TSTP Solution File: LCL026-10 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL026-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 : Sun Jul 17 13:43:29 EDT 2022
% Result : Unsatisfiable 4.91s 5.22s
% Output : Refutation 4.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL026-10 : TPTP v8.1.0. Released v7.3.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 4 13:46:38 EDT 2022
% 0.14/0.35 % CPUTime :
% 4.91/5.22 ============================== Prover9 ===============================
% 4.91/5.22 Prover9 (32) version 2009-11A, November 2009.
% 4.91/5.22 Process 7160 was started by sandbox2 on n004.cluster.edu,
% 4.91/5.22 Mon Jul 4 13:46:38 2022
% 4.91/5.22 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_7007_n004.cluster.edu".
% 4.91/5.22 ============================== end of head ===========================
% 4.91/5.22
% 4.91/5.22 ============================== INPUT =================================
% 4.91/5.22
% 4.91/5.22 % Reading from file /tmp/Prover9_7007_n004.cluster.edu
% 4.91/5.22
% 4.91/5.22 set(prolog_style_variables).
% 4.91/5.22 set(auto2).
% 4.91/5.22 % set(auto2) -> set(auto).
% 4.91/5.22 % set(auto) -> set(auto_inference).
% 4.91/5.22 % set(auto) -> set(auto_setup).
% 4.91/5.22 % set(auto_setup) -> set(predicate_elim).
% 4.91/5.22 % set(auto_setup) -> assign(eq_defs, unfold).
% 4.91/5.22 % set(auto) -> set(auto_limits).
% 4.91/5.22 % set(auto_limits) -> assign(max_weight, "100.000").
% 4.91/5.22 % set(auto_limits) -> assign(sos_limit, 20000).
% 4.91/5.22 % set(auto) -> set(auto_denials).
% 4.91/5.22 % set(auto) -> set(auto_process).
% 4.91/5.22 % set(auto2) -> assign(new_constants, 1).
% 4.91/5.22 % set(auto2) -> assign(fold_denial_max, 3).
% 4.91/5.22 % set(auto2) -> assign(max_weight, "200.000").
% 4.91/5.22 % set(auto2) -> assign(max_hours, 1).
% 4.91/5.22 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.91/5.22 % set(auto2) -> assign(max_seconds, 0).
% 4.91/5.22 % set(auto2) -> assign(max_minutes, 5).
% 4.91/5.22 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.91/5.22 % set(auto2) -> set(sort_initial_sos).
% 4.91/5.22 % set(auto2) -> assign(sos_limit, -1).
% 4.91/5.22 % set(auto2) -> assign(lrs_ticks, 3000).
% 4.91/5.22 % set(auto2) -> assign(max_megs, 400).
% 4.91/5.22 % set(auto2) -> assign(stats, some).
% 4.91/5.22 % set(auto2) -> clear(echo_input).
% 4.91/5.22 % set(auto2) -> set(quiet).
% 4.91/5.22 % set(auto2) -> clear(print_initial_clauses).
% 4.91/5.22 % set(auto2) -> clear(print_given).
% 4.91/5.22 assign(lrs_ticks,-1).
% 4.91/5.22 assign(sos_limit,10000).
% 4.91/5.22 assign(order,kbo).
% 4.91/5.22 set(lex_order_vars).
% 4.91/5.22 clear(print_given).
% 4.91/5.22
% 4.91/5.22 % formulas(sos). % not echoed (6 formulas)
% 4.91/5.22
% 4.91/5.22 ============================== end of input ==========================
% 4.91/5.22
% 4.91/5.22 % From the command line: assign(max_seconds, 300).
