.83/19.27 inference(rewrite,[status(thm)],[])).
% 29.83/19.27 tff(2,plain,
% 29.83/19.27 ((~![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))))) <=> (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A)))))),
% 29.83/19.27 inference(rewrite,[status(thm)],[])).
% 29.83/19.27 tff(3,plain,
% 29.83/19.27 ((~![A: $i] : (relation(A) => (![B: $i, C: $i] : (~in(ordered_pair(B, C), A)) => (A = empty_set)))) <=> (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A)))))),
% 29.83/19.27 inference(rewrite,[status(thm)],[])).
% 29.83/19.27 tff(4,axiom,(~![A: $i] : (relation(A) => (![B: $i, C: $i] : (~in(ordered_pair(B, C), A)) => (A = empty_set)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t56_relat_1')).
% 29.83/19.27 tff(5,plain,
% 29.83/19.27 (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))))),
% 29.83/19.27 inference(modus_ponens,[status(thm)],[4, 3])).
% 29.83/19.27 tff(6,plain,
% 29.83/19.27 (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))))),
% 29.83/19.27 inference(modus_ponens,[status(thm)],[5, 2])).
% 29.83/19.27 tff(7,plain,
% 29.83/19.27 (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))))),
% 29.83/19.27 inference(modus_ponens,[status(thm)],[6, 2])).
% 29.83/19.27 tff(8,plain,
% 29.83/19.27 (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))))),
% 29.83/19.27 inference(modus_ponens,[status(thm)],[7, 2])).
% 29.83/19.27 tff(9,plain,
% 29.83/19.27 (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))))),
% 29.83/19.27 inference(modus_ponens,[status(thm)],[8, 2])).
% 29.83/19.27 tff(10,plain,
% 29.83/19.27 (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))))),
% 29.83/19.27 inference(modus_ponens,[status(thm)],[9, 2])).
% 29.83/19.27 tff(11,plain,
% 29.83/19.27 (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))))),
% 29.83/19.27 inference(modus_ponens,[status(thm)],[10, 2])).
% 29.83/19.27 tff(12,plain,
% 29.83/19.27 ((~(A!46 = empty_set)) & relation(A!46) & ![B: $i, C: $i] : (~in(ordered_pair(B, C), A!46))),
% 29.83/19.27 inference(modus_ponens,[status(thm)],[11, 1])).
% 29.83/19.27 tff(13,plain,
% 29.83/19.27 (relation(A!46)),
% 29.83/19.27 inference(and_elim,[status(thm)],[12])).
% 29.83/19.27 tff(14,plain,
% 29.83/19.27 (^[A: $i] : refl(((~relation(A)) | relation(relation_inverse(A))) <=> ((~relation(A)) | relation(relation_inverse(A))))),
% 29.83/19.27 inference(bind,[status(th)],[])).
% 29.83/19.27 tff(15,plain,
% 29.83/19.27 (![A: $i] : ((~relation(A)) | relation(relation_inverse(A))) <=> ![A: $i] : ((~relation(A)) | relation(relation_inverse(A)))),
% 29.83/19.27 inference(quant_intro,[status(thm)],[14])).
% 29.83/19.27 tff(16,plain,
% 29.83/19.27 (![A: $i] : ((~relation(A)) | relation(relation_inverse(A))) <=> ![A: $i] : ((~relation(A)) | relation(relation_inverse(A)))),
% 29.83/19.27 inference(rewrite,[status(thm)],[])).
% 29.83/19.27 tff(17,plain,
% 29.83/19.27 (^[A: $i] : rewrite((relation(A) => relation(relation_inverse(A))) <=> ((~relation(A)) | relation(relation_inverse(A))))),
% 29.83/19.27 inference(bind,[status(th)],[])).
% 29.83/19.27 tff(18,plain,
% 29.83/19.27 (![A: $i] : (relation(A) => relation(relation_inverse(A))) <=> ![A: $i] : ((~relation(A)) | relation(relation_inverse(A)))),
% 29.83/19.27 inference(quant_intro,[status(thm)],[17])).
% 29.83/19.27 tff(19,axiom,(![A: $i] : (relation(A) => relation(relation_inverse(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k4_relat_1')).
% 29.83/19.27 tff(20,plain,
% 29.83/19.27 (![A: $i] : ((~relation(A)) | relation(relation_inverse(A)))),
% 29.83/19.27 inference(modus_ponens,[status(thm)],[19, 18])).
% 29.83/19.27 tff(21,plain,
% 29.83/19.27 (![A: $i] : ((~relation(A)) | relation(relation_inverse(A)))),
% 29.83/19.27 inference(modus_ponens,[status(thm)],[20, 16])).
