TSTP Solution File: GRP433-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP433-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 11:19:04 EDT 2022
% Result : Unsatisfiable 0.80s 1.09s
% Output : Refutation 0.80s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP433-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 15:24:59 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.80/1.09 ============================== Prover9 ===============================
% 0.80/1.09 Prover9 (32) version 2009-11A, November 2009.
% 0.80/1.09 Process 26217 was started by sandbox on n013.cluster.edu,
% 0.80/1.09 Mon Jun 13 15:24:59 2022
% 0.80/1.09 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_26064_n013.cluster.edu".
% 0.80/1.09 ============================== end of head ===========================
% 0.80/1.09
% 0.80/1.09 ============================== INPUT =================================
% 0.80/1.09
% 0.80/1.09 % Reading from file /tmp/Prover9_26064_n013.cluster.edu
% 0.80/1.09
% 0.80/1.09 set(prolog_style_variables).
% 0.80/1.09 set(auto2).
% 0.80/1.09 % set(auto2) -> set(auto).
% 0.80/1.09 % set(auto) -> set(auto_inference).
% 0.80/1.09 % set(auto) -> set(auto_setup).
% 0.80/1.09 % set(auto_setup) -> set(predicate_elim).
% 0.80/1.09 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.80/1.09 % set(auto) -> set(auto_limits).
% 0.80/1.09 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.80/1.09 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.80/1.09 % set(auto) -> set(auto_denials).
% 0.80/1.09 % set(auto) -> set(auto_process).
% 0.80/1.09 % set(auto2) -> assign(new_constants, 1).
% 0.80/1.09 % set(auto2) -> assign(fold_denial_max, 3).
% 0.80/1.09 % set(auto2) -> assign(max_weight, "200.000").
% 0.80/1.09 % set(auto2) -> assign(max_hours, 1).
% 0.80/1.09 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.80/1.09 % set(auto2) -> assign(max_seconds, 0).
% 0.80/1.09 % set(auto2) -> assign(max_minutes, 5).
% 0.80/1.09 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.80/1.09 % set(auto2) -> set(sort_initial_sos).
% 0.80/1.09 % set(auto2) -> assign(sos_limit, -1).
% 0.80/1.09 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.80/1.09 % set(auto2) -> assign(max_megs, 400).
% 0.80/1.09 % set(auto2) -> assign(stats, some).
% 0.80/1.09 % set(auto2) -> clear(echo_input).
% 0.80/1.09 % set(auto2) -> set(quiet).
% 0.80/1.09 % set(auto2) -> clear(print_initial_clauses).
% 0.80/1.09 % set(auto2) -> clear(print_given).
% 0.80/1.09 assign(lrs_ticks,-1).
% 0.80/1.09 assign(sos_limit,10000).
% 0.80/1.09 assign(order,kbo).
% 0.80/1.09 set(lex_order_vars).
% 0.80/1.09 clear(print_given).
% 0.80/1.09
% 0.80/1.09 % formulas(sos). % not echoed (2 formulas)
% 0.80/1.09
% 0.80/1.09 ============================== end of input ==========================
% 0.80/1.09
% 0.80/1.09 % From the command line: assign(max_seconds, 300).
% 0.80/1.09
% 0.80/1.09 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.80/1.09
% 0.80/1.09 % Formulas that are not ordinary clauses:
% 0.80/1.09
% 0.80/1.09 ============================== end of process non-clausal formulas ===
% 0.80/1.09
% 0.80/1.09 ============================== PROCESS INITIAL CLAUSES ===============
% 0.80/1.09
% 0.80/1.09 ============================== PREDICATE ELIMINATION =================
% 0.80/1.09
% 0.80/1.09 ============================== end predicate elimination =============
% 0.80/1.09
% 0.80/1.09 Auto_denials:
% 0.80/1.09 % copying label prove_these_axioms_1 to answer in negative clause
% 0.80/1.09
% 0.80/1.09 Term ordering decisions:
% 0.80/1.09
% 0.80/1.09 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 0.80/1.09 Function symbol KB weights: a1=1. b1=1. multiply=1. inverse=0.
% 0.80/1.09
% 0.80/1.09 ============================== end of process initial clauses ========
% 0.80/1.09
% 0.80/1.09 ============================== CLAUSES FOR SEARCH ====================
% 0.80/1.09
% 0.80/1.09 ============================== end of clauses for search =============
% 0.80/1.09
% 0.80/1.09 ============================== SEARCH ================================
% 0.80/1.09
% 0.80/1.09 % Starting search at 0.01 seconds.
% 0.80/1.09
% 0.80/1.09 ============================== PROOF =================================
% 0.80/1.09 % SZS status Unsatisfiable
% 0.80/1.09 % SZS output start Refutation
% 0.80/1.09
% 0.80/1.09 % Proof 1 at 0.05 (+ 0.00) seconds: prove_these_axioms_1.
% 0.80/1.09 % Length of proof is 48.
% 0.80/1.09 % Level of proof is 17.
% 0.80/1.09 % Maximum clause weight is 34.000.
% 0.80/1.09 % Given clauses 35.
