TSTP Solution File: LCL154-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL154-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n014.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 13:44:25 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
% 0.03/0.12 % Problem : LCL154-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 3 12:14:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.73/1.04 ============================== Prover9 ===============================
% 0.73/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.73/1.04 Process 1997 was started by sandbox on n014.cluster.edu,
% 0.73/1.04 Sun Jul 3 12:14:25 2022
% 0.73/1.04 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_1841_n014.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_1841_n014.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 (17 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
% 0.73/1.04 ============================== end predicate elimination =============
% 0.73/1.04
% 0.73/1.04 Auto_denials:
% 0.73/1.04 % copying label prove_alternative_wajsberg_axiom to answer in negative clause
% 0.73/1.04
% 0.73/1.04 Term ordering decisions:
% 0.73/1.04
% 0.73/1.04 % Assigning unary symbol not kb_weight 0 and highest precedence (10).
% 0.73/1.04 Function symbol KB weights: truth=1. falsehood=1. x=1. implies=1. or=1. and=1. and_star=1. xor=1. not=0.
% 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 0.05 (+ 0.00) seconds: prove_alternative_wajsberg_axiom.
% 0.73/1.04 % Length of proof is 39.
% 0.73/1.04 % Level of proof is 11.
% 0.73/1.04 % Maximum clause weight is 22.000.
% 0.73/1.04 % Given clauses 34.
% 0.73/1.04
% 0.73/1.04 1 not(truth) = falsehood # label(false_definition) # label(axiom). [assumption].
% 0.73/1.04 2 falsehood = not(truth). [copy(1),flip(a)].
% 0.73/1.04 3 implies(truth,A) = A # label(wajsberg_1) # label(axiom). [assumption].
% 0.73/1.04 4 or(A,B) = or(B,A) # label(or_commutativity) # label(axiom). [assumption].
% 0.73/1.04 5 and(A,B) = and(B,A) # label(and_commutativity) # label(axiom). [assumption].
% 0.73/1.04 8 or(A,B) = implies(not(A),B) # label(or_definition) # label(axiom). [assumption].
% 0.73/1.04 9 and(A,B) = not(or(not(A),not(B))) # label(and_definition) # label(axiom). [assumption].
% 0.73/1.04 10 and(A,B) = not(implies(not(not(A)),not(B))). [copy(9),rewrite([8(4)])].
% 0.73/1.04 13 implies(implies(A,B),B) = implies(implies(B,A),A) # label(wajsberg_3) # label(axiom). [assumption].
% 0.73/1.04 14 implies(implies(not(A),not(B)),implies(B,A)) = truth # label(wajsberg_4) # label(axiom). [assumption].
% 0.73/1.04 15 or(or(A,B),C) = or(A,or(B,C)) # label(or_associativity) # label(axiom). [assumption].
% 0.73/1.04 16 implies(not(A),implies(not(B),C)) = implies(not(C),implies(not(A),B)). [copy(15),rewrite([8(1),4(3),8(3),8(5),8(7)]),flip(a)].
% 0.73/1.04 20 implies(implies(A,B),implies(implies(B,C),implies(A,C))) = truth # label(wajsberg_2) # label(axiom). [assumption].
% 0.73/1.04 21 xor(A,B) = or(and(A,not(B)),and(not(A),B)) # label(xor_definition) # label(axiom). [assumption].
% 0.73/1.04 22 xor(A,B) = implies(not(not(implies(not(not(A)),not(not(B))))),not(implies(not(not(B)),not(not(A))))). [copy(21),rewrite([10(3),5(9),10(9),8(14)])].
% 0.73/1.04 23 xor(x,falsehood) != x # label(prove_alternative_wajsberg_axiom) # label(negated_conjecture) # answer(prove_alternative_wajsberg_axiom). [assumption].
% 0.73/1.04 24 implies(not(not(implies(not(not(x)),not(not(not(truth)))))),not(implies(not(not(not(truth))),not(not(x))))) != x # answer(prove_alternative_wajsberg_axiom). [copy(23),rewrite([2(2),22(4)])].
