TSTP Solution File: CAT008-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : CAT008-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 00:06:14 EDT 2022
% Result : Unsatisfiable 0.73s 1.04s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT008-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n029.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 20:30:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.73/1.04 ============================== Prover9 ===============================
% 0.73/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.73/1.04 Process 25937 was started by sandbox2 on n029.cluster.edu,
% 0.73/1.04 Sun May 29 20:30:59 2022
% 0.73/1.04 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_25675_n029.cluster.edu".
% 0.73/1.04 ============================== end of head ===========================
% 0.73/1.04
% 0.73/1.04 ============================== INPUT =================================
% 0.73/1.04
% 0.73/1.04 % Reading from file /tmp/Prover9_25675_n029.cluster.edu
% 0.73/1.04
% 0.73/1.04 set(prolog_style_variables).
% 0.73/1.04 set(auto2).
% 0.73/1.04 % set(auto2) -> set(auto).
% 0.73/1.04 % set(auto) -> set(auto_inference).
% 0.73/1.04 % set(auto) -> set(auto_setup).
% 0.73/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.73/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.73/1.04 % set(auto) -> set(auto_limits).
% 0.73/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.73/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.73/1.04 % set(auto) -> set(auto_denials).
% 0.73/1.04 % set(auto) -> set(auto_process).
% 0.73/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.73/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.73/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.73/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.73/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.73/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.73/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.73/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.73/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.73/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.73/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.73/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.73/1.04 % set(auto2) -> assign(stats, some).
% 0.73/1.04 % set(auto2) -> clear(echo_input).
% 0.73/1.04 % set(auto2) -> set(quiet).
% 0.73/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.73/1.04 % set(auto2) -> clear(print_given).
% 0.73/1.04 assign(lrs_ticks,-1).
% 0.73/1.04 assign(sos_limit,10000).
% 0.73/1.04 assign(order,kbo).
% 0.73/1.04 set(lex_order_vars).
% 0.73/1.04 clear(print_given).
% 0.73/1.04
% 0.73/1.04 % formulas(sos). % not echoed (20 formulas)
% 0.73/1.04
% 0.73/1.04 ============================== end of input ==========================
% 0.73/1.04
% 0.73/1.04 % From the command line: assign(max_seconds, 300).
% 0.73/1.04
% 0.73/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.73/1.04
% 0.73/1.04 % Formulas that are not ordinary clauses:
% 0.73/1.04
% 0.73/1.04 ============================== end of process non-clausal formulas ===
% 0.73/1.04
% 0.73/1.04 ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.04
% 0.73/1.04 ============================== PREDICATE ELIMINATION =================
% 0.73/1.04 1 -defined(A,B) | -identity_map(A) | product(A,B,B) # label(identity1) # label(axiom). [assumption].
% 0.73/1.04 2 identity_map(domain(A)) # label(domain_is_an_identity_map) # label(axiom). [assumption].
% 0.73/1.04 3 identity_map(codomain(A)) # label(codomain_is_an_identity_map) # label(axiom). [assumption].
% 0.73/1.04 Derived: -defined(domain(A),B) | product(domain(A),B,B). [resolve(1,b,2,a)].
% 0.73/1.04 Derived: -defined(codomain(A),B) | product(codomain(A),B,B). [resolve(1,b,3,a)].
% 0.73/1.04 4 -defined(A,B) | -identity_map(B) | product(A,B,A) # label(identity2) # label(axiom). [assumption].
% 0.73/1.04 Derived: -defined(A,domain(B)) | product(A,domain(B),A). [resolve(4,b,2,a)].
% 0.73/1.04 Derived: -defined(A,codomain(B)) | product(A,codomain(B),A). [resolve(4,b,3,a)].
% 0.73/1.04 5 -defined(A,B) | -defined(B,C) | -identity_map(B) | defined(A,C) # label(category_theory_axiom6) # label(axiom). [assumption].
% 0.73/1.04 Derived: -defined(A,domain(B)) | -defined(domain(B),C) | defined(A,C). [resolve(5,c,2,a)].
% 0.73/1.04 Derived: -defined(A,codomain(B)) | -defined(codomain(B),C) | defined(A,C). [resolve(5,c,3,a)].
% 0.73/1.04
% 0.73/1.04 ============================== end predicate elimination =============
% 0.73/1.04
% 0.73/1.04 Auto_denials:
% 0.73/1.04 % copying label prove_domain_of_a_equals_codomain_of_b to answer in negative clause
% 0.73/1.04
% 0.73/1.04 Term ordering decisions:
% 0.73/1.04 Function symbol KB weights: a=1. b=1. compose=1. codomain=1. domain=1.
% 0.73/1.04
% 0.73/1.04 ============================== end of process initial clauses ========
% 0.73/1.04
% 0.73/1.04 ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.04
% 0.73/1.04 ============================== end of clauses for search =============
% 0.73/1.04
% 0.73/1.04 ============================== SEARCH ================================
% 0.73/1.04
% 0.73/1.04 % Starting search at 0.01 seconds.
% 0.73/1.04
% 0.73/1.04 ============================== PROOF =================================
% 0.73/1.04 % SZS status Unsatisfiable
% 0.73/1.04 % SZS output start Refutation
% 0.73/1.04
% 0.73/1.04 % Proof 1 at 0.06 (+ 0.00) seconds: prove_domain_of_a_equals_codomain_of_b.
% 0.73/1.04 % Length of proof is 27.
