TSTP Solution File: LCL158-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL158-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 0.71s 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
% 0.00/0.11 % Problem : LCL158-1 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 2 19:01:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.71/1.01 ============================== Prover9 ===============================
% 0.71/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.71/1.01 Process 20492 was started by sandbox on n017.cluster.edu,
% 0.71/1.01 Sat Jul 2 19:01:41 2022
% 0.71/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_20338_n017.cluster.edu".
% 0.71/1.01 ============================== end of head ===========================
% 0.71/1.01
% 0.71/1.01 ============================== INPUT =================================
% 0.71/1.01
% 0.71/1.01 % Reading from file /tmp/Prover9_20338_n017.cluster.edu
% 0.71/1.01
% 0.71/1.01 set(prolog_style_variables).
% 0.71/1.01 set(auto2).
% 0.71/1.01 % set(auto2) -> set(auto).
% 0.71/1.01 % set(auto) -> set(auto_inference).
% 0.71/1.01 % set(auto) -> set(auto_setup).
% 0.71/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.71/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.71/1.01 % set(auto) -> set(auto_limits).
% 0.71/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.71/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.71/1.01 % set(auto) -> set(auto_denials).
% 0.71/1.01 % set(auto) -> set(auto_process).
% 0.71/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.71/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.71/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.71/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.71/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.71/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.71/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.71/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.71/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.71/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.71/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.71/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.71/1.01 % set(auto2) -> assign(stats, some).
% 0.71/1.01 % set(auto2) -> clear(echo_input).
% 0.71/1.01 % set(auto2) -> set(quiet).
% 0.71/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.71/1.01 % set(auto2) -> clear(print_given).
% 0.71/1.01 assign(lrs_ticks,-1).
% 0.71/1.01 assign(sos_limit,10000).
% 0.71/1.01 assign(order,kbo).
% 0.71/1.01 set(lex_order_vars).
% 0.71/1.01 clear(print_given).
% 0.71/1.01
% 0.71/1.01 % formulas(sos). % not echoed (17 formulas)
% 0.71/1.01
% 0.71/1.01 ============================== end of input ==========================
% 0.71/1.01
% 0.71/1.01 % From the command line: assign(max_seconds, 300).
% 0.71/1.01
% 0.71/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.71/1.01
% 0.71/1.01 % Formulas that are not ordinary clauses:
% 0.71/1.01
% 0.71/1.01 ============================== end of process non-clausal formulas ===
% 0.71/1.01
% 0.71/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.71/1.01
% 0.71/1.01 ============================== PREDICATE ELIMINATION =================
% 0.71/1.01
% 0.71/1.01 ============================== end predicate elimination =============
% 0.71/1.01
% 0.71/1.01 Auto_denials:
% 0.71/1.01 % copying label prove_alternative_wajsberg_axiom to answer in negative clause
% 0.71/1.01
% 0.71/1.01 Term ordering decisions:
% 0.71/1.01
% 0.71/1.01 % Assigning unary symbol not kb_weight 0 and highest precedence (10).
% 0.71/1.01 Function symbol KB weights: truth=1. falsehood=1. x=1. implies=1. or=1. and=1. and_star=1. xor=1. not=0.
% 0.71/1.01
% 0.71/1.01 ============================== end of process initial clauses ========
% 0.71/1.01
% 0.71/1.01 ============================== CLAUSES FOR SEARCH ====================
% 0.71/1.01
% 0.71/1.01 ============================== end of clauses for search =============
% 0.71/1.01
% 0.71/1.01 ============================== SEARCH ================================
% 0.71/1.01
% 0.71/1.01 % Starting search at 0.01 seconds.
% 0.71/1.01
% 0.71/1.01 ============================== 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 0.06 (+ 0.00) seconds: prove_alternative_wajsberg_axiom.
% 0.71/1.01 % Length of proof is 42.
% 0.71/1.01 % Level of proof is 11.
% 0.71/1.01 % Maximum clause weight is 27.000.
% 0.71/1.01 % Given clauses 33.
% 0.71/1.01
% 0.71/1.01 1 not(truth) = falsehood # label(false_definition) # label(axiom). [assumption].
% 0.71/1.01 2 falsehood = not(truth). [copy(1),flip(a)].
% 0.71/1.01 3 implies(truth,A) = A # label(wajsberg_1) # label(axiom). [assumption].
% 0.71/1.01 4 or(A,B) = or(B,A) # label(or_commutativity) # label(axiom). [assumption].
% 0.71/1.01 5 and(A,B) = and(B,A) # label(and_commutativity) # label(axiom). [assumption].
% 0.71/1.01 7 and_star(A,B) = and_star(B,A) # label(and_star_commutativity) # label(axiom). [assumption].
% 0.71/1.01 8 or(A,B) = implies(not(A),B) # label(or_definition) # label(axiom). [assumption].
% 0.71/1.01 9 and(A,B) = not(or(not(A),not(B))) # label(and_definition) # label(axiom). [assumption].
% 0.71/1.01 10 and(A,B) = not(implies(not(not(A)),not(B))). [copy(9),rewrite([8(4)])].
% 0.71/1.01 11 and_star(A,B) = not(or(not(A),not(B))) # label(and_star_definition) # label(axiom). [assumption].
% 0.71/1.01 12 and_star(A,B) = not(implies(not(not(A)),not(B))). [copy(11),rewrite([8(4)])].
