TSTP Solution File: SEU178+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU178+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 07:28:00 EDT 2022
% Result : Theorem 0.63s 0.68s
% Output : Proof 0.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU178+2 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 3 10:08:00 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.63/0.68 % SZS status Theorem
% 0.63/0.68 % SZS output start Proof
% 0.63/0.68 tff(in_type, type, (
% 0.63/0.68 in: ( $i * $i ) > $o)).
% 0.63/0.68 tff(relation_rng_type, type, (
% 0.63/0.68 relation_rng: $i > $i)).
% 0.63/0.68 tff(tptp_fun_A_36_type, type, (
% 0.63/0.68 tptp_fun_A_36: $i)).
% 0.63/0.68 tff(tptp_fun_D_0_type, type, (
% 0.63/0.68 tptp_fun_D_0: $i > $i)).
% 0.63/0.68 tff(tptp_fun_C_16_type, type, (
% 0.63/0.68 tptp_fun_C_16: ( $i * $i ) > $i)).
% 0.63/0.68 tff(cartesian_product2_type, type, (
% 0.63/0.68 cartesian_product2: ( $i * $i ) > $i)).
% 0.63/0.68 tff(relation_dom_type, type, (
% 0.63/0.68 relation_dom: $i > $i)).
% 0.63/0.68 tff(tptp_fun_C_1_type, type, (
% 0.63/0.68 tptp_fun_C_1: $i > $i)).
% 0.63/0.68 tff(ordered_pair_type, type, (
% 0.63/0.68 ordered_pair: ( $i * $i ) > $i)).
% 0.63/0.68 tff(relation_type, type, (
% 0.63/0.68 relation: $i > $o)).
% 0.63/0.68 tff(tptp_fun_B_2_type, type, (
% 0.63/0.68 tptp_fun_B_2: $i > $i)).
% 0.63/0.68 tff(subset_type, type, (
% 0.63/0.68 subset: ( $i * $i ) > $o)).
% 0.63/0.68 tff(1,plain,
% 0.63/0.68 (^[A: $i, B: $i, C: $i, D: $i] : refl((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))) <=> (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))))),
% 0.63/0.68 inference(bind,[status(th)],[])).
% 0.63/0.68 tff(2,plain,
% 0.63/0.68 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))),
% 0.63/0.68 inference(quant_intro,[status(thm)],[1])).
% 0.63/0.68 tff(3,plain,
% 0.63/0.68 (^[A: $i, B: $i, C: $i, D: $i] : rewrite((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))))),
% 0.63/0.68 inference(bind,[status(th)],[])).
% 0.63/0.68 tff(4,plain,
% 0.63/0.68 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))),
% 0.63/0.68 inference(quant_intro,[status(thm)],[3])).
% 0.63/0.68 tff(5,plain,
% 0.63/0.68 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.63/0.68 inference(rewrite,[status(thm)],[])).
% 0.63/0.68 tff(6,axiom,(![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l55_zfmisc_1')).
% 0.63/0.68 tff(7,plain,
% 0.63/0.68 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.63/0.68 tff(8,plain,(
% 0.63/0.68 ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.63/0.68 inference(skolemize,[status(sab)],[7])).
% 0.63/0.68 tff(9,plain,
% 0.63/0.68 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.63/0.68 tff(10,plain,
% 0.63/0.68 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.63/0.68 tff(11,plain,
% 0.63/0.68 ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), cartesian_product2(relation_dom(A!36), relation_rng(A!36))) <=> (~((~in(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_dom(A!36))) | (~in(tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_rng(A!36))))))),
% 0.63/0.68 inference(quant_inst,[status(thm)],[])).
% 0.63/0.68 tff(12,plain,
% 0.63/0.68 (in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), cartesian_product2(relation_dom(A!36), relation_rng(A!36))) <=> (~((~in(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_dom(A!36))) | (~in(tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_rng(A!36)))))),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.63/0.68 tff(13,plain,
% 0.63/0.68 (^[A: $i] : refl((~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))) <=> (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))))),
% 0.63/0.68 inference(bind,[status(th)],[])).
