TSTP Solution File: GRP116-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP116-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 : Sat Jul 16 11:17:13 EDT 2022
% Result : Unsatisfiable 0.74s 1.07s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP116-1 : TPTP v8.1.0. Released v1.2.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n007.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 : Mon Jun 13 18:10:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.74/1.07 ============================== Prover9 ===============================
% 0.74/1.07 Prover9 (32) version 2009-11A, November 2009.
% 0.74/1.07 Process 30536 was started by sandbox on n007.cluster.edu,
% 0.74/1.07 Mon Jun 13 18:10:54 2022
% 0.74/1.07 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_30381_n007.cluster.edu".
% 0.74/1.07 ============================== end of head ===========================
% 0.74/1.07
% 0.74/1.07 ============================== INPUT =================================
% 0.74/1.07
% 0.74/1.07 % Reading from file /tmp/Prover9_30381_n007.cluster.edu
% 0.74/1.07
% 0.74/1.07 set(prolog_style_variables).
% 0.74/1.07 set(auto2).
% 0.74/1.07 % set(auto2) -> set(auto).
% 0.74/1.07 % set(auto) -> set(auto_inference).
% 0.74/1.07 % set(auto) -> set(auto_setup).
% 0.74/1.07 % set(auto_setup) -> set(predicate_elim).
% 0.74/1.07 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.74/1.07 % set(auto) -> set(auto_limits).
% 0.74/1.07 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.74/1.07 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.74/1.07 % set(auto) -> set(auto_denials).
% 0.74/1.07 % set(auto) -> set(auto_process).
% 0.74/1.07 % set(auto2) -> assign(new_constants, 1).
% 0.74/1.07 % set(auto2) -> assign(fold_denial_max, 3).
% 0.74/1.07 % set(auto2) -> assign(max_weight, "200.000").
% 0.74/1.07 % set(auto2) -> assign(max_hours, 1).
% 0.74/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.74/1.07 % set(auto2) -> assign(max_seconds, 0).
% 0.74/1.07 % set(auto2) -> assign(max_minutes, 5).
% 0.74/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.74/1.07 % set(auto2) -> set(sort_initial_sos).
% 0.74/1.07 % set(auto2) -> assign(sos_limit, -1).
% 0.74/1.07 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.74/1.07 % set(auto2) -> assign(max_megs, 400).
% 0.74/1.07 % set(auto2) -> assign(stats, some).
% 0.74/1.07 % set(auto2) -> clear(echo_input).
% 0.74/1.07 % set(auto2) -> set(quiet).
% 0.74/1.07 % set(auto2) -> clear(print_initial_clauses).
% 0.74/1.07 % set(auto2) -> clear(print_given).
% 0.74/1.07 assign(lrs_ticks,-1).
% 0.74/1.07 assign(sos_limit,10000).
% 0.74/1.07 assign(order,kbo).
% 0.74/1.07 set(lex_order_vars).
% 0.74/1.07 clear(print_given).
% 0.74/1.07
% 0.74/1.07 % formulas(sos). % not echoed (2 formulas)
% 0.74/1.07
% 0.74/1.07 ============================== end of input ==========================
% 0.74/1.07
% 0.74/1.07 % From the command line: assign(max_seconds, 300).
% 0.74/1.07
% 0.74/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.74/1.07
% 0.74/1.07 % Formulas that are not ordinary clauses:
% 0.74/1.07
% 0.74/1.07 ============================== end of process non-clausal formulas ===
% 0.74/1.07
% 0.74/1.07 ============================== PROCESS INITIAL CLAUSES ===============
% 0.74/1.07
% 0.74/1.07 ============================== PREDICATE ELIMINATION =================
% 0.74/1.07
% 0.74/1.07 ============================== end predicate elimination =============
% 0.74/1.07
% 0.74/1.07 Auto_denials:
% 0.74/1.07 % copying label prove_order3 to answer in negative clause
% 0.74/1.07
% 0.74/1.07 Term ordering decisions:
% 0.74/1.07 Function symbol KB weights: identity=1. a=1. multiply=1.