% 0.71/1.01 13 implies(implies(A,B),B) = implies(implies(B,A),A) # label(wajsberg_3) # label(axiom). [assumption].
% 0.71/1.01 14 implies(implies(not(A),not(B)),implies(B,A)) = truth # label(wajsberg_4) # label(axiom). [assumption].
% 0.71/1.01 15 or(or(A,B),C) = or(A,or(B,C)) # label(or_associativity) # label(axiom). [assumption].
% 0.71/1.01 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)].
% 0.71/1.01 20 implies(implies(A,B),implies(implies(B,C),implies(A,C))) = truth # label(wajsberg_2) # label(axiom). [assumption].
% 0.71/1.01 21 xor(A,B) = or(and(A,not(B)),and(not(A),B)) # label(xor_definition) # label(axiom). [assumption].
% 0.71/1.01 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)])].
% 0.71/1.01 23 and_star(xor(truth,x),x) != falsehood # label(prove_alternative_wajsberg_axiom) # label(negated_conjecture) # answer(prove_alternative_wajsberg_axiom). [assumption].
% 0.71/1.01 24 not(implies(not(not(x)),not(implies(not(not(implies(not(not(truth)),not(not(x))))),not(implies(not(not(x)),not(not(truth)))))))) != not(truth) # answer(prove_alternative_wajsberg_axiom). [copy(23),rewrite([22(3),7(20),12(20),2(25)])].
% 0.71/1.01 25 implies(not(A),B) = implies(not(B),A). [back_rewrite(4),rewrite([8(1),8(3)])].
% 0.71/1.01 26 implies(implies(A,truth),truth) = implies(A,A). [para(3(a,1),13(a,1,1)),flip(a)].
% 0.71/1.01 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)].
% 0.71/1.01 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)].
% 0.71/1.01 67 implies(A,implies(implies(A,B),B)) = truth. [para(3(a,1),20(a,1,1)),rewrite([3(3)])].
% 0.71/1.01 68 implies(implies(A,truth),implies(B,implies(A,B))) = truth. [para(3(a,1),20(a,1,2,1))].
% 0.71/1.01 131 implies(A,A) = truth. [para(67(a,1),3(a,1)),rewrite([3(3)]),flip(a)].
% 0.71/1.01 143 implies(A,truth) = truth. [para(26(a,1),67(a,1,2)),rewrite([131(1)])].
% 0.71/1.01 151 implies(A,implies(B,A)) = truth. [back_rewrite(68),rewrite([143(2),3(4)])].
% 0.71/1.01 152 implies(not(not(A)),implies(not(B),A)) = truth. [para(131(a,1),16(a,1,2)),rewrite([143(3)]),flip(a)].
% 0.71/1.01 155 implies(implies(implies(A,B),B),A) = implies(B,A). [para(27(a,1),13(a,1)),rewrite([151(5),3(6)])].
% 0.71/1.01 186 implies(A,implies(not(A),B)) = truth. [para(25(a,1),151(a,1,2))].
% 0.71/1.01 201 implies(not(A),not(truth)) = A. [para(3(a,1),29(a,1,1,1)),rewrite([186(5),3(6),3(6)])].
% 0.71/1.01 218 implies(implies(not(truth),not(A)),not(A)) = implies(A,not(truth)). [para(201(a,1),13(a,1,1)),flip(a)].
% 0.71/1.01 242 implies(not(A),not(not(truth))) = truth. [para(201(a,1),152(a,1,2)),rewrite([25(5)])].
% 0.71/1.01 245 not(implies(not(not(x)),not(implies(not(not(truth)),not(implies(not(not(truth)),not(not(x)))))))) != not(truth) # answer(prove_alternative_wajsberg_axiom). [back_rewrite(24),rewrite([242(19),25(15)])].
% 0.71/1.01 246 not(not(truth)) = truth. [para(242(a,1),13(a,1,1)),rewrite([3(5),25(8),201(8),131(6)])].
% 0.71/1.01 249 not(implies(not(not(x)),not(not(not(not(x)))))) != not(truth) # answer(prove_alternative_wajsberg_axiom). [back_rewrite(245),rewrite([246(6),246(7),3(9),3(9)])].
% 0.71/1.01 271 implies(implies(A,not(truth)),not(truth)) = A. [para(201(a,1),155(a,2)),rewrite([218(6)])].
% 0.71/1.01 275 implies(A,not(truth)) = not(A). [para(25(a,1),271(a,1,1)),rewrite([246(3),3(2)])].
% 0.71/1.01 277 not(not(A)) = A. [para(271(a,1),29(a,2)),rewrite([275(3),275(4),246(5),275(6),3(6),131(5),246(4),275(5),3(5),3(4)])].
% 0.71/1.01 291 $F # answer(prove_alternative_wajsberg_axiom). [back_rewrite(249),rewrite([277(3),277(4),277(4),131(3)]),xx(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=33. Generated=1011. Kept=282. proofs=1.
% 0.71/1.01 Usable=23. Sos=137. Demods=130. Limbo=14, Disabled=125. Hints=0.
% 0.71/1.01 Megabytes=0.38.
% 0.71/1.01 User_CPU=0.06, 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 20492 exit (max_proofs) Sat Jul 2 19:01:41 2022
% 0.71/1.01 Prover9 interrupted
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