TSTP Solution File: LCL109-3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL109-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 13:44:04 EDT 2022
% Result : Unsatisfiable 1.53s 1.79s
% Output : Refutation 1.53s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL109-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % 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 Jul 3 22:03:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.53/1.79 ============================== Prover9 ===============================
% 1.53/1.79 Prover9 (32) version 2009-11A, November 2009.
% 1.53/1.79 Process 28275 was started by sandbox on n018.cluster.edu,
% 1.53/1.79 Sun Jul 3 22:03:36 2022
% 1.53/1.79 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_28121_n018.cluster.edu".
% 1.53/1.79 ============================== end of head ===========================
% 1.53/1.79
% 1.53/1.79 ============================== INPUT =================================
% 1.53/1.79
% 1.53/1.79 % Reading from file /tmp/Prover9_28121_n018.cluster.edu
% 1.53/1.79
% 1.53/1.79 set(prolog_style_variables).
% 1.53/1.79 set(auto2).
% 1.53/1.79 % set(auto2) -> set(auto).
% 1.53/1.79 % set(auto) -> set(auto_inference).
% 1.53/1.79 % set(auto) -> set(auto_setup).
% 1.53/1.79 % set(auto_setup) -> set(predicate_elim).
% 1.53/1.79 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.53/1.79 % set(auto) -> set(auto_limits).
% 1.53/1.79 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.53/1.79 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.53/1.79 % set(auto) -> set(auto_denials).
% 1.53/1.79 % set(auto) -> set(auto_process).
% 1.53/1.79 % set(auto2) -> assign(new_constants, 1).
% 1.53/1.79 % set(auto2) -> assign(fold_denial_max, 3).
% 1.53/1.79 % set(auto2) -> assign(max_weight, "200.000").
% 1.53/1.79 % set(auto2) -> assign(max_hours, 1).
% 1.53/1.79 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.53/1.79 % set(auto2) -> assign(max_seconds, 0).
% 1.53/1.79 % set(auto2) -> assign(max_minutes, 5).
% 1.53/1.79 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.53/1.79 % set(auto2) -> set(sort_initial_sos).
% 1.53/1.79 % set(auto2) -> assign(sos_limit, -1).
% 1.53/1.79 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.53/1.79 % set(auto2) -> assign(max_megs, 400).
% 1.53/1.79 % set(auto2) -> assign(stats, some).
% 1.53/1.79 % set(auto2) -> clear(echo_input).
% 1.53/1.79 % set(auto2) -> set(quiet).
% 1.53/1.79 % set(auto2) -> clear(print_initial_clauses).
% 1.53/1.79 % set(auto2) -> clear(print_given).
% 1.53/1.79 assign(lrs_ticks,-1).
% 1.53/1.79 assign(sos_limit,10000).
% 1.53/1.79 assign(order,kbo).
% 1.53/1.79 set(lex_order_vars).
% 1.53/1.79 clear(print_given).
% 1.53/1.79
% 1.53/1.79 % formulas(sos). % not echoed (15 formulas)
% 1.53/1.79
% 1.53/1.79 ============================== end of input ==========================
% 1.53/1.79
% 1.53/1.79 % From the command line: assign(max_seconds, 300).
% 1.53/1.79
% 1.53/1.79 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.53/1.79
% 1.53/1.79 % Formulas that are not ordinary clauses:
% 1.53/1.79
% 1.53/1.79 ============================== end of process non-clausal formulas ===
% 1.53/1.79
% 1.53/1.79 ============================== PROCESS INITIAL CLAUSES ===============
% 1.53/1.79
% 1.53/1.79 ============================== PREDICATE ELIMINATION =================
% 1.53/1.79
% 1.53/1.79 ============================== end predicate elimination =============
% 1.53/1.79
% 1.53/1.79 Auto_denials:
% 1.53/1.79 % copying label prove_wajsberg_mv_4 to answer in negative clause
% 1.53/1.79
% 1.53/1.79 Term ordering decisions:
% 1.53/1.79
% 1.53/1.79 % Assigning unary symbol not kb_weight 0 and highest precedence (6).
% 1.53/1.79 Function symbol KB weights: truth=1. a=1. b=1. implies=1. not=0.
