TSTP Solution File: CAT003-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : CAT003-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 00:06:13 EDT 2022
% Result : Unsatisfiable 0.41s 0.97s
% Output : Refutation 0.41s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : CAT003-2 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.33 % Computer : n028.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun May 29 17:25:33 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.41/0.97 ============================== Prover9 ===============================
% 0.41/0.97 Prover9 (32) version 2009-11A, November 2009.
% 0.41/0.97 Process 1247 was started by sandbox2 on n028.cluster.edu,
% 0.41/0.97 Sun May 29 17:25:34 2022
% 0.41/0.97 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_1088_n028.cluster.edu".
% 0.41/0.97 ============================== end of head ===========================
% 0.41/0.97
% 0.41/0.97 ============================== INPUT =================================
% 0.41/0.97
% 0.41/0.97 % Reading from file /tmp/Prover9_1088_n028.cluster.edu
% 0.41/0.97
% 0.41/0.97 set(prolog_style_variables).
% 0.41/0.97 set(auto2).
% 0.41/0.97 % set(auto2) -> set(auto).
% 0.41/0.97 % set(auto) -> set(auto_inference).
% 0.41/0.97 % set(auto) -> set(auto_setup).
% 0.41/0.97 % set(auto_setup) -> set(predicate_elim).
% 0.41/0.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/0.97 % set(auto) -> set(auto_limits).
% 0.41/0.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/0.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/0.97 % set(auto) -> set(auto_denials).
% 0.41/0.97 % set(auto) -> set(auto_process).
% 0.41/0.97 % set(auto2) -> assign(new_constants, 1).
% 0.41/0.97 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/0.97 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/0.97 % set(auto2) -> assign(max_hours, 1).
% 0.41/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/0.97 % set(auto2) -> assign(max_seconds, 0).
% 0.41/0.97 % set(auto2) -> assign(max_minutes, 5).
% 0.41/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/0.97 % set(auto2) -> set(sort_initial_sos).
% 0.41/0.97 % set(auto2) -> assign(sos_limit, -1).
% 0.41/0.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/0.97 % set(auto2) -> assign(max_megs, 400).
% 0.41/0.97 % set(auto2) -> assign(stats, some).
% 0.41/0.97 % set(auto2) -> clear(echo_input).
% 0.41/0.97 % set(auto2) -> set(quiet).
% 0.41/0.97 % set(auto2) -> clear(print_initial_clauses).
% 0.41/0.97 % set(auto2) -> clear(print_given).
% 0.41/0.97 assign(lrs_ticks,-1).
% 0.41/0.97 assign(sos_limit,10000).
% 0.41/0.97 assign(order,kbo).
% 0.41/0.97 set(lex_order_vars).
% 0.41/0.97 clear(print_given).
% 0.41/0.97
% 0.41/0.97 % formulas(sos). % not echoed (13 formulas)
% 0.41/0.97
% 0.41/0.97 ============================== end of input ==========================
% 0.41/0.97
% 0.41/0.97 % From the command line: assign(max_seconds, 300).
% 0.41/0.97
% 0.41/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/0.97
% 0.41/0.97 % Formulas that are not ordinary clauses:
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% 0.41/0.97 ============================== end of process non-clausal formulas ===
% 0.41/0.97
% 0.41/0.97 ============================== PROCESS INITIAL CLAUSES ===============
% 0.41/0.97
% 0.41/0.97 ============================== PREDICATE ELIMINATION =================
% 0.41/0.97
% 0.41/0.97 ============================== end predicate elimination =============
% 0.41/0.97
% 0.41/0.97 Auto_denials:
% 0.41/0.97 % copying label prove_g_equals_h to answer in negative clause
% 0.41/0.97
% 0.41/0.97 Term ordering decisions:
% 0.41/0.97 Function symbol KB weights: b=1. a=1. g=1. h=1. compose=1. codomain=1. domain=1.
% 0.41/0.97
% 0.41/0.97 ============================== end of process initial clauses ========
% 0.41/0.97
% 0.41/0.97 ============================== CLAUSES FOR SEARCH ====================
% 0.41/0.97
% 0.41/0.97 ============================== end of clauses for search =============
% 0.41/0.97
% 0.41/0.97 ============================== SEARCH ================================
% 0.41/0.97
% 0.41/0.97 % Starting search at 0.01 seconds.
