TSTP Solution File: CAT009-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : CAT009-1 : 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 00:06:15 EDT 2022
% Result : Unsatisfiable 0.72s 1.06s
% Output : Refutation 0.72s
% 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 : CAT009-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun May 29 19:22:28 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.72/1.06 ============================== Prover9 ===============================
% 0.72/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.72/1.06 Process 18232 was started by sandbox2 on n021.cluster.edu,
% 0.72/1.06 Sun May 29 19:22:28 2022
% 0.72/1.06 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_18077_n021.cluster.edu".
% 0.72/1.06 ============================== end of head ===========================
% 0.72/1.06
% 0.72/1.06 ============================== INPUT =================================
% 0.72/1.06
% 0.72/1.06 % Reading from file /tmp/Prover9_18077_n021.cluster.edu
% 0.72/1.06
% 0.72/1.06 set(prolog_style_variables).
% 0.72/1.06 set(auto2).
% 0.72/1.06 % set(auto2) -> set(auto).
% 0.72/1.06 % set(auto) -> set(auto_inference).
% 0.72/1.06 % set(auto) -> set(auto_setup).
% 0.72/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.72/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.72/1.06 % set(auto) -> set(auto_limits).
% 0.72/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.72/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.72/1.06 % set(auto) -> set(auto_denials).
% 0.72/1.06 % set(auto) -> set(auto_process).
% 0.72/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.72/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.72/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.72/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.72/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.72/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.72/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.72/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.72/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.72/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.72/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.72/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.72/1.06 % set(auto2) -> assign(stats, some).
% 0.72/1.06 % set(auto2) -> clear(echo_input).
% 0.72/1.06 % set(auto2) -> set(quiet).
% 0.72/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.72/1.06 % set(auto2) -> clear(print_given).
% 0.72/1.06 assign(lrs_ticks,-1).
% 0.72/1.06 assign(sos_limit,10000).
% 0.72/1.06 assign(order,kbo).
% 0.72/1.06 set(lex_order_vars).
% 0.72/1.06 clear(print_given).
% 0.72/1.06
% 0.72/1.06 % formulas(sos). % not echoed (20 formulas)
% 0.72/1.06
% 0.72/1.06 ============================== end of input ==========================
% 0.72/1.06
% 0.72/1.06 % From the command line: assign(max_seconds, 300).
% 0.72/1.06
% 0.72/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.72/1.06
% 0.72/1.06 % Formulas that are not ordinary clauses:
% 0.72/1.06
% 0.72/1.06 ============================== end of process non-clausal formulas ===
% 0.72/1.06
% 0.72/1.06 ============================== PROCESS INITIAL CLAUSES ===============
% 0.72/1.06
% 0.72/1.06 ============================== PREDICATE ELIMINATION =================
% 0.72/1.06 1 -defined(A,B) | -identity_map(A) | product(A,B,B) # label(identity1) # label(axiom). [assumption].
% 0.72/1.06 2 identity_map(domain(A)) # label(domain_is_an_identity_map) # label(axiom). [assumption].
% 0.72/1.06 3 identity_map(codomain(A)) # label(codomain_is_an_identity_map) # label(axiom). [assumption].
% 0.72/1.06 Derived: -defined(domain(A),B) | product(domain(A),B,B). [resolve(1,b,2,a)].
% 0.72/1.06 Derived: -defined(codomain(A),B) | product(codomain(A),B,B). [resolve(1,b,3,a)].
% 0.72/1.06 4 -defined(A,B) | -identity_map(B) | product(A,B,A) # label(identity2) # label(axiom). [assumption].
% 0.72/1.06 Derived: -defined(A,domain(B)) | product(A,domain(B),A). [resolve(4,b,2,a)].
% 0.72/1.06 Derived: -defined(A,codomain(B)) | product(A,codomain(B),A). [resolve(4,b,3,a)].