% 1.53/1.79
% 1.53/1.79 ============================== end of process initial clauses ========
% 1.53/1.79
% 1.53/1.79 ============================== CLAUSES FOR SEARCH ====================
% 1.53/1.79
% 1.53/1.79 ============================== end of clauses for search =============
% 1.53/1.79
% 1.53/1.79 ============================== SEARCH ================================
% 1.53/1.79
% 1.53/1.79 % Starting search at 0.01 seconds.
% 1.53/1.79
% 1.53/1.79 ============================== PROOF =================================
% 1.53/1.79 % SZS status Unsatisfiable
% 1.53/1.79 % SZS output start Refutation
% 1.53/1.79
% 1.53/1.79 % Proof 1 at 0.79 (+ 0.02) seconds: prove_wajsberg_mv_4.
% 1.53/1.79 % Length of proof is 38.
% 1.53/1.79 % Level of proof is 7.
% 1.53/1.79 % Maximum clause weight is 17.000.
% 1.53/1.79 % Given clauses 264.
% 1.53/1.79
% 1.53/1.79 1 implies(truth,A) = A # label(wajsberg_1) # label(axiom). [assumption].
% 1.53/1.79 3 implies(A,truth) = truth # label(lemma_3) # label(axiom). [assumption].
% 1.53/1.79 4 not(not(A)) = A # label(lemma_9) # label(axiom). [assumption].
% 1.53/1.79 5 implies(A,implies(B,A)) = truth # label(lemma_4) # label(axiom). [assumption].
% 1.53/1.79 6 implies(A,not(truth)) = not(A) # label(lemma_8) # label(axiom). [assumption].
% 1.53/1.79 7 implies(not(A),not(B)) = implies(B,A) # label(lemma_10) # label(axiom). [assumption].
% 1.53/1.79 8 implies(implies(A,B),B) = implies(implies(B,A),A) # label(wajsberg_3) # label(axiom). [assumption].
% 1.53/1.79 9 implies(implies(not(A),not(B)),implies(B,A)) = truth # label(wajsberg_4) # label(axiom). [assumption].
% 1.53/1.79 10 implies(A,implies(B,C)) = implies(B,implies(A,C)) # label(lemma_7) # label(axiom). [assumption].
% 1.53/1.79 11 implies(implies(A,B),implies(implies(B,C),implies(A,C))) = truth # label(wajsberg_2) # label(axiom). [assumption].
% 1.53/1.79 12 implies(A,implies(implies(A,B),implies(implies(B,C),C))) = truth. [copy(11),rewrite([10(4),10(5)])].
% 1.53/1.79 15 implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth # label(prove_wajsberg_mv_4) # label(negated_conjecture) # answer(prove_wajsberg_mv_4). [assumption].
% 1.53/1.79 16 implies(b,implies(implies(b,implies(implies(a,b),a)),a)) != truth # answer(prove_wajsberg_mv_4). [copy(15),rewrite([10(7),10(11)])].
% 1.53/1.79 17 implies(A,B) != implies(B,A) | A = B # label(lemma_2) # label(axiom). [assumption].
% 1.53/1.79 18 implies(A,B) != implies(B,C) | implies(A,C) = truth # label(lemma_5) # label(axiom). [assumption].
% 1.53/1.79 19 implies(A,B) != implies(C,A) | implies(C,B) = truth. [copy(18),flip(a)].
% 1.53/1.79 20 implies(A,implies(implies(not(B),not(A)),B)) = truth. [back_rewrite(9),rewrite([10(5)])].
% 1.53/1.79 22 implies(A,not(B)) = implies(B,not(A)). [para(4(a,1),7(a,1,1))].
% 1.53/1.79 23 implies(not(A),B) = implies(not(B),A). [para(4(a,1),7(a,1,2))].
% 1.53/1.79 24 implies(A,implies(not(A),B)) = truth. [para(7(a,1),5(a,1,2)),rewrite([10(3)])].
% 1.53/1.79 25 implies(A,implies(implies(A,B),B)) = truth. [back_rewrite(20),rewrite([22(3),4(2)])].
% 1.53/1.79 27 implies(implies(implies(A,B),B),A) = implies(B,A). [para(8(a,1),8(a,1,1)),rewrite([5(5),10(6),1(5)])].