% 0.73/1.04 % Level of proof is 6.
% 0.73/1.04 % Maximum clause weight is 16.000.
% 0.73/1.04 % Given clauses 102.
% 0.73/1.04
% 0.73/1.04 1 -defined(A,B) | -identity_map(A) | product(A,B,B) # label(identity1) # label(axiom). [assumption].
% 0.73/1.04 2 identity_map(domain(A)) # label(domain_is_an_identity_map) # label(axiom). [assumption].
% 0.73/1.04 3 identity_map(codomain(A)) # label(codomain_is_an_identity_map) # label(axiom). [assumption].
% 0.73/1.04 4 -defined(A,B) | -identity_map(B) | product(A,B,A) # label(identity2) # label(axiom). [assumption].
% 0.73/1.04 6 defined(a,b) # label(ab_defined) # label(hypothesis). [assumption].
% 0.73/1.04 9 product(A,domain(A),A) # label(product_on_domain) # label(axiom). [assumption].
% 0.73/1.04 10 product(codomain(A),A,A) # label(product_on_codomain) # label(axiom). [assumption].
% 0.73/1.04 11 domain(a) != codomain(b) # label(prove_domain_of_a_equals_codomain_of_b) # label(negated_conjecture) # answer(prove_domain_of_a_equals_codomain_of_b). [assumption].
% 0.73/1.04 14 -product(A,B,C) | -defined(C,D) | defined(B,D) # label(associative_property2) # label(axiom). [assumption].
% 0.73/1.04 15 -product(A,B,C) | -defined(D,C) | defined(D,A) # label(category_theory_axiom3) # label(axiom). [assumption].
% 0.73/1.04 16 -product(A,B,C) | -product(A,B,D) | C = D # label(composition_is_well_defined) # label(axiom). [assumption].
% 0.73/1.04 19 -product(A,B,C) | -product(C,D,E) | -product(B,D,F) | product(A,F,E) # label(category_theory_axiom2) # label(axiom). [assumption].
% 0.73/1.04 20 -product(A,B,C) | -product(D,C,E) | -product(D,A,F) | product(F,B,E) # label(category_theory_axiom5) # label(axiom). [assumption].
% 0.73/1.04 21 -defined(domain(A),B) | product(domain(A),B,B). [resolve(1,b,2,a)].
% 0.73/1.04 24 -defined(A,codomain(B)) | product(A,codomain(B),A). [resolve(4,b,3,a)].
% 0.73/1.04 27 domain(a) = c_0. [new_symbol(11)].
% 0.73/1.04 28 codomain(b) != c_0 # answer(prove_domain_of_a_equals_codomain_of_b). [back_rewrite(11),rewrite([27(2)]),flip(a)].
% 0.73/1.04 34 defined(c_0,b). [hyper(14,a,9,a,b,6,a),rewrite([27(2)])].
% 0.73/1.04 41 product(A,domain(domain(A)),A). [hyper(20,a,9,a,b,9,a,c,9,a)].
% 0.73/1.04 50 -defined(c_0,A) | product(c_0,A,A). [para(27(a,1),21(a,1)),rewrite([27(4)])].
% 0.73/1.04 56 -product(codomain(b),domain(codomain(b)),c_0) # answer(prove_domain_of_a_equals_codomain_of_b). [ur(16,a,9,a,c,28,a)].
% 0.73/1.04 69 -product(codomain(b),domain(domain(codomain(b))),c_0) # answer(prove_domain_of_a_equals_codomain_of_b). [ur(19,a,9,a,c,9,a,d,56,a)].
% 0.73/1.04 70 defined(c_0,codomain(b)). [hyper(15,a,10,a,b,34,a)].
% 0.73/1.04 95 product(c_0,codomain(b),c_0). [hyper(24,a,70,a)].
% 0.73/1.04 269 -product(c_0,codomain(b),codomain(b)) # answer(prove_domain_of_a_equals_codomain_of_b). [ur(20,a,41,a,b,95,a,d,69,a)].
% 0.73/1.04 423 product(c_0,codomain(b),codomain(b)). [hyper(50,a,70,a)].
% 0.73/1.04 424 $F # answer(prove_domain_of_a_equals_codomain_of_b). [resolve(423,a,269,a)].
% 0.73/1.04
% 0.73/1.04 % SZS output end Refutation
% 0.73/1.04 ============================== end of proof ==========================
% 0.73/1.04
% 0.73/1.04 ============================== STATISTICS ============================
% 0.73/1.04
% 0.73/1.04 Given=102. Generated=1768. Kept=418. proofs=1.
% 0.73/1.04 Usable=59. Sos=52. Demods=7. Limbo=2, Disabled=330. Hints=0.
% 0.73/1.04 Megabytes=0.23.
% 0.73/1.04 User_CPU=0.07, System_CPU=0.00, Wall_clock=0.
% 0.73/1.04
% 0.73/1.04 ============================== end of statistics =====================
% 0.73/1.04
% 0.73/1.04 ============================== end of search =========================
% 0.73/1.04
% 0.73/1.04 THEOREM PROVED
% 0.73/1.04 % SZS status Unsatisfiable
% 0.73/1.04
% 0.73/1.04 Exiting with 1 proof.
% 0.73/1.04
% 0.73/1.04 Process 25937 exit (max_proofs) Sun May 29 20:30:59 2022
% 0.73/1.04 Prover9 interrupted
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