% 4.91/5.22
% 4.91/5.22 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.91/5.22
% 4.91/5.22 % Formulas that are not ordinary clauses:
% 4.91/5.22
% 4.91/5.22 ============================== end of process non-clausal formulas ===
% 4.91/5.22
% 4.91/5.22 ============================== PROCESS INITIAL CLAUSES ===============
% 4.91/5.22
% 4.91/5.22 ============================== PREDICATE ELIMINATION =================
% 4.91/5.22
% 4.91/5.22 ============================== end predicate elimination =============
% 4.91/5.22
% 4.91/5.22 Auto_denials:
% 4.91/5.22 % copying label prove_c0_3 to answer in negative clause
% 4.91/5.22
% 4.91/5.22 Term ordering decisions:
% 4.91/5.22
% 4.91/5.22 % Assigning unary symbol is_a_theorem kb_weight 0 and highest precedence (8).
% 4.91/5.22 Function symbol KB weights: true=1. falsehood=1. a=1. b=1. implies=1. ifeq=1. is_a_theorem=0.
% 4.91/5.22
% 4.91/5.22 ============================== end of process initial clauses ========
% 4.91/5.22
% 4.91/5.22 ============================== CLAUSES FOR SEARCH ====================
% 4.91/5.22
% 4.91/5.22 ============================== end of clauses for search =============
% 4.91/5.22
% 4.91/5.22 ============================== SEARCH ================================
% 4.91/5.22
% 4.91/5.22 % Starting search at 0.01 seconds.
% 4.91/5.22
% 4.91/5.22 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 78 (0.00 of 1.17 sec).
% 4.91/5.22
% 4.91/5.22 Low Water (keep): wt=44.000, iters=3333
% 4.91/5.22
% 4.91/5.22 Low Water (keep): wt=30.000, iters=3348
% 4.91/5.22
% 4.91/5.22 Low Water (keep): wt=26.000, iters=3386
% 4.91/5.22
% 4.91/5.22 Low Water (keep): wt=24.000, iters=3361
% 4.91/5.22
% 4.91/5.22 Low Water (keep): wt=22.000, iters=3401
% 4.91/5.22
% 4.91/5.22 Low Water (keep): wt=21.000, iters=3346
% 4.91/5.22
% 4.91/5.22 Low Water (keep): wt=20.000, iters=3334
% 4.91/5.22
% 4.91/5.22 ============================== PROOF =================================
% 4.91/5.22 % SZS status Unsatisfiable
% 4.91/5.22 % SZS output start Refutation
% 4.91/5.22
% 4.91/5.22 % Proof 1 at 3.77 (+ 0.33) seconds: prove_c0_3.
% 4.91/5.22 % Length of proof is 40.
% 4.91/5.22 % Level of proof is 15.
% 4.91/5.22 % Maximum clause weight is 22.000.
% 4.91/5.22 % Given clauses 1188.
% 4.91/5.22
% 4.91/5.22 1 ifeq(A,A,B,C) = B # label(ifeq_axiom) # label(axiom). [assumption].
% 4.91/5.22 2 is_a_theorem(implies(A,implies(B,A))) = true # label(c0_2) # label(axiom). [assumption].
% 4.91/5.22 3 is_a_theorem(implies(implies(implies(A,falsehood),falsehood),A)) = true # label(c0_5) # label(axiom). [assumption].
% 4.91/5.22 4 ifeq(is_a_theorem(implies(A,B)),true,ifeq(is_a_theorem(A),true,is_a_theorem(B),true),true) = true # label(condensed_detachment) # label(axiom). [assumption].
% 4.91/5.22 5 is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C)))) = true # label(c0_6) # label(axiom). [assumption].
% 4.91/5.22 6 is_a_theorem(implies(implies(implies(a,b),a),a)) != true # label(prove_c0_3) # label(negated_conjecture) # answer(prove_c0_3). [assumption].
% 4.91/5.22 7 ifeq(is_a_theorem(A),true,is_a_theorem(implies(B,A)),true) = true. [para(2(a,1),4(a,1,1)),rewrite([1(10)])].
% 4.91/5.22 8 ifeq(is_a_theorem(implies(implies(A,implies(B,A)),C)),true,is_a_theorem(C),true) = true. [para(2(a,1),4(a,1,3,1)),rewrite([1(10)])].
