TSTP Solution File: CAT018-4 by Prover9---1109a
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- Process Solution
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% File : Prover9---1109a
% Problem : CAT018-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 00:06:17 EDT 2022
% Result : Unsatisfiable 0.75s 1.06s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : CAT018-4 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun May 29 16:13:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.75/1.06 ============================== Prover9 ===============================
% 0.75/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.75/1.06 Process 5439 was started by sandbox on n017.cluster.edu,
% 0.75/1.06 Sun May 29 16:13:25 2022
% 0.75/1.06 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_5254_n017.cluster.edu".
% 0.75/1.06 ============================== end of head ===========================
% 0.75/1.06
% 0.75/1.06 ============================== INPUT =================================
% 0.75/1.06
% 0.75/1.06 % Reading from file /tmp/Prover9_5254_n017.cluster.edu
% 0.75/1.06
% 0.75/1.06 set(prolog_style_variables).
% 0.75/1.06 set(auto2).
% 0.75/1.06 % set(auto2) -> set(auto).
% 0.75/1.06 % set(auto) -> set(auto_inference).
% 0.75/1.06 % set(auto) -> set(auto_setup).
% 0.75/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.75/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.75/1.06 % set(auto) -> set(auto_limits).
% 0.75/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.75/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.75/1.06 % set(auto) -> set(auto_denials).
% 0.75/1.06 % set(auto) -> set(auto_process).
% 0.75/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.75/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.75/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.75/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.75/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.75/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.75/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.75/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.75/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.75/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.75/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.75/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.75/1.06 % set(auto2) -> assign(stats, some).
% 0.75/1.06 % set(auto2) -> clear(echo_input).
% 0.75/1.06 % set(auto2) -> set(quiet).
% 0.75/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.75/1.06 % set(auto2) -> clear(print_given).
% 0.75/1.06 assign(lrs_ticks,-1).
% 0.75/1.06 assign(sos_limit,10000).
% 0.75/1.06 assign(order,kbo).
% 0.75/1.06 set(lex_order_vars).
% 0.75/1.06 clear(print_given).
% 0.75/1.06
% 0.75/1.06 % formulas(sos). % not echoed (14 formulas)
% 0.75/1.06
% 0.75/1.06 ============================== end of input ==========================
% 0.75/1.06
% 0.75/1.06 % From the command line: assign(max_seconds, 300).
% 0.75/1.06
% 0.75/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.75/1.06
% 0.75/1.06 % Formulas that are not ordinary clauses:
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% 0.75/1.06 ============================== end of process non-clausal formulas ===
% 0.75/1.06
% 0.75/1.06 ============================== PROCESS INITIAL CLAUSES ===============
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% 0.75/1.06 ============================== PREDICATE ELIMINATION =================
% 0.75/1.06 1 -there_exists(A) | A != B | equivalent(A,B) # label(existence_and_equality_implies_equivalence1) # label(axiom). [assumption].
% 0.75/1.06 2 -equivalent(A,B) | there_exists(A) # label(equivalence_implies_existence1) # label(axiom). [assumption].
% 0.75/1.06 3 -equivalent(A,B) | A = B # label(equivalence_implies_existence2) # label(axiom). [assumption].
% 0.75/1.06
% 0.75/1.06 ============================== end predicate elimination =============
% 0.75/1.06
% 0.75/1.06 Auto_denials:
% 0.75/1.06 % copying label prove_a_bc_exists to answer in negative clause
% 0.75/1.06
% 0.75/1.06 Term ordering decisions:
% 0.75/1.06 Function symbol KB weights: b=1. a=1. c=1. compose=1. domain=1. codomain=1.
% 0.75/1.06
% 0.75/1.06 ============================== end of process initial clauses ========
% 0.75/1.06
% 0.75/1.06 ============================== CLAUSES FOR SEARCH ====================
% 0.75/1.06
% 0.75/1.06 ============================== end of clauses for search =============
% 0.75/1.06
% 0.75/1.06 ============================== SEARCH ================================
% 0.75/1.06
% 0.75/1.06 % Starting search at 0.01 seconds.
% 0.75/1.06
% 0.75/1.06 ============================== PROOF =================================
% 0.75/1.06 % SZS status Unsatisfiable
% 0.75/1.06 % SZS output start Refutation
% 0.75/1.06
% 0.75/1.06 % Proof 1 at 0.06 (+ 0.00) seconds: prove_a_bc_exists.
% 0.75/1.06 % Length of proof is 23.
% 0.75/1.06 % Level of proof is 5.
