TSTP Solution File: CAT010-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : CAT010-1 : 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 00:06:15 EDT 2022
% Result : Unsatisfiable 0.82s 1.09s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT010-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n027.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun May 29 16:58:00 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.82/1.09 ============================== Prover9 ===============================
% 0.82/1.09 Prover9 (32) version 2009-11A, November 2009.
% 0.82/1.09 Process 32663 was started by sandbox2 on n027.cluster.edu,
% 0.82/1.09 Sun May 29 16:58:01 2022
% 0.82/1.09 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_32284_n027.cluster.edu".
% 0.82/1.09 ============================== end of head ===========================
% 0.82/1.09
% 0.82/1.09 ============================== INPUT =================================
% 0.82/1.09
% 0.82/1.09 % Reading from file /tmp/Prover9_32284_n027.cluster.edu
% 0.82/1.09
% 0.82/1.09 set(prolog_style_variables).
% 0.82/1.09 set(auto2).
% 0.82/1.09 % set(auto2) -> set(auto).
% 0.82/1.09 % set(auto) -> set(auto_inference).
% 0.82/1.09 % set(auto) -> set(auto_setup).
% 0.82/1.09 % set(auto_setup) -> set(predicate_elim).
% 0.82/1.09 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.82/1.09 % set(auto) -> set(auto_limits).
% 0.82/1.09 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.82/1.09 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.82/1.09 % set(auto) -> set(auto_denials).
% 0.82/1.09 % set(auto) -> set(auto_process).
% 0.82/1.09 % set(auto2) -> assign(new_constants, 1).
% 0.82/1.09 % set(auto2) -> assign(fold_denial_max, 3).
% 0.82/1.09 % set(auto2) -> assign(max_weight, "200.000").
% 0.82/1.09 % set(auto2) -> assign(max_hours, 1).
% 0.82/1.09 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.82/1.09 % set(auto2) -> assign(max_seconds, 0).
% 0.82/1.09 % set(auto2) -> assign(max_minutes, 5).
% 0.82/1.09 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.82/1.09 % set(auto2) -> set(sort_initial_sos).
% 0.82/1.09 % set(auto2) -> assign(sos_limit, -1).
% 0.82/1.09 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.82/1.09 % set(auto2) -> assign(max_megs, 400).
% 0.82/1.09 % set(auto2) -> assign(stats, some).
% 0.82/1.09 % set(auto2) -> clear(echo_input).
% 0.82/1.09 % set(auto2) -> set(quiet).
% 0.82/1.09 % set(auto2) -> clear(print_initial_clauses).
% 0.82/1.09 % set(auto2) -> clear(print_given).
% 0.82/1.09 assign(lrs_ticks,-1).
% 0.82/1.09 assign(sos_limit,10000).
% 0.82/1.09 assign(order,kbo).
% 0.82/1.09 set(lex_order_vars).
% 0.82/1.09 clear(print_given).
% 0.82/1.09
% 0.82/1.09 % formulas(sos). % not echoed (20 formulas)
% 0.82/1.09
% 0.82/1.09 ============================== end of input ==========================
% 0.82/1.09
% 0.82/1.09 % From the command line: assign(max_seconds, 300).
% 0.82/1.09
% 0.82/1.09 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.82/1.09
% 0.82/1.09 % Formulas that are not ordinary clauses:
% 0.82/1.09
% 0.82/1.09 ============================== end of process non-clausal formulas ===
% 0.82/1.09
% 0.82/1.09 ============================== PROCESS INITIAL CLAUSES ===============
% 0.82/1.09
% 0.82/1.09 ============================== PREDICATE ELIMINATION =================
% 0.82/1.09 1 -defined(A,B) | -identity_map(A) | product(A,B,B) # label(identity1) # label(axiom). [assumption].
% 0.82/1.09 2 identity_map(domain(A)) # label(domain_is_an_identity_map) # label(axiom). [assumption].
% 0.82/1.09 3 identity_map(codomain(A)) # label(codomain_is_an_identity_map) # label(axiom). [assumption].
% 0.82/1.09 Derived: -defined(domain(A),B) | product(domain(A),B,B). [resolve(1,b,2,a)].
