TSTP Solution File: BOO002-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 23:47:56 EDT 2022
% Result : Unsatisfiable 6.95s 7.24s
% Output : Refutation 6.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : BOO002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 1 19:39:40 EDT 2022
% 0.13/0.35 % CPUTime :
% 3.92/4.26 ============================== Prover9 ===============================
% 3.92/4.26 Prover9 (32) version 2009-11A, November 2009.
% 3.92/4.26 Process 26133 was started by sandbox on n019.cluster.edu,
% 3.92/4.26 Wed Jun 1 19:39:41 2022
% 3.92/4.26 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_25980_n019.cluster.edu".
% 3.92/4.26 ============================== end of head ===========================
% 3.92/4.26
% 3.92/4.26 ============================== INPUT =================================
% 3.92/4.26
% 3.92/4.26 % Reading from file /tmp/Prover9_25980_n019.cluster.edu
% 3.92/4.26
% 3.92/4.26 set(prolog_style_variables).
% 3.92/4.26 set(auto2).
% 3.92/4.26 % set(auto2) -> set(auto).
% 3.92/4.26 % set(auto) -> set(auto_inference).
% 3.92/4.26 % set(auto) -> set(auto_setup).
% 3.92/4.26 % set(auto_setup) -> set(predicate_elim).
% 3.92/4.26 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.92/4.26 % set(auto) -> set(auto_limits).
% 3.92/4.26 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.92/4.26 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.92/4.26 % set(auto) -> set(auto_denials).
% 3.92/4.26 % set(auto) -> set(auto_process).
% 3.92/4.26 % set(auto2) -> assign(new_constants, 1).
% 3.92/4.26 % set(auto2) -> assign(fold_denial_max, 3).
% 3.92/4.26 % set(auto2) -> assign(max_weight, "200.000").
% 3.92/4.26 % set(auto2) -> assign(max_hours, 1).
% 3.92/4.26 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.92/4.26 % set(auto2) -> assign(max_seconds, 0).
% 3.92/4.26 % set(auto2) -> assign(max_minutes, 5).
% 3.92/4.26 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.92/4.26 % set(auto2) -> set(sort_initial_sos).
% 3.92/4.26 % set(auto2) -> assign(sos_limit, -1).
% 3.92/4.26 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.92/4.26 % set(auto2) -> assign(max_megs, 400).
% 3.92/4.26 % set(auto2) -> assign(stats, some).
% 3.92/4.26 % set(auto2) -> clear(echo_input).
% 3.92/4.26 % set(auto2) -> set(quiet).
% 3.92/4.26 % set(auto2) -> clear(print_initial_clauses).
% 3.92/4.26 % set(auto2) -> clear(print_given).
% 3.92/4.26 assign(lrs_ticks,-1).
% 3.92/4.26 assign(sos_limit,10000).
% 3.92/4.26 assign(order,kbo).
% 3.92/4.26 set(lex_order_vars).
% 3.92/4.26 clear(print_given).
% 3.92/4.26
% 3.92/4.26 % formulas(sos). % not echoed (5 formulas)
% 3.92/4.26
% 3.92/4.26 ============================== end of input ==========================
% 3.92/4.26
% 3.92/4.26 % From the command line: assign(max_seconds, 300).
% 3.92/4.26
% 3.92/4.26 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.92/4.26
% 3.92/4.26 % Formulas that are not ordinary clauses:
% 3.92/4.26
% 3.92/4.26 ============================== end of process non-clausal formulas ===
% 3.92/4.26
% 3.92/4.26 ============================== PROCESS INITIAL CLAUSES ===============
% 3.92/4.26
% 3.92/4.26 ============================== PREDICATE ELIMINATION =================
% 3.92/4.26
% 3.92/4.26 ============================== end predicate elimination =============
% 3.92/4.26
% 3.92/4.26 Auto_denials:
% 3.92/4.26 % copying label prove_equation to answer in negative clause
% 3.92/4.26
% 3.92/4.26 Term ordering decisions:
% 3.92/4.26
% 3.92/4.26 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 3.92/4.26 Function symbol KB weights: a=1. b=1. multiply=1. inverse=0.
% 3.92/4.26
% 3.92/4.26 ============================== end of process initial clauses ========
% 3.92/4.26
% 3.92/4.26 ============================== CLAUSES FOR SEARCH ====================
% 3.92/4.26
% 3.92/4.26 ============================== end of clauses for search =============
% 3.92/4.26
% 3.92/4.26 ============================== SEARCH ================================
% 3.92/4.26
% 3.92/4.26 % Starting search at 0.01 seconds.
