TSTP Solution File: CAT004-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : CAT004-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 : 600s
% DateTime : Fri Jul 15 00:06:13 EDT 2022
% Result : Unsatisfiable 0.66s 0.98s
% Output : Refutation 0.66s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11 % Problem : CAT004-2 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun May 29 15:30:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.66/0.98 ============================== Prover9 ===============================
% 0.66/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.66/0.98 Process 1465 was started by sandbox2 on n019.cluster.edu,
% 0.66/0.98 Sun May 29 15:30:56 2022
% 0.66/0.98 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_1309_n019.cluster.edu".
% 0.66/0.98 ============================== end of head ===========================
% 0.66/0.98
% 0.66/0.98 ============================== INPUT =================================
% 0.66/0.98
% 0.66/0.98 % Reading from file /tmp/Prover9_1309_n019.cluster.edu
% 0.66/0.98
% 0.66/0.98 set(prolog_style_variables).
% 0.66/0.98 set(auto2).
% 0.66/0.98 % set(auto2) -> set(auto).
% 0.66/0.98 % set(auto) -> set(auto_inference).
% 0.66/0.98 % set(auto) -> set(auto_setup).
% 0.66/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.66/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.66/0.98 % set(auto) -> set(auto_limits).
% 0.66/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.66/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.66/0.98 % set(auto) -> set(auto_denials).
% 0.66/0.98 % set(auto) -> set(auto_process).
% 0.66/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.66/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.66/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.66/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.66/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.66/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.66/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.66/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.66/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.66/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.66/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.66/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.66/0.98 % set(auto2) -> assign(stats, some).
% 0.66/0.98 % set(auto2) -> clear(echo_input).
% 0.66/0.98 % set(auto2) -> set(quiet).
% 0.66/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.66/0.98 % set(auto2) -> clear(print_given).
% 0.66/0.98 assign(lrs_ticks,-1).
% 0.66/0.98 assign(sos_limit,10000).
% 0.66/0.98 assign(order,kbo).
% 0.66/0.98 set(lex_order_vars).
% 0.66/0.98 clear(print_given).
% 0.66/0.98
% 0.66/0.98 % formulas(sos). % not echoed (14 formulas)
% 0.66/0.98
% 0.66/0.98 ============================== end of input ==========================
% 0.66/0.98
% 0.66/0.98 % From the command line: assign(max_seconds, 300).
% 0.66/0.98
% 0.66/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.66/0.98
% 0.66/0.98 % Formulas that are not ordinary clauses:
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% 0.66/0.98 ============================== end of process non-clausal formulas ===
% 0.66/0.98
% 0.66/0.98 ============================== PROCESS INITIAL CLAUSES ===============
% 0.66/0.98
% 0.66/0.98 ============================== PREDICATE ELIMINATION =================
% 0.66/0.98
% 0.66/0.98 ============================== end predicate elimination =============
% 0.66/0.98
% 0.66/0.98 Auto_denials:
% 0.66/0.98 % copying label prove_h_equals_g to answer in negative clause
% 0.66/0.98
% 0.66/0.98 Term ordering decisions:
% 0.66/0.98 Function symbol KB weights: a=1. b=1. g=1. h=1. compose=1. codomain=1. domain=1.
% 0.66/0.98
% 0.66/0.98 ============================== end of process initial clauses ========
% 0.66/0.98
% 0.66/0.98 ============================== CLAUSES FOR SEARCH ====================
% 0.66/0.98
% 0.66/0.98 ============================== end of clauses for search =============
% 0.66/0.98
% 0.66/0.98 ============================== SEARCH ================================
% 0.66/0.98
% 0.66/0.98 % Starting search at 0.01 seconds.
% 0.66/0.98
% 0.66/0.98 ============================== PROOF =================================
% 0.66/0.98 % SZS status Unsatisfiable
% 0.66/0.98 % SZS output start Refutation
% 0.66/0.98
% 0.66/0.98 % Proof 1 at 0.02 (+ 0.00) seconds: prove_h_equals_g.
% 0.66/0.98 % Length of proof is 31.
% 0.66/0.98 % Level of proof is 7.
% 0.66/0.98 % Maximum clause weight is 23.000.
% 0.66/0.98 % Given clauses 29.
% 0.66/0.98
% 0.66/0.98 1 codomain(a) = domain(b) # label(codomain_of_a_equals_domain_of_b) # label(hypothesis). [assumption].
% 0.66/0.98 2 domain(b) = codomain(a). [copy(1),flip(a)].
% 0.66/0.98 4 domain(codomain(A)) = codomain(A) # label(domain_of_codomain_is_codomain) # label(axiom). [assumption].
% 0.66/0.98 6 compose(A,codomain(A)) = A # label(codomain_composition) # label(axiom). [assumption].
% 0.66/0.98 7 codomain(compose(a,b)) = domain(h) # label(codomain_of_ab_equals_domain_of_h) # label(hypothesis). [assumption].
% 0.66/0.98 8 codomain(compose(a,b)) = domain(g) # label(codomain_of_ab_equals_domain_of_g) # label(hypothesis). [assumption].
% 0.66/0.98 9 domain(h) = domain(g). [copy(8),rewrite([7(4)])].
