TSTP Solution File: SEU247+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU247+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 07:28:29 EDT 2022
% Result : Theorem 0.19s 0.54s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU247+2 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33 % Computer : n022.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sat Sep 3 11:04:24 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.19/0.54 % SZS status Theorem
% 0.19/0.54 % SZS output start Proof
% 0.19/0.54 tff(relation_rng_restriction_type, type, (
% 0.19/0.54 relation_rng_restriction: ( $i * $i ) > $i)).
% 0.19/0.54 tff(relation_dom_restriction_type, type, (
% 0.19/0.54 relation_dom_restriction: ( $i * $i ) > $i)).
% 0.19/0.54 tff(tptp_fun_A_103_type, type, (
% 0.19/0.54 tptp_fun_A_103: $i)).
% 0.19/0.54 tff(tptp_fun_B_102_type, type, (
% 0.19/0.54 tptp_fun_B_102: $i)).
% 0.19/0.54 tff(relation_restriction_type, type, (
% 0.19/0.54 relation_restriction: ( $i * $i ) > $i)).
% 0.19/0.54 tff(relation_type, type, (
% 0.19/0.54 relation: $i > $o)).
% 0.19/0.54 tff(1,plain,
% 0.19/0.54 ((~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))) <=> (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A)))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(2,plain,
% 0.19/0.54 ((~![A: $i, B: $i] : (relation(B) => (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))) <=> (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A)))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(3,axiom,(~![A: $i, B: $i] : (relation(B) => (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t18_wellord1')).
% 0.19/0.54 tff(4,plain,
% 0.19/0.54 (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.54 tff(5,plain,
% 0.19/0.54 (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.54 tff(6,plain,
% 0.19/0.54 (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.54 tff(7,plain,
% 0.19/0.54 (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.54 tff(8,plain,
% 0.19/0.54 (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.19/0.54 tff(9,plain,
% 0.19/0.54 (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.19/0.54 tff(10,plain,
% 0.19/0.54 (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.19/0.54 tff(11,plain,(
% 0.19/0.54 ~((~relation(B!102)) | (relation_restriction(B!102, A!103) = relation_rng_restriction(A!103, relation_dom_restriction(B!102, A!103))))),
% 0.19/0.54 inference(skolemize,[status(sab)],[10])).
% 0.19/0.54 tff(12,plain,
% 0.19/0.54 (relation(B!102)),
% 0.19/0.54 inference(or_elim,[status(thm)],[11])).
% 0.19/0.54 tff(13,plain,
% 0.19/0.54 (^[A: $i, B: $i, C: $i] : refl(((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B)))) <=> ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B)))))),
% 0.19/0.54 inference(bind,[status(th)],[])).
% 0.19/0.54 tff(14,plain,
% 0.19/0.54 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))),
% 0.19/0.54 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.54 tff(15,plain,
% 0.19/0.54 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(16,plain,
% 0.19/0.54 (^[A: $i, B: $i, C: $i] : rewrite((relation(C) => (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B)))) <=> ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B)))))),
% 0.19/0.54 inference(bind,[status(th)],[])).
% 0.19/0.54 tff(17,plain,
% 0.19/0.54 (![A: $i, B: $i, C: $i] : (relation(C) => (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))),
% 0.19/0.54 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.54 tff(18,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t140_relat_1')).
% 0.19/0.54 tff(19,plain,
% 0.19/0.54 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.54 tff(20,plain,
% 0.19/0.54 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.19/0.54 tff(21,plain,(
% 0.19/0.54 ![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))),
% 0.19/0.54 inference(skolemize,[status(sab)],[20])).