% 3.92/4.26
% 3.92/4.26 Low Water (keep): wt=52.000, iters=3375
% 3.92/4.26
% 3.92/4.26 Low Water (keep): wt=49.000, iters=3384
% 3.92/4.26
% 3.92/4.26 Low Water (keep): wt=48.000, iters=3493
% 3.92/4.26
% 3.92/4.26 Low Water (keep): wt=46.000, iters=3380
% 3.92/4.26
% 3.92/4.26 Low Water (keep): wt=45.000, iters=3466
% 3.92/4.26
% 3.92/4.26 Low Water (keep): wt=44.000, iters=3345
% 3.92/4.26
% 3.92/4.26 Low Water (keep): wt=43.000, iters=3336
% 3.92/4.26
% 3.92/4.26 Low Water (keep): wt=42.000, iters=3336
% 3.92/4.26
% 3.92/4.26 Low Water (keep): wt=41.000, iters=3361
% 3.92/4.26
% 3.92/4.26 Low Water (keep): wt=40.000, iters=3336
% 3.92/4.26
% 3.92/4.26 Low Water (keep): wt=39.000, iters=3408
% 3.92/4.26
% 3.92/4.26 Low Water (keep): wt=37.000, iters=3369
% 3.92/4.26
% 3.92/4.26 Low Water (keep): wt=36.000, iters=3340
% 3.92/4.26
% 3.92/4.26 Low Water (keep): wt=35.000, iters=3367
% 3.92/4.26
% 3.92/4.26 Low Water (keep): wt=34.000, iters=3485
% 3.92/4.26
% 3.92/4.26 Low Water (keep): wt=33.000, iters=3335
% 3.92/4.26
% 3.92/4.26 Low Water (displace): id=5477, wt=84.000
% 3.92/4.26
% 3.92/4.26 Low Water (displace): id=4919, wt=80.000
% 3.92/4.26
% 3.92/4.26 Low Water (displace): id=4991, wt=76.000
% 3.92/4.26
% 3.92/4.26 Low Water (displace): id=5508, wt=75.000
% 3.92/4.26
% 3.92/4.26 Low Water (displace): id=4477, wt=72.000
% 3.92/4.26
% 3.92/4.26 Low Water (displace): id=5016, wt=71.000
% 3.92/4.26
% 3.92/4.26 Low Water (displace): id=3980, wt=69.000
% 3.92/4.26
% 3.92/4.26 Low Water (displace): id=6067, wt=68.000
% 3.92/4.26
% 3.92/4.26 Low Water (displace): id=5509, wt=67.000
% 3.92/4.26
% 3.92/4.26 Low Water (displace): id=5732, wt=66.000
% 3.92/4.26
% 3.92/4.26 Low Water (displace): id=10790, wt=32.000
% 6.95/7.24
% 6.95/7.24 Low Water (displace): id=10793, wt=27.000
% 6.95/7.24
% 6.95/7.24 Low Water (displace): id=10798, wt=23.000
% 6.95/7.24
% 6.95/7.24 Low Water (displace): id=10800, wt=22.000
% 6.95/7.24
% 6.95/7.24 Low Water (displace): id=10821, wt=20.000
% 6.95/7.24
% 6.95/7.24 Low Water (keep): wt=32.000, iters=3336
% 6.95/7.24
% 6.95/7.24 Low Water (keep): wt=31.000, iters=3340
% 6.95/7.24
% 6.95/7.24 Low Water (keep): wt=30.000, iters=3340
% 6.95/7.24
% 6.95/7.24 Low Water (displace): id=13527, wt=18.000
% 6.95/7.24
% 6.95/7.24 Low Water (keep): wt=29.000, iters=3414
% 6.95/7.24
% 6.95/7.24 ============================== PROOF =================================
% 6.95/7.24 % SZS status Unsatisfiable
% 6.95/7.24 % SZS output start Refutation
% 6.95/7.24
% 6.95/7.24 % Proof 1 at 6.12 (+ 0.13) seconds: prove_equation.
% 6.95/7.24 % Length of proof is 29.
% 6.95/7.24 % Level of proof is 12.
% 6.95/7.24 % Maximum clause weight is 21.000.
% 6.95/7.24 % Given clauses 277.
% 6.95/7.24
% 6.95/7.24 1 multiply(A,B,B) = B # label(ternary_multiply_1) # label(axiom). [assumption].
% 6.95/7.24 2 multiply(A,A,B) = A # label(ternary_multiply_2) # label(axiom). [assumption].
% 6.95/7.24 3 multiply(inverse(A),A,B) = B # label(left_inverse) # label(axiom). [assumption].
% 6.95/7.24 4 multiply(multiply(A,B,C),D,multiply(A,B,E)) = multiply(A,B,multiply(C,D,E)) # label(associativity) # label(axiom). [assumption].
% 6.95/7.24 5 multiply(a,inverse(a),b) != b # label(prove_equation) # label(negated_conjecture) # answer(prove_equation). [assumption].
% 6.95/7.24 6 multiply(A,B,multiply(C,multiply(A,B,D),D)) = multiply(A,B,D). [para(4(a,1),1(a,1))].
% 6.95/7.24 8 multiply(multiply(A,B,C),D,B) = multiply(A,B,multiply(C,D,B)). [para(1(a,1),4(a,1,3))].
% 6.95/7.24 9 multiply(A,B,multiply(C,multiply(A,B,C),D)) = multiply(A,B,C). [para(4(a,1),2(a,1))].
