TSTP Solution File: SEU247+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SEU247+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n028.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 0.12s 0.37s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SEU247+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.32  % Computer : n028.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Sat Sep  3 11:11:53 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33  Usage: tptp [options] [-file:]file
% 0.12/0.33    -h, -?       prints this message.
% 0.12/0.33    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.33    -m, -model   generate model.
% 0.12/0.33    -p, -proof   generate proof.
% 0.12/0.33    -c, -core    generate unsat core of named formulas.
% 0.12/0.33    -st, -statistics display statistics.
% 0.12/0.33    -t:timeout   set timeout (in second).
% 0.12/0.33    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.33    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33    -<param>:<value> configuration parameter and value.
% 0.12/0.33    -o:<output-file> file to place output in.
% 0.12/0.37  % SZS status Theorem
% 0.12/0.37  % SZS output start Proof
% 0.12/0.37  tff(relation_rng_restriction_type, type, (
% 0.12/0.37     relation_rng_restriction: ( $i * $i ) > $i)).
% 0.12/0.37  tff(relation_dom_restriction_type, type, (
% 0.12/0.37     relation_dom_restriction: ( $i * $i ) > $i)).
% 0.12/0.37  tff(tptp_fun_A_1_type, type, (
% 0.12/0.37     tptp_fun_A_1: $i)).
% 0.12/0.37  tff(tptp_fun_B_0_type, type, (
% 0.12/0.37     tptp_fun_B_0: $i)).
% 0.12/0.37  tff(relation_restriction_type, type, (
% 0.12/0.37     relation_restriction: ( $i * $i ) > $i)).
% 0.12/0.37  tff(relation_type, type, (
% 0.12/0.37     relation: $i > $o)).
% 0.12/0.37  tff(1,plain,
% 0.12/0.37      ((~![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)))))),
% 0.12/0.37      inference(rewrite,[status(thm)],[])).
% 0.12/0.37  tff(2,plain,
% 0.12/0.37      ((~![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)))))),
% 0.12/0.37      inference(rewrite,[status(thm)],[])).
% 0.12/0.37  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/sandbox2/benchmark/theBenchmark.p','t18_wellord1')).
% 0.12/0.37  tff(4,plain,
% 0.12/0.37      (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))),
% 0.12/0.37      inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.37  tff(5,plain,
% 0.12/0.37      (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))),
% 0.12/0.37      inference(modus_ponens,[status(thm)],[4, 1])).
% 0.12/0.37  tff(6,plain,
% 0.12/0.37      (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))),
% 0.12/0.37      inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.37  tff(7,plain,
% 0.12/0.37      (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))),
% 0.12/0.37      inference(modus_ponens,[status(thm)],[6, 1])).
% 0.12/0.37  tff(8,plain,
% 0.12/0.37      (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))),
% 0.12/0.37      inference(modus_ponens,[status(thm)],[7, 1])).
% 0.12/0.37  tff(9,plain,
% 0.12/0.37      (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))),
% 0.12/0.37      inference(modus_ponens,[status(thm)],[8, 1])).
% 0.12/0.37  tff(10,plain,
% 0.12/0.37      (~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_rng_restriction(A, relation_dom_restriction(B, A))))),
% 0.12/0.37      inference(modus_ponens,[status(thm)],[9, 1])).
% 0.12/0.37  tff(11,plain,(
% 0.12/0.37      ~((~relation(B!0)) | (relation_restriction(B!0, A!1) = relation_rng_restriction(A!1, relation_dom_restriction(B!0, A!1))))),
% 0.12/0.37      inference(skolemize,[status(sab)],[10])).
% 0.12/0.37  tff(12,plain,
% 0.12/0.37      (relation(B!0)),
% 0.12/0.37      inference(or_elim,[status(thm)],[11])).
% 0.12/0.37  tff(13,plain,
% 0.12/0.37      (^[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))))),
% 0.12/0.37      inference(bind,[status(th)],[])).