% 0.74/1.07
% 0.74/1.07 ============================== end of process initial clauses ========
% 0.74/1.07
% 0.74/1.07 ============================== CLAUSES FOR SEARCH ====================
% 0.74/1.07
% 0.74/1.07 ============================== end of clauses for search =============
% 0.74/1.07
% 0.74/1.07 ============================== SEARCH ================================
% 0.74/1.07
% 0.74/1.07 % Starting search at 0.01 seconds.
% 0.74/1.07
% 0.74/1.07 ============================== PROOF =================================
% 0.74/1.07 % SZS status Unsatisfiable
% 0.74/1.07 % SZS output start Refutation
% 0.74/1.07
% 0.74/1.07 % Proof 1 at 0.08 (+ 0.01) seconds: prove_order3.
% 0.74/1.07 % Length of proof is 42.
% 0.74/1.07 % Level of proof is 18.
% 0.74/1.07 % Maximum clause weight is 49.000.
% 0.74/1.07 % Given clauses 18.
% 0.74/1.07
% 0.74/1.07 1 multiply(A,multiply(multiply(A,multiply(multiply(A,B),C)),multiply(identity,multiply(C,C)))) = B # label(single_axiom) # label(axiom). [assumption].
% 0.74/1.07 2 multiply(identity,a) != a # label(prove_order3) # label(negated_conjecture) # answer(prove_order3). [assumption].
% 0.74/1.07 3 multiply(multiply(A,multiply(multiply(A,B),C)),multiply(identity,multiply(C,C))) = multiply(A,multiply(multiply(A,multiply(B,D)),multiply(identity,multiply(D,D)))). [para(1(a,1),1(a,1,2,1,2,1)),flip(a)].
% 0.74/1.07 5 multiply(A,multiply(B,multiply(identity,multiply(multiply(identity,multiply(C,C)),multiply(identity,multiply(C,C)))))) = multiply(multiply(A,B),C). [para(1(a,1),1(a,1,2,1))].
% 0.74/1.07 10 multiply(A,multiply(A,multiply(multiply(A,multiply(B,C)),multiply(identity,multiply(C,C))))) = B. [para(3(a,1),1(a,1,2))].
% 0.74/1.07 11 multiply(multiply(A,multiply(B,C)),multiply(identity,multiply(C,C))) = multiply(A,multiply(multiply(A,multiply(multiply(multiply(A,multiply(multiply(A,B),D)),multiply(identity,multiply(D,D))),E)),multiply(identity,multiply(E,E)))). [para(3(a,2),1(a,1,2,1,2,1)),flip(a)].
% 0.74/1.07 14 multiply(multiply(A,multiply(multiply(A,multiply(A,B)),C)),multiply(identity,multiply(C,C))) = B. [para(3(a,2),1(a,1))].
% 0.74/1.07 18 multiply(multiply(A,multiply(multiply(A,B),C)),multiply(identity,multiply(C,C))) = multiply(A,multiply(multiply(A,D),multiply(identity,multiply(multiply(multiply(B,multiply(multiply(B,D),E)),multiply(identity,multiply(E,E))),multiply(multiply(B,multiply(multiply(B,D),E)),multiply(identity,multiply(E,E))))))). [para(1(a,1),3(a,2,2,1,2))].
% 0.74/1.07 24 multiply(multiply(A,multiply(multiply(multiply(A,multiply(multiply(A,B),C)),multiply(identity,multiply(C,C))),D)),multiply(identity,multiply(D,D))) = multiply(A,multiply(multiply(A,multiply(multiply(multiply(A,multiply(B,E)),multiply(identity,multiply(E,E))),F)),multiply(identity,multiply(F,F)))). [para(3(a,2),3(a,1,1,2,1))].
% 0.74/1.07 55 multiply(A,multiply(multiply(A,multiply(A,B)),C)) = multiply(D,multiply(multiply(D,multiply(D,B)),C)). [para(14(a,1),10(a,1,2,2,1,2)),rewrite([5(12)])].
