TSTP Solution File: ALG012-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ALG012-1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.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 : Thu Jul 14 17:53:36 EDT 2022
% Result : Unsatisfiable 2.66s 2.93s
% Output : Refutation 2.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG012-1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n020.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 : Tue Jun 7 22:56:21 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.66/2.93 ============================== Prover9 ===============================
% 2.66/2.93 Prover9 (32) version 2009-11A, November 2009.
% 2.66/2.93 Process 4782 was started by sandbox on n020.cluster.edu,
% 2.66/2.93 Tue Jun 7 22:56:22 2022
% 2.66/2.93 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4627_n020.cluster.edu".
% 2.66/2.93 ============================== end of head ===========================
% 2.66/2.93
% 2.66/2.93 ============================== INPUT =================================
% 2.66/2.93
% 2.66/2.93 % Reading from file /tmp/Prover9_4627_n020.cluster.edu
% 2.66/2.93
% 2.66/2.93 set(prolog_style_variables).
% 2.66/2.93 set(auto2).
% 2.66/2.93 % set(auto2) -> set(auto).
% 2.66/2.93 % set(auto) -> set(auto_inference).
% 2.66/2.93 % set(auto) -> set(auto_setup).
% 2.66/2.93 % set(auto_setup) -> set(predicate_elim).
% 2.66/2.93 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.66/2.93 % set(auto) -> set(auto_limits).
% 2.66/2.93 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.66/2.93 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.66/2.93 % set(auto) -> set(auto_denials).
% 2.66/2.93 % set(auto) -> set(auto_process).
% 2.66/2.93 % set(auto2) -> assign(new_constants, 1).
% 2.66/2.93 % set(auto2) -> assign(fold_denial_max, 3).
% 2.66/2.93 % set(auto2) -> assign(max_weight, "200.000").
% 2.66/2.93 % set(auto2) -> assign(max_hours, 1).
% 2.66/2.93 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.66/2.93 % set(auto2) -> assign(max_seconds, 0).
% 2.66/2.93 % set(auto2) -> assign(max_minutes, 5).
% 2.66/2.93 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.66/2.93 % set(auto2) -> set(sort_initial_sos).
% 2.66/2.93 % set(auto2) -> assign(sos_limit, -1).
% 2.66/2.93 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.66/2.93 % set(auto2) -> assign(max_megs, 400).
% 2.66/2.93 % set(auto2) -> assign(stats, some).
% 2.66/2.93 % set(auto2) -> clear(echo_input).
% 2.66/2.93 % set(auto2) -> set(quiet).
% 2.66/2.93 % set(auto2) -> clear(print_initial_clauses).
% 2.66/2.93 % set(auto2) -> clear(print_given).
% 2.66/2.93 assign(lrs_ticks,-1).
% 2.66/2.93 assign(sos_limit,10000).
% 2.66/2.93 assign(order,kbo).
% 2.66/2.93 set(lex_order_vars).
% 2.66/2.93 clear(print_given).
% 2.66/2.93
% 2.66/2.93 % formulas(sos). % not echoed (11 formulas)
% 2.66/2.93
% 2.66/2.93 ============================== end of input ==========================
% 2.66/2.93
% 2.66/2.93 % From the command line: assign(max_seconds, 300).
% 2.66/2.93
% 2.66/2.93 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.66/2.93
% 2.66/2.93 % Formulas that are not ordinary clauses:
% 2.66/2.93
% 2.66/2.93 ============================== end of process non-clausal formulas ===
% 2.66/2.93
% 2.66/2.93 ============================== PROCESS INITIAL CLAUSES ===============
% 2.66/2.93
% 2.66/2.93 ============================== PREDICATE ELIMINATION =================
% 2.66/2.93
% 2.66/2.93 ============================== end predicate elimination =============
% 2.66/2.93
% 2.66/2.93 Auto_denials: (non-Horn, no changes).
% 2.66/2.93
% 2.66/2.93 Term ordering decisions:
% 2.66/2.93 Function symbol KB weights: a1=1. a2=1. a3=1. f=1.
% 2.66/2.93
% 2.66/2.93 ============================== end of process initial clauses ========
% 2.66/2.93
% 2.66/2.93 ============================== CLAUSES FOR SEARCH ====================
% 2.66/2.93
% 2.66/2.93 ============================== end of clauses for search =============
% 2.66/2.93
% 2.66/2.93 ============================== SEARCH ================================
% 2.66/2.93
% 2.66/2.93 % Starting search at 0.01 seconds.