% 0.82/1.09 Derived: -defined(codomain(A),B) | product(codomain(A),B,B). [resolve(1,b,3,a)].
% 0.82/1.09 4 -defined(A,B) | -identity_map(B) | product(A,B,A) # label(identity2) # label(axiom). [assumption].
% 0.82/1.09 Derived: -defined(A,domain(B)) | product(A,domain(B),A). [resolve(4,b,2,a)].
% 0.82/1.09 Derived: -defined(A,codomain(B)) | product(A,codomain(B),A). [resolve(4,b,3,a)].
% 0.82/1.09 5 -defined(A,B) | -defined(B,C) | -identity_map(B) | defined(A,C) # label(category_theory_axiom6) # label(axiom). [assumption].
% 0.82/1.09 Derived: -defined(A,domain(B)) | -defined(domain(B),C) | defined(A,C). [resolve(5,c,2,a)].
% 0.82/1.09 Derived: -defined(A,codomain(B)) | -defined(codomain(B),C) | defined(A,C). [resolve(5,c,3,a)].
% 0.82/1.09
% 0.82/1.09 ============================== end predicate elimination =============
% 0.82/1.09
% 0.82/1.09 Auto_denials:
% 0.82/1.09 % copying label prove_codomain_of_ba_equals_codomain_of_b to answer in negative clause
% 0.82/1.09
% 0.82/1.09 Term ordering decisions:
% 0.82/1.09 Function symbol KB weights: a=1. b=1. compose=1. codomain=1. domain=1.
% 0.82/1.09
% 0.82/1.09 ============================== end of process initial clauses ========
% 0.82/1.09
% 0.82/1.09 ============================== CLAUSES FOR SEARCH ====================
% 0.82/1.09
% 0.82/1.09 ============================== end of clauses for search =============
% 0.82/1.09
% 0.82/1.09 ============================== SEARCH ================================
% 0.82/1.09
% 0.82/1.09 % Starting search at 0.01 seconds.
% 0.82/1.09
% 0.82/1.09 ============================== PROOF =================================
% 0.82/1.09 % SZS status Unsatisfiable
% 0.82/1.09 % SZS output start Refutation
% 0.82/1.09
% 0.82/1.09 % Proof 1 at 0.08 (+ 0.01) seconds: prove_codomain_of_ba_equals_codomain_of_b.
% 0.82/1.09 % Length of proof is 30.
% 0.82/1.09 % Level of proof is 6.
% 0.82/1.09 % Maximum clause weight is 16.000.
% 0.82/1.09 % Given clauses 108.
% 0.82/1.09
% 0.82/1.09 1 -defined(A,B) | -identity_map(A) | product(A,B,B) # label(identity1) # label(axiom). [assumption].
% 0.82/1.09 3 identity_map(codomain(A)) # label(codomain_is_an_identity_map) # label(axiom). [assumption].
% 0.82/1.09 4 -defined(A,B) | -identity_map(B) | product(A,B,A) # label(identity2) # label(axiom). [assumption].
% 0.82/1.09 6 defined(b,a) # label(ba_defined) # label(hypothesis). [assumption].
% 0.82/1.09 7 defined(A,domain(A)) # label(mapping_from_x_to_its_domain) # label(axiom). [assumption].
% 0.82/1.09 8 defined(codomain(A),A) # label(mapping_from_codomain_of_x_to_x) # label(axiom). [assumption].
% 0.82/1.09 9 product(A,domain(A),A) # label(product_on_domain) # label(axiom). [assumption].
% 0.82/1.09 10 product(codomain(A),A,A) # label(product_on_codomain) # label(axiom). [assumption].
% 0.82/1.09 11 codomain(compose(b,a)) != codomain(b) # label(prove_codomain_of_ba_equals_codomain_of_b) # label(negated_conjecture) # answer(prove_codomain_of_ba_equals_codomain_of_b). [assumption].
% 0.82/1.09 13 -defined(A,B) | product(A,B,compose(A,B)) # label(closure_of_composition) # label(axiom). [assumption].
% 0.82/1.09 15 -product(A,B,C) | -defined(D,C) | defined(D,A) # label(category_theory_axiom3) # label(axiom). [assumption].