% 0.19/0.54 tff(22,plain,
% 0.19/0.54 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.19/0.54 tff(23,plain,
% 0.19/0.54 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))) | ((~relation(B!102)) | (relation_dom_restriction(relation_rng_restriction(A!103, B!102), A!103) = relation_rng_restriction(A!103, relation_dom_restriction(B!102, A!103))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))) | (~relation(B!102)) | (relation_dom_restriction(relation_rng_restriction(A!103, B!102), A!103) = relation_rng_restriction(A!103, relation_dom_restriction(B!102, A!103))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(24,plain,
% 0.19/0.54 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))) | ((~relation(B!102)) | (relation_dom_restriction(relation_rng_restriction(A!103, B!102), A!103) = relation_rng_restriction(A!103, relation_dom_restriction(B!102, A!103))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(25,plain,
% 0.19/0.54 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))) | (~relation(B!102)) | (relation_dom_restriction(relation_rng_restriction(A!103, B!102), A!103) = relation_rng_restriction(A!103, relation_dom_restriction(B!102, A!103)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.54 tff(26,plain,
% 0.19/0.54 (relation_dom_restriction(relation_rng_restriction(A!103, B!102), A!103) = relation_rng_restriction(A!103, relation_dom_restriction(B!102, A!103))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[25, 22, 12])).
% 0.19/0.54 tff(27,plain,
% 0.19/0.54 (^[A: $i, B: $i] : refl(((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A))) <=> ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A))))),
% 0.19/0.54 inference(bind,[status(th)],[])).
% 0.19/0.54 tff(28,plain,
% 0.19/0.54 (![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A))) <=> ![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.19/0.54 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.54 tff(29,plain,
% 0.19/0.54 (![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A))) <=> ![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(30,plain,
% 0.19/0.54 (^[A: $i, B: $i] : rewrite((relation(B) => (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A))) <=> ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A))))),
% 0.19/0.54 inference(bind,[status(th)],[])).
% 0.19/0.54 tff(31,plain,
% 0.19/0.54 (![A: $i, B: $i] : (relation(B) => (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A))) <=> ![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.19/0.54 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.54 tff(32,axiom,(![A: $i, B: $i] : (relation(B) => (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t17_wellord1')).
% 0.19/0.54 tff(33,plain,
% 0.19/0.54 (![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.54 tff(34,plain,
% 0.19/0.54 (![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.19/0.54 tff(35,plain,(
% 0.19/0.54 ![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.19/0.54 inference(skolemize,[status(sab)],[34])).
% 0.19/0.54 tff(36,plain,
% 0.19/0.54 (![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.19/0.54 tff(37,plain,
% 0.19/0.54 (((~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))) | ((~relation(B!102)) | (relation_restriction(B!102, A!103) = relation_dom_restriction(relation_rng_restriction(A!103, B!102), A!103)))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))) | (~relation(B!102)) | (relation_restriction(B!102, A!103) = relation_dom_restriction(relation_rng_restriction(A!103, B!102), A!103)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(38,plain,
% 0.19/0.54 ((~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))) | ((~relation(B!102)) | (relation_restriction(B!102, A!103) = relation_dom_restriction(relation_rng_restriction(A!103, B!102), A!103)))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(39,plain,
% 0.19/0.54 ((~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))) | (~relation(B!102)) | (relation_restriction(B!102, A!103) = relation_dom_restriction(relation_rng_restriction(A!103, B!102), A!103))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.54 tff(40,plain,
% 0.19/0.54 (relation_restriction(B!102, A!103) = relation_dom_restriction(relation_rng_restriction(A!103, B!102), A!103)),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[39, 36, 12])).
% 0.19/0.54 tff(41,plain,
% 0.19/0.54 (relation_restriction(B!102, A!103) = relation_rng_restriction(A!103, relation_dom_restriction(B!102, A!103))),
% 0.19/0.54 inference(transitivity,[status(thm)],[40, 26])).
% 0.19/0.56 tff(42,plain,
% 0.19/0.56 (~(relation_restriction(B!102, A!103) = relation_rng_restriction(A!103, relation_dom_restriction(B!102, A!103)))),
% 0.19/0.56 inference(or_elim,[status(thm)],[11])).
% 0.19/0.56 tff(43,plain,
% 0.19/0.56 ($false),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.19/0.56 % SZS output end Proof
%------------------------------------------------------------------------------