TSTP Solution File: CAT001-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : CAT001-1 : 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 00:06:12 EDT 2022
% Result : Unsatisfiable 0.80s 1.10s
% 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
% 0.07/0.12 % Problem : CAT001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n025.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 23:03:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.80/1.10 ============================== Prover9 ===============================
% 0.80/1.10 Prover9 (32) version 2009-11A, November 2009.
% 0.80/1.10 Process 25384 was started by sandbox on n025.cluster.edu,
% 0.80/1.10 Sun May 29 23:03:42 2022
% 0.80/1.10 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_25231_n025.cluster.edu".
% 0.80/1.10 ============================== end of head ===========================
% 0.80/1.10
% 0.80/1.10 ============================== INPUT =================================
% 0.80/1.10
% 0.80/1.10 % Reading from file /tmp/Prover9_25231_n025.cluster.edu
% 0.80/1.10
% 0.80/1.10 set(prolog_style_variables).
% 0.80/1.10 set(auto2).
% 0.80/1.10 % set(auto2) -> set(auto).
% 0.80/1.10 % set(auto) -> set(auto_inference).
% 0.80/1.10 % set(auto) -> set(auto_setup).
% 0.80/1.10 % set(auto_setup) -> set(predicate_elim).
% 0.80/1.10 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.80/1.10 % set(auto) -> set(auto_limits).
% 0.80/1.10 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.80/1.10 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.80/1.10 % set(auto) -> set(auto_denials).
% 0.80/1.10 % set(auto) -> set(auto_process).
% 0.80/1.10 % set(auto2) -> assign(new_constants, 1).
% 0.80/1.10 % set(auto2) -> assign(fold_denial_max, 3).
% 0.80/1.10 % set(auto2) -> assign(max_weight, "200.000").
% 0.80/1.10 % set(auto2) -> assign(max_hours, 1).
% 0.80/1.10 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.80/1.10 % set(auto2) -> assign(max_seconds, 0).
% 0.80/1.10 % set(auto2) -> assign(max_minutes, 5).
% 0.80/1.10 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.80/1.10 % set(auto2) -> set(sort_initial_sos).
% 0.80/1.10 % set(auto2) -> assign(sos_limit, -1).
% 0.80/1.10 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.80/1.10 % set(auto2) -> assign(max_megs, 400).
% 0.80/1.10 % set(auto2) -> assign(stats, some).
% 0.80/1.10 % set(auto2) -> clear(echo_input).
% 0.80/1.10 % set(auto2) -> set(quiet).
% 0.80/1.10 % set(auto2) -> clear(print_initial_clauses).
% 0.80/1.10 % set(auto2) -> clear(print_given).
% 0.80/1.10 assign(lrs_ticks,-1).
% 0.80/1.10 assign(sos_limit,10000).
% 0.80/1.10 assign(order,kbo).
% 0.80/1.10 set(lex_order_vars).
% 0.80/1.10 clear(print_given).
% 0.80/1.10
% 0.80/1.10 % formulas(sos). % not echoed (23 formulas)
% 0.80/1.10
% 0.80/1.10 ============================== end of input ==========================
% 0.80/1.10
% 0.80/1.10 % From the command line: assign(max_seconds, 300).
% 0.80/1.10
% 0.80/1.10 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.80/1.10
% 0.80/1.10 % Formulas that are not ordinary clauses:
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% 0.80/1.10 ============================== end of process non-clausal formulas ===
% 0.80/1.10
% 0.80/1.10 ============================== PROCESS INITIAL CLAUSES ===============
% 0.80/1.10
% 0.80/1.10 ============================== PREDICATE ELIMINATION =================
% 0.80/1.10 1 -defined(A,B) | -identity_map(A) | product(A,B,B) # label(identity1) # label(axiom). [assumption].
% 0.80/1.10 2 identity_map(domain(A)) # label(domain_is_an_identity_map) # label(axiom). [assumption].
% 0.80/1.10 3 identity_map(codomain(A)) # label(codomain_is_an_identity_map) # label(axiom). [assumption].
% 0.80/1.10 Derived: -defined(domain(A),B) | product(domain(A),B,B). [resolve(1,b,2,a)].
% 0.80/1.10 Derived: -defined(codomain(A),B) | product(codomain(A),B,B). [resolve(1,b,3,a)].
% 0.80/1.10 4 -defined(A,B) | -identity_map(B) | product(A,B,A) # label(identity2) # label(axiom). [assumption].
% 0.80/1.10 Derived: -defined(A,domain(B)) | product(A,domain(B),A). [resolve(4,b,2,a)].
% 0.80/1.10 Derived: -defined(A,codomain(B)) | product(A,codomain(B),A). [resolve(4,b,3,a)].
% 0.80/1.10 5 -defined(A,B) | -defined(B,C) | -identity_map(B) | defined(A,C) # label(category_theory_axiom6) # label(axiom). [assumption].
% 0.80/1.10 Derived: -defined(A,domain(B)) | -defined(domain(B),C) | defined(A,C). [resolve(5,c,2,a)].
% 0.80/1.10 Derived: -defined(A,codomain(B)) | -defined(codomain(B),C) | defined(A,C). [resolve(5,c,3,a)].
% 0.80/1.10
% 0.80/1.10 ============================== end predicate elimination =============
% 0.80/1.10
% 0.80/1.10 Auto_denials:
% 0.80/1.10 % copying label prove_h_equals_g to answer in negative clause
% 0.80/1.10
% 0.80/1.10 Term ordering decisions:
% 0.80/1.10 Function symbol KB weights: b=1. c=1. d=1. a=1. g=1. h=1. compose=1. codomain=1. domain=1.