% 0.63/0.68 tff(14,plain,
% 0.63/0.68 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))) <=> ![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))),
% 0.63/0.68 inference(quant_intro,[status(thm)],[13])).
% 0.63/0.68 tff(15,plain,
% 0.63/0.68 (^[A: $i] : rewrite((~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))) <=> (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))))),
% 0.63/0.68 inference(bind,[status(th)],[])).
% 0.63/0.68 tff(16,plain,
% 0.63/0.68 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))) <=> ![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))),
% 0.63/0.68 inference(quant_intro,[status(thm)],[15])).
% 0.63/0.68 tff(17,plain,
% 0.63/0.68 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))) <=> ![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))),
% 0.63/0.68 inference(transitivity,[status(thm)],[16, 14])).
% 0.63/0.68 tff(18,plain,
% 0.63/0.68 (^[A: $i] : trans(monotonicity(rewrite(((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) <=> ((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))), rewrite((relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))) <=> (relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))), ((((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))) <=> (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))), rewrite((((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))) <=> (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))), ((((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))) <=> (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))))),
% 0.63/0.68 inference(bind,[status(th)],[])).
% 0.63/0.68 tff(19,plain,
% 0.63/0.68 (![A: $i] : (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))) <=> ![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))),
% 0.63/0.68 inference(quant_intro,[status(thm)],[18])).
% 0.63/0.68 tff(20,plain,
% 0.63/0.68 (^[A: $i] : rewrite((((~relation(A)) | ![B: $i] : ((~in(B, A)) | (~(~(B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))))) & (relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))) <=> (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))),
% 0.63/0.68 inference(bind,[status(th)],[])).
% 0.63/0.68 tff(21,plain,
% 0.63/0.68 (![A: $i] : (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (~(~(B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))))) & (relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))) <=> ![A: $i] : (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))),
% 0.63/0.68 inference(quant_intro,[status(thm)],[20])).
% 0.63/0.68 tff(22,plain,
% 0.63/0.68 (![A: $i] : (relation(A) <=> ![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(B = ordered_pair(C, D)))))) <=> ![A: $i] : (relation(A) <=> ![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(B = ordered_pair(C, D))))))),
% 0.63/0.68 inference(rewrite,[status(thm)],[])).
% 0.63/0.68 tff(23,axiom,(![A: $i] : (relation(A) <=> ![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(B = ordered_pair(C, D))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_relat_1')).
% 0.63/0.68 tff(24,plain,
% 0.63/0.68 (![A: $i] : (relation(A) <=> ![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(B = ordered_pair(C, D))))))),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.63/0.68 tff(25,plain,(
% 0.63/0.68 ![A: $i] : (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (~(~(B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))))) & (relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))),
% 0.63/0.68 inference(skolemize,[status(sab)],[24])).
% 0.63/0.68 tff(26,plain,
% 0.63/0.68 (![A: $i] : (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.63/0.68 tff(27,plain,
% 0.63/0.68 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.63/0.68 tff(28,plain,
% 0.63/0.68 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.63/0.69 tff(29,plain,
% 0.63/0.69 ((~![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))) | (~((~((~relation(A!36)) | ![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A!36) | (~((~in(tptp_fun_B_2(A!36), A!36)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A!36) = ordered_pair(C, D))))))))))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(30,plain,
% 0.63/0.69 (~((~((~relation(A!36)) | ![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A!36) | (~((~in(tptp_fun_B_2(A!36), A!36)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A!36) = ordered_pair(C, D)))))))))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.63/0.69 tff(31,plain,
% 0.63/0.69 (((~((~relation(A!36)) | ![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A!36) | (~((~in(tptp_fun_B_2(A!36), A!36)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A!36) = ordered_pair(C, D))))))))) | ((~relation(A!36)) | ![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))),
% 0.63/0.69 inference(tautology,[status(thm)],[])).
