TSTP Solution File: CAT005-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : CAT005-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 00:06:14 EDT 2022
% Result : Unsatisfiable 0.63s 0.98s
% Output : Refutation 0.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : CAT005-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.10 % Command : tptp2X_and_run_prover9 %d %s
% 0.10/0.29 % Computer : n025.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Sun May 29 16:14:56 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.63/0.96 ============================== Prover9 ===============================
% 0.63/0.96 Prover9 (32) version 2009-11A, November 2009.
% 0.63/0.96 Process 31343 was started by sandbox2 on n025.cluster.edu,
% 0.63/0.96 Sun May 29 16:14:57 2022
% 0.63/0.96 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_31189_n025.cluster.edu".
% 0.63/0.96 ============================== end of head ===========================
% 0.63/0.96
% 0.63/0.96 ============================== INPUT =================================
% 0.63/0.96
% 0.63/0.96 % Reading from file /tmp/Prover9_31189_n025.cluster.edu
% 0.63/0.96
% 0.63/0.96 set(prolog_style_variables).
% 0.63/0.96 set(auto2).
% 0.63/0.96 % set(auto2) -> set(auto).
% 0.63/0.96 % set(auto) -> set(auto_inference).
% 0.63/0.96 % set(auto) -> set(auto_setup).
% 0.63/0.96 % set(auto_setup) -> set(predicate_elim).
% 0.63/0.96 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.63/0.96 % set(auto) -> set(auto_limits).
% 0.63/0.96 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.63/0.96 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.63/0.96 % set(auto) -> set(auto_denials).
% 0.63/0.96 % set(auto) -> set(auto_process).
% 0.63/0.96 % set(auto2) -> assign(new_constants, 1).
% 0.63/0.96 % set(auto2) -> assign(fold_denial_max, 3).
% 0.63/0.96 % set(auto2) -> assign(max_weight, "200.000").
% 0.63/0.96 % set(auto2) -> assign(max_hours, 1).
% 0.63/0.96 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.63/0.96 % set(auto2) -> assign(max_seconds, 0).
% 0.63/0.96 % set(auto2) -> assign(max_minutes, 5).
% 0.63/0.96 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.63/0.96 % set(auto2) -> set(sort_initial_sos).
% 0.63/0.96 % set(auto2) -> assign(sos_limit, -1).
% 0.63/0.96 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.63/0.96 % set(auto2) -> assign(max_megs, 400).
% 0.63/0.96 % set(auto2) -> assign(stats, some).
% 0.63/0.96 % set(auto2) -> clear(echo_input).
% 0.63/0.96 % set(auto2) -> set(quiet).
% 0.63/0.96 % set(auto2) -> clear(print_initial_clauses).
% 0.63/0.96 % set(auto2) -> clear(print_given).
% 0.63/0.96 assign(lrs_ticks,-1).
% 0.63/0.96 assign(sos_limit,10000).
% 0.63/0.96 assign(order,kbo).
% 0.63/0.96 set(lex_order_vars).
% 0.63/0.96 clear(print_given).
% 0.63/0.96
% 0.63/0.96 % formulas(sos). % not echoed (21 formulas)
% 0.63/0.96
% 0.63/0.96 ============================== end of input ==========================
% 0.63/0.96
% 0.63/0.96 % From the command line: assign(max_seconds, 300).
% 0.63/0.96
% 0.63/0.96 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.63/0.96
% 0.63/0.96 % Formulas that are not ordinary clauses:
% 0.63/0.96
% 0.63/0.96 ============================== end of process non-clausal formulas ===
% 0.63/0.96
% 0.63/0.96 ============================== PROCESS INITIAL CLAUSES ===============
% 0.63/0.96
% 0.63/0.96 ============================== PREDICATE ELIMINATION =================
% 0.63/0.96 1 -defined(A,B) | -identity_map(A) | product(A,B,B) # label(identity1) # label(axiom). [assumption].
% 0.63/0.96 2 identity_map(d) # label(d_is_identity_map) # label(hypothesis). [assumption].
% 0.63/0.96 3 identity_map(domain(A)) # label(domain_is_an_identity_map) # label(axiom). [assumption].
% 0.63/0.96 4 identity_map(codomain(A)) # label(codomain_is_an_identity_map) # label(axiom). [assumption].
% 0.63/0.96 Derived: -defined(d,A) | product(d,A,A). [resolve(1,b,2,a)].
% 0.63/0.96 Derived: -defined(domain(A),B) | product(domain(A),B,B). [resolve(1,b,3,a)].
% 0.63/0.96 Derived: -defined(codomain(A),B) | product(codomain(A),B,B). [resolve(1,b,4,a)].
% 0.63/0.96 5 -defined(A,B) | -identity_map(B) | product(A,B,A) # label(identity2) # label(axiom). [assumption].
% 0.63/0.96 Derived: -defined(A,d) | product(A,d,A). [resolve(5,b,2,a)].
% 0.63/0.96 Derived: -defined(A,domain(B)) | product(A,domain(B),A). [resolve(5,b,3,a)].
% 0.63/0.96 Derived: -defined(A,codomain(B)) | product(A,codomain(B),A). [resolve(5,b,4,a)].
% 0.63/0.96 6 -defined(A,B) | -defined(B,C) | -identity_map(B) | defined(A,C) # label(category_theory_axiom6) # label(axiom). [assumption].
% 0.63/0.96 Derived: -defined(A,d) | -defined(d,B) | defined(A,B). [resolve(6,c,2,a)].
% 0.63/0.96 Derived: -defined(A,domain(B)) | -defined(domain(B),C) | defined(A,C). [resolve(6,c,3,a)].