% 0.80/1.10
% 0.80/1.10 ============================== end of process initial clauses ========
% 0.80/1.10
% 0.80/1.10 ============================== CLAUSES FOR SEARCH ====================
% 0.80/1.10
% 0.80/1.10 ============================== end of clauses for search =============
% 0.80/1.10
% 0.80/1.10 ============================== SEARCH ================================
% 0.80/1.10
% 0.80/1.10 % Starting search at 0.01 seconds.
% 0.80/1.10
% 0.80/1.10 ============================== PROOF =================================
% 0.80/1.10 % SZS status Unsatisfiable
% 0.80/1.10 % SZS output start Refutation
% 0.80/1.10
% 0.80/1.10 % Proof 1 at 0.11 (+ 0.00) seconds: prove_h_equals_g.
% 0.80/1.10 % Length of proof is 25.
% 0.80/1.10 % Level of proof is 7.
% 0.80/1.10 % Maximum clause weight is 16.000.
% 0.80/1.10 % Given clauses 162.
% 0.80/1.10
% 0.80/1.10 2 identity_map(domain(A)) # label(domain_is_an_identity_map) # label(axiom). [assumption].
% 0.80/1.10 5 -defined(A,B) | -defined(B,C) | -identity_map(B) | defined(A,C) # label(category_theory_axiom6) # label(axiom). [assumption].
% 0.80/1.10 8 product(a,b,c) # label(ab_equals_c) # label(hypothesis). [assumption].
% 0.80/1.10 9 product(b,h,d) # label(bh_equals_d) # label(hypothesis). [assumption].
% 0.80/1.10 10 product(b,g,d) # label(bg_equals_d) # label(hypothesis). [assumption].
% 0.80/1.10 11 product(A,domain(A),A) # label(product_on_domain) # label(axiom). [assumption].
% 0.80/1.10 13 h != g # label(prove_h_equals_g) # label(negated_conjecture) # answer(prove_h_equals_g). [assumption].
% 0.80/1.10 14 -product(A,B,C) | defined(A,B) # label(associative_property1) # label(axiom). [assumption].
% 0.80/1.10 15 -defined(A,B) | product(A,B,compose(A,B)) # label(closure_of_composition) # label(axiom). [assumption].
% 0.80/1.10 16 -product(A,B,C) | -defined(C,D) | defined(B,D) # label(associative_property2) # label(axiom). [assumption].
% 0.80/1.10 19 -product(c,A,B) | -product(c,C,B) | A = C # label(cancellation_for_product) # label(hypothesis). [assumption].
% 0.80/1.10 21 -product(A,B,C) | -product(D,A,E) | -defined(D,C) | defined(E,B) # label(category_theory_axiom4) # label(axiom). [assumption].
% 0.80/1.10 22 -product(A,B,C) | -product(C,D,E) | -product(B,D,F) | product(A,F,E) # label(category_theory_axiom2) # label(axiom). [assumption].
% 0.80/1.10 23 -product(A,B,C) | -product(D,C,E) | -product(D,A,F) | product(F,B,E) # label(category_theory_axiom5) # label(axiom). [assumption].
% 0.80/1.10 28 -defined(A,domain(B)) | -defined(domain(B),C) | defined(A,C). [resolve(5,c,2,a)].
% 0.80/1.10 31 defined(b,h). [hyper(14,a,9,a)].
% 0.80/1.10 32 defined(a,b). [hyper(14,a,8,a)].
% 0.80/1.10 74 defined(domain(b),h). [hyper(16,a,11,a,b,31,a)].
% 0.80/1.10 76 defined(c,domain(b)). [hyper(21,a,11,a,b,8,a,c,32,a)].
% 0.80/1.10 173 defined(c,h). [hyper(28,a,76,a,b,74,a)].
% 0.80/1.10 182 product(c,h,compose(c,h)). [hyper(15,a,173,a)].
% 0.80/1.10 704 product(a,d,compose(c,h)). [hyper(22,a,8,a,b,182,a,c,9,a)].
% 0.80/1.10 712 -product(c,g,compose(c,h)) # answer(prove_h_equals_g). [ur(19,b,182,a,c,13,a(flip))].
% 0.80/1.10 762 -product(a,d,compose(c,h)) # answer(prove_h_equals_g). [ur(23,a,10,a,c,8,a,d,712,a)].
% 0.80/1.10 763 $F # answer(prove_h_equals_g). [resolve(762,a,704,a)].
% 0.80/1.10
% 0.80/1.10 % SZS output end Refutation
% 0.80/1.10 ============================== end of proof ==========================
% 0.80/1.10
% 0.80/1.10 ============================== STATISTICS ============================
% 0.80/1.10
% 0.80/1.10 Given=162. Generated=3200. Kept=757. proofs=1.
% 0.80/1.10 Usable=101. Sos=107. Demods=21. Limbo=2, Disabled=575. Hints=0.
% 0.80/1.10 Megabytes=0.35.
% 0.80/1.10 User_CPU=0.11, System_CPU=0.00, Wall_clock=0.
% 0.80/1.10
% 0.80/1.10 ============================== end of statistics =====================
% 0.80/1.10
% 0.80/1.10 ============================== end of search =========================
% 0.80/1.10
% 0.80/1.10 THEOREM PROVED
% 0.80/1.10 % SZS status Unsatisfiable
% 0.80/1.10
% 0.80/1.10 Exiting with 1 proof.
% 0.80/1.10
% 0.80/1.10 Process 25384 exit (max_proofs) Sun May 29 23:03:42 2022
% 0.80/1.10 Prover9 interrupted
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