% 0.63/0.69 tff(32,plain,
% 0.63/0.69 ((~relation(A!36)) | ![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.63/0.69 tff(33,plain,
% 0.63/0.69 ((~![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))) <=> (~![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A)))))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(34,plain,
% 0.63/0.69 ((~![A: $i] : (relation(A) => subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))) <=> (~![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A)))))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(35,axiom,(~![A: $i] : (relation(A) => subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t21_relat_1')).
% 0.63/0.69 tff(36,plain,
% 0.63/0.69 (~![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.63/0.69 tff(37,plain,
% 0.63/0.69 (~![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[36, 33])).
% 0.63/0.69 tff(38,plain,
% 0.63/0.69 (~![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.63/0.69 tff(39,plain,
% 0.63/0.69 (~![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.63/0.69 tff(40,plain,
% 0.63/0.69 (~![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[39, 33])).
% 0.63/0.69 tff(41,plain,
% 0.63/0.69 (~![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.63/0.69 tff(42,plain,
% 0.63/0.69 (~![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[41, 33])).
% 0.63/0.69 tff(43,plain,(
% 0.63/0.69 ~((~relation(A!36)) | subset(A!36, cartesian_product2(relation_dom(A!36), relation_rng(A!36))))),
% 0.63/0.69 inference(skolemize,[status(sab)],[42])).
% 0.63/0.69 tff(44,plain,
% 0.63/0.69 (relation(A!36)),
% 0.63/0.69 inference(or_elim,[status(thm)],[43])).
% 0.63/0.69 tff(45,plain,
% 0.63/0.69 ((~((~relation(A!36)) | ![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~relation(A!36)) | ![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))),
% 0.63/0.69 inference(tautology,[status(thm)],[])).
% 0.63/0.69 tff(46,plain,
% 0.63/0.69 ((~((~relation(A!36)) | ![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | ![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.63/0.69 tff(47,plain,
% 0.63/0.69 (![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[46, 32])).
% 0.63/0.69 tff(48,plain,
% 0.63/0.69 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(49,plain,
% 0.63/0.69 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[48])).
% 0.63/0.69 tff(50,plain,
% 0.63/0.69 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(51,plain,
% 0.63/0.69 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[50])).
% 0.63/0.69 tff(52,plain,
% 0.63/0.69 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))),
% 0.63/0.69 inference(transitivity,[status(thm)],[51, 49])).
% 0.63/0.69 tff(53,plain,
% 0.63/0.69 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(54,plain,
% 0.63/0.69 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[53])).
% 0.63/0.69 tff(55,plain,
% 0.63/0.69 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(56,plain,
% 0.63/0.69 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(57,plain,
% 0.63/0.69 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[56])).
% 0.63/0.69 tff(58,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 0.63/0.69 tff(59,plain,
% 0.63/0.69 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.63/0.69 tff(60,plain,
% 0.63/0.69 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.63/0.69 tff(61,plain,(
% 0.63/0.69 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))),
% 0.63/0.69 inference(skolemize,[status(sab)],[60])).
% 0.63/0.69 tff(62,plain,
% 0.63/0.69 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.63/0.69 tff(63,plain,
% 0.63/0.69 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[62, 52])).
% 0.63/0.69 tff(64,plain,
% 0.63/0.69 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_16(B, A), A)) | in(tptp_fun_C_16(B, A), B)))))))) | (~((~((~subset(A!36, cartesian_product2(relation_dom(A!36), relation_rng(A!36)))) | ![C: $i] : ((~in(C, A!36)) | in(C, cartesian_product2(relation_dom(A!36), relation_rng(A!36)))))) | (~(subset(A!36, cartesian_product2(relation_dom(A!36), relation_rng(A!36))) | (~((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))))))))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(65,plain,
% 0.63/0.69 (~((~((~subset(A!36, cartesian_product2(relation_dom(A!36), relation_rng(A!36)))) | ![C: $i] : ((~in(C, A!36)) | in(C, cartesian_product2(relation_dom(A!36), relation_rng(A!36)))))) | (~(subset(A!36, cartesian_product2(relation_dom(A!36), relation_rng(A!36))) | (~((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36))))))))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.63/0.69 tff(66,plain,
% 0.63/0.69 (((~((~subset(A!36, cartesian_product2(relation_dom(A!36), relation_rng(A!36)))) | ![C: $i] : ((~in(C, A!36)) | in(C, cartesian_product2(relation_dom(A!36), relation_rng(A!36)))))) | (~(subset(A!36, cartesian_product2(relation_dom(A!36), relation_rng(A!36))) | (~((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))))))) | (subset(A!36, cartesian_product2(relation_dom(A!36), relation_rng(A!36))) | (~((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36))))))),
% 0.63/0.69 inference(tautology,[status(thm)],[])).
