TSTP Solution File: CAT006-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : CAT006-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n032.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 0.46s 0.81s
% Output : Refutation 0.46s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : CAT006-1 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.10 % Command : tptp2X_and_run_prover9 %d %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Sun May 29 18:54:41 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.46/0.79 ============================== Prover9 ===============================
% 0.46/0.79 Prover9 (32) version 2009-11A, November 2009.
% 0.46/0.79 Process 20790 was started by sandbox2 on n032.cluster.edu,
% 0.46/0.79 Sun May 29 18:54:42 2022
% 0.46/0.79 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_20637_n032.cluster.edu".
% 0.46/0.79 ============================== end of head ===========================
% 0.46/0.79
% 0.46/0.79 ============================== INPUT =================================
% 0.46/0.79
% 0.46/0.79 % Reading from file /tmp/Prover9_20637_n032.cluster.edu
% 0.46/0.79
% 0.46/0.79 set(prolog_style_variables).
% 0.46/0.79 set(auto2).
% 0.46/0.79 % set(auto2) -> set(auto).
% 0.46/0.79 % set(auto) -> set(auto_inference).
% 0.46/0.79 % set(auto) -> set(auto_setup).
% 0.46/0.79 % set(auto_setup) -> set(predicate_elim).
% 0.46/0.79 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/0.79 % set(auto) -> set(auto_limits).
% 0.46/0.79 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/0.79 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/0.79 % set(auto) -> set(auto_denials).
% 0.46/0.79 % set(auto) -> set(auto_process).
% 0.46/0.79 % set(auto2) -> assign(new_constants, 1).
% 0.46/0.79 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/0.79 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/0.79 % set(auto2) -> assign(max_hours, 1).
% 0.46/0.79 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/0.79 % set(auto2) -> assign(max_seconds, 0).
% 0.46/0.79 % set(auto2) -> assign(max_minutes, 5).
% 0.46/0.79 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/0.79 % set(auto2) -> set(sort_initial_sos).
% 0.46/0.79 % set(auto2) -> assign(sos_limit, -1).
% 0.46/0.79 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/0.79 % set(auto2) -> assign(max_megs, 400).
% 0.46/0.79 % set(auto2) -> assign(stats, some).
% 0.46/0.79 % set(auto2) -> clear(echo_input).
% 0.46/0.79 % set(auto2) -> set(quiet).
% 0.46/0.79 % set(auto2) -> clear(print_initial_clauses).
% 0.46/0.79 % set(auto2) -> clear(print_given).
% 0.46/0.79 assign(lrs_ticks,-1).
% 0.46/0.79 assign(sos_limit,10000).
% 0.46/0.79 assign(order,kbo).
% 0.46/0.79 set(lex_order_vars).
% 0.46/0.79 clear(print_given).
% 0.46/0.79
% 0.46/0.79 % formulas(sos). % not echoed (21 formulas)
% 0.46/0.79
% 0.46/0.79 ============================== end of input ==========================
% 0.46/0.79
% 0.46/0.79 % From the command line: assign(max_seconds, 300).
% 0.46/0.79
% 0.46/0.79 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/0.79
% 0.46/0.79 % Formulas that are not ordinary clauses:
% 0.46/0.79
% 0.46/0.79 ============================== end of process non-clausal formulas ===
% 0.46/0.79
% 0.46/0.79 ============================== PROCESS INITIAL CLAUSES ===============
% 0.46/0.79
% 0.46/0.79 ============================== PREDICATE ELIMINATION =================
% 0.46/0.79 1 -defined(A,B) | -identity_map(A) | product(A,B,B) # label(identity1) # label(axiom). [assumption].
% 0.46/0.79 2 identity_map(h) # label(h_is_the_identity_map) # label(hypothesis). [assumption].
% 0.46/0.79 3 identity_map(domain(A)) # label(domain_is_an_identity_map) # label(axiom). [assumption].
% 0.46/0.79 4 identity_map(codomain(A)) # label(codomain_is_an_identity_map) # label(axiom). [assumption].
% 0.46/0.79 Derived: -defined(h,A) | product(h,A,A). [resolve(1,b,2,a)].
% 0.46/0.79 Derived: -defined(domain(A),B) | product(domain(A),B,B). [resolve(1,b,3,a)].
% 0.46/0.79 Derived: -defined(codomain(A),B) | product(codomain(A),B,B). [resolve(1,b,4,a)].
% 0.46/0.79 5 -defined(A,B) | -identity_map(B) | product(A,B,A) # label(identity2) # label(axiom). [assumption].
% 0.46/0.79 Derived: -defined(A,h) | product(A,h,A). [resolve(5,b,2,a)].
% 0.46/0.79 Derived: -defined(A,domain(B)) | product(A,domain(B),A). [resolve(5,b,3,a)].
% 0.46/0.79 Derived: -defined(A,codomain(B)) | product(A,codomain(B),A). [resolve(5,b,4,a)].
% 0.46/0.79 6 -defined(A,B) | -defined(B,C) | -identity_map(B) | defined(A,C) # label(category_theory_axiom6) # label(axiom). [assumption].
% 0.46/0.79 Derived: -defined(A,h) | -defined(h,B) | defined(A,B). [resolve(6,c,2,a)].
% 0.46/0.79 Derived: -defined(A,domain(B)) | -defined(domain(B),C) | defined(A,C). [resolve(6,c,3,a)].
% 0.46/0.79 Derived: -defined(A,codomain(B)) | -defined(codomain(B),C) | defined(A,C). [resolve(6,c,4,a)].