% 0.73/1.04 25 implies(not(A),B) = implies(not(B),A). [back_rewrite(4),rewrite([8(1),8(3)])].
% 0.73/1.04 26 implies(implies(A,truth),truth) = implies(A,A). [para(3(a,1),13(a,1,1)),flip(a)].
% 0.73/1.04 27 implies(implies(implies(A,B),B),B) = implies(implies(implies(B,A),A),B). [para(13(a,1),13(a,1,1)),rewrite([13(7)]),flip(a)].
% 0.73/1.04 29 implies(implies(implies(A,B),implies(not(B),not(A))),implies(not(B),not(A))) = implies(A,B). [para(14(a,1),13(a,1,1)),rewrite([3(3)]),flip(a)].
% 0.73/1.04 67 implies(A,implies(implies(A,B),B)) = truth. [para(3(a,1),20(a,1,1)),rewrite([3(3)])].
% 0.73/1.04 68 implies(implies(A,truth),implies(B,implies(A,B))) = truth. [para(3(a,1),20(a,1,2,1))].
% 0.73/1.04 131 implies(A,A) = truth. [para(67(a,1),3(a,1)),rewrite([3(3)]),flip(a)].
% 0.73/1.04 143 implies(A,truth) = truth. [para(26(a,1),67(a,1,2)),rewrite([131(1)])].
% 0.73/1.04 151 implies(A,implies(B,A)) = truth. [back_rewrite(68),rewrite([143(2),3(4)])].
% 0.73/1.04 152 implies(not(not(A)),implies(not(B),A)) = truth. [para(131(a,1),16(a,1,2)),rewrite([143(3)]),flip(a)].
% 0.73/1.04 155 implies(implies(implies(A,B),B),A) = implies(B,A). [para(27(a,1),13(a,1)),rewrite([151(5),3(6)])].
% 0.73/1.04 186 implies(A,implies(not(A),B)) = truth. [para(25(a,1),151(a,1,2))].
% 0.73/1.04 201 implies(not(A),not(truth)) = A. [para(3(a,1),29(a,1,1,1)),rewrite([186(5),3(6),3(6)])].
% 0.73/1.04 218 implies(implies(not(truth),not(A)),not(A)) = implies(A,not(truth)). [para(201(a,1),13(a,1,1)),flip(a)].
% 0.73/1.04 242 implies(not(A),not(not(truth))) = truth. [para(201(a,1),152(a,1,2)),rewrite([25(5)])].
% 0.73/1.04 245 not(not(truth)) = truth. [para(242(a,1),13(a,1,1)),rewrite([3(5),25(8),201(8),131(6)])].
% 0.73/1.04 249 implies(not(not(not(x))),not(implies(not(truth),not(not(x))))) != x # answer(prove_alternative_wajsberg_axiom). [back_rewrite(24),rewrite([245(6),25(6),245(3),3(4),245(7)])].
% 0.73/1.04 268 not(not(x)) != x # answer(prove_alternative_wajsberg_axiom). [para(25(a,1),249(a,1,2,1)),rewrite([143(10),25(7),245(3),3(5)])].
% 0.73/1.04 271 implies(implies(A,not(truth)),not(truth)) = A. [para(201(a,1),155(a,2)),rewrite([218(6)])].
% 0.73/1.04 275 implies(A,not(truth)) = not(A). [para(25(a,1),271(a,1,1)),rewrite([245(3),3(2)])].
% 0.73/1.04 277 not(not(A)) = A. [para(271(a,1),29(a,2)),rewrite([275(3),275(4),245(5),275(6),3(6),131(5),245(4),275(5),3(5),3(4)])].
% 0.73/1.04 278 $F # answer(prove_alternative_wajsberg_axiom). [resolve(277,a,268,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=34. Generated=968. Kept=269. proofs=1.
% 0.73/1.04 Usable=29. Sos=157. Demods=145. Limbo=5, Disabled=94. Hints=0.
% 0.73/1.04 Megabytes=0.37.
% 0.73/1.04 User_CPU=0.05, 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 1997 exit (max_proofs) Sun Jul 3 12:14:25 2022
% 0.73/1.04 Prover9 interrupted
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