% 4.91/5.22 13 ifeq(is_a_theorem(implies(A,implies(B,C))),true,is_a_theorem(implies(implies(A,B),implies(A,C))),true) = true. [para(5(a,1),4(a,1,1)),rewrite([1(14)])].
% 4.91/5.22 16 is_a_theorem(implies(A,implies(B,implies(C,B)))) = true. [para(2(a,1),7(a,1,1)),rewrite([1(8)])].
% 4.91/5.22 18 is_a_theorem(implies(A,implies(implies(implies(B,falsehood),falsehood),B))) = true. [para(3(a,1),7(a,1,1)),rewrite([1(11)])].
% 4.91/5.22 21 ifeq(is_a_theorem(implies(implies(A,implies(B,implies(C,B))),D)),true,is_a_theorem(D),true) = true. [para(16(a,1),4(a,1,3,1)),rewrite([1(11)])].
% 4.91/5.22 27 is_a_theorem(implies(implies(A,B),implies(A,A))) = true. [para(5(a,1),8(a,1,1)),rewrite([1(8)])].
% 4.91/5.22 31 is_a_theorem(implies(A,A)) = true. [para(27(a,1),8(a,1,1)),rewrite([1(6)])].
% 4.91/5.22 33 ifeq(is_a_theorem(implies(implies(A,A),B)),true,is_a_theorem(B),true) = true. [para(31(a,1),4(a,1,3,1)),rewrite([1(9)])].
% 4.91/5.22 41 is_a_theorem(implies(implies(implies(A,B),A),implies(implies(A,B),B))) = true. [para(5(a,1),33(a,1,1)),rewrite([1(10)])].
% 4.91/5.22 50 ifeq(is_a_theorem(implies(implies(implies(implies(A,B),A),implies(implies(A,B),B)),C)),true,is_a_theorem(C),true) = true. [para(41(a,1),4(a,1,3,1)),rewrite([1(13)])].
% 4.91/5.22 51 is_a_theorem(implies(A,implies(implies(implies(B,C),B),implies(implies(B,C),C)))) = true. [para(41(a,1),7(a,1,1)),rewrite([1(11)])].
% 4.91/5.22 53 is_a_theorem(implies(implies(implies(A,implies(B,C)),implies(A,B)),implies(implies(A,implies(B,C)),implies(A,C)))) = true. [para(5(a,1),13(a,1,1)),rewrite([1(14)])].
% 4.91/5.22 55 is_a_theorem(implies(implies(A,implies(implies(B,falsehood),falsehood)),implies(A,B))) = true. [para(18(a,1),13(a,1,1)),rewrite([1(12)])].
% 4.91/5.22 91 is_a_theorem(implies(falsehood,A)) = true. [para(55(a,1),8(a,1,1)),rewrite([1(7)])].
% 4.91/5.22 100 is_a_theorem(implies(A,implies(falsehood,B))) = true. [para(91(a,1),7(a,1,1)),rewrite([1(8)])].
% 4.91/5.22 103 is_a_theorem(implies(implies(A,falsehood),implies(A,B))) = true. [para(100(a,1),13(a,1,1)),rewrite([1(9)])].
% 4.91/5.22 110 is_a_theorem(implies(A,implies(implies(B,falsehood),implies(B,C)))) = true. [para(103(a,1),7(a,1,1)),rewrite([1(10)])].
% 4.91/5.22 126 is_a_theorem(implies(implies(A,implies(B,falsehood)),implies(A,implies(B,C)))) = true. [para(110(a,1),13(a,1,1)),rewrite([1(11)])].
% 4.91/5.22 230 ifeq(is_a_theorem(implies(A,implies(B,falsehood))),true,is_a_theorem(implies(A,implies(B,C))),true) = true. [para(126(a,1),4(a,1,1)),rewrite([1(14)])].
% 4.91/5.22 383 is_a_theorem(implies(implies(implies(A,falsehood),A),A)) = true. [para(55(a,1),50(a,1,1)),rewrite([1(9)])].
