TSTP Solution File: LCL159-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL159-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.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 13:44:26 EDT 2022
% Result : Unsatisfiable 0.73s 1.06s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL159-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n010.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 : Sat Jul 2 10:08:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.73/1.06 ============================== Prover9 ===============================
% 0.73/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.73/1.06 Process 28897 was started by sandbox on n010.cluster.edu,
% 0.73/1.06 Sat Jul 2 10:08:34 2022
% 0.73/1.06 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_28744_n010.cluster.edu".
% 0.73/1.06 ============================== end of head ===========================
% 0.73/1.06
% 0.73/1.06 ============================== INPUT =================================
% 0.73/1.06
% 0.73/1.06 % Reading from file /tmp/Prover9_28744_n010.cluster.edu
% 0.73/1.06
% 0.73/1.06 set(prolog_style_variables).
% 0.73/1.06 set(auto2).
% 0.73/1.06 % set(auto2) -> set(auto).
% 0.73/1.06 % set(auto) -> set(auto_inference).
% 0.73/1.06 % set(auto) -> set(auto_setup).
% 0.73/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.73/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.73/1.06 % set(auto) -> set(auto_limits).
% 0.73/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.73/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.73/1.06 % set(auto) -> set(auto_denials).
% 0.73/1.06 % set(auto) -> set(auto_process).
% 0.73/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.73/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.73/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.73/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.73/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.73/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.73/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.73/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.73/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.73/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.73/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.73/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.73/1.06 % set(auto2) -> assign(stats, some).
% 0.73/1.06 % set(auto2) -> clear(echo_input).
% 0.73/1.06 % set(auto2) -> set(quiet).
% 0.73/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.73/1.06 % set(auto2) -> clear(print_given).
% 0.73/1.06 assign(lrs_ticks,-1).
% 0.73/1.06 assign(sos_limit,10000).
% 0.73/1.06 assign(order,kbo).
% 0.73/1.06 set(lex_order_vars).
% 0.73/1.06 clear(print_given).
% 0.73/1.06
% 0.73/1.06 % formulas(sos). % not echoed (17 formulas)
% 0.73/1.06
% 0.73/1.06 ============================== end of input ==========================
% 0.73/1.06
% 0.73/1.06 % From the command line: assign(max_seconds, 300).
% 0.73/1.06
% 0.73/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.73/1.06
% 0.73/1.06 % Formulas that are not ordinary clauses:
% 0.73/1.06
% 0.73/1.06 ============================== end of process non-clausal formulas ===
% 0.73/1.06
% 0.73/1.06 ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.06
% 0.73/1.06 ============================== PREDICATE ELIMINATION =================
% 0.73/1.06
% 0.73/1.06 ============================== end predicate elimination =============
% 0.73/1.06
% 0.73/1.06 Auto_denials:
% 0.73/1.06 % copying label prove_alternative_wajsberg_axiom to answer in negative clause
% 0.73/1.06
% 0.73/1.06 Term ordering decisions:
% 0.73/1.06
% 0.73/1.06 % Assigning unary symbol not kb_weight 0 and highest precedence (11).
% 0.73/1.06 Function symbol KB weights: truth=1. falsehood=1. x=1. y=1. implies=1. or=1. and=1. and_star=1. xor=1. not=0.
% 0.73/1.06
% 0.73/1.06 ============================== end of process initial clauses ========
% 0.73/1.06
% 0.73/1.06 ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.06
% 0.73/1.06 ============================== end of clauses for search =============
% 0.73/1.06
% 0.73/1.06 ============================== SEARCH ================================
% 0.73/1.06
% 0.73/1.06 % Starting search at 0.01 seconds.
% 0.73/1.06
% 0.73/1.06 ============================== PROOF =================================
% 0.73/1.06 % SZS status Unsatisfiable
% 0.73/1.06 % SZS output start Refutation
% 0.73/1.06
% 0.73/1.06 % Proof 1 at 0.08 (+ 0.01) seconds: prove_alternative_wajsberg_axiom.
% 0.73/1.06 % Length of proof is 36.
% 0.73/1.06 % Level of proof is 9.
% 0.73/1.06 % Maximum clause weight is 97.000.
% 0.73/1.06 % Given clauses 38.