% 2.66/2.93
% 2.66/2.93 Low Water (keep): wt=48.000, iters=3337
% 2.66/2.93
% 2.66/2.93 Low Water (keep): wt=46.000, iters=3380
% 2.66/2.93
% 2.66/2.93 Low Water (keep): wt=40.000, iters=3338
% 2.66/2.93
% 2.66/2.93 Low Water (keep): wt=38.000, iters=3333
% 2.66/2.93
% 2.66/2.93 Low Water (keep): wt=34.000, iters=4797
% 2.66/2.93
% 2.66/2.93 Low Water (keep): wt=32.000, iters=3945
% 2.66/2.93
% 2.66/2.93 Low Water (keep): wt=30.000, iters=3336
% 2.66/2.93
% 2.66/2.93 ============================== PROOF =================================
% 2.66/2.93 % SZS status Unsatisfiable
% 2.66/2.93 % SZS output start Refutation
% 2.66/2.93
% 2.66/2.93 % Proof 1 at 1.92 (+ 0.03) seconds.
% 2.66/2.93 % Length of proof is 53.
% 2.66/2.93 % Level of proof is 16.
% 2.66/2.93 % Maximum clause weight is 24.000.
% 2.66/2.93 % Given clauses 277.
% 2.66/2.93
% 2.66/2.93 2 d1(a2) # label(partition_d1_not_empty) # label(hypothesis). [assumption].
% 2.66/2.93 3 d2(a3) # label(partition_d2_not_empty) # label(hypothesis). [assumption].
% 2.66/2.93 4 c(A) | d1(A) | d2(A) # label(partitions_union) # label(axiom). [assumption].
% 2.66/2.93 5 f(A,f(B,C)) = f(f(A,B),C) # label(f_is_associative) # label(axiom). [assumption].
% 2.66/2.93 6 f(f(A,B),C) = f(A,f(B,C)). [copy(5),flip(a)].
% 2.66/2.93 7 -c(A) | -d1(A) # label(partitions_exclusive_c_d1) # label(hypothesis). [assumption].
% 2.66/2.93 8 -c(A) | -d2(A) # label(partitions_exclusive_c_d2) # label(hypothesis). [assumption].
% 2.66/2.93 10 c(f(A,B)) | -d1(A) | -d1(B) # label(conjecture_2) # label(negated_conjecture). [assumption].
% 2.66/2.93 11 c(f(A,B)) | -d2(A) | -d2(B) # label(conjecture_3) # label(negated_conjecture). [assumption].
% 2.66/2.93 12 d2(f(A,B)) | d1(f(A,B)) | -c(A) | -c(B) # label(conjecture_1) # label(negated_conjecture). [assumption].
% 2.66/2.93 13 c(f(A,A)) | -d1(A). [factor(10,b,c)].
% 2.66/2.93 14 c(f(A,A)) | -d2(A). [factor(11,b,c)].
% 2.66/2.93 15 d2(f(A,A)) | d1(f(A,A)) | -c(A). [factor(12,c,d)].
% 2.66/2.93 16 -c(a2). [resolve(7,b,2,a)].
% 2.66/2.93 22 c(f(a2,A)) | -d1(A). [resolve(10,b,2,a)].
% 2.66/2.93 23 c(f(A,a2)) | -d1(A). [resolve(10,c,2,a)].
% 2.66/2.93 27 c(f(A,a3)) | -d2(A). [resolve(11,c,3,a)].
% 2.66/2.93 30 c(f(a2,a2)). [resolve(13,b,2,a)].
% 2.66/2.93 31 c(f(A,A)) | c(A) | d1(A). [resolve(14,b,4,c)].
% 2.66/2.93 32 c(f(a3,a3)). [resolve(14,b,3,a)].
% 2.66/2.93 34 d2(f(a2,f(a2,f(a2,a2)))) | d1(f(a2,f(a2,f(a2,a2)))). [resolve(30,a,15,c),rewrite([6(7),6(15)])].
% 2.66/2.93 36 d2(f(a2,f(a2,A))) | d1(f(a2,f(a2,A))) | -c(A). [resolve(30,a,12,c),rewrite([6(4),6(9)])].
% 2.66/2.93 45 c(f(A,a3)) | c(A) | d1(A). [resolve(27,b,4,c)].
% 2.66/2.93 48 c(f(A,A)) | c(A). [resolve(31,c,13,b),merge(c)].
% 2.66/2.93 51 c(A) | d2(f(A,f(A,B))) | d1(f(A,f(A,B))) | -c(B). [resolve(48,a,12,c),rewrite([6(3),6(6)])].
% 2.66/2.93 52 c(f(A,f(B,f(A,B)))) | c(f(A,B)). [para(6(a,1),48(a,1))].
% 2.66/2.93 66 c(f(A,a3)) | c(A) | c(f(a2,A)). [resolve(45,c,22,b)].
% 2.66/2.93 88 d1(f(a2,f(a2,f(a2,a2)))) | c(f(a2,f(a2,f(a2,f(a2,a3))))). [resolve(34,a,27,b),rewrite([6(17),6(16),6(15)])].
% 2.66/2.93 92 d1(f(a2,f(a2,f(a2,a2)))) | c(f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,a2)))))))). [resolve(34,a,14,b),rewrite([6(23),6(22),6(21)])].
% 2.66/2.93 128 c(f(A,f(B,a3))) | c(f(A,B)) | c(f(a2,f(A,B))). [para(6(a,1),66(a,1))].