% 0.12/0.37  tff(14,plain,
% 0.12/0.37      (![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)))),
% 0.12/0.37      inference(quant_intro,[status(thm)],[13])).
% 0.12/0.37  tff(15,plain,
% 0.12/0.37      (![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)))),
% 0.12/0.37      inference(rewrite,[status(thm)],[])).
% 0.12/0.37  tff(16,plain,
% 0.12/0.37      (^[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))))),
% 0.12/0.38      inference(bind,[status(th)],[])).
% 0.12/0.38  tff(17,plain,
% 0.12/0.38      (![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)))),
% 0.12/0.38      inference(quant_intro,[status(thm)],[16])).
% 0.12/0.38  tff(18,axiom,(![A: $i, B: $i] : (relation(B) => (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t17_wellord1')).
% 0.12/0.38  tff(19,plain,
% 0.12/0.38      (![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.12/0.38      inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.38  tff(20,plain,
% 0.12/0.38      (![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.12/0.38      inference(modus_ponens,[status(thm)],[19, 15])).
% 0.12/0.38  tff(21,plain,(
% 0.12/0.38      ![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.12/0.38      inference(skolemize,[status(sab)],[20])).
% 0.12/0.38  tff(22,plain,
% 0.12/0.38      (![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))),
% 0.12/0.38      inference(modus_ponens,[status(thm)],[21, 14])).
% 0.12/0.38  tff(23,plain,
% 0.12/0.38      (((~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))) | ((~relation(B!0)) | (relation_restriction(B!0, A!1) = relation_dom_restriction(relation_rng_restriction(A!1, B!0), A!1)))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))) | (~relation(B!0)) | (relation_restriction(B!0, A!1) = relation_dom_restriction(relation_rng_restriction(A!1, B!0), A!1)))),
% 0.12/0.38      inference(rewrite,[status(thm)],[])).
% 0.12/0.38  tff(24,plain,
% 0.12/0.38      ((~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))) | ((~relation(B!0)) | (relation_restriction(B!0, A!1) = relation_dom_restriction(relation_rng_restriction(A!1, B!0), A!1)))),
% 0.12/0.38      inference(quant_inst,[status(thm)],[])).
% 0.12/0.38  tff(25,plain,
% 0.12/0.38      ((~![A: $i, B: $i] : ((~relation(B)) | (relation_restriction(B, A) = relation_dom_restriction(relation_rng_restriction(A, B), A)))) | (~relation(B!0)) | (relation_restriction(B!0, A!1) = relation_dom_restriction(relation_rng_restriction(A!1, B!0), A!1))),
% 0.12/0.38      inference(modus_ponens,[status(thm)],[24, 23])).
% 0.12/0.38  tff(26,plain,
% 0.12/0.38      (relation_restriction(B!0, A!1) = relation_dom_restriction(relation_rng_restriction(A!1, B!0), A!1)),
% 0.12/0.38      inference(unit_resolution,[status(thm)],[25, 22, 12])).
% 0.12/0.38  tff(27,plain,
% 0.12/0.38      ((relation_restriction(B!0, A!1) = relation_rng_restriction(A!1, relation_dom_restriction(B!0, A!1))) <=> (relation_dom_restriction(relation_rng_restriction(A!1, B!0), A!1) = relation_rng_restriction(A!1, relation_dom_restriction(B!0, A!1)))),
% 0.12/0.38      inference(monotonicity,[status(thm)],[26])).
% 0.12/0.38  tff(28,plain,
% 0.12/0.38      ((relation_dom_restriction(relation_rng_restriction(A!1, B!0), A!1) = relation_rng_restriction(A!1, relation_dom_restriction(B!0, A!1))) <=> (relation_restriction(B!0, A!1) = relation_rng_restriction(A!1, relation_dom_restriction(B!0, A!1)))),
% 0.12/0.38      inference(symmetry,[status(thm)],[27])).
% 0.12/0.38  tff(29,plain,
% 0.12/0.38      (^[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)))))),
% 0.12/0.38      inference(bind,[status(th)],[])).
