TSTP Solution File: GRP512-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP512-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 11:19:24 EDT 2022
% Result : Unsatisfiable 0.75s 1.03s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP512-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n024.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 06:17:33 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.75/1.03 ============================== Prover9 ===============================
% 0.75/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.75/1.03 Process 8521 was started by sandbox on n024.cluster.edu,
% 0.75/1.03 Mon Jun 13 06:17:34 2022
% 0.75/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_8368_n024.cluster.edu".
% 0.75/1.03 ============================== end of head ===========================
% 0.75/1.03
% 0.75/1.03 ============================== INPUT =================================
% 0.75/1.03
% 0.75/1.03 % Reading from file /tmp/Prover9_8368_n024.cluster.edu
% 0.75/1.03
% 0.75/1.03 set(prolog_style_variables).
% 0.75/1.03 set(auto2).
% 0.75/1.03 % set(auto2) -> set(auto).
% 0.75/1.03 % set(auto) -> set(auto_inference).
% 0.75/1.03 % set(auto) -> set(auto_setup).
% 0.75/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.75/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.75/1.03 % set(auto) -> set(auto_limits).
% 0.75/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.75/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.75/1.03 % set(auto) -> set(auto_denials).
% 0.75/1.03 % set(auto) -> set(auto_process).
% 0.75/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.75/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.75/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.75/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.75/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.75/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.75/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.75/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.75/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.75/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.75/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.75/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.75/1.03 % set(auto2) -> assign(stats, some).
% 0.75/1.03 % set(auto2) -> clear(echo_input).
% 0.75/1.03 % set(auto2) -> set(quiet).
% 0.75/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.75/1.03 % set(auto2) -> clear(print_given).
% 0.75/1.03 assign(lrs_ticks,-1).
% 0.75/1.03 assign(sos_limit,10000).
% 0.75/1.03 assign(order,kbo).
% 0.75/1.03 set(lex_order_vars).
% 0.75/1.03 clear(print_given).
% 0.75/1.03
% 0.75/1.03 % formulas(sos). % not echoed (2 formulas)
% 0.75/1.03
% 0.75/1.03 ============================== end of input ==========================
% 0.75/1.03
% 0.75/1.03 % From the command line: assign(max_seconds, 300).
% 0.75/1.03
% 0.75/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.75/1.03
% 0.75/1.03 % Formulas that are not ordinary clauses:
% 0.75/1.03
% 0.75/1.03 ============================== end of process non-clausal formulas ===
% 0.75/1.03
% 0.75/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.75/1.03
% 0.75/1.03 ============================== PREDICATE ELIMINATION =================
% 0.75/1.03
% 0.75/1.03 ============================== end predicate elimination =============
% 0.75/1.03
% 0.75/1.03 Auto_denials:
% 0.75/1.03 % copying label prove_these_axioms_4 to answer in negative clause
% 0.75/1.03
% 0.75/1.03 Term ordering decisions:
% 0.75/1.03
% 0.75/1.03 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 0.75/1.03 Function symbol KB weights: a=1. b=1. multiply=1. inverse=0.
% 0.75/1.03
% 0.75/1.03 ============================== end of process initial clauses ========
% 0.75/1.03
% 0.75/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.75/1.03
% 0.75/1.03 ============================== end of clauses for search =============
% 0.75/1.03
% 0.75/1.03 ============================== SEARCH ================================
% 0.75/1.03
% 0.75/1.03 % Starting search at 0.01 seconds.
% 0.75/1.03
% 0.75/1.03 ============================== PROOF =================================
% 0.75/1.03 % SZS status Unsatisfiable
% 0.75/1.03 % SZS output start Refutation
% 0.75/1.03
% 0.75/1.03 % Proof 1 at 0.02 (+ 0.01) seconds: prove_these_axioms_4.
% 0.75/1.03 % Length of proof is 42.
% 0.75/1.03 % Level of proof is 14.
% 0.75/1.03 % Maximum clause weight is 19.000.
% 0.75/1.03 % Given clauses 23.
% 0.75/1.03
% 0.75/1.03 1 multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B # label(single_axiom) # label(axiom). [assumption].
% 0.75/1.03 2 multiply(a,b) != multiply(b,a) # label(prove_these_axioms_4) # label(negated_conjecture) # answer(prove_these_axioms_4). [assumption].
% 0.75/1.03 3 multiply(b,a) != multiply(a,b) # answer(prove_these_axioms_4). [copy(2),flip(a)].
% 0.75/1.03 4 multiply(b,a) = c_0. [new_symbol(3)].
% 0.75/1.03 5 multiply(a,b) != c_0 # answer(prove_these_axioms_4). [back_rewrite(3),rewrite([4(3)]),flip(a)].
% 0.75/1.03 6 multiply(multiply(A,B),inverse(multiply(multiply(multiply(C,A),D),B))) = inverse(multiply(C,D)). [para(1(a,1),1(a,1,1,1))].
% 0.75/1.03 7 multiply(A,inverse(multiply(multiply(B,A),inverse(multiply(B,C))))) = C. [para(1(a,1),1(a,1,1))].