% 29.83/19.27 tff(22,plain,(
% 29.83/19.27 ![A: $i] : ((~relation(A)) | relation(relation_inverse(A)))),
% 29.83/19.27 inference(skolemize,[status(sab)],[21])).
% 29.83/19.27 tff(23,plain,
% 29.83/19.27 (![A: $i] : ((~relation(A)) | relation(relation_inverse(A)))),
% 29.83/19.27 inference(modus_ponens,[status(thm)],[22, 15])).
% 29.83/19.27 tff(24,plain,
% 29.83/19.27 (((~![A: $i] : ((~relation(A)) | relation(relation_inverse(A)))) | ((~relation(A!46)) | relation(relation_inverse(A!46)))) <=> ((~![A: $i] : ((~relation(A)) | relation(relation_inverse(A)))) | (~relation(A!46)) | relation(relation_inverse(A!46)))),
% 29.83/19.27 inference(rewrite,[status(thm)],[])).
% 29.83/19.27 tff(25,plain,
% 29.83/19.27 ((~![A: $i] : ((~relation(A)) | relation(relation_inverse(A)))) | ((~relation(A!46)) | relation(relation_inverse(A!46)))),
% 29.83/19.27 inference(quant_inst,[status(thm)],[])).
% 29.83/19.27 tff(26,plain,
% 29.83/19.27 ((~![A: $i] : ((~relation(A)) | relation(relation_inverse(A)))) | (~relation(A!46)) | relation(relation_inverse(A!46))),
% 29.83/19.27 inference(modus_ponens,[status(thm)],[25, 24])).
% 29.83/19.27 tff(27,plain,
% 29.83/19.27 (relation(relation_inverse(A!46))),
% 29.83/19.27 inference(unit_resolution,[status(thm)],[26, 23, 13])).
% 29.83/19.27 tff(28,plain,
% 29.83/19.27 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | ((~in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B)) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | ((~in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B)) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))))))),
% 29.83/19.27 inference(bind,[status(th)],[])).
% 29.83/19.27 tff(29,plain,
% 29.83/19.27 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | ((~in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B)) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | ((~in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B)) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A))))))))),
% 29.83/19.27 inference(quant_intro,[status(thm)],[28])).
% 29.83/19.27 tff(30,plain,
% 29.83/19.27 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | ((~in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B)) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | ((~in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B)) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))))))),
% 29.83/19.27 inference(bind,[status(th)],[])).
% 29.83/19.27 tff(31,plain,
% 29.83/19.27 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | ((~in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B)) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | ((~in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B)) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A))))))))),
% 29.83/19.28 inference(quant_intro,[status(thm)],[30])).
% 29.83/19.28 tff(32,plain,
% 29.83/19.28 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | ((~in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B)) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | ((~in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B)) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A))))))))),
% 29.83/19.28 inference(transitivity,[status(thm)],[31, 29])).
% 29.83/19.28 tff(33,plain,
% 29.83/19.28 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((~relation(B)) | (((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))) & ((B = relation_inverse(A)) | ((~in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B)) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | ((~in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B)) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))))))),
% 29.83/19.28 inference(bind,[status(th)],[])).
% 29.83/19.28 tff(34,plain,
% 29.83/19.28 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))) & ((B = relation_inverse(A)) | ((~in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B)) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | ((~in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B)) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A))))))))),
% 29.83/19.28 inference(quant_intro,[status(thm)],[33])).
% 29.83/19.28 tff(35,plain,
% 29.83/19.28 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((~relation(B)) | (((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))) & ((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))) & ((B = relation_inverse(A)) | ((~in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B)) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))))),
% 29.83/19.28 inference(bind,[status(th)],[])).
% 29.83/19.28 tff(36,plain,
% 29.83/19.28 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))) & ((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))) & ((B = relation_inverse(A)) | ((~in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B)) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A))))))),
% 29.83/19.28 inference(quant_intro,[status(thm)],[35])).
% 29.83/19.28 tff(37,plain,
% 29.83/19.28 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))))),
% 29.83/19.28 inference(rewrite,[status(thm)],[])).
% 29.83/19.28 tff(38,plain,
% 29.83/19.28 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite(((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))) <=> ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))), ((relation(B) => ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) <=> (relation(B) => ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))))), rewrite((relation(B) => ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) <=> ((~relation(B)) | ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))))), ((relation(B) => ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) <=> ((~relation(B)) | ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))))))), (![B: $i] : (relation(B) => ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) <=> ![B: $i] : ((~relation(B)) | ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))))), ((relation(A) => ![B: $i] : (relation(B) => ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))))) <=> (relation(A) => ![B: $i] : ((~relation(B)) | ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))))))), rewrite((relation(A) => ![B: $i] : ((~relation(B)) | ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))))), ((relation(A) => ![B: $i] : (relation(B) => ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))))))),
% 29.83/19.28 inference(bind,[status(th)],[])).
