TSTP Solution File: LCL153-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL153-1 : 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 : Sun Jul 17 13:44:24 EDT 2022
% Result : Unsatisfiable 0.71s 1.01s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : LCL153-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.31 % Computer : n028.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 600
% 0.12/0.31 % DateTime : Sun Jul 3 21:23:19 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.71/1.00 ============================== Prover9 ===============================
% 0.71/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.71/1.00 Process 17259 was started by sandbox on n028.cluster.edu,
% 0.71/1.00 Sun Jul 3 21:23:19 2022
% 0.71/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_17105_n028.cluster.edu".
% 0.71/1.00 ============================== end of head ===========================
% 0.71/1.00
% 0.71/1.00 ============================== INPUT =================================
% 0.71/1.00
% 0.71/1.00 % Reading from file /tmp/Prover9_17105_n028.cluster.edu
% 0.71/1.00
% 0.71/1.00 set(prolog_style_variables).
% 0.71/1.00 set(auto2).
% 0.71/1.00 % set(auto2) -> set(auto).
% 0.71/1.00 % set(auto) -> set(auto_inference).
% 0.71/1.00 % set(auto) -> set(auto_setup).
% 0.71/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.71/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.71/1.00 % set(auto) -> set(auto_limits).
% 0.71/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.71/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.71/1.00 % set(auto) -> set(auto_denials).
% 0.71/1.00 % set(auto) -> set(auto_process).
% 0.71/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.71/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.71/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.71/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.71/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.71/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.71/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.71/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.71/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.71/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.71/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.71/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.71/1.00 % set(auto2) -> assign(stats, some).
% 0.71/1.00 % set(auto2) -> clear(echo_input).
% 0.71/1.00 % set(auto2) -> set(quiet).
% 0.71/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.71/1.00 % set(auto2) -> clear(print_given).
% 0.71/1.00 assign(lrs_ticks,-1).
% 0.71/1.00 assign(sos_limit,10000).
% 0.71/1.00 assign(order,kbo).
% 0.71/1.00 set(lex_order_vars).
% 0.71/1.00 clear(print_given).
% 0.71/1.00
% 0.71/1.00 % formulas(sos). % not echoed (17 formulas)
% 0.71/1.00
% 0.71/1.00 ============================== end of input ==========================
% 0.71/1.00
% 0.71/1.00 % From the command line: assign(max_seconds, 300).
% 0.71/1.00
% 0.71/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.71/1.00
% 0.71/1.00 % Formulas that are not ordinary clauses:
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% 0.71/1.00 ============================== end of process non-clausal formulas ===
% 0.71/1.00
% 0.71/1.00 ============================== PROCESS INITIAL CLAUSES ===============
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% 0.71/1.00 ============================== PREDICATE ELIMINATION =================
% 0.71/1.00
% 0.71/1.00 ============================== end predicate elimination =============
% 0.71/1.00
% 0.71/1.00 Auto_denials:
% 0.71/1.00 % copying label prove_alternative_wajsberg_axiom to answer in negative clause
% 0.71/1.00
% 0.71/1.00 Term ordering decisions:
% 0.71/1.00
% 0.71/1.00 % Assigning unary symbol not kb_weight 0 and highest precedence (10).
% 0.71/1.00 Function symbol KB weights: truth=1. falsehood=1. x=1. implies=1. or=1. and=1. and_star=1. xor=1. not=0.
% 0.71/1.00
% 0.71/1.00 ============================== end of process initial clauses ========
% 0.71/1.00
% 0.71/1.00 ============================== CLAUSES FOR SEARCH ====================
% 0.71/1.00
% 0.71/1.00 ============================== end of clauses for search =============
% 0.71/1.00
% 0.71/1.00 ============================== SEARCH ================================
% 0.71/1.00
% 0.71/1.00 % Starting search at 0.01 seconds.
% 0.71/1.00
% 0.71/1.00 ============================== PROOF =================================
% 0.71/1.01 % SZS status Unsatisfiable
% 0.71/1.01 % SZS output start Refutation
% 0.71/1.01
% 0.71/1.01 % Proof 1 at 0.05 (+ 0.00) seconds: prove_alternative_wajsberg_axiom.
% 0.71/1.01 % Length of proof is 32.
% 0.71/1.01 % Level of proof is 9.
% 0.71/1.01 % Maximum clause weight is 22.000.
% 0.71/1.01 % Given clauses 27.
% 0.71/1.01
% 0.71/1.01 1 not(truth) = falsehood # label(false_definition) # label(axiom). [assumption].
% 0.71/1.01 2 implies(truth,A) = A # label(wajsberg_1) # label(axiom). [assumption].
% 0.71/1.01 3 or(A,B) = or(B,A) # label(or_commutativity) # label(axiom). [assumption].
% 0.71/1.01 4 and(A,B) = and(B,A) # label(and_commutativity) # label(axiom). [assumption].
% 0.71/1.01 5 xor(A,B) = xor(B,A) # label(xor_commutativity) # label(axiom). [assumption].
% 0.71/1.01 7 or(A,B) = implies(not(A),B) # label(or_definition) # label(axiom). [assumption].