% 4.91/5.22 386 ifeq(is_a_theorem(implies(implies(A,falsehood),A)),true,is_a_theorem(A),true) = true. [para(383(a,1),4(a,1,1)),rewrite([1(12)])].
% 4.91/5.22 422 is_a_theorem(implies(implies(A,implies(implies(B,A),C)),implies(A,C))) = true. [para(53(a,1),21(a,1,1)),rewrite([1(10)])].
% 4.91/5.22 630 ifeq(is_a_theorem(implies(A,implies(implies(B,A),C))),true,is_a_theorem(implies(A,C)),true) = true. [para(422(a,1),4(a,1,1)),rewrite([1(13)])].
% 4.91/5.22 3400 is_a_theorem(implies(implies(A,implies(implies(B,A),falsehood)),implies(A,C))) = true. [para(422(a,1),230(a,1,1)),rewrite([1(11)])].
% 4.91/5.22 3480 is_a_theorem(implies(A,implies(implies(B,implies(implies(C,B),falsehood)),implies(B,D)))) = true. [para(3400(a,1),7(a,1,1)),rewrite([1(12)])].
% 4.91/5.22 4930 is_a_theorem(implies(A,implies(implies(A,B),B))) = true. [para(51(a,1),630(a,1,1)),rewrite([1(8)])].
% 4.91/5.22 4934 is_a_theorem(implies(implies(implies(A,B),falsehood),implies(B,C))) = true. [para(3480(a,1),630(a,1,1)),rewrite([1(10)])].
% 4.91/5.22 4945 is_a_theorem(implies(A,implies(B,implies(implies(B,C),C)))) = true. [para(4930(a,1),7(a,1,1)),rewrite([1(9)])].
% 4.91/5.22 4989 is_a_theorem(implies(implies(A,B),implies(A,implies(implies(B,C),C)))) = true. [para(4945(a,1),13(a,1,1)),rewrite([1(10)])].
% 4.91/5.22 6039 ifeq(is_a_theorem(implies(A,B)),true,is_a_theorem(implies(A,implies(implies(B,C),C))),true) = true. [para(4989(a,1),4(a,1,1)),rewrite([1(13)])].
% 4.91/5.22 9969 is_a_theorem(implies(implies(implies(A,B),falsehood),implies(implies(implies(B,C),D),D))) = true. [para(4934(a,1),6039(a,1,1)),rewrite([1(12)])].
% 4.91/5.22 10054 is_a_theorem(implies(implies(implies(A,B),A),A)) = true. [para(9969(a,1),386(a,1,1)),rewrite([1(8)])].
% 4.91/5.22 10055 $F # answer(prove_c0_3). [resolve(10054,a,6,a)].
% 4.91/5.22
% 4.91/5.22 % SZS output end Refutation
% 4.91/5.22 ============================== end of proof ==========================
% 4.91/5.22
% 4.91/5.22 ============================== STATISTICS ============================
% 4.91/5.22
% 4.91/5.22 Given=1188. Generated=597829. Kept=10054. proofs=1.
% 4.91/5.22 Usable=1163. Sos=8696. Demods=9862. Limbo=4, Disabled=196. Hints=0.
% 4.91/5.22 Megabytes=10.62.
% 4.91/5.22 User_CPU=3.77, System_CPU=0.33, Wall_clock=5.
% 4.91/5.22
% 4.91/5.22 ============================== end of statistics =====================
% 4.91/5.22
% 4.91/5.22 ============================== end of search =========================
% 4.91/5.22
% 4.91/5.22 THEOREM PROVED
% 4.91/5.22 % SZS status Unsatisfiable
% 4.91/5.22
% 4.91/5.22 Exiting with 1 proof.
% 4.91/5.22
% 4.91/5.22 Process 7160 exit (max_proofs) Mon Jul 4 13:46:43 2022
% 4.91/5.22 Prover9 interrupted
%------------------------------------------------------------------------------