TSTP Solution File: SEU200+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU200+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 07:28:08 EDT 2022
% Result : Theorem 0.14s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU200+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Sep 3 10:16:59 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.14/0.41 % SZS status Theorem
% 0.14/0.41 % SZS output start Proof
% 0.14/0.41 tff(subset_type, type, (
% 0.14/0.41 subset: ( $i * $i ) > $o)).
% 0.14/0.41 tff(relation_rng_type, type, (
% 0.14/0.41 relation_rng: $i > $i)).
% 0.14/0.41 tff(tptp_fun_B_7_type, type, (
% 0.14/0.41 tptp_fun_B_7: $i)).
% 0.14/0.41 tff(relation_rng_restriction_type, type, (
% 0.14/0.41 relation_rng_restriction: ( $i * $i ) > $i)).
% 0.14/0.41 tff(tptp_fun_A_8_type, type, (
% 0.14/0.41 tptp_fun_A_8: $i)).
% 0.14/0.41 tff(relation_dom_type, type, (
% 0.14/0.41 relation_dom: $i > $i)).
% 0.14/0.41 tff(relation_type, type, (
% 0.14/0.41 relation: $i > $o)).
% 0.14/0.41 tff(1,plain,
% 0.14/0.41 ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), relation_rng(B)))) <=> (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), relation_rng(B))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(2,plain,
% 0.14/0.41 ((~![A: $i, B: $i] : (relation(B) => subset(relation_rng(relation_rng_restriction(A, B)), relation_rng(B)))) <=> (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), relation_rng(B))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(3,axiom,(~![A: $i, B: $i] : (relation(B) => subset(relation_rng(relation_rng_restriction(A, B)), relation_rng(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t118_relat_1')).
% 0.14/0.41 tff(4,plain,
% 0.14/0.41 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), relation_rng(B)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.14/0.41 tff(5,plain,
% 0.14/0.41 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), relation_rng(B)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.14/0.41 tff(6,plain,
% 0.14/0.41 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), relation_rng(B)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.14/0.41 tff(7,plain,
% 0.14/0.41 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), relation_rng(B)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.14/0.41 tff(8,plain,
% 0.14/0.41 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), relation_rng(B)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.14/0.41 tff(9,plain,
% 0.14/0.41 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), relation_rng(B)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.14/0.41 tff(10,plain,
% 0.14/0.41 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), relation_rng(B)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.14/0.41 tff(11,plain,(
% 0.14/0.41 ~((~relation(B!7)) | subset(relation_rng(relation_rng_restriction(A!8, B!7)), relation_rng(B!7)))),
% 0.14/0.41 inference(skolemize,[status(sab)],[10])).
% 0.14/0.41 tff(12,plain,
% 0.14/0.41 (~subset(relation_rng(relation_rng_restriction(A!8, B!7)), relation_rng(B!7))),
% 0.14/0.41 inference(or_elim,[status(thm)],[11])).
% 0.14/0.41 tff(13,plain,
% 0.14/0.41 (((~subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B!7))) | (~subset(relation_rng(relation_rng_restriction(A!8, B!7)), relation_rng(B!7)))) | subset(relation_rng(relation_rng_restriction(A!8, B!7)), relation_rng(B!7))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(14,plain,
% 0.14/0.41 ((~subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B!7))) | (~subset(relation_rng(relation_rng_restriction(A!8, B!7)), relation_rng(B!7)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.14/0.41 tff(15,plain,
% 0.14/0.41 (relation(B!7)),
% 0.14/0.41 inference(or_elim,[status(thm)],[11])).
% 0.14/0.41 tff(16,plain,
% 0.14/0.41 (^[A: $i, B: $i] : refl(((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ((~relation(B)) | relation(relation_rng_restriction(A, B))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(17,plain,
% 0.14/0.41 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[16])).
% 0.14/0.41 tff(18,plain,
% 0.14/0.41 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(19,plain,
% 0.14/0.41 (^[A: $i, B: $i] : rewrite((relation(B) => relation(relation_rng_restriction(A, B))) <=> ((~relation(B)) | relation(relation_rng_restriction(A, B))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(20,plain,
% 0.14/0.41 (![A: $i, B: $i] : (relation(B) => relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[19])).
% 0.14/0.41 tff(21,axiom,(![A: $i, B: $i] : (relation(B) => relation(relation_rng_restriction(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k8_relat_1')).
% 0.14/0.41 tff(22,plain,
% 0.14/0.41 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.14/0.41 tff(23,plain,
% 0.14/0.41 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.14/0.41 tff(24,plain,(
% 0.14/0.41 ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.14/0.41 inference(skolemize,[status(sab)],[23])).
