TSTP Solution File: CAT004-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : CAT004-1 : TPTP v8.1.0. Released v1.0.0.
% 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 00:06:13 EDT 2022
% Result : Unsatisfiable 0.80s 1.14s
% Output : Refutation 0.80s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : CAT004-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % 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 17:07:42 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.80/1.14 ============================== Prover9 ===============================
% 0.80/1.14 Prover9 (32) version 2009-11A, November 2009.
% 0.80/1.14 Process 29467 was started by sandbox2 on n023.cluster.edu,
% 0.80/1.14 Sun May 29 17:07:43 2022
% 0.80/1.14 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_29312_n023.cluster.edu".
% 0.80/1.14 ============================== end of head ===========================
% 0.80/1.14
% 0.80/1.14 ============================== INPUT =================================
% 0.80/1.14
% 0.80/1.14 % Reading from file /tmp/Prover9_29312_n023.cluster.edu
% 0.80/1.14
% 0.80/1.14 set(prolog_style_variables).
% 0.80/1.14 set(auto2).
% 0.80/1.14 % set(auto2) -> set(auto).
% 0.80/1.14 % set(auto) -> set(auto_inference).
% 0.80/1.14 % set(auto) -> set(auto_setup).
% 0.80/1.14 % set(auto_setup) -> set(predicate_elim).
% 0.80/1.14 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.80/1.14 % set(auto) -> set(auto_limits).
% 0.80/1.14 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.80/1.14 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.80/1.14 % set(auto) -> set(auto_denials).
% 0.80/1.14 % set(auto) -> set(auto_process).
% 0.80/1.14 % set(auto2) -> assign(new_constants, 1).
% 0.80/1.14 % set(auto2) -> assign(fold_denial_max, 3).
% 0.80/1.14 % set(auto2) -> assign(max_weight, "200.000").
% 0.80/1.14 % set(auto2) -> assign(max_hours, 1).
% 0.80/1.14 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.80/1.14 % set(auto2) -> assign(max_seconds, 0).
% 0.80/1.14 % set(auto2) -> assign(max_minutes, 5).
% 0.80/1.14 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.80/1.14 % set(auto2) -> set(sort_initial_sos).
% 0.80/1.14 % set(auto2) -> assign(sos_limit, -1).
% 0.80/1.14 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.80/1.14 % set(auto2) -> assign(max_megs, 400).
% 0.80/1.14 % set(auto2) -> assign(stats, some).
% 0.80/1.14 % set(auto2) -> clear(echo_input).
% 0.80/1.14 % set(auto2) -> set(quiet).
% 0.80/1.14 % set(auto2) -> clear(print_initial_clauses).
% 0.80/1.14 % set(auto2) -> clear(print_given).
% 0.80/1.14 assign(lrs_ticks,-1).
% 0.80/1.14 assign(sos_limit,10000).
% 0.80/1.14 assign(order,kbo).
% 0.80/1.14 set(lex_order_vars).
% 0.80/1.14 clear(print_given).
% 0.80/1.14
% 0.80/1.14 % formulas(sos). % not echoed (24 formulas)
% 0.80/1.14
% 0.80/1.14 ============================== end of input ==========================
% 0.80/1.14
% 0.80/1.14 % From the command line: assign(max_seconds, 300).
% 0.80/1.14
% 0.80/1.14 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.80/1.14
% 0.80/1.14 % Formulas that are not ordinary clauses:
% 0.80/1.14
% 0.80/1.14 ============================== end of process non-clausal formulas ===
% 0.80/1.14
% 0.80/1.14 ============================== PROCESS INITIAL CLAUSES ===============
% 0.80/1.14
% 0.80/1.14 ============================== PREDICATE ELIMINATION =================
% 0.80/1.14 1 -defined(A,B) | -identity_map(A) | product(A,B,B) # label(identity1) # label(axiom). [assumption].
% 0.80/1.14 2 identity_map(domain(A)) # label(domain_is_an_identity_map) # label(axiom). [assumption].
% 0.80/1.14 3 identity_map(codomain(A)) # label(codomain_is_an_identity_map) # label(axiom). [assumption].