% 0.66/0.98 10 compose(compose(a,b),h) = compose(compose(a,b),g) # label(ab_h_equals_ab_g) # label(hypothesis). [assumption].
% 0.66/0.98 11 h != g # label(prove_h_equals_g) # label(negated_conjecture) # answer(prove_h_equals_g). [assumption].
% 0.66/0.98 12 codomain(A) != domain(B) | domain(compose(A,B)) = domain(A) # label(codomain_domain1) # label(axiom). [assumption].
% 0.66/0.98 13 codomain(A) != domain(B) | codomain(compose(A,B)) = codomain(B) # label(codomain_domain2) # label(axiom). [assumption].
% 0.66/0.98 14 codomain(A) != domain(B) | codomain(B) != domain(C) | compose(A,compose(B,C)) = compose(compose(A,B),C) # label(star_property) # label(axiom). [assumption].
% 0.66/0.98 15 codomain(A) != domain(B) | codomain(B) != domain(C) | compose(compose(A,B),C) = compose(A,compose(B,C)). [copy(14),flip(c)].
% 0.66/0.98 16 codomain(a) != domain(A) | compose(a,A) != B | codomain(a) != domain(C) | compose(a,C) != B | A = C # label(epimorphism1) # label(hypothesis). [assumption].
% 0.66/0.98 17 codomain(b) != domain(A) | compose(b,A) != B | codomain(b) != domain(C) | compose(b,C) != B | A = C # label(epimorphism2) # label(hypothesis). [assumption].
% 0.66/0.98 18 codomain(compose(a,b)) = domain(g). [back_rewrite(7),rewrite([9(6)])].
% 0.66/0.98 31 domain(g) = codomain(b). [hyper(13,a,2,a(flip)),rewrite([18(4)])].
% 0.66/0.98 39 domain(h) = codomain(b). [back_rewrite(9),rewrite([31(4)])].
% 0.66/0.98 54 compose(compose(a,b),g) = compose(a,compose(b,g)). [hyper(15,a,2,a(flip),b,31,a(flip))].
% 0.66/0.98 55 compose(compose(b,g),codomain(g)) = compose(b,g). [hyper(15,a,31,a(flip),b,4,a(flip)),rewrite([6(11)])].
% 0.66/0.98 56 codomain(compose(b,g)) = codomain(g). [hyper(13,a,31,a(flip))].
% 0.66/0.98 57 domain(compose(b,g)) = codomain(a). [hyper(12,a,31,a(flip)),rewrite([2(6)])].
% 0.66/0.98 63 compose(compose(a,b),h) = compose(a,compose(b,g)). [back_rewrite(10),rewrite([54(10)])].
% 0.66/0.98 65 compose(a,compose(b,h)) = compose(a,compose(b,g)). [hyper(15,a,2,a(flip),b,39,a(flip)),rewrite([63(5)]),flip(a)].
% 0.66/0.98 66 compose(compose(b,h),codomain(h)) = compose(b,h). [hyper(15,a,39,a(flip),b,4,a(flip)),rewrite([6(11)])].
% 0.66/0.98 67 codomain(compose(b,h)) = codomain(h). [hyper(13,a,39,a(flip))].
% 0.66/0.98 68 domain(compose(b,h)) = codomain(a). [hyper(12,a,39,a(flip)),rewrite([2(6)])].
% 0.66/0.98 69 compose(b,h) != compose(b,g) # answer(prove_h_equals_g). [ur(17,a,31,a(flip),c,39,a(flip),d,6,a(flip),e,11,a(flip)),rewrite([67(10),66(9)]),flip(a)].
% 0.66/0.98 87 compose(compose(a,compose(b,g)),codomain(g)) = compose(a,compose(b,g)). [hyper(15,a,57,a(flip),b,4,a(flip)),rewrite([56(9),56(16),55(15)])].
% 0.66/0.98 88 codomain(compose(a,compose(b,g))) = codomain(g). [hyper(13,a,57,a(flip)),rewrite([56(10)])].
% 0.66/0.98 99 $F # answer(prove_h_equals_g). [ur(16,a,57,a(flip),c,68,a(flip),d,6,a(flip),e,69,a(flip)),rewrite([65(10),65(15),88(16),87(13)]),xx(a)].
% 0.66/0.98
% 0.66/0.98 % SZS output end Refutation
% 0.66/0.98 ============================== end of proof ==========================
% 0.66/0.98
% 0.66/0.98 ============================== STATISTICS ============================
% 0.66/0.98
% 0.66/0.98 Given=29. Generated=275. Kept=95. proofs=1.
% 0.66/0.98 Usable=27. Sos=59. Demods=35. Limbo=2, Disabled=21. Hints=0.
% 0.66/0.98 Megabytes=0.13.
% 0.66/0.98 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.66/0.98
% 0.66/0.98 ============================== end of statistics =====================
% 0.66/0.98
% 0.66/0.98 ============================== end of search =========================
% 0.66/0.98
% 0.66/0.98 THEOREM PROVED
% 0.66/0.98 % SZS status Unsatisfiable
% 0.66/0.98
% 0.66/0.98 Exiting with 1 proof.
% 0.66/0.98
% 0.66/0.98 Process 1465 exit (max_proofs) Sun May 29 15:30:56 2022
% 0.66/0.98 Prover9 interrupted
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