% 29.83/19.28 tff(39,plain,
% 29.83/19.28 (![A: $i] : (relation(A) => ![B: $i] : (relation(B) => ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))))),
% 29.83/19.28 inference(quant_intro,[status(thm)],[38])).
% 29.83/19.28 tff(40,axiom,(![A: $i] : (relation(A) => ![B: $i] : (relation(B) => ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d7_relat_1')).
% 29.83/19.28 tff(41,plain,
% 29.83/19.28 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))))),
% 29.83/19.28 inference(modus_ponens,[status(thm)],[40, 39])).
% 29.83/19.28 tff(42,plain,
% 29.83/19.28 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ((B = relation_inverse(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))))),
% 29.83/19.28 inference(modus_ponens,[status(thm)],[41, 37])).
% 29.83/19.28 tff(43,plain,(
% 29.83/19.28 ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))) & ((B = relation_inverse(A)) | (~(in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A)))))))),
% 30.00/19.28 inference(skolemize,[status(sab)],[42])).
% 30.00/19.28 tff(44,plain,
% 30.00/19.28 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A))) & ((B = relation_inverse(A)) | ((~in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B)) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A))))))),
% 30.00/19.28 inference(modus_ponens,[status(thm)],[43, 36])).
% 30.00/19.28 tff(45,plain,
% 30.00/19.28 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | ((~in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B)) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A))))))))),
% 30.00/19.28 inference(modus_ponens,[status(thm)],[44, 34])).
% 30.00/19.28 tff(46,plain,
% 30.00/19.28 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | ((~in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B)) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A))))))))),
% 30.00/19.28 inference(modus_ponens,[status(thm)],[45, 32])).
% 30.00/19.28 tff(47,plain,
% 30.00/19.28 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | ((~in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B)) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A))))))))) | ((~relation(relation_inverse(A!46))) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((B = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B)) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | ((~in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B)) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A))))))))) | (~relation(relation_inverse(A!46))) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((B = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B)) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46)))))))))),
% 30.00/19.28 inference(rewrite,[status(thm)],[])).
% 30.00/19.28 tff(48,plain,
% 30.00/19.28 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | ((~in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B)) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A))))))))) | ((~relation(relation_inverse(A!46))) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((B = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B)) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46)))))))))),
% 30.00/19.28 inference(quant_inst,[status(thm)],[])).
% 30.00/19.28 tff(49,plain,
% 30.00/19.28 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), A)))) | (~((B = relation_inverse(A)) | ((~in(ordered_pair(tptp_fun_C_29(B, A), tptp_fun_D_28(B, A)), B)) <=> in(ordered_pair(tptp_fun_D_28(B, A), tptp_fun_C_29(B, A)), A))))))))) | (~relation(relation_inverse(A!46))) | ![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((B = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B)) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46))))))))),
% 30.00/19.28 inference(modus_ponens,[status(thm)],[48, 47])).
% 30.00/19.28 tff(50,plain,
% 30.00/19.28 (![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((B = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B)) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46))))))))),
% 30.00/19.28 inference(unit_resolution,[status(thm)],[49, 46, 27])).
% 30.00/19.28 tff(51,plain,
% 30.00/19.28 (((~![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((B = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B)) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46))))))))) | ((~relation(A!46)) | (~((~((~(A!46 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((A!46 = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(A!46, relation_inverse(A!46)), tptp_fun_D_28(A!46, relation_inverse(A!46))), A!46)) <=> in(ordered_pair(tptp_fun_D_28(A!46, relation_inverse(A!46)), tptp_fun_C_29(A!46, relation_inverse(A!46))), relation_inverse(A!46))))))))) <=> ((~![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((B = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B)) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46))))))))) | (~relation(A!46)) | (~((~((~(A!46 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((A!46 = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(A!46, relation_inverse(A!46)), tptp_fun_D_28(A!46, relation_inverse(A!46))), A!46)) <=> in(ordered_pair(tptp_fun_D_28(A!46, relation_inverse(A!46)), tptp_fun_C_29(A!46, relation_inverse(A!46))), relation_inverse(A!46))))))))),
% 30.00/19.28 inference(rewrite,[status(thm)],[])).
