TSTP Solution File: CAT012-1 by Prover9---1109a
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- Process Solution
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% File : Prover9---1109a
% Problem : CAT012-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 00:06:16 EDT 2022
% Result : Unsatisfiable 0.70s 0.96s
% 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
% 0.03/0.12 % Problem : CAT012-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun May 29 22:36:15 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.70/0.96 ============================== Prover9 ===============================
% 0.70/0.96 Prover9 (32) version 2009-11A, November 2009.
% 0.70/0.96 Process 29913 was started by sandbox2 on n027.cluster.edu,
% 0.70/0.96 Sun May 29 22:36:16 2022
% 0.70/0.96 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_29759_n027.cluster.edu".
% 0.70/0.96 ============================== end of head ===========================
% 0.70/0.96
% 0.70/0.96 ============================== INPUT =================================
% 0.70/0.96
% 0.70/0.96 % Reading from file /tmp/Prover9_29759_n027.cluster.edu
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% 0.70/0.96 set(prolog_style_variables).
% 0.70/0.96 set(auto2).
% 0.70/0.96 % set(auto2) -> set(auto).
% 0.70/0.96 % set(auto) -> set(auto_inference).
% 0.70/0.96 % set(auto) -> set(auto_setup).
% 0.70/0.96 % set(auto_setup) -> set(predicate_elim).
% 0.70/0.96 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.70/0.96 % set(auto) -> set(auto_limits).
% 0.70/0.96 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.70/0.96 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.70/0.96 % set(auto) -> set(auto_denials).
% 0.70/0.96 % set(auto) -> set(auto_process).
% 0.70/0.96 % set(auto2) -> assign(new_constants, 1).
% 0.70/0.96 % set(auto2) -> assign(fold_denial_max, 3).
% 0.70/0.96 % set(auto2) -> assign(max_weight, "200.000").
% 0.70/0.96 % set(auto2) -> assign(max_hours, 1).
% 0.70/0.96 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.70/0.96 % set(auto2) -> assign(max_seconds, 0).
% 0.70/0.96 % set(auto2) -> assign(max_minutes, 5).
% 0.70/0.96 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.70/0.96 % set(auto2) -> set(sort_initial_sos).
% 0.70/0.96 % set(auto2) -> assign(sos_limit, -1).
% 0.70/0.96 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.70/0.96 % set(auto2) -> assign(max_megs, 400).
% 0.70/0.96 % set(auto2) -> assign(stats, some).
% 0.70/0.96 % set(auto2) -> clear(echo_input).
% 0.70/0.96 % set(auto2) -> set(quiet).
% 0.70/0.96 % set(auto2) -> clear(print_initial_clauses).
% 0.70/0.96 % set(auto2) -> clear(print_given).
% 0.70/0.96 assign(lrs_ticks,-1).
% 0.70/0.96 assign(sos_limit,10000).
% 0.70/0.96 assign(order,kbo).
% 0.70/0.96 set(lex_order_vars).
% 0.70/0.96 clear(print_given).
% 0.70/0.96
% 0.70/0.96 % formulas(sos). % not echoed (19 formulas)
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% 0.70/0.96 ============================== end of input ==========================
% 0.70/0.96
% 0.70/0.96 % From the command line: assign(max_seconds, 300).
% 0.70/0.96
% 0.70/0.96 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.70/0.96
% 0.70/0.96 % Formulas that are not ordinary clauses:
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% 0.70/0.96 ============================== end of process non-clausal formulas ===
% 0.70/0.96
% 0.70/0.96 ============================== PROCESS INITIAL CLAUSES ===============
% 0.70/0.96
% 0.70/0.96 ============================== PREDICATE ELIMINATION =================
% 0.70/0.96 1 -defined(A,B) | -identity_map(A) | product(A,B,B) # label(identity1) # label(axiom). [assumption].
% 0.70/0.96 2 identity_map(domain(A)) # label(domain_is_an_identity_map) # label(axiom). [assumption].
% 0.70/0.96 3 identity_map(codomain(A)) # label(codomain_is_an_identity_map) # label(axiom). [assumption].
% 0.70/0.96 Derived: -defined(domain(A),B) | product(domain(A),B,B). [resolve(1,b,2,a)].
% 0.70/0.96 Derived: -defined(codomain(A),B) | product(codomain(A),B,B). [resolve(1,b,3,a)].
% 0.70/0.96 4 -defined(A,B) | -identity_map(B) | product(A,B,A) # label(identity2) # label(axiom). [assumption].
% 0.70/0.96 Derived: -defined(A,domain(B)) | product(A,domain(B),A). [resolve(4,b,2,a)].
% 0.70/0.96 Derived: -defined(A,codomain(B)) | product(A,codomain(B),A). [resolve(4,b,3,a)].
% 0.70/0.96 5 -defined(A,B) | -defined(B,C) | -identity_map(B) | defined(A,C) # label(category_theory_axiom6) # label(axiom). [assumption].