% 0.82/1.09 16 -product(A,B,C) | -product(A,B,D) | C = D # label(composition_is_well_defined) # label(axiom). [assumption].
% 0.82/1.09 17 -product(A,B,C) | -product(B,D,E) | -defined(C,D) | defined(A,E) # label(category_theory_axiom1) # label(axiom). [assumption].
% 0.82/1.09 19 -product(A,B,C) | -product(C,D,E) | -product(B,D,F) | product(A,F,E) # label(category_theory_axiom2) # label(axiom). [assumption].
% 0.82/1.09 20 -product(A,B,C) | -product(D,C,E) | -product(D,A,F) | product(F,B,E) # label(category_theory_axiom5) # label(axiom). [assumption].
% 0.82/1.09 22 -defined(codomain(A),B) | product(codomain(A),B,B). [resolve(1,b,3,a)].
% 0.82/1.09 24 -defined(A,codomain(B)) | product(A,codomain(B),A). [resolve(4,b,3,a)].
% 0.82/1.09 29 product(b,a,compose(b,a)). [hyper(13,a,6,a)].
% 0.82/1.09 33 defined(codomain(A),codomain(A)). [hyper(15,a,10,a,b,8,a)].
% 0.82/1.09 39 -product(codomain(compose(b,a)),domain(codomain(compose(b,a))),codomain(b)) # answer(prove_codomain_of_ba_equals_codomain_of_b). [ur(16,b,9,a,c,11,a(flip))].
% 0.82/1.09 45 product(codomain(A),domain(codomain(A)),domain(codomain(A))). [hyper(22,a,7,a)].
% 0.82/1.09 97 product(codomain(A),codomain(A),codomain(A)). [hyper(24,a,33,a)].
% 0.82/1.09 142 defined(codomain(b),compose(b,a)). [hyper(17,a,10,a,b,29,a,c,6,a)].
% 0.82/1.09 344 domain(codomain(A)) = codomain(A). [hyper(16,a,9,a,b,45,a),flip(a)].
% 0.82/1.09 345 -product(codomain(compose(b,a)),codomain(compose(b,a)),codomain(b)) # answer(prove_codomain_of_ba_equals_codomain_of_b). [ur(19,a,45,a,c,9,a,d,39,a),rewrite([344(5),344(9),344(9)])].
% 0.82/1.09 382 defined(codomain(b),codomain(compose(b,a))). [hyper(15,a,10,a,b,142,a)].
% 0.82/1.09 428 product(codomain(b),codomain(compose(b,a)),codomain(b)). [hyper(24,a,382,a)].
% 0.82/1.09 429 product(codomain(b),codomain(compose(b,a)),codomain(compose(b,a))). [hyper(22,a,382,a)].
% 0.82/1.09 450 -product(codomain(b),codomain(compose(b,a)),codomain(compose(b,a))) # answer(prove_codomain_of_ba_equals_codomain_of_b). [ur(20,a,97,a,b,428,a,d,345,a)].
% 0.82/1.09 451 $F # answer(prove_codomain_of_ba_equals_codomain_of_b). [resolve(450,a,429,a)].
% 0.82/1.09
% 0.82/1.09 % SZS output end Refutation
% 0.82/1.09 ============================== end of proof ==========================
% 0.82/1.09
% 0.82/1.09 ============================== STATISTICS ============================
% 0.82/1.09
% 0.82/1.09 Given=108. Generated=2275. Kept=445. proofs=1.
% 0.82/1.09 Usable=54. Sos=14. Demods=11. Limbo=0, Disabled=402. Hints=0.
% 0.82/1.09 Megabytes=0.25.
% 0.82/1.09 User_CPU=0.08, System_CPU=0.01, Wall_clock=0.
% 0.82/1.09
% 0.82/1.09 ============================== end of statistics =====================
% 0.82/1.09
% 0.82/1.09 ============================== end of search =========================
% 0.82/1.09
% 0.82/1.09 THEOREM PROVED
% 0.82/1.09 % SZS status Unsatisfiable
% 0.82/1.09
% 0.82/1.09 Exiting with 1 proof.
% 0.82/1.09
% 0.82/1.09 Process 32663 exit (max_proofs) Sun May 29 16:58:01 2022
% 0.82/1.09 Prover9 interrupted
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