% 0.46/0.79
% 0.46/0.79 ============================== end predicate elimination =============
% 0.46/0.79
% 0.46/0.79 Auto_denials:
% 0.46/0.79 % copying label prove_codomain_of_a_is_h to answer in negative clause
% 0.46/0.79
% 0.46/0.79 Term ordering decisions:
% 0.46/0.79 Function symbol KB weights: h=1. a=1. compose=1. codomain=1. domain=1.
% 0.46/0.79
% 0.46/0.79 ============================== end of process initial clauses ========
% 0.46/0.79
% 0.46/0.79 ============================== CLAUSES FOR SEARCH ====================
% 0.46/0.79
% 0.46/0.79 ============================== end of clauses for search =============
% 0.46/0.81
% 0.46/0.81 ============================== SEARCH ================================
% 0.46/0.81
% 0.46/0.81 % Starting search at 0.01 seconds.
% 0.46/0.81
% 0.46/0.81 ============================== PROOF =================================
% 0.46/0.81 % SZS status Unsatisfiable
% 0.46/0.81 % SZS output start Refutation
% 0.46/0.81
% 0.46/0.81 % Proof 1 at 0.03 (+ 0.00) seconds: prove_codomain_of_a_is_h.
% 0.46/0.81 % Length of proof is 22.
% 0.46/0.81 % Level of proof is 4.
% 0.46/0.81 % Maximum clause weight is 16.000.
% 0.46/0.81 % Given clauses 69.
% 0.46/0.81
% 0.46/0.81 1 -defined(A,B) | -identity_map(A) | product(A,B,B) # label(identity1) # label(axiom). [assumption].
% 0.46/0.81 2 identity_map(h) # label(h_is_the_identity_map) # label(hypothesis). [assumption].
% 0.46/0.81 4 identity_map(codomain(A)) # label(codomain_is_an_identity_map) # label(axiom). [assumption].
% 0.46/0.81 5 -defined(A,B) | -identity_map(B) | product(A,B,A) # label(identity2) # label(axiom). [assumption].
% 0.46/0.81 7 defined(h,a) # label(ha_defined) # label(hypothesis). [assumption].
% 0.46/0.81 10 product(A,domain(A),A) # label(product_on_domain) # label(axiom). [assumption].
% 0.46/0.81 11 product(codomain(A),A,A) # label(product_on_codomain) # label(axiom). [assumption].
% 0.46/0.81 12 codomain(a) != h # label(prove_codomain_of_a_is_h) # label(negated_conjecture) # answer(prove_codomain_of_a_is_h). [assumption].
% 0.46/0.81 16 -product(A,B,C) | -defined(D,C) | defined(D,A) # label(category_theory_axiom3) # label(axiom). [assumption].
% 0.46/0.81 17 -product(A,B,C) | -product(A,B,D) | C = D # label(composition_is_well_defined) # label(axiom). [assumption].
% 0.46/0.81 20 -product(A,B,C) | -product(C,D,E) | -product(B,D,F) | product(A,F,E) # label(category_theory_axiom2) # label(axiom). [assumption].
% 0.46/0.81 21 -product(A,B,C) | -product(D,C,E) | -product(D,A,F) | product(F,B,E) # label(category_theory_axiom5) # label(axiom). [assumption].
% 0.46/0.81 22 -defined(h,A) | product(h,A,A). [resolve(1,b,2,a)].
% 0.46/0.81 27 -defined(A,codomain(B)) | product(A,codomain(B),A). [resolve(5,b,4,a)].
% 0.46/0.81 39 defined(h,codomain(a)). [hyper(16,a,11,a,b,7,a)].
% 0.46/0.81 43 -product(codomain(a),domain(codomain(a)),h) # answer(prove_codomain_of_a_is_h). [ur(17,b,10,a,c,12,a(flip))].
% 0.46/0.81 47 product(A,domain(domain(A)),A). [hyper(21,a,10,a,b,10,a,c,10,a)].
% 0.46/0.81 71 -product(codomain(a),domain(domain(codomain(a))),h) # answer(prove_codomain_of_a_is_h). [ur(20,a,10,a,c,10,a,d,43,a)].
% 0.46/0.81 79 product(h,codomain(a),h). [hyper(27,a,39,a)].
% 0.46/0.81 80 product(h,codomain(a),codomain(a)). [hyper(22,a,39,a)].
% 0.46/0.81 311 -product(h,codomain(a),codomain(a)) # answer(prove_codomain_of_a_is_h). [ur(21,a,47,a,b,79,a,d,71,a)].
% 0.46/0.81 312 $F # answer(prove_codomain_of_a_is_h). [resolve(311,a,80,a)].
% 0.46/0.81
% 0.46/0.81 % SZS output end Refutation
% 0.46/0.81 ============================== end of proof ==========================
% 0.46/0.81
% 0.46/0.81 ============================== STATISTICS ============================
% 0.46/0.81
% 0.46/0.81 Given=69. Generated=863. Kept=305. proofs=1.
% 0.46/0.81 Usable=66. Sos=202. Demods=3. Limbo=1, Disabled=65. Hints=0.
% 0.46/0.81 Megabytes=0.19.
% 0.46/0.81 User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.46/0.81
% 0.46/0.81 ============================== end of statistics =====================
% 0.46/0.81
% 0.46/0.81 ============================== end of search =========================
% 0.46/0.81
% 0.46/0.81 THEOREM PROVED
% 0.46/0.81 % SZS status Unsatisfiable
% 0.46/0.81
% 0.46/0.81 Exiting with 1 proof.
% 0.46/0.81
% 0.46/0.81 Process 20790 exit (max_proofs) Sun May 29 18:54:42 2022
% 0.46/0.81 Prover9 interrupted
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