% 0.80/1.14 Derived: -defined(domain(A),B) | product(domain(A),B,B). [resolve(1,b,2,a)].
% 0.80/1.14 Derived: -defined(codomain(A),B) | product(codomain(A),B,B). [resolve(1,b,3,a)].
% 0.80/1.14 4 -defined(A,B) | -identity_map(B) | product(A,B,A) # label(identity2) # label(axiom). [assumption].
% 0.80/1.14 Derived: -defined(A,domain(B)) | product(A,domain(B),A). [resolve(4,b,2,a)].
% 0.80/1.14 Derived: -defined(A,codomain(B)) | product(A,codomain(B),A). [resolve(4,b,3,a)].
% 0.80/1.14 5 -defined(A,B) | -defined(B,C) | -identity_map(B) | defined(A,C) # label(category_theory_axiom6) # label(axiom). [assumption].
% 0.80/1.14 Derived: -defined(A,domain(B)) | -defined(domain(B),C) | defined(A,C). [resolve(5,c,2,a)].
% 0.80/1.14 Derived: -defined(A,codomain(B)) | -defined(codomain(B),C) | defined(A,C). [resolve(5,c,3,a)].
% 0.80/1.14
% 0.80/1.14 ============================== end predicate elimination =============
% 0.80/1.14
% 0.80/1.14 Auto_denials:
% 0.80/1.14 % copying label prove_h_equals_g to answer in negative clause
% 0.80/1.14
% 0.80/1.14 Term ordering decisions:
% 0.80/1.14 Function symbol KB weights: a=1. b=1. c=1. d=1. g=1. h=1. compose=1. codomain=1. domain=1.
% 0.80/1.14
% 0.80/1.14 ============================== end of process initial clauses ========
% 0.80/1.14
% 0.80/1.14 ============================== CLAUSES FOR SEARCH ====================
% 0.80/1.14
% 0.80/1.14 ============================== end of clauses for search =============
% 0.80/1.14
% 0.80/1.14 ============================== SEARCH ================================
% 0.80/1.14
% 0.80/1.14 % Starting search at 0.01 seconds.
% 0.80/1.14
% 0.80/1.14 ============================== PROOF =================================
% 0.80/1.14 % SZS status Unsatisfiable
% 0.80/1.14 % SZS output start Refutation
% 0.80/1.14
% 0.80/1.14 % Proof 1 at 0.11 (+ 0.01) seconds: prove_h_equals_g.
% 0.80/1.14 % Length of proof is 33.
% 0.80/1.14 % Level of proof is 7.
% 0.80/1.14 % Maximum clause weight is 16.000.
% 0.80/1.14 % Given clauses 185.
% 0.80/1.14
% 0.80/1.14 1 -defined(A,B) | -identity_map(A) | product(A,B,B) # label(identity1) # label(axiom). [assumption].
% 0.80/1.14 3 identity_map(codomain(A)) # label(codomain_is_an_identity_map) # label(axiom). [assumption].
% 0.80/1.14 8 product(a,b,c) # label(ab_equals_c) # label(hypothesis). [assumption].
% 0.80/1.14 9 product(h,c,d) # label(hc_equals_d) # label(hypothesis). [assumption].
% 0.80/1.14 10 product(g,c,d) # label(gc_equals_d) # label(hypothesis). [assumption].
% 0.80/1.14 12 product(codomain(A),A,A) # label(product_on_codomain) # label(axiom). [assumption].
% 0.80/1.14 13 h != g # label(prove_h_equals_g) # label(negated_conjecture) # answer(prove_h_equals_g). [assumption].
% 0.80/1.14 14 -product(A,B,C) | defined(A,B) # label(associative_property1) # label(axiom). [assumption].
% 0.80/1.14 15 -defined(A,B) | product(A,B,compose(A,B)) # label(closure_of_composition) # label(axiom). [assumption].
% 0.80/1.14 17 -product(A,B,C) | -defined(D,C) | defined(D,A) # label(category_theory_axiom3) # label(axiom). [assumption].
% 0.80/1.14 19 -product(A,a,B) | -product(C,a,B) | A = C # label(cancellation_for_product1) # label(hypothesis). [assumption].