% 0.71/1.01 8 and(A,B) = not(or(not(A),not(B))) # label(and_definition) # label(axiom). [assumption].
% 0.71/1.01 9 and(A,B) = not(implies(not(not(A)),not(B))). [copy(8),rewrite([7(4)])].
% 0.71/1.01 12 implies(implies(A,B),B) = implies(implies(B,A),A) # label(wajsberg_3) # label(axiom). [assumption].
% 0.71/1.01 13 implies(implies(not(A),not(B)),implies(B,A)) = truth # label(wajsberg_4) # label(axiom). [assumption].
% 0.71/1.01 19 implies(implies(A,B),implies(implies(B,C),implies(A,C))) = truth # label(wajsberg_2) # label(axiom). [assumption].
% 0.71/1.01 20 xor(A,B) = or(and(A,not(B)),and(not(A),B)) # label(xor_definition) # label(axiom). [assumption].
% 0.71/1.01 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)])].
% 0.71/1.01 22 not(x) != xor(x,truth) # label(prove_alternative_wajsberg_axiom) # label(negated_conjecture) # answer(prove_alternative_wajsberg_axiom). [assumption].
% 0.71/1.01 23 implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(x)),not(falsehood)))) != not(x) # answer(prove_alternative_wajsberg_axiom). [copy(22),rewrite([5(5),21(5),1(4),1(15)]),flip(a)].
% 0.71/1.01 24 implies(not(A),B) = implies(not(B),A). [back_rewrite(3),rewrite([7(1),7(3)])].
% 0.71/1.01 25 implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))) != not(x) # answer(prove_alternative_wajsberg_axiom). [back_rewrite(23),rewrite([24(14)])].
% 0.71/1.01 26 implies(implies(A,truth),truth) = implies(A,A). [para(2(a,1),12(a,1,1)),flip(a)].
% 0.71/1.01 29 implies(implies(not(A),falsehood),A) = truth. [para(1(a,1),13(a,1,1,2)),rewrite([2(5)])].
% 0.71/1.01 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)].
% 0.71/1.01 74 implies(A,implies(implies(A,B),B)) = truth. [para(2(a,1),19(a,1,1)),rewrite([2(3)])].
% 0.71/1.01 102 implies(not(A),truth) = implies(falsehood,A). [para(1(a,1),24(a,1,1)),flip(a)].
% 0.71/1.01 132 implies(implies(falsehood,not(falsehood)),not(falsehood)) = truth. [para(29(a,1),12(a,1)),flip(a)].
% 0.71/1.01 194 implies(A,A) = truth. [para(74(a,1),2(a,1)),rewrite([2(3)]),flip(a)].
% 0.71/1.01 206 implies(A,truth) = truth. [para(26(a,1),74(a,1,2)),rewrite([194(1)])].
% 0.71/1.01 207 implies(falsehood,A) = truth. [para(102(a,2),74(a,1,2,1)),rewrite([206(4),2(3)])].
% 0.71/1.01 224 not(falsehood) = truth. [back_rewrite(132),rewrite([207(4),2(4)])].
% 0.71/1.01 232 not(not(not(x))) != not(x) # answer(prove_alternative_wajsberg_axiom). [back_rewrite(25),rewrite([224(2),2(5),224(7),1(7),207(9),1(7),24(7),224(2),2(6)])].
% 0.71/1.01 237 implies(not(A),falsehood) = A. [para(224(a,1),24(a,1,1)),rewrite([2(2)]),flip(a)].
% 0.71/1.01 259 implies(A,falsehood) = not(A). [para(237(a,1),12(a,1,1)),rewrite([207(5),2(5)])].
% 0.71/1.01 265 not(not(A)) = A. [para(237(a,1),30(a,2)),rewrite([259(3),224(4),2(6),194(5),224(3),2(5),2(4)])].
% 0.71/1.01 266 $F # answer(prove_alternative_wajsberg_axiom). [resolve(265,a,232,a)].
% 0.71/1.01
% 0.71/1.01 % SZS output end Refutation
% 0.71/1.01 ============================== end of proof ==========================
% 0.71/1.01
% 0.71/1.01 ============================== STATISTICS ============================
% 0.71/1.01
% 0.71/1.01 Given=27. Generated=698. Kept=258. proofs=1.
% 0.71/1.01 Usable=21. Sos=121. Demods=95. Limbo=6, Disabled=126. Hints=0.
% 0.71/1.01 Megabytes=0.34.
% 0.71/1.01 User_CPU=0.05, System_CPU=0.00, Wall_clock=0.
% 0.71/1.01
% 0.71/1.01 ============================== end of statistics =====================
% 0.71/1.01
% 0.71/1.01 ============================== end of search =========================
% 0.71/1.01
% 0.71/1.01 THEOREM PROVED
% 0.71/1.01 % SZS status Unsatisfiable
% 0.71/1.01
% 0.71/1.01 Exiting with 1 proof.
% 0.71/1.01
% 0.71/1.01 Process 17259 exit (max_proofs) Sun Jul 3 21:23:19 2022
% 0.71/1.01 Prover9 interrupted
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