% 30.00/19.28 tff(52,plain,
% 30.00/19.28 ((~![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((B = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B)) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46))))))))) | ((~relation(A!46)) | (~((~((~(A!46 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((A!46 = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(A!46, relation_inverse(A!46)), tptp_fun_D_28(A!46, relation_inverse(A!46))), A!46)) <=> in(ordered_pair(tptp_fun_D_28(A!46, relation_inverse(A!46)), tptp_fun_C_29(A!46, relation_inverse(A!46))), relation_inverse(A!46))))))))),
% 30.00/19.28 inference(quant_inst,[status(thm)],[])).
% 30.00/19.28 tff(53,plain,
% 30.00/19.28 ((~![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((B = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B)) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46))))))))) | (~relation(A!46)) | (~((~((~(A!46 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((A!46 = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(A!46, relation_inverse(A!46)), tptp_fun_D_28(A!46, relation_inverse(A!46))), A!46)) <=> in(ordered_pair(tptp_fun_D_28(A!46, relation_inverse(A!46)), tptp_fun_C_29(A!46, relation_inverse(A!46))), relation_inverse(A!46)))))))),
% 30.00/19.28 inference(modus_ponens,[status(thm)],[52, 51])).
% 30.00/19.28 tff(54,plain,
% 30.00/19.28 (~((~((~(A!46 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((A!46 = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(A!46, relation_inverse(A!46)), tptp_fun_D_28(A!46, relation_inverse(A!46))), A!46)) <=> in(ordered_pair(tptp_fun_D_28(A!46, relation_inverse(A!46)), tptp_fun_C_29(A!46, relation_inverse(A!46))), relation_inverse(A!46))))))),
% 30.00/19.28 inference(unit_resolution,[status(thm)],[53, 13, 50])).
% 30.00/19.28 tff(55,plain,
% 30.00/19.28 (((~((~(A!46 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((A!46 = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(A!46, relation_inverse(A!46)), tptp_fun_D_28(A!46, relation_inverse(A!46))), A!46)) <=> in(ordered_pair(tptp_fun_D_28(A!46, relation_inverse(A!46)), tptp_fun_C_29(A!46, relation_inverse(A!46))), relation_inverse(A!46)))))) | ((~(A!46 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46))))),
% 30.00/19.28 inference(tautology,[status(thm)],[])).
% 30.00/19.28 tff(56,plain,
% 30.00/19.28 ((~(A!46 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46)))),
% 30.00/19.28 inference(unit_resolution,[status(thm)],[55, 54])).
% 30.00/19.28 tff(57,plain,
% 30.00/19.28 (^[A: $i] : refl(((~relation(A)) | (relation_inverse(relation_inverse(A)) = A)) <=> ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A)))),
% 30.00/19.28 inference(bind,[status(th)],[])).
% 30.00/19.28 tff(58,plain,
% 30.00/19.28 (![A: $i] : ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A)) <=> ![A: $i] : ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A))),
% 30.00/19.28 inference(quant_intro,[status(thm)],[57])).
% 30.00/19.28 tff(59,plain,
% 30.00/19.28 (![A: $i] : ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A)) <=> ![A: $i] : ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A))),
% 30.00/19.28 inference(rewrite,[status(thm)],[])).
% 30.00/19.28 tff(60,plain,
% 30.00/19.28 (^[A: $i] : rewrite((relation(A) => (relation_inverse(relation_inverse(A)) = A)) <=> ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A)))),
% 30.00/19.28 inference(bind,[status(th)],[])).
% 30.00/19.28 tff(61,plain,
% 30.00/19.28 (![A: $i] : (relation(A) => (relation_inverse(relation_inverse(A)) = A)) <=> ![A: $i] : ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A))),
% 30.00/19.28 inference(quant_intro,[status(thm)],[60])).
% 30.00/19.28 tff(62,axiom,(![A: $i] : (relation(A) => (relation_inverse(relation_inverse(A)) = A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','involutiveness_k4_relat_1')).
% 30.00/19.28 tff(63,plain,
% 30.00/19.28 (![A: $i] : ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A))),
% 30.00/19.28 inference(modus_ponens,[status(thm)],[62, 61])).
% 30.00/19.28 tff(64,plain,
% 30.00/19.28 (![A: $i] : ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A))),
% 30.00/19.28 inference(modus_ponens,[status(thm)],[63, 59])).
% 30.00/19.28 tff(65,plain,(
% 30.00/19.28 ![A: $i] : ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A))),
% 30.00/19.28 inference(skolemize,[status(sab)],[64])).
% 30.00/19.28 tff(66,plain,
% 30.00/19.28 (![A: $i] : ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A))),
% 30.00/19.28 inference(modus_ponens,[status(thm)],[65, 58])).