% 6.95/7.24 10 multiply(A,B,A) = A. [para(2(a,1),4(a,1,1)),rewrite([2(1),2(3)])].
% 6.95/7.24 13 multiply(A,B,multiply(A,B,C)) = multiply(A,B,C). [para(2(a,1),6(a,1,3))].
% 6.95/7.24 18 multiply(A,B,multiply(A,C,D)) = multiply(A,C,multiply(A,B,D)). [para(10(a,1),4(a,1,1))].
% 6.95/7.24 19 multiply(multiply(A,B,C),D,A) = multiply(A,B,multiply(C,D,A)). [para(10(a,1),4(a,1,3))].
% 6.95/7.24 21 multiply(A,B,multiply(C,D,multiply(A,B,E))) = multiply(A,B,multiply(C,D,E)). [para(13(a,1),4(a,1,3)),rewrite([4(3)]),flip(a)].
% 6.95/7.24 46 multiply(A,B,multiply(A,C,B)) = multiply(A,C,B). [para(10(a,1),8(a,1,1)),flip(a)].
% 6.95/7.24 169 multiply(multiply(A,B,multiply(C,D,A)),E,D) = multiply(multiply(A,B,C),D,multiply(A,E,D)). [para(19(a,1),8(a,1,1))].
% 6.95/7.24 199 multiply(A,multiply(B,C,A),multiply(B,C,D)) = multiply(B,C,A). [para(9(a,1),21(a,1,3)),rewrite([1(3)]),flip(a)].
% 6.95/7.24 266 multiply(A,multiply(B,C,A),C) = multiply(B,C,A). [para(1(a,1),199(a,1,3))].
% 6.95/7.24 273 multiply(A,multiply(B,C,A),B) = multiply(B,C,A). [para(10(a,1),199(a,1,3))].
% 6.95/7.24 284 multiply(A,multiply(B,C,A),multiply(B,D,C)) = multiply(B,C,A). [para(46(a,1),199(a,1,3))].
% 6.95/7.24 371 multiply(A,multiply(B,C,A),multiply(A,D,B)) = multiply(A,D,multiply(B,C,A)). [para(273(a,1),18(a,1,3)),flip(a)].
% 6.95/7.24 373 multiply(A,multiply(B,C,A),multiply(B,D,A)) = multiply(multiply(B,C,A),D,A). [para(273(a,1),19(a,1,1)),flip(a)].
% 6.95/7.24 744 multiply(multiply(A,B,C),multiply(A,C,D),D) = multiply(A,C,D). [para(284(a,1),273(a,1,2)),rewrite([284(6)])].
% 6.95/7.24 1721 multiply(multiply(A,B,C),D,multiply(C,D,A)) = multiply(C,D,A). [para(266(a,1),744(a,1,2)),rewrite([169(4),266(3),266(5)])].
% 6.95/7.24 2058 multiply(multiply(A,B,C),D,multiply(B,D,C)) = multiply(B,D,C). [para(266(a,1),1721(a,1,1))].
% 6.95/7.24 2097 multiply(multiply(A,inverse(B),C),B,C) = C. [para(3(a,1),2058(a,1,3)),rewrite([3(5)])].
% 6.95/7.24 14384 multiply(multiply(A,B,C),D,C) = multiply(multiply(A,D,C),B,C). [para(273(a,1),371(a,1,3)),rewrite([373(3),373(5)])].
% 6.95/7.24 14521 multiply(multiply(A,B,C),inverse(B),C) = C. [para(14384(a,1),2097(a,1))].
% 6.95/7.24 14855 multiply(A,inverse(A),B) = B. [para(2(a,1),14521(a,1,1))].
% 6.95/7.24 14856 $F # answer(prove_equation). [resolve(14855,a,5,a)].
% 6.95/7.24
% 6.95/7.24 % SZS output end Refutation
% 6.95/7.24 ============================== end of proof ==========================
% 6.95/7.24
% 6.95/7.24 ============================== STATISTICS ============================
% 6.95/7.24
% 6.95/7.24 Given=277. Generated=216547. Kept=14855. proofs=1.
% 6.95/7.24 Usable=254. Sos=9999. Demods=9396. Limbo=0, Disabled=4606. Hints=0.
% 6.95/7.24 Megabytes=16.55.
% 6.95/7.24 User_CPU=6.12, System_CPU=0.13, Wall_clock=6.
% 6.95/7.24
% 6.95/7.24 ============================== end of statistics =====================
% 6.95/7.24
% 6.95/7.24 ============================== end of search =========================
% 6.95/7.24
% 6.95/7.24 THEOREM PROVED
% 6.95/7.24 % SZS status Unsatisfiable
% 6.95/7.24
% 6.95/7.24 Exiting with 1 proof.
% 6.95/7.24
% 6.95/7.24 Process 26133 exit (max_proofs) Wed Jun 1 19:39:47 2022
% 6.95/7.24 Prover9 interrupted
%------------------------------------------------------------------------------