TSTP Solution File: LDA002-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LDA002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 16:45:34 EDT 2022
% Result : Unsatisfiable 0.79s 1.12s
% Output : Refutation 0.79s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LDA002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon May 30 02:52:28 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.79/1.12 ============================== Prover9 ===============================
% 0.79/1.12 Prover9 (32) version 2009-11A, November 2009.
% 0.79/1.12 Process 19334 was started by sandbox on n021.cluster.edu,
% 0.79/1.12 Mon May 30 02:52:29 2022
% 0.79/1.12 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_19171_n021.cluster.edu".
% 0.79/1.12 ============================== end of head ===========================
% 0.79/1.12
% 0.79/1.12 ============================== INPUT =================================
% 0.79/1.12
% 0.79/1.12 % Reading from file /tmp/Prover9_19171_n021.cluster.edu
% 0.79/1.12
% 0.79/1.12 set(prolog_style_variables).
% 0.79/1.12 set(auto2).
% 0.79/1.12 % set(auto2) -> set(auto).
% 0.79/1.12 % set(auto) -> set(auto_inference).
% 0.79/1.12 % set(auto) -> set(auto_setup).
% 0.79/1.12 % set(auto_setup) -> set(predicate_elim).
% 0.79/1.12 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.79/1.12 % set(auto) -> set(auto_limits).
% 0.79/1.12 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.79/1.12 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.79/1.12 % set(auto) -> set(auto_denials).
% 0.79/1.12 % set(auto) -> set(auto_process).
% 0.79/1.12 % set(auto2) -> assign(new_constants, 1).
% 0.79/1.12 % set(auto2) -> assign(fold_denial_max, 3).
% 0.79/1.12 % set(auto2) -> assign(max_weight, "200.000").
% 0.79/1.12 % set(auto2) -> assign(max_hours, 1).
% 0.79/1.12 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.79/1.12 % set(auto2) -> assign(max_seconds, 0).
% 0.79/1.12 % set(auto2) -> assign(max_minutes, 5).
% 0.79/1.12 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.79/1.12 % set(auto2) -> set(sort_initial_sos).
% 0.79/1.12 % set(auto2) -> assign(sos_limit, -1).
% 0.79/1.12 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.79/1.12 % set(auto2) -> assign(max_megs, 400).
% 0.79/1.12 % set(auto2) -> assign(stats, some).
% 0.79/1.12 % set(auto2) -> clear(echo_input).
% 0.79/1.12 % set(auto2) -> set(quiet).
% 0.79/1.12 % set(auto2) -> clear(print_initial_clauses).
% 0.79/1.12 % set(auto2) -> clear(print_given).
% 0.79/1.12 assign(lrs_ticks,-1).
% 0.79/1.12 assign(sos_limit,10000).
% 0.79/1.12 assign(order,kbo).
% 0.79/1.12 set(lex_order_vars).
% 0.79/1.12 clear(print_given).
% 0.79/1.12
% 0.79/1.12 % formulas(sos). % not echoed (12 formulas)
% 0.79/1.12
% 0.79/1.12 ============================== end of input ==========================
% 0.79/1.12
% 0.79/1.12 % From the command line: assign(max_seconds, 300).
% 0.79/1.12
% 0.79/1.12 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.79/1.12
% 0.79/1.12 % Formulas that are not ordinary clauses:
% 0.79/1.12
% 0.79/1.12 ============================== end of process non-clausal formulas ===
% 0.79/1.12
% 0.79/1.12 ============================== PROCESS INITIAL CLAUSES ===============
% 0.79/1.12
% 0.79/1.12 ============================== PREDICATE ELIMINATION =================
% 0.79/1.12
% 0.79/1.12 ============================== end predicate elimination =============
% 0.79/1.12
% 0.79/1.12 Auto_denials:
% 0.79/1.12 % copying label prove_equation to answer in negative clause
% 0.79/1.12
% 0.79/1.12 Term ordering decisions:
% 0.79/1.12 Function symbol KB weights: n2=1. u=1. n1=1. n3=1. uu=1. u1=1. u2=1. u3=1. a=1. b=1. v=1. f=1.
% 0.79/1.12
% 0.79/1.12 ============================== end of process initial clauses ========
% 0.79/1.12
% 0.79/1.12 ============================== CLAUSES FOR SEARCH ====================
% 0.79/1.12
% 0.79/1.12 ============================== end of clauses for search =============
% 0.79/1.12
% 0.79/1.12 ============================== SEARCH ================================
% 0.79/1.12
% 0.79/1.12 % Starting search at 0.01 seconds.
% 0.79/1.12
% 0.79/1.12 ============================== PROOF =================================
% 0.79/1.12 % SZS status Unsatisfiable
% 0.79/1.12 % SZS output start Refutation
% 0.79/1.12
% 0.79/1.12 % Proof 1 at 0.03 (+ 0.00) seconds: prove_equation.
