TSTP Solution File: CAT003-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : CAT003-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 00:06:12 EDT 2022
% Result : Unsatisfiable 0.70s 1.05s
% Output : Refutation 0.70s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : CAT003-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n021.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 19:11:43 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.70/1.05 ============================== Prover9 ===============================
% 0.70/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.70/1.05 Process 12019 was started by sandbox on n021.cluster.edu,
% 0.70/1.05 Sun May 29 19:11:43 2022
% 0.70/1.05 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_11852_n021.cluster.edu".
% 0.70/1.05 ============================== end of head ===========================
% 0.70/1.05
% 0.70/1.05 ============================== INPUT =================================
% 0.70/1.05
% 0.70/1.05 % Reading from file /tmp/Prover9_11852_n021.cluster.edu
% 0.70/1.05
% 0.70/1.05 set(prolog_style_variables).
% 0.70/1.05 set(auto2).
% 0.70/1.05 % set(auto2) -> set(auto).
% 0.70/1.05 % set(auto) -> set(auto_inference).
% 0.70/1.05 % set(auto) -> set(auto_setup).
% 0.70/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.70/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.70/1.05 % set(auto) -> set(auto_limits).
% 0.70/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.70/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.70/1.05 % set(auto) -> set(auto_denials).
% 0.70/1.05 % set(auto) -> set(auto_process).
% 0.70/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.70/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.70/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.70/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.70/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.70/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.70/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.70/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.70/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.70/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.70/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.70/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.70/1.05 % set(auto2) -> assign(stats, some).
% 0.70/1.05 % set(auto2) -> clear(echo_input).
% 0.70/1.05 % set(auto2) -> set(quiet).
% 0.70/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.70/1.05 % set(auto2) -> clear(print_given).
% 0.70/1.05 assign(lrs_ticks,-1).
% 0.70/1.05 assign(sos_limit,10000).
% 0.70/1.05 assign(order,kbo).
% 0.70/1.05 set(lex_order_vars).
% 0.70/1.05 clear(print_given).
% 0.70/1.05
% 0.70/1.05 % formulas(sos). % not echoed (23 formulas)
% 0.70/1.05
% 0.70/1.05 ============================== end of input ==========================
% 0.70/1.05
% 0.70/1.05 % From the command line: assign(max_seconds, 300).
% 0.70/1.05
% 0.70/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.70/1.05
% 0.70/1.05 % Formulas that are not ordinary clauses:
% 0.70/1.05
% 0.70/1.05 ============================== end of process non-clausal formulas ===
% 0.70/1.05
% 0.70/1.05 ============================== PROCESS INITIAL CLAUSES ===============
% 0.70/1.05
% 0.70/1.05 ============================== PREDICATE ELIMINATION =================
% 0.70/1.05 1 -defined(A,B) | -identity_map(A) | product(A,B,B) # label(identity1) # label(axiom). [assumption].
% 0.70/1.05 2 identity_map(domain(A)) # label(domain_is_an_identity_map) # label(axiom). [assumption].
% 0.70/1.05 3 identity_map(codomain(A)) # label(codomain_is_an_identity_map) # label(axiom). [assumption].
% 0.70/1.05 Derived: -defined(domain(A),B) | product(domain(A),B,B). [resolve(1,b,2,a)].
% 0.70/1.05 Derived: -defined(codomain(A),B) | product(codomain(A),B,B). [resolve(1,b,3,a)].
% 0.70/1.05 4 -defined(A,B) | -identity_map(B) | product(A,B,A) # label(identity2) # label(axiom). [assumption].
% 0.70/1.05 Derived: -defined(A,domain(B)) | product(A,domain(B),A). [resolve(4,b,2,a)].
% 0.70/1.05 Derived: -defined(A,codomain(B)) | product(A,codomain(B),A). [resolve(4,b,3,a)].
% 0.70/1.05 5 -defined(A,B) | -defined(B,C) | -identity_map(B) | defined(A,C) # label(category_theory_axiom6) # label(axiom). [assumption].
% 0.70/1.05 Derived: -defined(A,domain(B)) | -defined(domain(B),C) | defined(A,C). [resolve(5,c,2,a)].
% 0.70/1.05 Derived: -defined(A,codomain(B)) | -defined(codomain(B),C) | defined(A,C). [resolve(5,c,3,a)].
% 0.70/1.05
% 0.70/1.05 ============================== end predicate elimination =============
% 0.70/1.05
% 0.70/1.05 Auto_denials:
% 0.70/1.05 % copying label prove_h_equals_g to answer in negative clause
% 0.70/1.05
% 0.70/1.05 Term ordering decisions:
% 0.70/1.05 Function symbol KB weights: a=1. c=1. d=1. b=1. g=1. h=1. compose=1. codomain=1. domain=1.
% 0.70/1.05
% 0.70/1.05 ============================== end of process initial clauses ========
% 0.70/1.05
% 0.70/1.05 ============================== CLAUSES FOR SEARCH ====================
% 0.70/1.05
% 0.70/1.05 ============================== end of clauses for search =============
% 0.70/1.05
% 0.70/1.05 ============================== SEARCH ================================
% 0.70/1.05
% 0.70/1.05 % Starting search at 0.01 seconds.