% 0.80/1.14 20 -product(A,b,B) | -product(C,b,B) | A = C # label(cancellation_for_product2) # label(hypothesis). [assumption].
% 0.80/1.14 21 -product(A,B,C) | -product(B,D,E) | -defined(C,D) | defined(A,E) # label(category_theory_axiom1) # label(axiom). [assumption].
% 0.80/1.14 23 -product(A,B,C) | -product(C,D,E) | -product(B,D,F) | product(A,F,E) # label(category_theory_axiom2) # label(axiom). [assumption].
% 0.80/1.14 24 -product(A,B,C) | -product(D,C,E) | -product(D,A,F) | product(F,B,E) # label(category_theory_axiom5) # label(axiom). [assumption].
% 0.80/1.14 26 -defined(codomain(A),B) | product(codomain(A),B,B). [resolve(1,b,3,a)].
% 0.80/1.14 31 defined(g,c). [hyper(14,a,10,a)].
% 0.80/1.14 32 defined(h,c). [hyper(14,a,9,a)].
% 0.80/1.14 67 defined(g,a). [hyper(17,a,8,a,b,31,a)].
% 0.80/1.14 74 defined(codomain(h),d). [hyper(21,a,12,a,b,9,a,c,32,a)].
% 0.80/1.14 76 defined(h,a). [hyper(17,a,8,a,b,32,a)].
% 0.80/1.14 86 product(g,a,compose(g,a)). [hyper(15,a,67,a)].
% 0.80/1.14 89 product(h,a,compose(h,a)). [hyper(15,a,76,a)].
% 0.80/1.14 171 defined(codomain(h),g). [hyper(17,a,10,a,b,74,a)].
% 0.80/1.14 265 product(codomain(h),g,g). [hyper(26,a,171,a)].
% 0.80/1.14 625 product(compose(g,a),b,d). [hyper(24,a,8,a,b,10,a,c,86,a)].
% 0.80/1.14 644 product(compose(h,a),b,d). [hyper(24,a,8,a,b,9,a,c,89,a)].
% 0.80/1.14 659 -product(g,a,compose(h,a)) # answer(prove_h_equals_g). [ur(19,b,89,a,c,13,a(flip))].
% 0.80/1.14 664 product(codomain(h),compose(g,a),compose(g,a)). [hyper(23,a,265,a,b,86,a,c,86,a)].
% 0.80/1.14 667 -product(codomain(h),compose(g,a),compose(h,a)) # answer(prove_h_equals_g). [ur(24,a,86,a,c,265,a,d,659,a)].
% 0.80/1.14 764 compose(h,a) = compose(g,a). [hyper(20,a,625,a,b,644,a),flip(a)].
% 0.80/1.14 765 -product(codomain(h),compose(g,a),compose(g,a)) # answer(prove_h_equals_g). [back_rewrite(667),rewrite([764(8)])].
% 0.80/1.14 766 $F # answer(prove_h_equals_g). [resolve(765,a,664,a)].
% 0.80/1.14
% 0.80/1.14 % SZS output end Refutation
% 0.80/1.14 ============================== end of proof ==========================
% 0.80/1.14
% 0.80/1.14 ============================== STATISTICS ============================
% 0.80/1.14
% 0.80/1.14 Given=185. Generated=3355. Kept=760. proofs=1.
% 0.80/1.14 Usable=119. Sos=89. Demods=25. Limbo=1, Disabled=580. Hints=0.
% 0.80/1.14 Megabytes=0.35.
% 0.80/1.14 User_CPU=0.11, System_CPU=0.01, Wall_clock=0.
% 0.80/1.14
% 0.80/1.14 ============================== end of statistics =====================
% 0.80/1.14
% 0.80/1.14 ============================== end of search =========================
% 0.80/1.14
% 0.80/1.14 THEOREM PROVED
% 0.80/1.14 % SZS status Unsatisfiable
% 0.80/1.14
% 0.80/1.14 Exiting with 1 proof.
% 0.80/1.14
% 0.80/1.14 Process 29467 exit (max_proofs) Sun May 29 17:07:43 2022
% 0.80/1.14 Prover9 interrupted
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