% 0.79/1.12 % Length of proof is 64.
% 0.79/1.12 % Level of proof is 12.
% 0.79/1.12 % Maximum clause weight is 15.000.
% 0.79/1.12 % Given clauses 99.
% 0.79/1.12
% 0.79/1.12 1 n2 = f(n1,n1) # label(clause_2) # label(axiom). [assumption].
% 0.79/1.12 2 f(n1,n1) = n2. [copy(1),flip(a)].
% 0.79/1.12 3 n3 = f(n2,n1) # label(clause_3) # label(axiom). [assumption].
% 0.79/1.12 4 f(n2,n1) = n3. [copy(3),flip(a)].
% 0.79/1.12 5 u = f(n2,n2) # label(clause_4) # label(axiom). [assumption].
% 0.79/1.12 6 f(n2,n2) = u. [copy(5),flip(a)].
% 0.79/1.12 7 u1 = f(u,n1) # label(clause_5) # label(axiom). [assumption].
% 0.79/1.12 8 f(u,n1) = u1. [copy(7),flip(a)].
% 0.79/1.12 9 u2 = f(u,n2) # label(clause_6) # label(axiom). [assumption].
% 0.79/1.12 10 f(u,n2) = u2. [copy(9),flip(a)].
% 0.79/1.12 11 u3 = f(u,n3) # label(clause_7) # label(axiom). [assumption].
% 0.79/1.12 12 f(u,n3) = u3. [copy(11),flip(a)].
% 0.79/1.12 13 uu = f(u,u) # label(clause_8) # label(axiom). [assumption].
% 0.79/1.12 14 f(u,u) = uu. [copy(13),flip(a)].
% 0.79/1.12 15 b = f(u1,u3) # label(clause_10) # label(axiom). [assumption].
% 0.79/1.12 16 f(u1,u3) = b. [copy(15),flip(a)].
% 0.79/1.12 17 v = f(uu,uu) # label(clause_11) # label(axiom). [assumption].
% 0.79/1.12 18 f(uu,uu) = v. [copy(17),flip(a)].
% 0.79/1.12 19 a = f(f(n3,n2),u2) # label(clause_9) # label(axiom). [assumption].
% 0.79/1.12 20 f(f(n3,n2),u2) = a. [copy(19),flip(a)].
% 0.79/1.12 21 f(A,f(B,C)) = f(f(A,B),f(A,C)) # label(a1) # label(axiom). [assumption].
% 0.79/1.12 22 f(f(A,B),f(A,C)) = f(A,f(B,C)). [copy(21),flip(a)].
% 0.79/1.12 23 f(a,v) != f(b,v) # label(prove_equation) # label(negated_conjecture) # answer(prove_equation). [assumption].
% 0.79/1.12 24 f(b,v) != f(a,v) # answer(prove_equation). [copy(23),flip(a)].
% 0.79/1.12 25 f(b,v) = c_0. [new_symbol(24)].
% 0.79/1.12 26 f(a,v) != c_0 # answer(prove_equation). [back_rewrite(24),rewrite([25(3)]),flip(a)].
% 0.79/1.12 27 f(n1,f(n1,A)) = f(n2,f(n1,A)). [para(2(a,1),22(a,1,1)),flip(a)].
% 0.79/1.12 29 f(n3,f(n2,A)) = f(n2,f(n1,A)). [para(4(a,1),22(a,1,1))].
% 0.79/1.12 31 f(u,f(n2,A)) = f(n2,f(n2,A)). [para(6(a,1),22(a,1,1))].
% 0.79/1.12 33 f(u1,f(u,A)) = f(u,f(n1,A)). [para(8(a,1),22(a,1,1))].
% 0.79/1.12 35 f(u2,f(u,A)) = f(n2,f(n2,A)). [para(10(a,1),22(a,1,1)),rewrite([31(8)])].
% 0.79/1.12 37 f(u3,f(u,A)) = f(u,f(n3,A)). [para(12(a,1),22(a,1,1))].
% 0.79/1.12 39 f(uu,f(u,A)) = f(u,f(u,A)). [para(14(a,1),22(a,1,1))].
% 0.79/1.12 41 f(b,f(u1,A)) = f(u1,f(u3,A)). [para(16(a,1),22(a,1,1))].
% 0.79/1.12 45 f(f(n3,n2),f(u2,A)) = f(a,f(f(n3,n2),A)). [para(20(a,1),22(a,1,1)),flip(a)].
% 0.79/1.12 51 f(n1,n2) = u. [para(2(a,1),27(a,1,2)),rewrite([2(7),6(6)])].
% 0.79/1.12 57 f(n1,u) = f(n2,u). [para(51(a,1),27(a,1,2)),rewrite([51(7)])].
% 0.79/1.12 68 f(n3,u) = f(n2,u). [para(6(a,1),29(a,1,2)),rewrite([51(7)])].
