TSTP Solution File: CAT009-3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : CAT009-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %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 : 600s
% DateTime : Fri Jul 15 00:06:15 EDT 2022
% Result : Unsatisfiable 0.73s 1.06s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : CAT009-3 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n028.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 20:27:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.73/1.06 ============================== Prover9 ===============================
% 0.73/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.73/1.06 Process 27287 was started by sandbox2 on n028.cluster.edu,
% 0.73/1.06 Sun May 29 20:27:19 2022
% 0.73/1.06 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_27133_n028.cluster.edu".
% 0.73/1.06 ============================== end of head ===========================
% 0.73/1.06
% 0.73/1.06 ============================== INPUT =================================
% 0.73/1.06
% 0.73/1.06 % Reading from file /tmp/Prover9_27133_n028.cluster.edu
% 0.73/1.06
% 0.73/1.06 set(prolog_style_variables).
% 0.73/1.06 set(auto2).
% 0.73/1.06 % set(auto2) -> set(auto).
% 0.73/1.06 % set(auto) -> set(auto_inference).
% 0.73/1.06 % set(auto) -> set(auto_setup).
% 0.73/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.73/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.73/1.06 % set(auto) -> set(auto_limits).
% 0.73/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.73/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.73/1.06 % set(auto) -> set(auto_denials).
% 0.73/1.06 % set(auto) -> set(auto_process).
% 0.73/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.73/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.73/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.73/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.73/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.73/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.73/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.73/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.73/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.73/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.73/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.73/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.73/1.06 % set(auto2) -> assign(stats, some).
% 0.73/1.06 % set(auto2) -> clear(echo_input).
% 0.73/1.06 % set(auto2) -> set(quiet).
% 0.73/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.73/1.06 % set(auto2) -> clear(print_given).
% 0.73/1.06 assign(lrs_ticks,-1).
% 0.73/1.06 assign(sos_limit,10000).
% 0.73/1.06 assign(order,kbo).
% 0.73/1.06 set(lex_order_vars).
% 0.73/1.06 clear(print_given).
% 0.73/1.06
% 0.73/1.06 % formulas(sos). % not echoed (19 formulas)
% 0.73/1.06
% 0.73/1.06 ============================== end of input ==========================
% 0.73/1.06
% 0.73/1.06 % From the command line: assign(max_seconds, 300).
% 0.73/1.06
% 0.73/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.73/1.06
% 0.73/1.06 % Formulas that are not ordinary clauses:
% 0.73/1.06
% 0.73/1.06 ============================== end of process non-clausal formulas ===
% 0.73/1.06
% 0.73/1.06 ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.06
% 0.73/1.06 ============================== PREDICATE ELIMINATION =================
% 0.73/1.06 1 -there_exists(A) | A != B | equivalent(A,B) # label(existence_and_equality_implies_equivalence1) # label(axiom). [assumption].
% 0.73/1.06 2 -equivalent(A,B) | there_exists(A) # label(equivalence_implies_existence1) # label(axiom). [assumption].
% 0.73/1.06 3 -equivalent(A,B) | there_exists(B) # label(equivalence_implies_existence3) # label(axiom). [assumption].
% 0.73/1.06 4 -equivalent(A,B) | A = B # label(equivalence_implies_existence2) # label(axiom). [assumption].
% 0.73/1.06 Derived: -there_exists(A) | A != B | there_exists(B). [resolve(1,c,3,a)].
% 0.73/1.06 5 -there_exists(A) | -there_exists(B) | A != B | equivalent(A,B) # label(existence_and_equality_implies_equivalence2) # label(axiom). [assumption].
% 0.73/1.06
% 0.73/1.06 ============================== end predicate elimination =============
% 0.73/1.06
% 0.73/1.06 Auto_denials: (non-Horn, no changes).
% 0.73/1.06
% 0.73/1.06 Term ordering decisions:
% 0.73/1.06 Function symbol KB weights: a=1. b=1. compose=1. f1=1. domain=1. codomain=1.
% 0.73/1.06
% 0.73/1.06 ============================== end of process initial clauses ========
% 0.73/1.06
% 0.73/1.06 ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.06
% 0.73/1.06 ============================== end of clauses for search =============
% 0.73/1.06
% 0.73/1.06 ============================== SEARCH ================================
% 0.73/1.06
% 0.73/1.06 % Starting search at 0.01 seconds.
% 0.73/1.06
% 0.73/1.06 ============================== PROOF =================================
% 0.73/1.06 % SZS status Unsatisfiable
% 0.73/1.06 % SZS output start Refutation
% 0.73/1.06
% 0.73/1.06 % Proof 1 at 0.08 (+ 0.00) seconds.
% 0.73/1.06 % Length of proof is 31.
% 0.73/1.06 % Level of proof is 7.
% 0.73/1.06 % Maximum clause weight is 14.000.
% 0.73/1.06 % Given clauses 143.
% 0.73/1.06
% 0.73/1.06 6 there_exists(compose(a,b)) # label(ab_exists) # label(hypothesis). [assumption].
% 0.73/1.06 7 compose(A,domain(A)) = A # label(compose_domain) # label(axiom). [assumption].
% 0.73/1.06 8 compose(codomain(A),A) = A # label(compose_codomain) # label(axiom). [assumption].
