TSTP Solution File: LCL146-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL146-1 : 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 13:44:21 EDT 2022
% Result : Unsatisfiable 0.68s 0.98s
% Output : Refutation 0.68s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL146-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % 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
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 3 18:27:02 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.68/0.97 ============================== Prover9 ===============================
% 0.68/0.97 Prover9 (32) version 2009-11A, November 2009.
% 0.68/0.97 Process 29131 was started by sandbox on n010.cluster.edu,
% 0.68/0.97 Sun Jul 3 18:27:03 2022
% 0.68/0.97 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_28978_n010.cluster.edu".
% 0.68/0.97 ============================== end of head ===========================
% 0.68/0.97
% 0.68/0.97 ============================== INPUT =================================
% 0.68/0.97
% 0.68/0.97 % Reading from file /tmp/Prover9_28978_n010.cluster.edu
% 0.68/0.97
% 0.68/0.97 set(prolog_style_variables).
% 0.68/0.97 set(auto2).
% 0.68/0.97 % set(auto2) -> set(auto).
% 0.68/0.97 % set(auto) -> set(auto_inference).
% 0.68/0.97 % set(auto) -> set(auto_setup).
% 0.68/0.97 % set(auto_setup) -> set(predicate_elim).
% 0.68/0.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.68/0.97 % set(auto) -> set(auto_limits).
% 0.68/0.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.68/0.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.68/0.97 % set(auto) -> set(auto_denials).
% 0.68/0.97 % set(auto) -> set(auto_process).
% 0.68/0.97 % set(auto2) -> assign(new_constants, 1).
% 0.68/0.97 % set(auto2) -> assign(fold_denial_max, 3).
% 0.68/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.68/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.68/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.68/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.68/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.68/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.68/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.68/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.68/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.68/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.68/0.98 % set(auto2) -> assign(stats, some).
% 0.68/0.98 % set(auto2) -> clear(echo_input).
% 0.68/0.98 % set(auto2) -> set(quiet).
% 0.68/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.68/0.98 % set(auto2) -> clear(print_given).
% 0.68/0.98 assign(lrs_ticks,-1).
% 0.68/0.98 assign(sos_limit,10000).
% 0.68/0.98 assign(order,kbo).
% 0.68/0.98 set(lex_order_vars).
% 0.68/0.98 clear(print_given).
% 0.68/0.98
% 0.68/0.98 % formulas(sos). % not echoed (9 formulas)
% 0.68/0.98
% 0.68/0.98 ============================== end of input ==========================
% 0.68/0.98
% 0.68/0.98 % From the command line: assign(max_seconds, 300).
% 0.68/0.98
% 0.68/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.68/0.98
% 0.68/0.98 % Formulas that are not ordinary clauses:
% 0.68/0.98
% 0.68/0.98 ============================== end of process non-clausal formulas ===
% 0.68/0.98
% 0.68/0.98 ============================== PROCESS INITIAL CLAUSES ===============
% 0.68/0.98
% 0.68/0.98 ============================== PREDICATE ELIMINATION =================
% 0.68/0.98 1 implies(A,B) != truth | ordered(A,B) # label(partial_order_definition2) # label(axiom). [assumption].
% 0.68/0.98 2 -ordered(A,B) | implies(A,B) = truth # label(partial_order_definition1) # label(axiom). [assumption].
% 0.68/0.98
% 0.68/0.98 ============================== end predicate elimination =============
% 0.68/0.98
% 0.68/0.98 Auto_denials:
% 0.68/0.98 % copying label prove_wajsberg_theorem to answer in negative clause
% 0.68/0.98
% 0.68/0.98 Term ordering decisions:
% 0.68/0.98
% 0.68/0.98 % Assigning unary symbol not kb_weight 0 and highest precedence (8).
% 0.68/0.98 Function symbol KB weights: truth=1. x=1. y=1. implies=1. big_V=1. big_hat=1. not=0.
% 0.68/0.98
% 0.68/0.98 ============================== end of process initial clauses ========
% 0.68/0.98
% 0.68/0.98 ============================== CLAUSES FOR SEARCH ====================
% 0.68/0.98
% 0.68/0.98 ============================== end of clauses for search =============
% 0.68/0.98
% 0.68/0.98 ============================== SEARCH ================================
% 0.68/0.98
% 0.68/0.98 % Starting search at 0.01 seconds.
% 0.68/0.98
% 0.68/0.98 ============================== PROOF =================================
% 0.68/0.98 % SZS status Unsatisfiable
% 0.68/0.98 % SZS output start Refutation
% 0.68/0.98
% 0.68/0.98 % Proof 1 at 0.03 (+ 0.00) seconds: prove_wajsberg_theorem.
% 0.68/0.98 % Length of proof is 29.
% 0.68/0.98 % Level of proof is 13.
% 0.68/0.98 % Maximum clause weight is 19.000.
% 0.68/0.98 % Given clauses 30.
% 0.68/0.98
% 0.68/0.98 3 implies(truth,A) = A # label(wajsberg_1) # label(axiom). [assumption].
% 0.68/0.98 4 big_V(A,B) = implies(implies(A,B),B) # label(big_V_definition) # label(axiom). [assumption].
% 0.68/0.98 5 big_hat(A,B) = not(big_V(not(A),not(B))) # label(big_hat_definition) # label(axiom). [assumption].