% 0.74/1.07 71 multiply(A,multiply(multiply(A,multiply(A,multiply(multiply(B,multiply(C,D)),multiply(identity,multiply(D,D))))),E)) = multiply(B,multiply(C,E)). [para(3(a,2),55(a,1,2,1,2)),rewrite([1(8)]),flip(a)].
% 0.74/1.07 75 multiply(A,multiply(B,multiply(multiply(B,multiply(B,C)),multiply(identity,multiply(C,C))))) = A. [para(55(a,1),10(a,1,2))].
% 0.74/1.07 79 multiply(multiply(A,multiply(multiply(A,multiply(A,B)),C)),multiply(multiply(multiply(A,multiply(multiply(A,multiply(A,B)),C)),B),D)) = multiply(E,multiply(multiply(E,multiply(E,multiply(identity,multiply(C,C)))),D)). [para(14(a,1),55(a,1,2,1,2))].
% 0.74/1.07 83 multiply(A,multiply(multiply(A,multiply(A,B)),identity)) = B. [para(75(a,1),1(a,1,2,1,2)),rewrite([75(18),75(11)])].
% 0.74/1.07 88 multiply(A,multiply(multiply(A,multiply(B,C)),multiply(identity,multiply(C,C)))) = multiply(multiply(A,multiply(A,B)),identity). [para(75(a,1),3(a,1,1,2)),rewrite([75(18),75(11)]),flip(a)].
% 0.74/1.07 91 multiply(A,multiply(multiply(A,B),multiply(identity,multiply(identity,identity)))) = multiply(multiply(A,multiply(A,B)),identity). [para(75(a,1),3(a,1)),rewrite([88(15)])].
% 0.74/1.07 95 multiply(multiply(A,multiply(multiply(A,B),C)),multiply(identity,multiply(C,C))) = multiply(A,multiply(A,multiply(B,multiply(identity,multiply(identity,identity))))). [para(75(a,1),3(a,2,2))].
% 0.74/1.07 104 multiply(A,multiply(B,multiply(multiply(B,C),multiply(identity,multiply(multiply(multiply(B,multiply(B,C)),identity),multiply(multiply(B,multiply(B,C)),identity)))))) = A. [para(10(a,1),75(a,1,2,2,1,2)),rewrite([88(9),88(13)])].
% 0.74/1.07 106 multiply(multiply(A,multiply(A,A)),identity) = multiply(B,multiply(B,multiply(B,multiply(identity,multiply(identity,identity))))). [para(75(a,1),14(a,1,1,2,1,2)),rewrite([95(7),88(15)]),flip(a)].
% 0.74/1.07 138 multiply(A,multiply(identity,multiply(identity,identity))) = multiply(A,identity). [back_rewrite(24),rewrite([95(7),95(14),91(14),83(11),88(19),88(13),83(11)])].
% 0.74/1.07 145 multiply(multiply(A,multiply(B,C)),multiply(identity,multiply(C,C))) = multiply(A,multiply(A,multiply(A,multiply(multiply(A,multiply(B,identity)),identity)))). [back_rewrite(11),rewrite([95(13),138(12),95(16),138(15)])].
% 0.74/1.07 148 multiply(multiply(A,multiply(A,B)),identity) = multiply(A,multiply(A,multiply(B,identity))). [back_rewrite(3),rewrite([95(7),138(6),88(11)]),flip(a)].
% 0.74/1.07 149 multiply(A,multiply(A,multiply(A,multiply(B,identity)))) = B. [back_rewrite(1),rewrite([95(7),138(6)])].
% 0.74/1.07 171 multiply(A,multiply(multiply(A,B),multiply(identity,multiply(multiply(C,multiply(C,multiply(B,identity))),multiply(C,multiply(C,multiply(B,identity))))))) = multiply(A,multiply(A,multiply(C,identity))). [back_rewrite(18),rewrite([95(7),138(6),95(13),138(12),95(17),138(16)]),flip(a)].
% 0.74/1.07 173 multiply(A,multiply(A,multiply(A,identity))) = c_0. [new_symbol(106),rewrite([148(4)])].
% 0.74/1.07 181 multiply(A,c_0) = A. [back_rewrite(104),rewrite([148(6),148(10),171(14),173(4)])].