% 0.80/1.09
% 0.80/1.09 1 inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),multiply(D,inverse(D)))) = C # label(single_axiom) # label(axiom). [assumption].
% 0.80/1.09 2 multiply(inverse(a1),a1) != multiply(inverse(b1),b1) # label(prove_these_axioms_1) # label(negated_conjecture) # answer(prove_these_axioms_1). [assumption].
% 0.80/1.09 3 multiply(inverse(b1),b1) != multiply(inverse(a1),a1) # answer(prove_these_axioms_1). [copy(2),flip(a)].
% 0.80/1.09 4 inverse(multiply(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C),multiply(D,inverse(D)))) = multiply(E,inverse(E)). [para(1(a,1),1(a,1,1,1,1,1))].
% 0.80/1.09 8 inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C),multiply(D,inverse(D)))),E)),F),inverse(F)),multiply(V6,inverse(V6)))) = E. [para(4(a,2),1(a,1,1,1,1,1,1,1))].
% 0.80/1.09 9 inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C),multiply(D,inverse(D))))),E),F),multiply(V6,inverse(V6)))) = inverse(multiply(E,F)). [para(4(a,2),1(a,1,1,1,1,1,1))].
% 0.80/1.09 15 multiply(A,inverse(A)) = multiply(B,inverse(B)). [para(4(a,1),4(a,1))].
% 0.80/1.09 21 multiply(A,inverse(A)) = c_0. [new_symbol(15)].
% 0.80/1.09 32 inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C),c_0))),D),E),c_0)) = inverse(multiply(D,E)). [back_rewrite(9),rewrite([21(8),21(14)])].
% 0.80/1.09 33 inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C),c_0)),D)),E),inverse(E)),c_0)) = D. [back_rewrite(8),rewrite([21(8),21(16)])].
% 0.80/1.09 37 inverse(multiply(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C),c_0)) = c_0. [back_rewrite(4),rewrite([21(8),21(11)])].
% 0.80/1.09 38 inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),c_0)) = C. [back_rewrite(1),rewrite([21(7)])].
% 0.80/1.09 39 inverse(multiply(multiply(multiply(inverse(multiply(c_0,A)),B),inverse(B)),c_0)) = A. [back_rewrite(33),rewrite([37(9)])].
% 0.80/1.09 40 inverse(multiply(multiply(multiply(inverse(c_0),A),B),c_0)) = inverse(multiply(A,B)). [back_rewrite(32),rewrite([37(9)])].
% 0.80/1.09 46 inverse(multiply(multiply(c_0,inverse(inverse(inverse(multiply(c_0,A))))),c_0)) = A. [para(21(a,1),39(a,1,1,1,1))].
% 0.80/1.09 49 inverse(multiply(multiply(c_0,inverse(inverse(inverse(c_0)))),c_0)) = inverse(c_0). [para(21(a,1),46(a,1,1,1,2,1,1,1))].
% 0.80/1.09 51 multiply(multiply(multiply(c_0,inverse(inverse(inverse(c_0)))),c_0),inverse(c_0)) = c_0. [para(49(a,1),21(a,1,2))].
% 0.80/1.09 64 inverse(multiply(multiply(c_0,A),c_0)) = inverse(multiply(inverse(inverse(c_0)),A)). [para(21(a,1),40(a,1,1,1,1))].
% 0.80/1.09 65 inverse(multiply(A,inverse(multiply(inverse(c_0),A)))) = inverse(multiply(c_0,c_0)). [para(21(a,1),40(a,1,1,1)),flip(a)].
% 0.80/1.09 67 inverse(multiply(inverse(inverse(c_0)),inverse(inverse(inverse(multiply(c_0,A)))))) = A. [para(46(a,1),40(a,2)),rewrite([40(15),64(10)])].
% 0.80/1.09 70 inverse(multiply(inverse(inverse(c_0)),inverse(c_0))) = inverse(multiply(c_0,c_0)). [para(21(a,1),64(a,1,1,1)),flip(a)].
% 0.80/1.09 73 multiply(multiply(inverse(inverse(c_0)),inverse(c_0)),inverse(multiply(c_0,c_0))) = c_0. [para(70(a,1),21(a,1,2))].
% 0.80/1.09 85 inverse(multiply(inverse(c_0),c_0)) = c_0. [para(65(a,1),39(a,1,1,1,1,1)),rewrite([39(10)]),flip(a)].
% 0.80/1.09 90 multiply(multiply(inverse(c_0),c_0),c_0) = c_0. [para(85(a,1),21(a,1,2))].
% 0.80/1.09 100 inverse(multiply(multiply(inverse(c_0),multiply(c_0,inverse(inverse(inverse(c_0))))),c_0)) = c_0. [para(51(a,1),37(a,1,1,1,1,2,1,1)),rewrite([40(17)])].
% 0.80/1.09 101 inverse(multiply(multiply(inverse(multiply(multiply(A,B),inverse(c_0))),A),B)) = c_0. [para(37(a,1),40(a,1)),flip(a)].