% 0.41/0.97
% 0.41/0.97 ============================== PROOF =================================
% 0.41/0.97 % SZS status Unsatisfiable
% 0.41/0.97 % SZS output start Refutation
% 0.41/0.97
% 0.41/0.97 % Proof 1 at 0.02 (+ 0.00) seconds: prove_g_equals_h.
% 0.41/0.97 % Length of proof is 19.
% 0.41/0.97 % Level of proof is 5.
% 0.41/0.97 % Maximum clause weight is 31.000.
% 0.41/0.97 % Given clauses 53.
% 0.41/0.97
% 0.41/0.97 1 codomain(a) = domain(b) # label(codomain_of_a_equals_domain_of_b) # label(hypothesis). [assumption].
% 0.41/0.97 2 domain(b) = codomain(a). [copy(1),flip(a)].
% 0.41/0.97 3 codomain(b) = domain(h) # label(codomain_of_b_equals_domain_of_h) # label(hypothesis). [assumption].
% 0.41/0.97 4 domain(h) = codomain(b). [copy(3),flip(a)].
% 0.41/0.97 5 codomain(b) = domain(g) # label(codomain_of_b_equals_domain_of_g) # label(hypothesis). [assumption].
% 0.41/0.97 6 domain(g) = codomain(b). [copy(5),flip(a)].
% 0.41/0.97 11 compose(b,h) = compose(b,g) # label(bh_equals_bg) # label(hypothesis). [assumption].
% 0.41/0.97 12 g != h # label(prove_g_equals_h) # label(negated_conjecture) # answer(prove_g_equals_h). [assumption].
% 0.41/0.97 13 h != g # answer(prove_g_equals_h). [copy(12),flip(a)].
% 0.41/0.97 15 codomain(A) != domain(B) | codomain(compose(A,B)) = codomain(B) # label(codomain_domain2) # label(axiom). [assumption].
% 0.41/0.97 16 codomain(A) != domain(B) | codomain(B) != domain(C) | compose(A,compose(B,C)) = compose(compose(A,B),C) # label(star_property) # label(axiom). [assumption].
% 0.41/0.97 17 codomain(A) != domain(B) | codomain(B) != domain(C) | compose(compose(A,B),C) = compose(A,compose(B,C)). [copy(16),flip(c)].
% 0.41/0.97 18 codomain(compose(a,b)) != domain(A) | compose(compose(a,b),A) != B | codomain(compose(a,b)) != domain(C) | compose(compose(a,b),C) != B | A = C # label(endomorphism) # label(hypothesis). [assumption].
% 0.41/0.97 37 codomain(compose(a,b)) = codomain(b). [hyper(15,a,2,a(flip))].
% 0.41/0.97 43 codomain(b) != domain(A) | compose(compose(a,b),A) != B | codomain(b) != domain(C) | compose(compose(a,b),C) != B | A = C. [back_rewrite(18),rewrite([37(4),37(13)])].
% 0.41/0.97 49 compose(compose(a,b),g) = compose(a,compose(b,g)). [hyper(17,a,2,a(flip),b,6,a(flip))].
% 0.41/0.97 50 compose(compose(a,b),h) = compose(a,compose(b,g)). [hyper(17,a,2,a(flip),b,4,a(flip)),rewrite([11(9)])].
% 0.41/0.97 164 h = g. [hyper(43,a,6,a(flip),b,49,a,c,4,a(flip),d,50,a),flip(a)].
% 0.41/0.97 165 $F # answer(prove_g_equals_h). [resolve(164,a,13,a)].
% 0.41/0.97
% 0.41/0.97 % SZS output end Refutation
% 0.41/0.97 ============================== end of proof ==========================
% 0.41/0.97
% 0.41/0.97 ============================== STATISTICS ============================
% 0.41/0.97
% 0.41/0.97 Given=53. Generated=429. Kept=159. proofs=1.
% 0.41/0.97 Usable=53. Sos=101. Demods=31. Limbo=0, Disabled=17. Hints=0.
% 0.41/0.97 Megabytes=0.19.
% 0.41/0.97 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.41/0.97
% 0.41/0.97 ============================== end of statistics =====================
% 0.41/0.97
% 0.41/0.97 ============================== end of search =========================
% 0.41/0.97
% 0.41/0.97 THEOREM PROVED
% 0.41/0.97 % SZS status Unsatisfiable
% 0.41/0.97
% 0.41/0.97 Exiting with 1 proof.
% 0.41/0.97
% 0.41/0.97 Process 1247 exit (max_proofs) Sun May 29 17:25:34 2022
% 0.41/0.97 Prover9 interrupted
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