% 0.14/0.41 tff(25,plain,
% 0.14/0.41 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.14/0.41 tff(26,plain,
% 0.14/0.41 (((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | ((~relation(B!7)) | relation(relation_rng_restriction(A!8, B!7)))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | (~relation(B!7)) | relation(relation_rng_restriction(A!8, B!7)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(27,plain,
% 0.14/0.41 ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | ((~relation(B!7)) | relation(relation_rng_restriction(A!8, B!7)))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(28,plain,
% 0.14/0.41 ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | (~relation(B!7)) | relation(relation_rng_restriction(A!8, B!7))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.14/0.41 tff(29,plain,
% 0.14/0.41 (relation(relation_rng_restriction(A!8, B!7))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[28, 25, 15])).
% 0.14/0.41 tff(30,plain,
% 0.14/0.41 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : ((~relation(B)) | (~subset(A, B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~subset(A, B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B))))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(31,plain,
% 0.14/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~subset(A, B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~subset(A, B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[30])).
% 0.14/0.41 tff(32,plain,
% 0.14/0.41 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((~relation(B)) | (~subset(A, B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~subset(A, B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B))))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(33,plain,
% 0.14/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~subset(A, B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~subset(A, B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[32])).
% 0.14/0.41 tff(34,plain,
% 0.14/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~subset(A, B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~subset(A, B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))),
% 0.14/0.41 inference(transitivity,[status(thm)],[33, 31])).
% 0.14/0.41 tff(35,plain,
% 0.14/0.41 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~relation(B)) | (~subset(A, B)))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~subset(A, B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B))))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(36,plain,
% 0.14/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~relation(B)) | (~subset(A, B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~subset(A, B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[35])).
% 0.14/0.41 tff(37,plain,
% 0.14/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~relation(B)) | (~subset(A, B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~relation(B)) | (~subset(A, B))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(38,plain,
% 0.14/0.41 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((subset(A, B) => (subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B)))) <=> ((~subset(A, B)) | (subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))))), ((relation(B) => (subset(A, B) => (subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))))) <=> (relation(B) => ((~subset(A, B)) | (subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))))))), rewrite((relation(B) => ((~subset(A, B)) | (subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))))) <=> ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~relation(B)) | (~subset(A, B)))), ((relation(B) => (subset(A, B) => (subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))))) <=> ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~relation(B)) | (~subset(A, B)))))), (![B: $i] : (relation(B) => (subset(A, B) => (subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))))) <=> ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~relation(B)) | (~subset(A, B))))), ((relation(A) => ![B: $i] : (relation(B) => (subset(A, B) => (subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B)))))) <=> (relation(A) => ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~relation(B)) | (~subset(A, B)))))), rewrite((relation(A) => ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~relation(B)) | (~subset(A, B)))) <=> ((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~relation(B)) | (~subset(A, B))))), ((relation(A) => ![B: $i] : (relation(B) => (subset(A, B) => (subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B)))))) <=> ((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~relation(B)) | (~subset(A, B))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(39,plain,
% 0.14/0.41 (![A: $i] : (relation(A) => ![B: $i] : (relation(B) => (subset(A, B) => (subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B)))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~relation(B)) | (~subset(A, B))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[38])).
% 0.14/0.41 tff(40,axiom,(![A: $i] : (relation(A) => ![B: $i] : (relation(B) => (subset(A, B) => (subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t25_relat_1')).
% 0.22/0.41 tff(41,plain,
% 0.22/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~relation(B)) | (~subset(A, B))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.22/0.41 tff(42,plain,
% 0.22/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~relation(B)) | (~subset(A, B))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.22/0.41 tff(43,plain,(
% 0.22/0.41 ![A: $i] : ((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~relation(B)) | (~subset(A, B))))),
% 0.22/0.41 inference(skolemize,[status(sab)],[42])).
% 0.22/0.41 tff(44,plain,
% 0.22/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~subset(A, B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.22/0.41 tff(45,plain,
% 0.22/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~subset(A, B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[44, 34])).
% 0.22/0.41 tff(46,plain,
% 0.22/0.41 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~subset(A, B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))) | ((~relation(relation_rng_restriction(A!8, B!7))) | ![B: $i] : ((~relation(B)) | (~subset(relation_rng_restriction(A!8, B!7), B)) | (~((~subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B))) | (~subset(relation_rng(relation_rng_restriction(A!8, B!7)), relation_rng(B)))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~subset(A, B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))) | (~relation(relation_rng_restriction(A!8, B!7))) | ![B: $i] : ((~relation(B)) | (~subset(relation_rng_restriction(A!8, B!7), B)) | (~((~subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B))) | (~subset(relation_rng(relation_rng_restriction(A!8, B!7)), relation_rng(B)))))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(47,plain,
% 0.22/0.41 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~subset(A, B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))) | ((~relation(relation_rng_restriction(A!8, B!7))) | ![B: $i] : ((~relation(B)) | (~subset(relation_rng_restriction(A!8, B!7), B)) | (~((~subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B))) | (~subset(relation_rng(relation_rng_restriction(A!8, B!7)), relation_rng(B)))))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(48,plain,
% 0.22/0.41 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~subset(A, B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))) | (~relation(relation_rng_restriction(A!8, B!7))) | ![B: $i] : ((~relation(B)) | (~subset(relation_rng_restriction(A!8, B!7), B)) | (~((~subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B))) | (~subset(relation_rng(relation_rng_restriction(A!8, B!7)), relation_rng(B))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.22/0.41 tff(49,plain,
% 0.22/0.41 (![B: $i] : ((~relation(B)) | (~subset(relation_rng_restriction(A!8, B!7), B)) | (~((~subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B))) | (~subset(relation_rng(relation_rng_restriction(A!8, B!7)), relation_rng(B))))))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[48, 45, 29])).