% 0.63/0.69 tff(67,plain,
% 0.63/0.69 (subset(A!36, cartesian_product2(relation_dom(A!36), relation_rng(A!36))) | (~((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.63/0.69 tff(68,plain,
% 0.63/0.69 (~subset(A!36, cartesian_product2(relation_dom(A!36), relation_rng(A!36)))),
% 0.63/0.69 inference(or_elim,[status(thm)],[43])).
% 0.63/0.69 tff(69,plain,
% 0.63/0.69 ((~(subset(A!36, cartesian_product2(relation_dom(A!36), relation_rng(A!36))) | (~((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36))))))) | subset(A!36, cartesian_product2(relation_dom(A!36), relation_rng(A!36))) | (~((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))))),
% 0.63/0.69 inference(tautology,[status(thm)],[])).
% 0.63/0.69 tff(70,plain,
% 0.63/0.69 ((~(subset(A!36, cartesian_product2(relation_dom(A!36), relation_rng(A!36))) | (~((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36))))))) | (~((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.63/0.69 tff(71,plain,
% 0.63/0.69 (~((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36))))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[70, 67])).
% 0.63/0.69 tff(72,plain,
% 0.63/0.69 (((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))) | in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)),
% 0.63/0.69 inference(tautology,[status(thm)],[])).
% 0.63/0.69 tff(73,plain,
% 0.63/0.69 (in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.63/0.69 tff(74,plain,
% 0.63/0.69 (((~![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) | ((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | (tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36) = ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)))))) <=> ((~![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) | (~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | (tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36) = ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)))))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(75,plain,
% 0.63/0.69 ((~![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) | ((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | (tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36) = ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)))))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(76,plain,
% 0.63/0.69 ((~![B: $i] : ((~in(B, A!36)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) | (~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | (tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36) = ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.63/0.69 tff(77,plain,
% 0.63/0.69 (tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36) = ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[76, 73, 47])).
% 0.63/0.69 tff(78,plain,
% 0.63/0.69 (ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))) = tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)),
% 0.63/0.69 inference(symmetry,[status(thm)],[77])).
% 0.63/0.69 tff(79,plain,
% 0.63/0.69 (in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), cartesian_product2(relation_dom(A!36), relation_rng(A!36))) <=> in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))),
% 0.63/0.69 inference(monotonicity,[status(thm)],[78])).
% 0.63/0.69 tff(80,plain,
% 0.63/0.69 (in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36))) <=> in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))),
% 0.63/0.69 inference(symmetry,[status(thm)],[79])).
% 0.63/0.69 tff(81,plain,
% 0.63/0.69 ((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))) <=> (~in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), cartesian_product2(relation_dom(A!36), relation_rng(A!36))))),
% 0.63/0.69 inference(monotonicity,[status(thm)],[80])).
% 0.63/0.69 tff(82,plain,
% 0.63/0.69 (((~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)) | in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))) | (~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36))))),
% 0.63/0.69 inference(tautology,[status(thm)],[])).
% 0.63/0.69 tff(83,plain,
% 0.63/0.69 (~in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[82, 71])).
% 0.63/0.69 tff(84,plain,
% 0.63/0.69 (~in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), cartesian_product2(relation_dom(A!36), relation_rng(A!36)))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[83, 81])).
% 0.63/0.69 tff(85,plain,
% 0.63/0.69 (in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), A!36) <=> in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36)),
% 0.63/0.69 inference(monotonicity,[status(thm)],[78])).