% 0.73/1.06
% 0.73/1.06 1 not(truth) = falsehood # label(false_definition) # label(axiom). [assumption].
% 0.73/1.06 2 implies(truth,A) = A # label(wajsberg_1) # label(axiom). [assumption].
% 0.73/1.06 3 or(A,B) = or(B,A) # label(or_commutativity) # label(axiom). [assumption].
% 0.73/1.06 4 and(A,B) = and(B,A) # label(and_commutativity) # label(axiom). [assumption].
% 0.73/1.06 5 xor(A,B) = xor(B,A) # label(xor_commutativity) # label(axiom). [assumption].
% 0.73/1.06 7 or(A,B) = implies(not(A),B) # label(or_definition) # label(axiom). [assumption].
% 0.73/1.06 8 and(A,B) = not(or(not(A),not(B))) # label(and_definition) # label(axiom). [assumption].
% 0.73/1.06 9 and(A,B) = not(implies(not(not(A)),not(B))). [copy(8),rewrite([7(4)])].
% 0.73/1.06 12 implies(implies(A,B),B) = implies(implies(B,A),A) # label(wajsberg_3) # label(axiom). [assumption].
% 0.73/1.06 13 implies(implies(not(A),not(B)),implies(B,A)) = truth # label(wajsberg_4) # label(axiom). [assumption].
% 0.73/1.06 16 and(and(A,B),C) = and(A,and(B,C)) # label(and_associativity) # label(axiom). [assumption].
% 0.73/1.06 17 not(implies(not(not(A)),not(not(implies(not(not(B)),not(C)))))) = not(implies(not(not(C)),not(not(implies(not(not(A)),not(B)))))). [copy(16),rewrite([9(1),4(6),9(6),9(11),9(16)]),flip(a)].
% 0.73/1.06 19 implies(implies(A,B),implies(implies(B,C),implies(A,C))) = truth # label(wajsberg_2) # label(axiom). [assumption].
% 0.73/1.06 20 xor(A,B) = or(and(A,not(B)),and(not(A),B)) # label(xor_definition) # label(axiom). [assumption].
% 0.73/1.06 21 xor(A,B) = implies(not(not(implies(not(not(A)),not(not(B))))),not(implies(not(not(B)),not(not(A))))). [copy(20),rewrite([9(3),4(9),9(9),7(14)])].
% 0.73/1.06 22 xor(x,xor(truth,y)) != xor(xor(x,truth),y) # label(prove_alternative_wajsberg_axiom) # label(negated_conjecture) # answer(prove_alternative_wajsberg_axiom). [assumption].
% 0.73/1.06 23 implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(x)),not(falsehood))))))))),not(implies(not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(x)),not(falsehood)))))),not(not(y))))) != implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(y)),not(falsehood))))))))),not(implies(not(not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(y)),not(falsehood)))))),not(not(x))))) # answer(prove_alternative_wajsberg_axiom). [copy(22),rewrite([21(4),1(3),1(14),21(18),5(51),21(51),1(50),1(61),5(66),21(66)]),flip(a)].
% 0.73/1.06 24 implies(not(A),B) = implies(not(B),A). [back_rewrite(3),rewrite([7(1),7(3)])].
% 0.73/1.06 25 implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),not(implies(not(not(not(y))),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))) != implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))) # answer(prove_alternative_wajsberg_axiom). [back_rewrite(23),rewrite([24(17),24(38),24(46),24(65),24(86),24(94)])].
% 0.73/1.06 26 implies(implies(A,truth),truth) = implies(A,A). [para(2(a,1),12(a,1,1)),flip(a)].
% 0.73/1.06 29 implies(implies(not(A),falsehood),A) = truth. [para(1(a,1),13(a,1,1,2)),rewrite([2(5)])].
% 0.73/1.06 30 implies(implies(implies(A,B),implies(not(B),not(A))),implies(not(B),not(A))) = implies(A,B). [para(13(a,1),12(a,1,1)),rewrite([2(3)]),flip(a)].
% 0.73/1.06 74 implies(A,implies(implies(A,B),B)) = truth. [para(2(a,1),19(a,1,1)),rewrite([2(3)])].
% 0.73/1.06 102 implies(not(A),truth) = implies(falsehood,A). [para(1(a,1),24(a,1,1)),flip(a)].