% 30.00/19.28 tff(67,plain,
% 30.00/19.28 (((~![A: $i] : ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A))) | ((~relation(A!46)) | (relation_inverse(relation_inverse(A!46)) = A!46))) <=> ((~![A: $i] : ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A))) | (~relation(A!46)) | (relation_inverse(relation_inverse(A!46)) = A!46))),
% 30.00/19.28 inference(rewrite,[status(thm)],[])).
% 30.00/19.28 tff(68,plain,
% 30.00/19.28 ((~![A: $i] : ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A))) | ((~relation(A!46)) | (relation_inverse(relation_inverse(A!46)) = A!46))),
% 30.00/19.28 inference(quant_inst,[status(thm)],[])).
% 30.00/19.28 tff(69,plain,
% 30.00/19.28 ((~![A: $i] : ((~relation(A)) | (relation_inverse(relation_inverse(A)) = A))) | (~relation(A!46)) | (relation_inverse(relation_inverse(A!46)) = A!46)),
% 30.00/19.28 inference(modus_ponens,[status(thm)],[68, 67])).
% 30.00/19.28 tff(70,plain,
% 30.00/19.28 (relation_inverse(relation_inverse(A!46)) = A!46),
% 30.00/19.28 inference(unit_resolution,[status(thm)],[69, 66, 13])).
% 30.00/19.28 tff(71,plain,
% 30.00/19.28 (A!46 = relation_inverse(relation_inverse(A!46))),
% 30.00/19.28 inference(symmetry,[status(thm)],[70])).
% 30.00/19.28 tff(72,plain,
% 30.00/19.28 ((~((~(A!46 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~(A!46 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46)))),
% 30.00/19.28 inference(tautology,[status(thm)],[])).
% 30.00/19.28 tff(73,plain,
% 30.00/19.28 ((~((~(A!46 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46)))),
% 30.00/19.28 inference(unit_resolution,[status(thm)],[72, 71])).
% 30.00/19.28 tff(74,plain,
% 30.00/19.28 (![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46)))),
% 30.00/19.28 inference(unit_resolution,[status(thm)],[73, 56])).
% 30.00/19.28 tff(75,plain,
% 30.00/19.28 ((~![C: $i, D: $i] : (in(ordered_pair(C, D), A!46) <=> in(ordered_pair(D, C), relation_inverse(A!46)))) | (in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!46) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46)))),
% 30.00/19.28 inference(quant_inst,[status(thm)],[])).
% 30.00/19.28 tff(76,plain,
% 30.00/19.28 (in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!46) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46))),
% 30.00/19.28 inference(unit_resolution,[status(thm)],[75, 74])).
% 30.00/19.28 tff(77,plain,
% 30.00/19.28 (^[B: $i, C: $i] : refl((~in(ordered_pair(B, C), A!46)) <=> (~in(ordered_pair(B, C), A!46)))),
% 30.00/19.28 inference(bind,[status(th)],[])).
% 30.00/19.28 tff(78,plain,
% 30.00/19.28 (![B: $i, C: $i] : (~in(ordered_pair(B, C), A!46)) <=> ![B: $i, C: $i] : (~in(ordered_pair(B, C), A!46))),
% 30.00/19.28 inference(quant_intro,[status(thm)],[77])).
% 30.00/19.28 tff(79,plain,
% 30.00/19.28 (![B: $i, C: $i] : (~in(ordered_pair(B, C), A!46))),
% 30.00/19.28 inference(and_elim,[status(thm)],[12])).
% 30.00/19.28 tff(80,plain,
% 30.00/19.28 (![B: $i, C: $i] : (~in(ordered_pair(B, C), A!46))),
% 30.00/19.28 inference(modus_ponens,[status(thm)],[79, 78])).
% 30.00/19.28 tff(81,plain,
% 30.00/19.28 ((~![B: $i, C: $i] : (~in(ordered_pair(B, C), A!46))) | (~in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!46))),
% 30.00/19.28 inference(quant_inst,[status(thm)],[])).
% 30.00/19.28 tff(82,plain,
% 30.00/19.28 (~in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!46)),
% 30.00/19.28 inference(unit_resolution,[status(thm)],[81, 80])).
% 30.00/19.28 tff(83,plain,
% 30.00/19.28 (?[A: $i] : (empty(A) & relation(A)) <=> ?[A: $i] : (empty(A) & relation(A))),
% 30.00/19.28 inference(rewrite,[status(thm)],[])).
% 30.00/19.28 tff(84,axiom,(?[A: $i] : (empty(A) & relation(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rc1_relat_1')).