% 0.68/0.98 6 big_hat(A,B) = not(implies(implies(not(A),not(B)),not(B))). [copy(5),rewrite([4(4)])].
% 0.68/0.98 7 implies(implies(A,B),B) = implies(implies(B,A),A) # label(wajsberg_3) # label(axiom). [assumption].
% 0.68/0.98 8 implies(implies(not(A),not(B)),implies(B,A)) = truth # label(wajsberg_4) # label(axiom). [assumption].
% 0.68/0.98 9 implies(implies(A,B),implies(implies(B,C),implies(A,C))) = truth # label(wajsberg_2) # label(axiom). [assumption].
% 0.68/0.98 10 not(big_hat(x,y)) != big_V(not(x),not(y)) # label(prove_wajsberg_theorem) # label(negated_conjecture) # answer(prove_wajsberg_theorem). [assumption].
% 0.68/0.98 11 not(not(implies(implies(not(x),not(y)),not(y)))) != implies(implies(not(x),not(y)),not(y)) # answer(prove_wajsberg_theorem). [copy(10),rewrite([6(3),4(15)])].
% 0.68/0.98 12 implies(implies(A,truth),truth) = implies(A,A). [para(3(a,1),7(a,1,1)),flip(a)].
% 0.68/0.98 13 implies(implies(implies(A,B),B),B) = implies(implies(implies(B,A),A),B). [para(7(a,1),4(a,2,1)),rewrite([4(2)])].
% 0.68/0.98 15 implies(implies(not(A),not(truth)),A) = truth. [para(3(a,1),8(a,1,2))].
% 0.68/0.98 19 implies(A,implies(implies(A,B),B)) = truth. [para(3(a,1),9(a,1,1)),rewrite([3(3)])].
% 0.68/0.98 20 implies(implies(A,truth),implies(B,implies(A,B))) = truth. [para(3(a,1),9(a,1,2,1))].
% 0.68/0.98 55 implies(A,A) = truth. [para(19(a,1),3(a,1)),rewrite([3(3)]),flip(a)].
% 0.68/0.98 64 implies(A,truth) = truth. [para(12(a,1),19(a,1,2)),rewrite([55(1)])].
% 0.68/0.98 65 implies(A,implies(B,A)) = truth. [back_rewrite(20),rewrite([64(2),3(4)])].
% 0.68/0.98 67 implies(implies(implies(A,B),B),A) = implies(B,A). [para(13(a,1),7(a,1)),rewrite([65(5),3(6)])].
% 0.68/0.98 83 implies(implies(implies(A,B),C),implies(B,C)) = truth. [para(65(a,1),9(a,1,1)),rewrite([3(6)])].
% 0.68/0.98 85 implies(not(truth),not(not(truth))) = not(not(truth)). [para(15(a,1),67(a,1,1)),rewrite([3(5)]),flip(a)].
% 0.68/0.98 107 implies(not(truth),A) = truth. [para(15(a,1),83(a,1,1)),rewrite([3(5)])].
% 0.68/0.98 115 not(not(truth)) = truth. [back_rewrite(85),rewrite([107(6)]),flip(a)].
% 0.68/0.98 116 implies(implies(A,not(truth)),not(truth)) = A. [para(107(a,1),7(a,1,1)),rewrite([3(2)]),flip(a)].
% 0.68/0.98 143 implies(not(implies(A,not(truth))),A) = truth. [para(116(a,1),8(a,1,2)),rewrite([115(3),3(6)])].
% 0.68/0.98 148 implies(A,implies(not(A),not(truth))) = truth. [para(143(a,1),8(a,1,1)),rewrite([3(7)])].
% 0.68/0.98 162 implies(not(A),not(truth)) = A. [para(148(a,1),7(a,1,1)),rewrite([3(6),15(9),3(6)])].
% 0.68/0.98 163 implies(A,not(truth)) = not(A). [para(162(a,1),7(a,1,1)),rewrite([107(7),3(6)])].
% 0.68/0.98 168 not(not(A)) = A. [para(162(a,1),67(a,2)),rewrite([107(4),3(3),163(4)])].
% 0.68/0.98 169 $F # answer(prove_wajsberg_theorem). [resolve(168,a,11,a)].
% 0.68/0.98
% 0.68/0.98 % SZS output end Refutation
% 0.68/0.98 ============================== end of proof ==========================
% 0.68/0.98
% 0.68/0.98 ============================== STATISTICS ============================
% 0.68/0.98
% 0.68/0.98 Given=30. Generated=906. Kept=164. proofs=1.
% 0.68/0.98 Usable=24. Sos=74. Demods=95. Limbo=5, Disabled=69. Hints=0.
% 0.68/0.98 Megabytes=0.20.
% 0.68/0.98 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.68/0.98
% 0.68/0.98 ============================== end of statistics =====================
% 0.68/0.98
% 0.68/0.98 ============================== end of search =========================
% 0.68/0.98
% 0.68/0.98 THEOREM PROVED
% 0.68/0.98 % SZS status Unsatisfiable
% 0.68/0.98
% 0.68/0.98 Exiting with 1 proof.
% 0.68/0.98
% 0.68/0.98 Process 29131 exit (max_proofs) Sun Jul 3 18:27:03 2022
% 0.68/0.98 Prover9 interrupted
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