TSTP Solution File: CAT010-10 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : CAT010-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 0.80s 1.12s
% Output : Refutation 0.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT010-10 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n023.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 22:40:12 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.80/1.12 ============================== Prover9 ===============================
% 0.80/1.12 Prover9 (32) version 2009-11A, November 2009.
% 0.80/1.12 Process 10872 was started by sandbox on n023.cluster.edu,
% 0.80/1.12 Sun May 29 22:40:13 2022
% 0.80/1.12 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_10719_n023.cluster.edu".
% 0.80/1.12 ============================== end of head ===========================
% 0.80/1.12
% 0.80/1.12 ============================== INPUT =================================
% 0.80/1.12
% 0.80/1.12 % Reading from file /tmp/Prover9_10719_n023.cluster.edu
% 0.80/1.12
% 0.80/1.12 set(prolog_style_variables).
% 0.80/1.12 set(auto2).
% 0.80/1.12 % set(auto2) -> set(auto).
% 0.80/1.12 % set(auto) -> set(auto_inference).
% 0.80/1.12 % set(auto) -> set(auto_setup).
% 0.80/1.12 % set(auto_setup) -> set(predicate_elim).
% 0.80/1.12 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.80/1.12 % set(auto) -> set(auto_limits).
% 0.80/1.12 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.80/1.12 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.80/1.12 % set(auto) -> set(auto_denials).
% 0.80/1.12 % set(auto) -> set(auto_process).
% 0.80/1.12 % set(auto2) -> assign(new_constants, 1).
% 0.80/1.12 % set(auto2) -> assign(fold_denial_max, 3).
% 0.80/1.12 % set(auto2) -> assign(max_weight, "200.000").
% 0.80/1.12 % set(auto2) -> assign(max_hours, 1).
% 0.80/1.12 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.80/1.12 % set(auto2) -> assign(max_seconds, 0).
% 0.80/1.12 % set(auto2) -> assign(max_minutes, 5).
% 0.80/1.12 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.80/1.12 % set(auto2) -> set(sort_initial_sos).
% 0.80/1.12 % set(auto2) -> assign(sos_limit, -1).
% 0.80/1.12 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.80/1.12 % set(auto2) -> assign(max_megs, 400).
% 0.80/1.12 % set(auto2) -> assign(stats, some).
% 0.80/1.12 % set(auto2) -> clear(echo_input).
% 0.80/1.12 % set(auto2) -> set(quiet).
% 0.80/1.12 % set(auto2) -> clear(print_initial_clauses).
% 0.80/1.12 % set(auto2) -> clear(print_given).
% 0.80/1.12 assign(lrs_ticks,-1).
% 0.80/1.12 assign(sos_limit,10000).
% 0.80/1.12 assign(order,kbo).
% 0.80/1.12 set(lex_order_vars).
% 0.80/1.12 clear(print_given).
% 0.80/1.12
% 0.80/1.12 % formulas(sos). % not echoed (16 formulas)
% 0.80/1.12
% 0.80/1.12 ============================== end of input ==========================
% 0.80/1.12
% 0.80/1.12 % From the command line: assign(max_seconds, 300).
% 0.80/1.12
% 0.80/1.12 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.80/1.12
% 0.80/1.12 % Formulas that are not ordinary clauses:
% 0.80/1.12
% 0.80/1.12 ============================== end of process non-clausal formulas ===
% 0.80/1.12
% 0.80/1.12 ============================== PROCESS INITIAL CLAUSES ===============
% 0.80/1.12
% 0.80/1.12 ============================== PREDICATE ELIMINATION =================
% 0.80/1.12
% 0.80/1.12 ============================== end predicate elimination =============
% 0.80/1.12
% 0.80/1.12 Auto_denials:
% 0.80/1.12 % copying label prove_codomain_of_ab_equals_codomain_of_a to answer in negative clause
% 0.80/1.12
% 0.80/1.12 Term ordering decisions:
% 0.80/1.12 Function symbol KB weights: true=1. a=1. b=1. compose=1. equivalent=1. there_exists=1. domain=1. codomain=1. ifeq=1. ifeq2=1. ifeq3=1.
% 0.80/1.12
% 0.80/1.12 ============================== end of process initial clauses ========
% 0.80/1.12
% 0.80/1.12 ============================== CLAUSES FOR SEARCH ====================
% 0.80/1.12
% 0.80/1.12 ============================== end of clauses for search =============
% 0.80/1.12
% 0.80/1.12 ============================== SEARCH ================================
% 0.80/1.12
% 0.80/1.12 % Starting search at 0.01 seconds.