% 0.70/0.96 Derived: -defined(A,domain(B)) | -defined(domain(B),C) | defined(A,C). [resolve(5,c,2,a)].
% 0.70/0.96 Derived: -defined(A,codomain(B)) | -defined(codomain(B),C) | defined(A,C). [resolve(5,c,3,a)].
% 0.70/0.96
% 0.70/0.96 ============================== end predicate elimination =============
% 0.70/0.96
% 0.70/0.96 Auto_denials:
% 0.70/0.96 % copying label prove_codomain_of_domain_is_domain to answer in negative clause
% 0.70/0.96
% 0.70/0.96 Term ordering decisions:
% 0.70/0.96 Function symbol KB weights: a=1. compose=1. codomain=1. domain=1.
% 0.70/0.96
% 0.70/0.96 ============================== end of process initial clauses ========
% 0.70/0.96
% 0.70/0.96 ============================== CLAUSES FOR SEARCH ====================
% 0.70/0.96
% 0.70/0.96 ============================== end of clauses for search =============
% 0.70/0.96
% 0.70/0.96 ============================== SEARCH ================================
% 0.70/0.96
% 0.70/0.96 % Starting search at 0.01 seconds.
% 0.70/0.96
% 0.70/0.96 ============================== PROOF =================================
% 0.70/0.96 % SZS status Unsatisfiable
% 0.70/0.96 % SZS output start Refutation
% 0.70/0.96
% 0.70/0.96 % Proof 1 at 0.02 (+ 0.00) seconds: prove_codomain_of_domain_is_domain.
% 0.70/0.96 % Length of proof is 13.
% 0.70/0.96 % Level of proof is 5.
% 0.70/0.96 % Maximum clause weight is 11.000.
% 0.70/0.96 % Given clauses 23.
% 0.70/0.96
% 0.70/0.96 2 identity_map(domain(A)) # label(domain_is_an_identity_map) # label(axiom). [assumption].
% 0.70/0.96 4 -defined(A,B) | -identity_map(B) | product(A,B,A) # label(identity2) # label(axiom). [assumption].
% 0.70/0.96 7 defined(codomain(A),A) # label(mapping_from_codomain_of_x_to_x) # label(axiom). [assumption].
% 0.70/0.96 9 product(codomain(A),A,A) # label(product_on_codomain) # label(axiom). [assumption].
% 0.70/0.96 10 codomain(domain(a)) != domain(a) # label(prove_codomain_of_domain_is_domain) # label(negated_conjecture) # answer(prove_codomain_of_domain_is_domain). [assumption].
% 0.70/0.96 15 -product(A,B,C) | -product(A,B,D) | C = D # label(composition_is_well_defined) # label(axiom). [assumption].
% 0.70/0.96 22 -defined(A,domain(B)) | product(A,domain(B),A). [resolve(4,b,2,a)].
% 0.70/0.96 26 codomain(domain(a)) = c_0. [new_symbol(10)].
% 0.70/0.96 27 domain(a) != c_0 # answer(prove_codomain_of_domain_is_domain). [back_rewrite(10),rewrite([26(3)]),flip(a)].
% 0.70/0.96 44 defined(c_0,domain(a)). [para(26(a,1),7(a,1))].
% 0.70/0.96 51 -product(c_0,domain(a),c_0) # answer(prove_codomain_of_domain_is_domain). [ur(15,a,9,a,c,27,a),rewrite([26(3)])].
% 0.70/0.96 63 -defined(c_0,domain(a)) # answer(prove_codomain_of_domain_is_domain). [ur(22,b,51,a)].
% 0.70/0.96 64 $F # answer(prove_codomain_of_domain_is_domain). [resolve(63,a,44,a)].
% 0.70/0.96
% 0.70/0.96 % SZS output end Refutation
% 0.70/0.96 ============================== end of proof ==========================
% 0.70/0.96
% 0.70/0.96 ============================== STATISTICS ============================
% 0.70/0.96
% 0.70/0.96 Given=23. Generated=98. Kept=58. proofs=1.
% 0.70/0.96 Usable=22. Sos=25. Demods=2. Limbo=0, Disabled=35. Hints=0.
% 0.70/0.96 Megabytes=0.06.
% 0.70/0.96 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.70/0.96
% 0.70/0.96 ============================== end of statistics =====================
% 0.70/0.96
% 0.70/0.96 ============================== end of search =========================
% 0.70/0.96
% 0.70/0.96 THEOREM PROVED
% 0.70/0.96 % SZS status Unsatisfiable
% 0.70/0.96
% 0.70/0.96 Exiting with 1 proof.
% 0.70/0.96
% 0.70/0.96 Process 29913 exit (max_proofs) Sun May 29 22:36:16 2022
% 0.70/0.96 Prover9 interrupted
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