% 1.53/1.79 30 implies(implies(implies(A,B),C),C) = implies(A,implies(implies(A,implies(C,B)),B)). [para(10(a,1),8(a,1,1)),rewrite([10(4)]),flip(a)].
% 1.53/1.79 58 implies(A,B) != A | truth = B. [para(1(a,1),19(a,2)),rewrite([1(4)]),flip(b)].
% 1.53/1.79 64 implies(implies(A,B),B) != implies(A,C) | implies(implies(B,A),C) = truth. [para(8(a,1),19(a,2)),flip(a)].
% 1.53/1.79 75 implies(not(A),B) != implies(A,not(B)) | not(A) = B. [para(22(a,1),17(a,1)),flip(a),flip(b)].
% 1.53/1.79 100 implies(A,implies(implies(implies(not(A),B),C),C)) = truth. [para(24(a,1),12(a,1,2,1)),rewrite([1(6)])].
% 1.53/1.79 122 implies(not(A),B) != not(B) | truth = A. [para(23(a,1),58(a,1))].
% 1.53/1.79 133 implies(A,B) != truth | implies(implies(B,A),A) = B. [para(25(a,1),17(a,1)),rewrite([27(4)]),flip(a),flip(b)].
% 1.53/1.79 223 not(implies(A,B)) != truth | truth = A. [para(24(a,1),122(a,1)),rewrite([4(3)]),flip(a)].
% 1.53/1.79 354 not(implies(implies(implies(A,B),C),C)) != truth | truth = A. [para(30(a,2),223(a,1,1))].
% 1.53/1.79 771 implies(not(A),implies(implies(implies(A,B),C),C)) = truth. [para(4(a,1),100(a,1,2,1,1,1))].
% 1.53/1.79 1435 implies(A,implies(not(B),implies(implies(A,implies(implies(B,C),D)),D))) = truth. [para(10(a,1),771(a,1,2,1)),rewrite([10(6),10(7)])].
% 1.53/1.79 4659 implies(implies(A,not(A)),not(implies(not(A),A))) = truth. [hyper(64,a,22,a),rewrite([22(6)])].
% 1.53/1.79 4855 not(implies(not(A),A)) = implies(A,not(A)). [hyper(133,a,4659,a),rewrite([10(6),22(5),4(4),5(3),3(2),10(4),22(3),6(3)]),flip(a)].
% 1.53/1.79 4868 not(implies(A,not(A))) = implies(not(A),A). [para(4659(a,1),75(a,2)),rewrite([10(6),23(5),5(5),3(3)]),xx(a)].
% 1.53/1.79 4869 implies(not(A),A) != truth | truth = A. [para(4659(a,1),354(a,1,1,1)),rewrite([4855(4),10(4),22(3),6(3),4868(3)])].
% 1.53/1.79 4914 $F # answer(prove_wajsberg_mv_4). [ur(4869,b,16,a(flip)),rewrite([10(24),10(23),23(22),10(22),1435(22),3(10),3(3)]),xx(a)].
% 1.53/1.79
% 1.53/1.79 % SZS output end Refutation
% 1.53/1.79 ============================== end of proof ==========================
% 1.53/1.79
% 1.53/1.79 ============================== STATISTICS ============================
% 1.53/1.79
% 1.53/1.79 Given=264. Generated=24953. Kept=4909. proofs=1.
% 1.53/1.79 Usable=250. Sos=4323. Demods=1556. Limbo=37, Disabled=314. Hints=0.
% 1.53/1.79 Megabytes=5.22.
% 1.53/1.79 User_CPU=0.79, System_CPU=0.02, Wall_clock=0.
% 1.53/1.79
% 1.53/1.79 ============================== end of statistics =====================
% 1.53/1.79
% 1.53/1.79 ============================== end of search =========================
% 1.53/1.79
% 1.53/1.79 THEOREM PROVED
% 1.53/1.79 % SZS status Unsatisfiable
% 1.53/1.79
% 1.53/1.79 Exiting with 1 proof.
% 1.53/1.79
% 1.53/1.79 Process 28275 exit (max_proofs) Sun Jul 3 22:03:36 2022
% 1.53/1.79 Prover9 interrupted
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