% 2.66/2.93 143 c(f(A,f(B,f(C,f(A,f(B,C)))))) | c(f(A,f(B,C))). [para(6(a,1),52(a,1,2,2)),rewrite([6(5),6(8)])].
% 2.66/2.93 168 d2(f(a2,f(a2,f(a3,a3)))) | d1(f(a2,f(a2,f(a3,a3)))). [resolve(36,c,32,a)].
% 2.66/2.93 591 c(f(a2,f(a2,f(a2,f(a2,a3))))) | c(f(a2,f(a2,f(a2,f(a2,a2))))). [resolve(88,a,23,b),rewrite([6(19),6(18),6(17)])].
% 2.66/2.93 1234 c(f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,a2)))))))). [resolve(92,a,13,b),rewrite([6(31),6(30),6(29)]),merge(b)].
% 2.66/2.93 2538 d1(f(a2,f(a2,f(a3,a3)))) | -c(f(a2,f(a2,f(a3,a3)))). [resolve(168,a,8,b)].
% 2.66/2.93 6998 -d2(f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,a2)))))))). [ur(8,a,1234,a)].
% 2.66/2.93 6999 -d1(f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,a2)))))))). [ur(7,a,1234,a)].
% 2.66/2.93 7082 -c(f(a2,f(a2,f(a2,f(a2,f(a2,a2)))))). [ur(51,a,16,a,b,6998,a,c,6999,a)].
% 2.66/2.93 7092 -d1(f(a2,f(a2,f(a2,f(a2,a2))))). [ur(22,a,7082,a)].
% 2.66/2.93 7660 c(f(a2,f(a2,a2))). [resolve(143,a,7082,a)].
% 2.66/2.93 7678 d2(f(a2,f(a2,f(a2,f(a2,a2))))). [resolve(7660,a,36,c),unit_del(b,7092)].
% 2.66/2.93 7697 c(f(a2,f(a2,f(a2,f(a2,f(a2,a3)))))). [resolve(7678,a,27,b),rewrite([6(11),6(10),6(9),6(8)])].
% 2.66/2.93 7704 -c(f(a2,f(a2,f(a2,f(a2,a2))))). [resolve(7678,a,8,b)].
% 2.66/2.93 7717 c(f(a2,f(a2,f(a2,f(a2,a3))))). [back_unit_del(591),unit_del(b,7704)].
% 2.66/2.93 7883 -d2(f(a2,f(a2,f(a2,f(a2,a3))))). [ur(8,a,7717,a)].
% 2.66/2.93 7884 -d1(f(a2,f(a2,f(a2,f(a2,a3))))). [ur(7,a,7717,a)].
% 2.66/2.93 7900 -d2(f(a2,f(a2,f(a2,f(a2,f(a2,a3)))))). [ur(8,a,7697,a)].
% 2.66/2.93 7901 -d1(f(a2,f(a2,f(a2,f(a2,f(a2,a3)))))). [ur(7,a,7697,a)].
% 2.66/2.93 7915 -c(f(a2,f(a2,a3))). [ur(51,a,16,a,b,7883,a,c,7884,a)].
% 2.66/2.93 7992 -c(f(a2,f(a2,f(a2,a3)))). [ur(51,a,16,a,b,7900,a,c,7901,a)].
% 2.66/2.93 8001 c(f(a2,f(a2,f(a3,a3)))). [resolve(7992,a,128,c),rewrite([6(6)]),unit_del(b,7915)].
% 2.66/2.93 8003 d1(f(a2,f(a2,f(a3,a3)))). [back_unit_del(2538),unit_del(b,8001)].
% 2.66/2.93 8026 $F. [ur(7,a,8001,a),unit_del(a,8003)].
% 2.66/2.93
% 2.66/2.93 % SZS output end Refutation
% 2.66/2.93 ============================== end of proof ==========================
% 2.66/2.93
% 2.66/2.93 ============================== STATISTICS ============================
% 2.66/2.93
% 2.66/2.93 Given=277. Generated=23908. Kept=8024. proofs=1.
% 2.66/2.93 Usable=252. Sos=6787. Demods=1. Limbo=11, Disabled=985. Hints=0.
% 2.66/2.93 Megabytes=9.31.
% 2.66/2.93 User_CPU=1.92, System_CPU=0.03, Wall_clock=2.
% 2.66/2.93
% 2.66/2.93 ============================== end of statistics =====================
% 2.66/2.93
% 2.66/2.93 ============================== end of search =========================
% 2.66/2.93
% 2.66/2.93 THEOREM PROVED
% 2.66/2.93 % SZS status Unsatisfiable
% 2.66/2.93
% 2.66/2.93 Exiting with 1 proof.
% 2.66/2.93
% 2.66/2.93 Process 4782 exit (max_proofs) Tue Jun 7 22:56:24 2022
% 2.66/2.93 Prover9 interrupted
%------------------------------------------------------------------------------