% 0.63/0.69 tff(86,plain,
% 0.63/0.69 (in(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36), A!36) <=> in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), A!36)),
% 0.63/0.69 inference(symmetry,[status(thm)],[85])).
% 0.63/0.69 tff(87,plain,
% 0.63/0.69 (in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), A!36)),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[73, 86])).
% 0.63/0.69 tff(88,plain,
% 0.63/0.69 (^[A: $i, B: $i, C: $i] : refl(((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C)))))) <=> ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C)))))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(89,plain,
% 0.63/0.69 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C)))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[88])).
% 0.63/0.69 tff(90,plain,
% 0.63/0.69 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, relation_dom(C)) & in(B, relation_rng(C))) <=> (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C)))))), (((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ((~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))) | (~relation(C)) | (~in(ordered_pair(A, B), C))))), rewrite(((~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))), (((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(91,plain,
% 0.63/0.69 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[90])).
% 0.63/0.69 tff(92,plain,
% 0.63/0.69 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(93,plain,
% 0.63/0.69 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C)))) <=> ((~in(ordered_pair(A, B), C)) | (in(A, relation_dom(C)) & in(B, relation_rng(C))))), ((relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> (relation(C) => ((~in(ordered_pair(A, B), C)) | (in(A, relation_dom(C)) & in(B, relation_rng(C))))))), rewrite((relation(C) => ((~in(ordered_pair(A, B), C)) | (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))), ((relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(94,plain,
% 0.63/0.69 (![A: $i, B: $i, C: $i] : (relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> ![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[93])).
% 0.63/0.69 tff(95,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t20_relat_1')).
% 0.63/0.69 tff(96,plain,
% 0.63/0.69 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.63/0.69 tff(97,plain,
% 0.63/0.69 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.63/0.69 tff(98,plain,(
% 0.63/0.69 ![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 0.63/0.69 inference(skolemize,[status(sab)],[97])).
% 0.63/0.69 tff(99,plain,
% 0.63/0.69 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.63/0.69 tff(100,plain,
% 0.63/0.69 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[99, 89])).
% 0.63/0.69 tff(101,plain,
% 0.63/0.69 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))) | ((~relation(A!36)) | (~in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), A!36)) | (~((~in(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_dom(A!36))) | (~in(tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_rng(A!36))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))) | (~relation(A!36)) | (~in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), A!36)) | (~((~in(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_dom(A!36))) | (~in(tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_rng(A!36))))))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(102,plain,
% 0.63/0.69 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))) | ((~relation(A!36)) | (~in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), A!36)) | (~((~in(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_dom(A!36))) | (~in(tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_rng(A!36))))))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(103,plain,
% 0.63/0.69 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))) | (~relation(A!36)) | (~in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), A!36)) | (~((~in(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_dom(A!36))) | (~in(tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_rng(A!36)))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.63/0.69 tff(104,plain,
% 0.63/0.69 ((~in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), A!36)) | (~((~in(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_dom(A!36))) | (~in(tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_rng(A!36)))))),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[103, 100, 44])).
% 0.63/0.70 tff(105,plain,
% 0.63/0.70 (~((~in(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_dom(A!36))) | (~in(tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_rng(A!36))))),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[104, 87])).
% 0.63/0.70 tff(106,plain,
% 0.63/0.70 ((~(in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), cartesian_product2(relation_dom(A!36), relation_rng(A!36))) <=> (~((~in(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_dom(A!36))) | (~in(tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_rng(A!36))))))) | in(ordered_pair(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36))), cartesian_product2(relation_dom(A!36), relation_rng(A!36))) | ((~in(tptp_fun_C_1(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_dom(A!36))) | (~in(tptp_fun_D_0(tptp_fun_C_16(cartesian_product2(relation_dom(A!36), relation_rng(A!36)), A!36)), relation_rng(A!36))))),
% 0.63/0.70 inference(tautology,[status(thm)],[])).
% 0.63/0.70 tff(107,plain,
% 0.63/0.70 ($false),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[106, 105, 84, 12])).
% 0.63/0.70 % SZS output end Proof
%------------------------------------------------------------------------------