% 30.00/19.28 tff(85,plain,
% 30.00/19.28 (?[A: $i] : (empty(A) & relation(A))),
% 30.00/19.28 inference(modus_ponens,[status(thm)],[84, 83])).
% 30.00/19.28 tff(86,plain,(
% 30.00/19.28 empty(A!36) & relation(A!36)),
% 30.00/19.28 inference(skolemize,[status(sab)],[85])).
% 30.00/19.28 tff(87,plain,
% 30.00/19.28 (relation(A!36)),
% 30.00/19.28 inference(and_elim,[status(thm)],[86])).
% 30.00/19.28 tff(88,plain,
% 30.00/19.28 (((~![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((B = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B)) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46))))))))) | ((~relation(A!36)) | (~((~((~(A!36 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!36) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((A!36 = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36)) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46))))))))) <=> ((~![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((B = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B)) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46))))))))) | (~relation(A!36)) | (~((~((~(A!36 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!36) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((A!36 = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36)) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46))))))))),
% 30.00/19.28 inference(rewrite,[status(thm)],[])).
% 30.00/19.28 tff(89,plain,
% 30.00/19.28 ((~![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((B = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B)) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46))))))))) | ((~relation(A!36)) | (~((~((~(A!36 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!36) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((A!36 = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36)) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46))))))))),
% 30.00/19.28 inference(quant_inst,[status(thm)],[])).
% 30.00/19.28 tff(90,plain,
% 30.00/19.28 ((~![B: $i] : ((~relation(B)) | (~((~((~(B = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((B = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(B, relation_inverse(A!46)), tptp_fun_D_28(B, relation_inverse(A!46))), B)) <=> in(ordered_pair(tptp_fun_D_28(B, relation_inverse(A!46)), tptp_fun_C_29(B, relation_inverse(A!46))), relation_inverse(A!46))))))))) | (~relation(A!36)) | (~((~((~(A!36 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!36) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((A!36 = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36)) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46)))))))),
% 30.00/19.28 inference(modus_ponens,[status(thm)],[89, 88])).
% 30.00/19.28 tff(91,plain,
% 30.00/19.28 (~((~((~(A!36 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!36) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((A!36 = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36)) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46))))))),
% 30.00/19.28 inference(unit_resolution,[status(thm)],[90, 87, 50])).
% 30.00/19.28 tff(92,plain,
% 30.00/19.28 (((~((~(A!36 = relation_inverse(relation_inverse(A!46)))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), A!36) <=> in(ordered_pair(D, C), relation_inverse(A!46))))) | (~((A!36 = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36)) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46)))))) | ((A!36 = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36)) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46))))),
% 30.00/19.28 inference(tautology,[status(thm)],[])).
% 30.00/19.28 tff(93,plain,
% 30.00/19.28 ((A!36 = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36)) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46)))),
% 30.00/19.28 inference(unit_resolution,[status(thm)],[92, 91])).
% 30.00/19.28 tff(94,plain,
% 30.00/19.28 ((empty_set = A!46) <=> (A!46 = empty_set)),
% 30.00/19.28 inference(commutativity,[status(thm)],[])).
% 30.00/19.28 tff(95,plain,
% 30.00/19.28 (^[A: $i, B: $i] : refl(((A = B) | (~empty(A)) | (~empty(B))) <=> ((A = B) | (~empty(A)) | (~empty(B))))),
% 30.00/19.28 inference(bind,[status(th)],[])).
% 30.00/19.28 tff(96,plain,
% 30.00/19.28 (![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B))) <=> ![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 30.00/19.28 inference(quant_intro,[status(thm)],[95])).
% 30.00/19.28 tff(97,plain,
% 30.00/19.28 (^[A: $i, B: $i] : trans(monotonicity(rewrite((empty(A) & (~(A = B)) & empty(B)) <=> (~((A = B) | (~empty(A)) | (~empty(B))))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> (~(~((A = B) | (~empty(A)) | (~empty(B))))))), rewrite((~(~((A = B) | (~empty(A)) | (~empty(B))))) <=> ((A = B) | (~empty(A)) | (~empty(B)))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> ((A = B) | (~empty(A)) | (~empty(B)))))),
% 30.00/19.28 inference(bind,[status(th)],[])).
% 30.00/19.28 tff(98,plain,
% 30.00/19.28 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 30.00/19.28 inference(quant_intro,[status(thm)],[97])).
% 30.00/19.28 tff(99,plain,
% 30.00/19.28 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 30.00/19.29 inference(rewrite,[status(thm)],[])).