% 0.63/0.96 Derived: -defined(A,codomain(B)) | -defined(codomain(B),C) | defined(A,C). [resolve(6,c,4,a)].
% 0.63/0.96
% 0.63/0.96 ============================== end predicate elimination =============
% 0.63/0.96
% 0.63/0.96 Auto_denials:
% 0.63/0.96 % copying label prove_domain_of_a_is_d to answer in negative clause
% 0.63/0.96
% 0.63/0.96 Term ordering decisions:
% 0.63/0.96 Function symbol KB weights: d=1. a=1. compose=1. codomain=1. domain=1.
% 0.63/0.96
% 0.63/0.96 ============================== end of process initial clauses ========
% 0.63/0.96
% 0.63/0.96 ============================== CLAUSES FOR SEARCH ====================
% 0.63/0.96
% 0.63/0.96 ============================== end of clauses for search =============
% 0.63/0.98
% 0.63/0.98 ============================== SEARCH ================================
% 0.63/0.98
% 0.63/0.98 % Starting search at 0.01 seconds.
% 0.63/0.98
% 0.63/0.98 ============================== PROOF =================================
% 0.63/0.98 % SZS status Unsatisfiable
% 0.63/0.98 % SZS output start Refutation
% 0.63/0.98
% 0.63/0.98 % Proof 1 at 0.03 (+ 0.00) seconds: prove_domain_of_a_is_d.
% 0.63/0.98 % Length of proof is 22.
% 0.63/0.98 % Level of proof is 7.
% 0.63/0.98 % Maximum clause weight is 16.000.
% 0.63/0.98 % Given clauses 60.
% 0.63/0.98
% 0.63/0.98 1 -defined(A,B) | -identity_map(A) | product(A,B,B) # label(identity1) # label(axiom). [assumption].
% 0.63/0.98 2 identity_map(d) # label(d_is_identity_map) # label(hypothesis). [assumption].
% 0.63/0.98 3 identity_map(domain(A)) # label(domain_is_an_identity_map) # label(axiom). [assumption].
% 0.63/0.98 5 -defined(A,B) | -identity_map(B) | product(A,B,A) # label(identity2) # label(axiom). [assumption].
% 0.63/0.98 7 defined(a,d) # label(ad_defined) # label(hypothesis). [assumption].
% 0.63/0.98 10 product(A,domain(A),A) # label(product_on_domain) # label(axiom). [assumption].
% 0.63/0.98 12 domain(a) != d # label(prove_domain_of_a_is_d) # label(negated_conjecture) # answer(prove_domain_of_a_is_d). [assumption].
% 0.63/0.98 15 -product(A,B,C) | -defined(C,D) | defined(B,D) # label(associative_property2) # label(axiom). [assumption].
% 0.63/0.98 17 -product(A,B,C) | -product(A,B,D) | C = D # label(composition_is_well_defined) # label(axiom). [assumption].
% 0.63/0.98 21 -product(A,B,C) | -product(D,C,E) | -product(D,A,F) | product(F,B,E) # label(category_theory_axiom5) # label(axiom). [assumption].
% 0.63/0.98 23 -defined(domain(A),B) | product(domain(A),B,B). [resolve(1,b,3,a)].
% 0.63/0.98 25 -defined(A,d) | product(A,d,A). [resolve(5,b,2,a)].
% 0.63/0.98 36 defined(domain(a),d). [hyper(15,a,10,a,b,7,a)].
% 0.63/0.98 42 -product(d,domain(d),domain(a)) # answer(prove_domain_of_a_is_d). [ur(17,b,10,a,c,12,a)].
% 0.63/0.98 52 product(a,d,a). [hyper(25,a,7,a)].
% 0.63/0.98 74 product(domain(a),d,domain(a)). [hyper(25,a,36,a)].
% 0.63/0.98 75 product(domain(a),d,d). [hyper(23,a,36,a)].
% 0.63/0.98 86 defined(d,d). [hyper(15,a,52,a,b,7,a)].
% 0.63/0.98 87 product(d,d,d). [hyper(25,a,86,a)].
% 0.63/0.98 115 -product(d,d,domain(a)) # answer(prove_domain_of_a_is_d). [ur(21,a,10,a,c,87,a,d,42,a)].
% 0.63/0.98 264 -product(domain(a),d,domain(a)) # answer(prove_domain_of_a_is_d). [ur(21,a,87,a,c,75,a,d,115,a)].
% 0.63/0.98 265 $F # answer(prove_domain_of_a_is_d). [resolve(264,a,74,a)].
% 0.63/0.98
% 0.63/0.98 % SZS output end Refutation
% 0.63/0.98 ============================== end of proof ==========================
% 0.63/0.98
% 0.63/0.98 ============================== STATISTICS ============================
% 0.63/0.98
% 0.63/0.98 Given=60. Generated=664. Kept=258. proofs=1.
% 0.63/0.98 Usable=57. Sos=165. Demods=3. Limbo=4, Disabled=61. Hints=0.
% 0.63/0.98 Megabytes=0.17.
% 0.63/0.98 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.63/0.98
% 0.63/0.98 ============================== end of statistics =====================
% 0.63/0.98
% 0.63/0.98 ============================== end of search =========================
% 0.63/0.98
% 0.63/0.98 THEOREM PROVED
% 0.63/0.98 % SZS status Unsatisfiable
% 0.63/0.98
% 0.63/0.98 Exiting with 1 proof.
% 0.63/0.98
% 0.63/0.98 Process 31343 exit (max_proofs) Sun May 29 16:14:57 2022
% 0.63/0.98 Prover9 interrupted
%------------------------------------------------------------------------------