% 0.80/1.09 136 inverse(multiply(multiply(multiply(inverse(multiply(c_0,A)),multiply(multiply(inverse(c_0),multiply(c_0,inverse(inverse(inverse(c_0))))),c_0)),c_0),c_0)) = A. [para(100(a,1),39(a,1,1,1,2))].
% 0.80/1.09 140 inverse(multiply(inverse(inverse(c_0)),multiply(c_0,inverse(inverse(inverse(c_0)))))) = c_0. [para(100(a,1),38(a,1,1,1,1,1)),rewrite([21(4),64(11)])].
% 0.80/1.09 141 multiply(multiply(inverse(inverse(c_0)),multiply(c_0,inverse(inverse(inverse(c_0))))),c_0) = c_0. [para(140(a,1),21(a,1,2))].
% 0.80/1.09 145 inverse(multiply(multiply(inverse(c_0),A),inverse(A))) = c_0. [para(21(a,1),101(a,1,1,1,1,1,1)),rewrite([21(4)])].
% 0.80/1.09 152 inverse(multiply(multiply(inverse(c_0),multiply(inverse(inverse(c_0)),inverse(c_0))),inverse(multiply(c_0,c_0)))) = c_0. [para(73(a,1),101(a,1,1,1,1,1,1)),rewrite([21(4)])].
% 0.80/1.09 202 inverse(multiply(inverse(inverse(c_0)),A)) = inverse(A). [para(145(a,1),38(a,1,1,1,1,1)),rewrite([21(4),64(5)])].
% 0.80/1.09 205 inverse(multiply(c_0,c_0)) = c_0. [para(145(a,1),101(a,1,1,1,1)),rewrite([21(4)])].
% 0.80/1.09 220 inverse(inverse(c_0)) = c_0. [back_rewrite(70),rewrite([202(7),205(7)])].
% 0.80/1.09 222 inverse(multiply(c_0,inverse(inverse(inverse(multiply(c_0,A)))))) = A. [back_rewrite(67),rewrite([220(3)])].
% 0.80/1.09 223 inverse(multiply(multiply(c_0,A),c_0)) = inverse(multiply(c_0,A)). [back_rewrite(64),rewrite([220(8)])].
% 0.80/1.09 228 inverse(c_0) = c_0. [back_rewrite(152),rewrite([220(5),21(6),205(8),90(6)])].
% 0.80/1.09 246 inverse(multiply(c_0,A)) = inverse(A). [back_rewrite(202),rewrite([228(2),228(2)])].
% 0.80/1.09 252 multiply(multiply(c_0,multiply(c_0,c_0)),c_0) = c_0. [back_rewrite(141),rewrite([228(2),228(2),228(4),228(4),228(4)])].
% 0.80/1.09 255 inverse(multiply(multiply(multiply(inverse(A),c_0),c_0),c_0)) = A. [back_rewrite(136),rewrite([246(3),228(3),228(5),228(5),228(5),252(8)])].
% 0.80/1.09 324 inverse(multiply(multiply(c_0,A),c_0)) = inverse(A). [back_rewrite(223),rewrite([246(8)])].
% 0.80/1.09 325 inverse(inverse(inverse(inverse(A)))) = A. [back_rewrite(222),rewrite([246(4),246(6)])].
% 0.80/1.09 354 multiply(inverse(inverse(inverse(A))),A) = c_0. [para(325(a,1),21(a,1,2))].
% 0.80/1.09 357 multiply(c_0,A) = A. [para(246(a,1),325(a,1,1,1,1)),rewrite([325(4)]),flip(a)].
% 0.80/1.09 371 inverse(multiply(A,c_0)) = inverse(A). [back_rewrite(324),rewrite([357(2)])].
% 0.80/1.09 395 inverse(inverse(A)) = A. [back_rewrite(255),rewrite([371(8),371(6),371(4)])].
% 0.80/1.09 406 multiply(inverse(A),A) = c_0. [back_rewrite(354),rewrite([395(2)])].
% 0.80/1.09 407 $F # answer(prove_these_axioms_1). [back_rewrite(3),rewrite([406(4),406(5)]),xx(a)].
% 0.80/1.09
% 0.80/1.09 % SZS output end Refutation
% 0.80/1.09 ============================== end of proof ==========================
% 0.80/1.09
% 0.80/1.09 ============================== STATISTICS ============================
% 0.80/1.09
% 0.80/1.09 Given=35. Generated=753. Kept=405. proofs=1.
% 0.80/1.09 Usable=2. Sos=36. Demods=39. Limbo=1, Disabled=368. Hints=0.
% 0.80/1.09 Megabytes=0.46.
% 0.80/1.09 User_CPU=0.06, System_CPU=0.00, Wall_clock=0.
% 0.80/1.09
% 0.80/1.09 ============================== end of statistics =====================
% 0.80/1.09
% 0.80/1.09 ============================== end of search =========================
% 0.80/1.09
% 0.80/1.09 THEOREM PROVED
% 0.80/1.09 % SZS status Unsatisfiable
% 0.80/1.09
% 0.80/1.09 Exiting with 1 proof.
% 0.80/1.09
% 0.80/1.09 Process 26217 exit (max_proofs) Mon Jun 13 15:24:59 2022
% 0.80/1.09 Prover9 interrupted
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