% 30.00/19.29 tff(100,plain,
% 30.00/19.29 (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 30.00/19.29 inference(bind,[status(th)],[])).
% 30.00/19.29 tff(101,plain,
% 30.00/19.29 (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 30.00/19.29 inference(quant_intro,[status(thm)],[100])).
% 30.00/19.29 tff(102,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_boole')).
% 30.00/19.29 tff(103,plain,
% 30.00/19.29 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 30.00/19.29 inference(modus_ponens,[status(thm)],[102, 101])).
% 30.00/19.29 tff(104,plain,
% 30.00/19.29 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 30.00/19.29 inference(modus_ponens,[status(thm)],[103, 99])).
% 30.00/19.29 tff(105,plain,(
% 30.00/19.29 ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 30.00/19.29 inference(skolemize,[status(sab)],[104])).
% 30.00/19.29 tff(106,plain,
% 30.00/19.29 (![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 30.00/19.29 inference(modus_ponens,[status(thm)],[105, 98])).
% 30.00/19.29 tff(107,plain,
% 30.00/19.29 (![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 30.00/19.29 inference(modus_ponens,[status(thm)],[106, 96])).
% 30.00/19.29 tff(108,plain,
% 30.00/19.29 (empty(A!36)),
% 30.00/19.29 inference(and_elim,[status(thm)],[86])).
% 30.00/19.29 tff(109,plain,
% 30.00/19.29 (empty(empty_set) <=> empty(empty_set)),
% 30.00/19.29 inference(rewrite,[status(thm)],[])).
% 30.00/19.29 tff(110,axiom,(empty(empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_xboole_0')).
% 30.00/19.29 tff(111,plain,
% 30.00/19.29 (empty(empty_set)),
% 30.00/19.29 inference(modus_ponens,[status(thm)],[110, 109])).
% 30.00/19.29 tff(112,plain,
% 30.00/19.29 (((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | ((empty_set = A!36) | (~empty(empty_set)) | (~empty(A!36)))) <=> ((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | (empty_set = A!36) | (~empty(empty_set)) | (~empty(A!36)))),
% 30.00/19.29 inference(rewrite,[status(thm)],[])).
% 30.00/19.29 tff(113,plain,
% 30.00/19.29 ((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | ((empty_set = A!36) | (~empty(empty_set)) | (~empty(A!36)))),
% 30.00/19.29 inference(quant_inst,[status(thm)],[])).
% 30.00/19.29 tff(114,plain,
% 30.00/19.29 ((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | (empty_set = A!36) | (~empty(empty_set)) | (~empty(A!36))),
% 30.00/19.29 inference(modus_ponens,[status(thm)],[113, 112])).
% 30.00/19.29 tff(115,plain,
% 30.00/19.29 (empty_set = A!36),
% 30.00/19.29 inference(unit_resolution,[status(thm)],[114, 111, 108, 107])).
% 30.00/19.29 tff(116,plain,
% 30.00/19.29 (A!36 = empty_set),
% 30.00/19.29 inference(symmetry,[status(thm)],[115])).
% 30.00/19.29 tff(117,plain,
% 30.00/19.29 ((A!36 = relation_inverse(relation_inverse(A!46))) <=> (empty_set = A!46)),
% 30.00/19.29 inference(monotonicity,[status(thm)],[116, 70])).
% 30.00/19.29 tff(118,plain,
% 30.00/19.29 ((A!36 = relation_inverse(relation_inverse(A!46))) <=> (A!46 = empty_set)),
% 30.00/19.29 inference(transitivity,[status(thm)],[117, 94])).
% 30.00/19.29 tff(119,plain,
% 30.00/19.29 ((A!46 = empty_set) <=> (A!36 = relation_inverse(relation_inverse(A!46)))),
% 30.00/19.29 inference(symmetry,[status(thm)],[118])).
% 30.00/19.29 tff(120,plain,
% 30.00/19.29 ((~(A!46 = empty_set)) <=> (~(A!36 = relation_inverse(relation_inverse(A!46))))),
% 30.00/19.29 inference(monotonicity,[status(thm)],[119])).
% 30.00/19.29 tff(121,plain,
% 30.00/19.29 (~(A!46 = empty_set)),
% 30.00/19.29 inference(and_elim,[status(thm)],[12])).
% 30.00/19.29 tff(122,plain,
% 30.00/19.29 (~(A!36 = relation_inverse(relation_inverse(A!46)))),
% 30.00/19.29 inference(modus_ponens,[status(thm)],[121, 120])).