% 0.70/1.05
% 0.70/1.05 ============================== PROOF =================================
% 0.70/1.05 % SZS status Unsatisfiable
% 0.70/1.05 % SZS output start Refutation
% 0.70/1.05
% 0.70/1.05 % Proof 1 at 0.10 (+ 0.00) seconds: prove_h_equals_g.
% 0.70/1.05 % Length of proof is 25.
% 0.70/1.05 % Level of proof is 7.
% 0.70/1.05 % Maximum clause weight is 16.000.
% 0.70/1.05 % Given clauses 155.
% 0.70/1.05
% 0.70/1.05 3 identity_map(codomain(A)) # label(codomain_is_an_identity_map) # label(axiom). [assumption].
% 0.70/1.05 5 -defined(A,B) | -defined(B,C) | -identity_map(B) | defined(A,C) # label(category_theory_axiom6) # label(axiom). [assumption].
% 0.70/1.05 8 product(a,b,c) # label(ab_equals_c) # label(hypothesis). [assumption].
% 0.70/1.05 9 product(h,a,d) # label(ha_equals_d) # label(hypothesis). [assumption].
% 0.70/1.05 10 product(g,a,d) # label(ga_equals_d) # label(hypothesis). [assumption].
% 0.70/1.05 12 product(codomain(A),A,A) # label(product_on_codomain) # label(axiom). [assumption].
% 0.70/1.05 13 h != g # label(prove_h_equals_g) # label(negated_conjecture) # answer(prove_h_equals_g). [assumption].
% 0.70/1.05 14 -product(A,B,C) | defined(A,B) # label(associative_property1) # label(axiom). [assumption].
% 0.70/1.05 15 -defined(A,B) | product(A,B,compose(A,B)) # label(closure_of_composition) # label(axiom). [assumption].
% 0.70/1.05 17 -product(A,B,C) | -defined(D,C) | defined(D,A) # label(category_theory_axiom3) # label(axiom). [assumption].
% 0.70/1.05 19 -product(A,c,B) | -product(C,c,B) | A = C # label(cancellation_for_product) # label(hypothesis). [assumption].
% 0.70/1.05 20 -product(A,B,C) | -product(B,D,E) | -defined(C,D) | defined(A,E) # label(category_theory_axiom1) # label(axiom). [assumption].
% 0.70/1.05 22 -product(A,B,C) | -product(C,D,E) | -product(B,D,F) | product(A,F,E) # label(category_theory_axiom2) # label(axiom). [assumption].
% 0.70/1.05 23 -product(A,B,C) | -product(D,C,E) | -product(D,A,F) | product(F,B,E) # label(category_theory_axiom5) # label(axiom). [assumption].
% 0.70/1.05 29 -defined(A,codomain(B)) | -defined(codomain(B),C) | defined(A,C). [resolve(5,c,3,a)].
% 0.70/1.05 31 defined(h,a). [hyper(14,a,9,a)].
% 0.70/1.05 32 defined(a,b). [hyper(14,a,8,a)].
% 0.70/1.05 73 defined(h,codomain(a)). [hyper(17,a,12,a,b,31,a)].
% 0.70/1.05 77 defined(codomain(a),c). [hyper(20,a,12,a,b,8,a,c,32,a)].
% 0.70/1.05 180 defined(h,c). [hyper(29,a,73,a,b,77,a)].
% 0.70/1.05 194 product(h,c,compose(h,c)). [hyper(15,a,180,a)].
% 0.70/1.05 686 product(d,b,compose(h,c)). [hyper(23,a,8,a,b,194,a,c,9,a)].
% 0.70/1.05 697 -product(g,c,compose(h,c)) # answer(prove_h_equals_g). [ur(19,b,194,a,c,13,a(flip))].
% 0.70/1.05 709 -product(d,b,compose(h,c)) # answer(prove_h_equals_g). [ur(22,a,10,a,c,8,a,d,697,a)].
% 0.70/1.05 710 $F # answer(prove_h_equals_g). [resolve(709,a,686,a)].
% 0.70/1.05
% 0.70/1.05 % SZS output end Refutation
% 0.70/1.05 ============================== end of proof ==========================
% 0.70/1.05
% 0.70/1.05 ============================== STATISTICS ============================
% 0.70/1.05
% 0.70/1.05 Given=155. Generated=3010. Kept=704. proofs=1.
% 0.70/1.05 Usable=98. Sos=82. Demods=19. Limbo=1, Disabled=551. Hints=0.
% 0.70/1.05 Megabytes=0.32.
% 0.70/1.05 User_CPU=0.10, System_CPU=0.00, Wall_clock=1.
% 0.70/1.05
% 0.70/1.05 ============================== end of statistics =====================
% 0.70/1.05
% 0.70/1.05 ============================== end of search =========================
% 0.70/1.05
% 0.70/1.05 THEOREM PROVED
% 0.70/1.05 % SZS status Unsatisfiable
% 0.70/1.05
% 0.70/1.05 Exiting with 1 proof.
% 0.70/1.05
% 0.70/1.05 Process 12019 exit (max_proofs) Sun May 29 19:11:44 2022
% 0.70/1.05 Prover9 interrupted
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