% 0.12/0.38  tff(30,plain,
% 0.12/0.38      (![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))))),
% 0.12/0.38      inference(quant_intro,[status(thm)],[29])).
% 0.12/0.38  tff(31,plain,
% 0.12/0.38      (![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))))),
% 0.12/0.38      inference(rewrite,[status(thm)],[])).
% 0.12/0.38  tff(32,plain,
% 0.12/0.38      (^[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)))))),
% 0.12/0.38      inference(bind,[status(th)],[])).
% 0.12/0.38  tff(33,plain,
% 0.12/0.38      (![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))))),
% 0.12/0.38      inference(quant_intro,[status(thm)],[32])).
% 0.12/0.38  tff(34,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/sandbox2/benchmark/theBenchmark.p','t140_relat_1')).
% 0.12/0.38  tff(35,plain,
% 0.12/0.38      (![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))))),
% 0.12/0.38      inference(modus_ponens,[status(thm)],[34, 33])).
% 0.12/0.38  tff(36,plain,
% 0.12/0.38      (![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))))),
% 0.12/0.38      inference(modus_ponens,[status(thm)],[35, 31])).
% 0.12/0.38  tff(37,plain,(
% 0.12/0.38      ![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))))),
% 0.12/0.38      inference(skolemize,[status(sab)],[36])).
% 0.12/0.38  tff(38,plain,
% 0.12/0.38      (![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))))),
% 0.12/0.38      inference(modus_ponens,[status(thm)],[37, 30])).
% 0.12/0.38  tff(39,plain,
% 0.12/0.38      (((~![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!0)) | (relation_dom_restriction(relation_rng_restriction(A!1, B!0), A!1) = relation_rng_restriction(A!1, relation_dom_restriction(B!0, A!1))))) <=> ((~![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!0)) | (relation_dom_restriction(relation_rng_restriction(A!1, B!0), A!1) = relation_rng_restriction(A!1, relation_dom_restriction(B!0, A!1))))),
% 0.12/0.38      inference(rewrite,[status(thm)],[])).
% 0.12/0.38  tff(40,plain,
% 0.12/0.38      ((~![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!0)) | (relation_dom_restriction(relation_rng_restriction(A!1, B!0), A!1) = relation_rng_restriction(A!1, relation_dom_restriction(B!0, A!1))))),
% 0.12/0.38      inference(quant_inst,[status(thm)],[])).
% 0.12/0.38  tff(41,plain,
% 0.12/0.38      ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))) | (~relation(B!0)) | (relation_dom_restriction(relation_rng_restriction(A!1, B!0), A!1) = relation_rng_restriction(A!1, relation_dom_restriction(B!0, A!1)))),
% 0.12/0.38      inference(modus_ponens,[status(thm)],[40, 39])).
% 0.12/0.38  tff(42,plain,
% 0.12/0.38      (relation_dom_restriction(relation_rng_restriction(A!1, B!0), A!1) = relation_rng_restriction(A!1, relation_dom_restriction(B!0, A!1))),
% 0.12/0.38      inference(unit_resolution,[status(thm)],[41, 38, 12])).
% 0.12/0.38  tff(43,plain,
% 0.12/0.38      (relation_restriction(B!0, A!1) = relation_rng_restriction(A!1, relation_dom_restriction(B!0, A!1))),
% 0.12/0.38      inference(modus_ponens,[status(thm)],[42, 28])).
% 0.12/0.38  tff(44,plain,
% 0.12/0.38      (~(relation_restriction(B!0, A!1) = relation_rng_restriction(A!1, relation_dom_restriction(B!0, A!1)))),
% 0.12/0.38      inference(or_elim,[status(thm)],[11])).
% 0.12/0.38  tff(45,plain,
% 0.12/0.38      ($false),
% 0.12/0.38      inference(unit_resolution,[status(thm)],[44, 43])).
% 0.12/0.38  % SZS output end Proof
%------------------------------------------------------------------------------