% 0.74/1.07 188 multiply(A,multiply(multiply(A,B),identity)) = multiply(A,multiply(A,multiply(B,identity))). [back_rewrite(91),rewrite([138(7),148(8)])].
% 0.74/1.07 205 multiply(multiply(A,multiply(B,C)),multiply(identity,multiply(C,C))) = multiply(A,multiply(B,identity)). [back_rewrite(145),rewrite([188(12),149(13)])].
% 0.74/1.07 220 multiply(A,multiply(multiply(A,multiply(A,multiply(B,multiply(C,identity)))),D)) = multiply(B,multiply(C,D)). [back_rewrite(71),rewrite([205(6)])].
% 0.74/1.07 232 multiply(identity,identity) = c_0. [para(138(a,1),173(a,1))].
% 0.74/1.07 254 multiply(A,multiply(multiply(A,A),B)) = multiply(identity,multiply(identity,B)). [para(173(a,1),79(a,2,2,1,2)),rewrite([148(4),149(5),148(4),149(5),181(7)])].
% 0.74/1.07 270 multiply(A,multiply(A,A)) = identity. [para(232(a,1),149(a,1,2,2,2)),rewrite([181(2)])].
% 0.74/1.07 272 multiply(A,multiply(multiply(A,multiply(A,B)),C)) = multiply(B,multiply(identity,C)). [para(270(a,1),55(a,1,2,1)),flip(a)].
% 0.74/1.07 275 c_0 = identity. [para(181(a,1),270(a,1,2)),rewrite([181(3)])].
% 0.74/1.07 313 multiply(multiply(A,multiply(B,identity)),multiply(identity,C)) = multiply(A,multiply(B,C)). [back_rewrite(220),rewrite([272(7)])].
% 0.74/1.07 329 multiply(A,identity) = A. [back_rewrite(181),rewrite([275(1)])].
% 0.74/1.07 343 multiply(multiply(A,B),multiply(identity,C)) = multiply(A,multiply(B,C)). [back_rewrite(313),rewrite([329(2)])].
% 0.74/1.07 353 multiply(A,multiply(multiply(B,C),multiply(C,C))) = multiply(A,B). [back_rewrite(205),rewrite([343(6),329(6)])].
% 0.74/1.07 360 multiply(A,multiply(A,multiply(A,B))) = B. [back_rewrite(149),rewrite([329(2)])].
% 0.74/1.07 376 multiply(identity,multiply(identity,A)) = A. [para(270(a,1),254(a,1,2)),rewrite([329(2),353(6)]),flip(a)].
% 0.74/1.07 378 multiply(identity,A) = A. [para(254(a,1),254(a,2,2)),rewrite([329(4),343(4),360(3),376(5)]),flip(a)].
% 0.74/1.07 379 $F # answer(prove_order3). [resolve(378,a,2,a)].
% 0.74/1.07
% 0.74/1.07 % SZS output end Refutation
% 0.74/1.07 ============================== end of proof ==========================
% 0.74/1.07
% 0.74/1.07 ============================== STATISTICS ============================
% 0.74/1.07
% 0.74/1.07 Given=18. Generated=682. Kept=378. proofs=1.
% 0.74/1.07 Usable=5. Sos=35. Demods=41. Limbo=2, Disabled=337. Hints=0.
% 0.74/1.07 Megabytes=0.49.
% 0.74/1.07 User_CPU=0.08, System_CPU=0.01, Wall_clock=1.
% 0.74/1.07
% 0.74/1.07 ============================== end of statistics =====================
% 0.74/1.07
% 0.74/1.07 ============================== end of search =========================
% 0.74/1.07
% 0.74/1.07 THEOREM PROVED
% 0.74/1.07 % SZS status Unsatisfiable
% 0.74/1.07
% 0.74/1.07 Exiting with 1 proof.
% 0.74/1.07
% 0.74/1.07 Process 30536 exit (max_proofs) Mon Jun 13 18:10:55 2022
% 0.74/1.07 Prover9 interrupted
%------------------------------------------------------------------------------