% 0.22/0.41 tff(50,plain,
% 0.22/0.41 (^[A: $i, B: $i] : refl(((~relation(B)) | subset(relation_rng_restriction(A, B), B)) <=> ((~relation(B)) | subset(relation_rng_restriction(A, B), B)))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(51,plain,
% 0.22/0.41 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B)) <=> ![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[50])).
% 0.22/0.41 tff(52,plain,
% 0.22/0.41 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B)) <=> ![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(53,plain,
% 0.22/0.41 (^[A: $i, B: $i] : rewrite((relation(B) => subset(relation_rng_restriction(A, B), B)) <=> ((~relation(B)) | subset(relation_rng_restriction(A, B), B)))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(54,plain,
% 0.22/0.41 (![A: $i, B: $i] : (relation(B) => subset(relation_rng_restriction(A, B), B)) <=> ![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[53])).
% 0.22/0.41 tff(55,axiom,(![A: $i, B: $i] : (relation(B) => subset(relation_rng_restriction(A, B), B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t117_relat_1')).
% 0.22/0.41 tff(56,plain,
% 0.22/0.41 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.22/0.41 tff(57,plain,
% 0.22/0.41 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.22/0.41 tff(58,plain,(
% 0.22/0.41 ![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 0.22/0.41 inference(skolemize,[status(sab)],[57])).
% 0.22/0.41 tff(59,plain,
% 0.22/0.41 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.22/0.41 tff(60,plain,
% 0.22/0.41 (((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))) | ((~relation(B!7)) | subset(relation_rng_restriction(A!8, B!7), B!7))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))) | (~relation(B!7)) | subset(relation_rng_restriction(A!8, B!7), B!7))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(61,plain,
% 0.22/0.41 ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))) | ((~relation(B!7)) | subset(relation_rng_restriction(A!8, B!7), B!7))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(62,plain,
% 0.22/0.41 ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))) | (~relation(B!7)) | subset(relation_rng_restriction(A!8, B!7), B!7)),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.22/0.41 tff(63,plain,
% 0.22/0.41 (subset(relation_rng_restriction(A!8, B!7), B!7)),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[62, 59, 15])).
% 0.22/0.41 tff(64,plain,
% 0.22/0.41 (((~![B: $i] : ((~relation(B)) | (~subset(relation_rng_restriction(A!8, B!7), B)) | (~((~subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B))) | (~subset(relation_rng(relation_rng_restriction(A!8, B!7)), relation_rng(B))))))) | ((~relation(B!7)) | (~subset(relation_rng_restriction(A!8, B!7), B!7)) | (~((~subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B!7))) | (~subset(relation_rng(relation_rng_restriction(A!8, B!7)), relation_rng(B!7))))))) <=> ((~![B: $i] : ((~relation(B)) | (~subset(relation_rng_restriction(A!8, B!7), B)) | (~((~subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B))) | (~subset(relation_rng(relation_rng_restriction(A!8, B!7)), relation_rng(B))))))) | (~relation(B!7)) | (~subset(relation_rng_restriction(A!8, B!7), B!7)) | (~((~subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B!7))) | (~subset(relation_rng(relation_rng_restriction(A!8, B!7)), relation_rng(B!7))))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(65,plain,
% 0.22/0.41 ((~![B: $i] : ((~relation(B)) | (~subset(relation_rng_restriction(A!8, B!7), B)) | (~((~subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B))) | (~subset(relation_rng(relation_rng_restriction(A!8, B!7)), relation_rng(B))))))) | ((~relation(B!7)) | (~subset(relation_rng_restriction(A!8, B!7), B!7)) | (~((~subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B!7))) | (~subset(relation_rng(relation_rng_restriction(A!8, B!7)), relation_rng(B!7))))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(66,plain,
% 0.22/0.42 ((~![B: $i] : ((~relation(B)) | (~subset(relation_rng_restriction(A!8, B!7), B)) | (~((~subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B))) | (~subset(relation_rng(relation_rng_restriction(A!8, B!7)), relation_rng(B))))))) | (~relation(B!7)) | (~subset(relation_rng_restriction(A!8, B!7), B!7)) | (~((~subset(relation_dom(relation_rng_restriction(A!8, B!7)), relation_dom(B!7))) | (~subset(relation_rng(relation_rng_restriction(A!8, B!7)), relation_rng(B!7)))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.22/0.42 tff(67,plain,
% 0.22/0.42 ($false),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[66, 15, 63, 49, 14])).
% 0.22/0.42 % SZS output end Proof
%------------------------------------------------------------------------------