% 30.00/19.29 tff(123,plain,
% 30.00/19.29 ((~((A!36 = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36)) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46))))) | (A!36 = relation_inverse(relation_inverse(A!46))) | ((~in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36)) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46)))),
% 30.00/19.29 inference(tautology,[status(thm)],[])).
% 30.00/19.29 tff(124,plain,
% 30.00/19.29 ((~in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36)) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46))),
% 30.00/19.29 inference(unit_resolution,[status(thm)],[123, 122, 93])).
% 30.00/19.29 tff(125,plain,
% 30.00/19.29 (^[A: $i, B: $i] : refl(((~empty(B)) | (~in(A, B))) <=> ((~empty(B)) | (~in(A, B))))),
% 30.00/19.29 inference(bind,[status(th)],[])).
% 30.00/19.29 tff(126,plain,
% 30.00/19.29 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 30.00/19.29 inference(quant_intro,[status(thm)],[125])).
% 30.00/19.29 tff(127,plain,
% 30.00/19.29 (^[A: $i, B: $i] : trans(monotonicity(rewrite((in(A, B) & empty(B)) <=> (~((~empty(B)) | (~in(A, B))))), ((~(in(A, B) & empty(B))) <=> (~(~((~empty(B)) | (~in(A, B))))))), rewrite((~(~((~empty(B)) | (~in(A, B))))) <=> ((~empty(B)) | (~in(A, B)))), ((~(in(A, B) & empty(B))) <=> ((~empty(B)) | (~in(A, B)))))),
% 30.00/19.29 inference(bind,[status(th)],[])).
% 30.00/19.29 tff(128,plain,
% 30.00/19.29 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 30.00/19.29 inference(quant_intro,[status(thm)],[127])).
% 30.00/19.29 tff(129,plain,
% 30.00/19.29 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 30.00/19.29 inference(rewrite,[status(thm)],[])).
% 30.00/19.29 tff(130,axiom,(![A: $i, B: $i] : (~(in(A, B) & empty(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t7_boole')).
% 30.00/19.29 tff(131,plain,
% 30.00/19.29 (![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 30.00/19.29 inference(modus_ponens,[status(thm)],[130, 129])).
% 30.00/19.29 tff(132,plain,(
% 30.00/19.29 ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 30.00/19.29 inference(skolemize,[status(sab)],[131])).
% 30.00/19.29 tff(133,plain,
% 30.00/19.29 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 30.00/19.29 inference(modus_ponens,[status(thm)],[132, 128])).
% 30.00/19.29 tff(134,plain,
% 30.00/19.29 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 30.00/19.29 inference(modus_ponens,[status(thm)],[133, 126])).
% 30.00/19.29 tff(135,plain,
% 30.00/19.29 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(A!36)) | (~in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(A!36)) | (~in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36)))),
% 30.00/19.29 inference(rewrite,[status(thm)],[])).
% 30.00/19.29 tff(136,plain,
% 30.00/19.29 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(A!36)) | (~in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36)))),
% 30.00/19.29 inference(quant_inst,[status(thm)],[])).
% 30.00/19.29 tff(137,plain,
% 30.00/19.29 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(A!36)) | (~in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36))),
% 30.00/19.29 inference(modus_ponens,[status(thm)],[136, 135])).
% 30.00/19.29 tff(138,plain,
% 30.00/19.29 (~in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36)),
% 30.00/19.29 inference(unit_resolution,[status(thm)],[137, 108, 134])).
% 30.00/19.29 tff(139,plain,
% 30.00/19.29 ((~((~in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36)) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46)))) | in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!36) | in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46))),
% 30.00/19.29 inference(tautology,[status(thm)],[])).
% 30.00/19.29 tff(140,plain,
% 30.00/19.29 (in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46))),
% 30.00/19.29 inference(unit_resolution,[status(thm)],[139, 138, 124])).
% 30.00/19.29 tff(141,plain,
% 30.00/19.29 ((~(in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!46) <=> in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46)))) | in(ordered_pair(tptp_fun_C_29(A!36, relation_inverse(A!46)), tptp_fun_D_28(A!36, relation_inverse(A!46))), A!46) | (~in(ordered_pair(tptp_fun_D_28(A!36, relation_inverse(A!46)), tptp_fun_C_29(A!36, relation_inverse(A!46))), relation_inverse(A!46)))),
% 30.02/19.31 inference(tautology,[status(thm)],[])).
% 30.02/19.31 tff(142,plain,
% 30.02/19.31 ($false),
% 30.02/19.31 inference(unit_resolution,[status(thm)],[141, 140, 82, 76])).
% 30.02/19.31 % SZS output end Proof
%------------------------------------------------------------------------------