% 0.75/1.06 % Maximum clause weight is 12.000.
% 0.75/1.06 % Given clauses 147.
% 0.75/1.06
% 0.75/1.06 4 there_exists(compose(a,b)) # label(assume_ab_exists) # label(hypothesis). [assumption].
% 0.75/1.06 5 there_exists(compose(b,c)) # label(assume_bc_exists) # label(hypothesis). [assumption].
% 0.75/1.06 7 compose(codomain(A),A) = A # label(compose_codomain) # label(axiom). [assumption].
% 0.75/1.06 8 compose(A,compose(B,C)) = compose(compose(A,B),C) # label(associativity_of_compose) # label(axiom). [assumption].
% 0.75/1.06 9 compose(compose(A,B),C) = compose(A,compose(B,C)). [copy(8),flip(a)].
% 0.75/1.06 10 -there_exists(compose(a,compose(b,c))) # label(prove_a_bc_exists) # label(negated_conjecture) # answer(prove_a_bc_exists). [assumption].
% 0.75/1.06 11 -there_exists(domain(A)) | there_exists(A) # label(domain_has_elements) # label(axiom). [assumption].
% 0.75/1.06 13 -there_exists(compose(A,B)) | there_exists(domain(A)) # label(composition_implies_domain) # label(axiom). [assumption].
% 0.75/1.06 14 -there_exists(compose(A,B)) | domain(A) = codomain(B) # label(domain_codomain_composition1) # label(axiom). [assumption].
% 0.75/1.06 15 -there_exists(compose(A,B)) | codomain(B) = domain(A). [copy(14),flip(b)].
% 0.75/1.06 16 -there_exists(domain(A)) | domain(A) != codomain(B) | there_exists(compose(A,B)) # label(domain_codomain_composition2) # label(axiom). [assumption].
% 0.75/1.06 17 -there_exists(domain(A)) | codomain(B) != domain(A) | there_exists(compose(A,B)). [copy(16),flip(b)].
% 0.75/1.06 20 compose(codomain(A),compose(A,B)) = compose(A,B). [para(7(a,1),9(a,1,1)),flip(a)].
% 0.75/1.06 23 there_exists(domain(b)). [hyper(13,a,5,a)].
% 0.75/1.06 24 there_exists(domain(a)). [hyper(13,a,4,a)].
% 0.75/1.06 29 codomain(b) = domain(a). [hyper(15,a,4,a)].
% 0.75/1.06 31 -there_exists(A) | domain(codomain(A)) = codomain(A). [para(7(a,1),15(a,1)),flip(b)].
% 0.75/1.06 45 there_exists(b). [hyper(11,a,23,a)].
% 0.75/1.06 48 codomain(compose(b,c)) != domain(a) # answer(prove_a_bc_exists). [ur(17,a,24,a,c,10,a)].
% 0.75/1.06 72 -there_exists(compose(A,B)) | codomain(compose(A,B)) = domain(codomain(A)). [para(20(a,1),15(a,1))].
% 0.75/1.06 186 domain(domain(a)) = domain(a). [hyper(31,a,45,a),rewrite([29(2),29(5)])].
% 0.75/1.06 467 codomain(compose(b,c)) = domain(a). [hyper(72,a,5,a),rewrite([29(6),186(7)])].
% 0.75/1.06 468 $F # answer(prove_a_bc_exists). [resolve(467,a,48,a)].
% 0.75/1.06
% 0.75/1.06 % SZS output end Refutation
% 0.75/1.06 ============================== end of proof ==========================
% 0.75/1.06
% 0.75/1.06 ============================== STATISTICS ============================
% 0.75/1.06
% 0.75/1.06 Given=147. Generated=1970. Kept=461. proofs=1.
% 0.75/1.06 Usable=135. Sos=255. Demods=107. Limbo=0, Disabled=84. Hints=0.
% 0.75/1.06 Megabytes=0.52.
% 0.75/1.06 User_CPU=0.06, System_CPU=0.00, Wall_clock=0.
% 0.75/1.06
% 0.75/1.06 ============================== end of statistics =====================
% 0.75/1.06
% 0.75/1.06 ============================== end of search =========================
% 0.75/1.06
% 0.75/1.06 THEOREM PROVED
% 0.75/1.06 % SZS status Unsatisfiable
% 0.75/1.06
% 0.75/1.06 Exiting with 1 proof.
% 0.75/1.06
% 0.75/1.06 Process 5439 exit (max_proofs) Sun May 29 16:13:25 2022
% 0.75/1.06 Prover9 interrupted
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