% 0.73/1.06 110 implies(not(not(implies(not(not(not(y))),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(not(implies(not(not(y)),not(implies(not(not(falsehood)),not(x))))))))) != implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))) # answer(prove_alternative_wajsberg_axiom). [para(17(a,2),25(a,1,1,1)),rewrite([24(19),24(48)])].
% 0.73/1.06 138 implies(not(not(implies(not(not(not(y))),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(not(implies(not(not(y)),not(implies(not(not(falsehood)),not(x))))))))) != implies(not(not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(not(implies(not(not(x)),not(implies(not(not(falsehood)),not(y))))))))) # answer(prove_alternative_wajsberg_axiom). [para(17(a,2),110(a,2,1,1)),rewrite([24(67),24(96)])].
% 0.73/1.06 140 implies(implies(falsehood,not(falsehood)),not(falsehood)) = truth. [para(29(a,1),12(a,1)),flip(a)].
% 0.73/1.06 202 implies(A,A) = truth. [para(74(a,1),2(a,1)),rewrite([2(3)]),flip(a)].
% 0.73/1.06 214 implies(A,truth) = truth. [para(26(a,1),74(a,1,2)),rewrite([202(1)])].
% 0.73/1.06 215 implies(falsehood,A) = truth. [para(102(a,2),74(a,1,2,1)),rewrite([214(4),2(3)])].
% 0.73/1.06 232 not(falsehood) = truth. [back_rewrite(140),rewrite([215(4),2(4)])].
% 0.73/1.06 237 implies(not(not(implies(not(not(not(y))),not(not(not(not(x))))))),not(implies(not(not(not(not(x)))),not(not(not(y)))))) != implies(not(not(implies(not(not(not(x))),not(not(not(not(y))))))),not(implies(not(not(not(not(x)))),not(not(not(y)))))) # answer(prove_alternative_wajsberg_axiom). [back_rewrite(138),rewrite([232(6),2(9),232(11),1(11),215(13),1(11),24(11),232(6),2(10),232(14),2(17),232(22),1(22),215(24),1(22),24(22),232(19),2(21),232(30),2(33),232(35),1(35),215(37),1(35),24(35),232(30),2(34),232(38),2(41),232(46),1(46),215(48),1(46),24(46),232(43),2(45),24(46)])].
% 0.73/1.06 253 implies(not(A),falsehood) = A. [para(232(a,1),24(a,1,1)),rewrite([2(2)]),flip(a)].
% 0.73/1.06 275 implies(A,falsehood) = not(A). [para(253(a,1),12(a,1,1)),rewrite([215(5),2(5)])].
% 0.73/1.06 281 not(not(A)) = A. [para(253(a,1),30(a,2)),rewrite([275(3),232(4),2(6),202(5),232(3),2(5),2(4)])].
% 0.73/1.06 313 $F # answer(prove_alternative_wajsberg_axiom). [back_rewrite(237),rewrite([281(3),281(5),281(5),24(4),281(6),281(7),281(7),281(8),281(13),281(15),281(15),281(16),281(17),281(17),281(18)]),xx(a)].
% 0.73/1.06
% 0.73/1.06 % SZS output end Refutation
% 0.73/1.06 ============================== end of proof ==========================
% 0.73/1.06
% 0.73/1.06 ============================== STATISTICS ============================
% 0.73/1.06
% 0.73/1.06 Given=38. Generated=973. Kept=305. proofs=1.
% 0.73/1.06 Usable=19. Sos=90. Demods=87. Limbo=32, Disabled=181. Hints=0.
% 0.73/1.06 Megabytes=0.43.
% 0.73/1.06 User_CPU=0.09, System_CPU=0.01, Wall_clock=0.
% 0.73/1.06
% 0.73/1.06 ============================== end of statistics =====================
% 0.73/1.06
% 0.73/1.06 ============================== end of search =========================
% 0.73/1.06
% 0.73/1.06 THEOREM PROVED
% 0.73/1.06 % SZS status Unsatisfiable
% 0.73/1.06
% 0.73/1.06 Exiting with 1 proof.
% 0.73/1.06
% 0.73/1.06 Process 28897 exit (max_proofs) Sat Jul 2 10:08:34 2022
% 0.73/1.06 Prover9 interrupted
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