% 0.79/1.12 77 f(f(n3,A),f(n2,u)) = f(n3,f(A,u)). [para(68(a,1),22(a,1,2))].
% 0.79/1.12 95 f(n2,u) = uu. [para(6(a,1),31(a,1,2)),rewrite([14(3),6(5)]),flip(a)].
% 0.79/1.12 102 f(f(n3,A),uu) = f(n3,f(A,u)). [back_rewrite(77),rewrite([95(5)])].
% 0.79/1.12 104 f(n3,u) = uu. [back_rewrite(68),rewrite([95(6)])].
% 0.79/1.12 108 f(n1,u) = uu. [back_rewrite(57),rewrite([95(6)])].
% 0.79/1.12 111 f(n3,uu) = f(n2,uu). [para(95(a,1),29(a,1,2)),rewrite([108(7)])].
% 0.79/1.12 113 f(u,uu) = f(n2,uu). [para(95(a,1),31(a,1,2)),rewrite([95(7)])].
% 0.79/1.12 114 f(n1,uu) = f(n2,uu). [para(108(a,1),27(a,1,2)),rewrite([108(7)])].
% 0.79/1.12 121 f(f(n3,A),f(n2,uu)) = f(n3,f(A,uu)). [para(111(a,1),22(a,1,2))].
% 0.79/1.12 129 f(u1,uu) = f(n2,uu). [para(14(a,1),33(a,1,2)),rewrite([108(7),113(6)])].
% 0.79/1.12 135 f(u1,f(n2,uu)) = f(n2,f(n2,uu)). [para(113(a,1),33(a,1,2)),rewrite([114(9),31(10)])].
% 0.79/1.12 162 f(u2,uu) = f(n2,uu). [para(14(a,1),35(a,1,2)),rewrite([95(7)])].
% 0.79/1.12 206 f(u3,uu) = f(n2,uu). [para(14(a,1),37(a,1,2)),rewrite([104(7),113(6)])].
% 0.79/1.12 254 f(n2,uu) = v. [para(14(a,1),39(a,1,2)),rewrite([18(3),14(5),113(4)]),flip(a)].
% 0.79/1.12 263 f(u3,uu) = v. [back_rewrite(206),rewrite([254(6)])].
% 0.79/1.12 268 f(u2,uu) = v. [back_rewrite(162),rewrite([254(6)])].
% 0.79/1.12 275 f(u1,v) = f(n2,v). [back_rewrite(135),rewrite([254(4),254(7)])].
% 0.79/1.12 276 f(u1,uu) = v. [back_rewrite(129),rewrite([254(6)])].
% 0.79/1.12 279 f(f(n3,A),v) = f(n3,f(A,uu)). [back_rewrite(121),rewrite([254(5)])].
% 0.79/1.12 281 f(n1,uu) = v. [back_rewrite(114),rewrite([254(6)])].
% 0.79/1.12 283 f(n3,uu) = v. [back_rewrite(111),rewrite([254(6)])].
% 0.79/1.12 286 f(n3,v) = f(n2,v). [para(254(a,1),29(a,1,2)),rewrite([281(7)])].
% 0.79/1.12 306 f(n2,v) = c_0. [para(263(a,1),41(a,2,2)),rewrite([276(4),25(3),275(4)]),flip(a)].
% 0.79/1.12 312 f(n3,v) = c_0. [back_rewrite(286),rewrite([306(6)])].
% 0.79/1.12 390 f(a,v) = c_0. [para(268(a,1),45(a,1,2)),rewrite([279(5),254(4),312(3),102(7),95(6),283(5)]),flip(a)].
% 0.79/1.12 391 $F # answer(prove_equation). [resolve(390,a,26,a)].
% 0.79/1.12
% 0.79/1.12 % SZS output end Refutation
% 0.79/1.12 ============================== end of proof ==========================
% 0.79/1.12
% 0.79/1.12 ============================== STATISTICS ============================
% 0.79/1.12
% 0.79/1.12 Given=99. Generated=867. Kept=378. proofs=1.
% 0.79/1.12 Usable=90. Sos=234. Demods=330. Limbo=7, Disabled=58. Hints=0.
% 0.79/1.12 Megabytes=0.30.
% 0.79/1.12 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.79/1.12
% 0.79/1.12 ============================== end of statistics =====================
% 0.79/1.12
% 0.79/1.12 ============================== end of search =========================
% 0.79/1.12
% 0.79/1.12 THEOREM PROVED
% 0.79/1.12 % SZS status Unsatisfiable
% 0.79/1.12
% 0.79/1.12 Exiting with 1 proof.
% 0.79/1.12
% 0.79/1.12 Process 19334 exit (max_proofs) Mon May 30 02:52:29 2022
% 0.79/1.12 Prover9 interrupted
%------------------------------------------------------------------------------