% 0.73/1.06 10 compose(A,compose(B,C)) = compose(compose(A,B),C) # label(associativity_of_compose) # label(axiom). [assumption].
% 0.73/1.06 11 compose(compose(A,B),C) = compose(A,compose(B,C)). [copy(10),flip(a)].
% 0.73/1.06 14 domain(compose(a,b)) != domain(b) # label(prove_domain_of_ab_equals_domain_of_b) # label(negated_conjecture). [assumption].
% 0.73/1.06 16 -there_exists(codomain(A)) | there_exists(A) # label(codomain_has_elements) # label(axiom). [assumption].
% 0.73/1.06 17 -there_exists(compose(A,B)) | there_exists(domain(A)) # label(composition_implies_domain) # label(axiom). [assumption].
% 0.73/1.06 19 -there_exists(compose(A,B)) | domain(A) = codomain(B) # label(domain_codomain_composition1) # label(axiom). [assumption].
% 0.73/1.06 20 -there_exists(compose(A,B)) | codomain(B) = domain(A). [copy(19),flip(b)].
% 0.73/1.06 21 -there_exists(domain(A)) | domain(A) != codomain(B) | there_exists(compose(A,B)) # label(domain_codomain_composition2) # label(axiom). [assumption].
% 0.73/1.06 22 -there_exists(domain(A)) | codomain(B) != domain(A) | there_exists(compose(A,B)). [copy(21),flip(b)].
% 0.73/1.06 26 compose(A,compose(B,domain(compose(A,B)))) = compose(A,B). [para(11(a,1),7(a,1))].
% 0.73/1.06 28 compose(codomain(A),compose(A,B)) = compose(A,B). [para(8(a,1),11(a,1,1)),flip(a)].
% 0.73/1.06 31 there_exists(domain(a)). [resolve(17,a,6,a)].
% 0.73/1.06 32 -there_exists(A) | there_exists(domain(A)). [para(7(a,1),17(a,1))].
% 0.73/1.06 39 codomain(b) = domain(a). [resolve(20,a,6,a)].
% 0.73/1.06 40 -there_exists(A) | codomain(domain(A)) = domain(A). [para(7(a,1),20(a,1))].
% 0.73/1.06 48 -there_exists(compose(A,B)) | codomain(compose(B,domain(compose(A,B)))) = domain(A). [para(26(a,1),20(a,1))].
% 0.73/1.06 55 there_exists(domain(domain(a))). [resolve(32,a,31,a)].
% 0.73/1.06 65 there_exists(domain(domain(domain(a)))). [resolve(55,a,32,a)].
% 0.73/1.06 86 compose(domain(a),b) = b. [para(39(a,1),8(a,1,1))].
% 0.73/1.06 87 there_exists(b). [para(39(a,1),16(a,1)),unit_del(a,31)].
% 0.73/1.06 88 compose(domain(a),compose(b,A)) = compose(b,A). [para(39(a,1),28(a,1,1))].
% 0.73/1.06 132 codomain(A) != domain(domain(domain(a))) | there_exists(compose(domain(domain(a)),A)). [resolve(65,a,22,a)].
% 0.73/1.06 219 domain(domain(a)) = domain(a). [para(86(a,1),20(a,1)),rewrite([39(4)]),flip(b),unit_del(a,87)].
% 0.73/1.06 223 codomain(A) != domain(a) | there_exists(compose(domain(a),A)). [back_rewrite(132),rewrite([219(4),219(4),219(7)])].
% 0.73/1.06 260 codomain(domain(compose(a,b))) = domain(compose(a,b)). [resolve(40,a,6,a)].
% 0.73/1.06 420 codomain(compose(b,domain(compose(a,b)))) = domain(a). [resolve(48,a,6,a)].
% 0.73/1.06 829 there_exists(compose(b,domain(compose(a,b)))). [resolve(420,a,223,a),rewrite([88(9)])].
% 0.73/1.06 842 $F. [resolve(829,a,20,a),rewrite([260(5)]),unit_del(a,14)].
% 0.73/1.06
% 0.73/1.06 % SZS output end Refutation
% 0.73/1.06 ============================== end of proof ==========================
% 0.73/1.06
% 0.73/1.06 ============================== STATISTICS ============================
% 0.73/1.06
% 0.73/1.06 Given=143. Generated=2451. Kept=831. proofs=1.
% 0.73/1.06 Usable=116. Sos=529. Demods=99. Limbo=9, Disabled=197. Hints=0.
% 0.73/1.06 Megabytes=0.76.
% 0.73/1.06 User_CPU=0.08, System_CPU=0.00, Wall_clock=0.
% 0.73/1.06
% 0.73/1.06 ============================== end of statistics =====================
% 0.73/1.06
% 0.73/1.06 ============================== end of search =========================
% 0.73/1.06
% 0.73/1.06 THEOREM PROVED
% 0.73/1.06 % SZS status Unsatisfiable
% 0.73/1.06
% 0.73/1.06 Exiting with 1 proof.
% 0.73/1.06
% 0.73/1.06 Process 27287 exit (max_proofs) Sun May 29 20:27:19 2022
% 0.73/1.06 Prover9 interrupted
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