% 0.72/1.06 5 -defined(A,B) | -defined(B,C) | -identity_map(B) | defined(A,C) # label(category_theory_axiom6) # label(axiom). [assumption].
% 0.72/1.06 Derived: -defined(A,domain(B)) | -defined(domain(B),C) | defined(A,C). [resolve(5,c,2,a)].
% 0.72/1.06 Derived: -defined(A,codomain(B)) | -defined(codomain(B),C) | defined(A,C). [resolve(5,c,3,a)].
% 0.72/1.06
% 0.72/1.06 ============================== end predicate elimination =============
% 0.72/1.06
% 0.72/1.06 Auto_denials:
% 0.72/1.06 % copying label prove_domain_of_ba_equals_domain_of_a to answer in negative clause
% 0.72/1.06
% 0.72/1.06 Term ordering decisions:
% 0.72/1.06 Function symbol KB weights: a=1. b=1. compose=1. codomain=1. domain=1.
% 0.72/1.06
% 0.72/1.06 ============================== end of process initial clauses ========
% 0.72/1.06
% 0.72/1.06 ============================== CLAUSES FOR SEARCH ====================
% 0.72/1.06
% 0.72/1.06 ============================== end of clauses for search =============
% 0.72/1.06
% 0.72/1.06 ============================== SEARCH ================================
% 0.72/1.06
% 0.72/1.06 % Starting search at 0.01 seconds.
% 0.72/1.06
% 0.72/1.06 ============================== PROOF =================================
% 0.72/1.06 % SZS status Unsatisfiable
% 0.72/1.06 % SZS output start Refutation
% 0.72/1.06
% 0.72/1.06 % Proof 1 at 0.08 (+ 0.00) seconds: prove_domain_of_ba_equals_domain_of_a.
% 0.72/1.06 % Length of proof is 30.
% 0.72/1.06 % Level of proof is 6.
% 0.72/1.06 % Maximum clause weight is 16.000.
% 0.72/1.06 % Given clauses 104.
% 0.72/1.06
% 0.72/1.06 1 -defined(A,B) | -identity_map(A) | product(A,B,B) # label(identity1) # label(axiom). [assumption].
% 0.72/1.06 2 identity_map(domain(A)) # label(domain_is_an_identity_map) # label(axiom). [assumption].
% 0.72/1.06 4 -defined(A,B) | -identity_map(B) | product(A,B,A) # label(identity2) # label(axiom). [assumption].
% 0.72/1.06 6 defined(b,a) # label(ba_defined) # label(hypothesis). [assumption].
% 0.72/1.06 7 defined(A,domain(A)) # label(mapping_from_x_to_its_domain) # label(axiom). [assumption].
% 0.72/1.06 9 product(A,domain(A),A) # label(product_on_domain) # label(axiom). [assumption].
% 0.72/1.06 11 domain(compose(b,a)) != domain(a) # label(prove_domain_of_ba_equals_domain_of_a) # label(negated_conjecture) # answer(prove_domain_of_ba_equals_domain_of_a). [assumption].
% 0.72/1.06 13 -defined(A,B) | product(A,B,compose(A,B)) # label(closure_of_composition) # label(axiom). [assumption].
% 0.72/1.06 14 -product(A,B,C) | -defined(C,D) | defined(B,D) # label(associative_property2) # label(axiom). [assumption].
% 0.72/1.06 16 -product(A,B,C) | -product(A,B,D) | C = D # label(composition_is_well_defined) # label(axiom). [assumption].
% 0.72/1.06 18 -product(A,B,C) | -product(D,A,E) | -defined(D,C) | defined(E,B) # label(category_theory_axiom4) # label(axiom). [assumption].
% 0.72/1.06 19 -product(A,B,C) | -product(C,D,E) | -product(B,D,F) | product(A,F,E) # label(category_theory_axiom2) # label(axiom). [assumption].