% 0.80/1.12
% 0.80/1.12 ============================== PROOF =================================
% 0.80/1.12 % SZS status Unsatisfiable
% 0.80/1.12 % SZS output start Refutation
% 0.80/1.12
% 0.80/1.12 % Proof 1 at 0.14 (+ 0.01) seconds: prove_codomain_of_ab_equals_codomain_of_a.
% 0.80/1.12 % Length of proof is 18.
% 0.80/1.12 % Level of proof is 5.
% 0.80/1.12 % Maximum clause weight is 18.000.
% 0.80/1.12 % Given clauses 192.
% 0.80/1.12
% 0.80/1.12 2 compose(codomain(A),A) = A # label(compose_codomain) # label(axiom). [assumption].
% 0.80/1.12 3 there_exists(compose(a,b)) = true # label(ab_exists) # label(hypothesis). [assumption].
% 0.80/1.12 5 ifeq2(A,A,B,C) = B # label(ifeq_axiom_001) # label(axiom). [assumption].
% 0.80/1.12 6 ifeq(A,A,B,C) = B # label(ifeq_axiom_002) # label(axiom). [assumption].
% 0.80/1.12 10 ifeq(there_exists(domain(A)),true,there_exists(A),true) = true # label(domain_has_elements) # label(axiom). [assumption].
% 0.80/1.12 12 compose(A,compose(B,C)) = compose(compose(A,B),C) # label(associativity_of_compose) # label(axiom). [assumption].
% 0.80/1.12 13 compose(compose(A,B),C) = compose(A,compose(B,C)). [copy(12),flip(a)].
% 0.80/1.12 14 ifeq(there_exists(compose(A,B)),true,there_exists(domain(A)),true) = true # label(composition_implies_domain) # label(axiom). [assumption].
% 0.80/1.12 15 ifeq2(there_exists(compose(A,B)),true,domain(A),codomain(B)) = codomain(B) # label(domain_codomain_composition1) # label(axiom). [assumption].
% 0.80/1.12 17 codomain(compose(a,b)) != codomain(a) # label(prove_codomain_of_ab_equals_codomain_of_a) # label(negated_conjecture) # answer(prove_codomain_of_ab_equals_codomain_of_a). [assumption].
% 0.80/1.12 24 compose(codomain(A),compose(A,B)) = compose(A,B). [para(2(a,1),13(a,1,1)),flip(a)].
% 0.80/1.12 27 there_exists(domain(a)) = true. [para(3(a,1),14(a,1,1)),rewrite([6(7)])].
% 0.80/1.12 30 ifeq2(there_exists(A),true,domain(codomain(A)),codomain(A)) = codomain(A). [para(2(a,1),15(a,1,1,1))].
% 0.80/1.12 38 there_exists(a) = true. [para(27(a,1),10(a,1,1)),rewrite([6(6)])].
% 0.80/1.12 90 ifeq2(there_exists(compose(A,B)),true,domain(codomain(A)),codomain(compose(A,B))) = codomain(compose(A,B)). [para(24(a,1),15(a,1,1,1))].
% 0.80/1.12 209 domain(codomain(a)) = codomain(a). [para(38(a,1),30(a,1,1)),rewrite([5(8)])].
% 0.80/1.12 1334 codomain(compose(a,b)) = codomain(a). [para(3(a,1),90(a,1,1)),rewrite([209(5),5(9)]),flip(a)].
% 0.80/1.12 1335 $F # answer(prove_codomain_of_ab_equals_codomain_of_a). [resolve(1334,a,17,a)].
% 0.80/1.12
% 0.80/1.12 % SZS output end Refutation
% 0.80/1.12 ============================== end of proof ==========================
% 0.80/1.12
% 0.80/1.12 ============================== STATISTICS ============================
% 0.80/1.12
% 0.80/1.12 Given=192. Generated=8012. Kept=1333. proofs=1.
% 0.80/1.12 Usable=172. Sos=1016. Demods=1187. Limbo=0, Disabled=160. Hints=0.
% 0.80/1.12 Megabytes=1.87.
% 0.80/1.12 User_CPU=0.14, System_CPU=0.01, Wall_clock=0.
% 0.80/1.12
% 0.80/1.12 ============================== end of statistics =====================
% 0.80/1.12
% 0.80/1.12 ============================== end of search =========================
% 0.80/1.12
% 0.80/1.12 THEOREM PROVED
% 0.80/1.12 % SZS status Unsatisfiable
% 0.80/1.12
% 0.80/1.12 Exiting with 1 proof.
% 0.80/1.12
% 0.80/1.12 Process 10872 exit (max_proofs) Sun May 29 22:40:13 2022
% 0.80/1.12 Prover9 interrupted
%------------------------------------------------------------------------------