% 0.72/1.06 20 -product(A,B,C) | -product(D,C,E) | -product(D,A,F) | product(F,B,E) # label(category_theory_axiom5) # label(axiom). [assumption].
% 0.72/1.06 21 -defined(domain(A),B) | product(domain(A),B,B). [resolve(1,b,2,a)].
% 0.72/1.06 23 -defined(A,domain(B)) | product(A,domain(B),A). [resolve(4,b,2,a)].
% 0.72/1.06 29 product(b,a,compose(b,a)). [hyper(13,a,6,a)].
% 0.72/1.06 31 defined(domain(A),domain(A)). [hyper(14,a,9,a,b,7,a)].
% 0.72/1.06 38 -product(domain(a),domain(domain(a)),domain(compose(b,a))) # answer(prove_domain_of_ba_equals_domain_of_a). [ur(16,b,9,a,c,11,a)].
% 0.72/1.06 43 product(A,domain(domain(A)),A). [hyper(20,a,9,a,b,9,a,c,9,a)].
% 0.72/1.06 44 product(domain(A),domain(domain(A)),domain(domain(A))). [hyper(21,a,7,a)].
% 0.72/1.06 82 product(domain(A),domain(A),domain(A)). [hyper(23,a,31,a)].
% 0.72/1.06 141 defined(compose(b,a),domain(a)). [hyper(18,a,9,a,b,29,a,c,6,a)].
% 0.72/1.06 230 -product(domain(a),domain(domain(domain(domain(a)))),domain(compose(b,a))) # answer(prove_domain_of_ba_equals_domain_of_a). [ur(19,a,9,a,c,43,a,d,38,a)].
% 0.72/1.06 298 domain(domain(A)) = domain(A). [hyper(16,a,9,a,b,44,a),flip(a)].
% 0.72/1.06 299 -product(domain(a),domain(a),domain(compose(b,a))) # answer(prove_domain_of_ba_equals_domain_of_a). [ur(20,a,44,a,c,43,a,d,230,a),rewrite([298(5),298(5),298(5)])].
% 0.72/1.06 377 defined(domain(compose(b,a)),domain(a)). [hyper(14,a,9,a,b,141,a)].
% 0.72/1.06 425 product(domain(compose(b,a)),domain(a),domain(compose(b,a))). [hyper(23,a,377,a)].
% 0.72/1.06 426 product(domain(compose(b,a)),domain(a),domain(a)). [hyper(21,a,377,a)].
% 0.72/1.06 437 -product(domain(compose(b,a)),domain(a),domain(compose(b,a))) # answer(prove_domain_of_ba_equals_domain_of_a). [ur(20,a,82,a,c,426,a,d,299,a)].
% 0.72/1.06 438 $F # answer(prove_domain_of_ba_equals_domain_of_a). [resolve(437,a,425,a)].
% 0.72/1.06
% 0.72/1.06 % SZS output end Refutation
% 0.72/1.06 ============================== end of proof ==========================
% 0.72/1.06
% 0.72/1.06 ============================== STATISTICS ============================
% 0.72/1.06
% 0.72/1.06 Given=104. Generated=2187. Kept=432. proofs=1.
% 0.72/1.06 Usable=53. Sos=15. Demods=10. Limbo=0, Disabled=389. Hints=0.
% 0.72/1.06 Megabytes=0.25.
% 0.72/1.06 User_CPU=0.08, System_CPU=0.00, Wall_clock=1.
% 0.72/1.06
% 0.72/1.06 ============================== end of statistics =====================
% 0.72/1.06
% 0.72/1.06 ============================== end of search =========================
% 0.72/1.06
% 0.72/1.06 THEOREM PROVED
% 0.72/1.06 % SZS status Unsatisfiable
% 0.72/1.06
% 0.72/1.06 Exiting with 1 proof.
% 0.72/1.06
% 0.72/1.06 Process 18232 exit (max_proofs) Sun May 29 19:22:29 2022
% 0.72/1.06 Prover9 interrupted
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