% 0.75/1.03 8 multiply(multiply(multiply(multiply(multiply(A,B),C),D),inverse(multiply(A,C))),inverse(B)) = D. [para(1(a,1),1(a,1,2,1))].
% 0.75/1.03 9 multiply(multiply(c_0,A),inverse(multiply(b,A))) = a. [para(4(a,1),1(a,1,1,1))].
% 0.75/1.03 10 multiply(multiply(multiply(b,A),a),inverse(c_0)) = A. [para(4(a,1),1(a,1,2,1))].
% 0.75/1.03 15 inverse(multiply(multiply(A,B),inverse(multiply(A,C)))) = multiply(multiply(C,D),inverse(multiply(B,D))). [para(1(a,1),6(a,1,2,1,1)),flip(a)].
% 0.75/1.03 24 multiply(multiply(c_0,a),inverse(c_0)) = a. [para(4(a,1),9(a,1,2,1))].
% 0.75/1.03 27 multiply(a,inverse(multiply(c_0,inverse(c_0)))) = a. [para(24(a,1),1(a,1,1))].
% 0.75/1.03 38 multiply(multiply(A,inverse(c_0)),inverse(A)) = inverse(c_0). [para(10(a,1),6(a,1,2,1)),rewrite([4(8)])].
% 0.75/1.03 46 inverse(multiply(A,multiply(B,inverse(multiply(multiply(A,B),C))))) = C. [para(7(a,1),6(a,1)),flip(a)].
% 0.75/1.03 54 multiply(inverse(multiply(c_0,inverse(c_0))),inverse(multiply(a,inverse(multiply(a,A))))) = A. [para(27(a,1),7(a,1,2,1,1))].
% 0.75/1.03 55 multiply(A,inverse(multiply(multiply(a,A),inverse(a)))) = inverse(multiply(c_0,inverse(c_0))). [para(27(a,1),7(a,1,2,1,2,1))].
% 0.75/1.03 59 inverse(multiply(multiply(A,B),inverse(multiply(A,C)))) = multiply(D,inverse(multiply(multiply(B,D),inverse(C)))). [para(7(a,1),7(a,1,2,1,2,1)),flip(a)].
% 0.75/1.03 65 inverse(multiply(A,inverse(A))) = multiply(multiply(inverse(c_0),B),inverse(multiply(inverse(c_0),B))). [para(38(a,1),6(a,1,2,1,1)),flip(a)].
% 0.75/1.03 66 multiply(multiply(A,inverse(multiply(B,A))),inverse(inverse(c_0))) = inverse(multiply(B,inverse(c_0))). [para(38(a,1),6(a,1,2,1))].
% 0.75/1.03 71 inverse(multiply(A,inverse(A))) = c_1. [new_symbol(65)].
% 0.75/1.03 74 multiply(A,inverse(multiply(multiply(a,A),inverse(a)))) = c_1. [back_rewrite(55),rewrite([71(12)])].
% 0.75/1.03 75 multiply(c_1,inverse(multiply(a,inverse(multiply(a,A))))) = A. [back_rewrite(54),rewrite([71(5)])].
% 0.75/1.03 80 multiply(multiply(multiply(A,B),inverse(A)),c_1) = B. [para(71(a,1),1(a,1,2))].
% 0.75/1.03 81 multiply(multiply(A,inverse(multiply(multiply(B,A),C))),c_1) = inverse(multiply(B,C)). [para(71(a,1),6(a,1,2))].
% 0.75/1.03 83 multiply(A,inverse(multiply(multiply(B,A),c_1))) = inverse(B). [para(71(a,1),7(a,1,2,1,2))].
% 0.75/1.03 84 multiply(A,c_1) = A. [para(71(a,1),7(a,1,2))].
% 0.75/1.03 86 multiply(A,inverse(multiply(B,A))) = inverse(B). [back_rewrite(83),rewrite([84(3)])].
% 0.75/1.03 88 multiply(A,inverse(multiply(multiply(B,A),C))) = inverse(multiply(B,C)). [back_rewrite(81),rewrite([84(6)])].
% 0.75/1.03 89 multiply(multiply(A,B),inverse(A)) = B. [back_rewrite(80),rewrite([84(5)])].
% 0.75/1.03 90 inverse(multiply(A,inverse(c_0))) = multiply(inverse(A),inverse(inverse(c_0))). [back_rewrite(66),rewrite([86(3)]),flip(a)].
% 0.75/1.03 91 multiply(A,inverse(A)) = c_1. [back_rewrite(74),rewrite([89(5)])].
% 0.75/1.03 94 inverse(multiply(multiply(A,B),inverse(multiply(A,C)))) = inverse(multiply(B,inverse(C))). [back_rewrite(59),rewrite([88(10)])].
% 0.75/1.03 97 inverse(multiply(A,inverse(multiply(A,B)))) = B. [back_rewrite(46),rewrite([88(4)])].
% 0.75/1.03 115 multiply(multiply(A,B),inverse(multiply(C,B))) = inverse(multiply(C,inverse(A))). [back_rewrite(15),rewrite([94(5)]),flip(a)].
% 0.75/1.03 116 multiply(c_1,A) = A. [back_rewrite(75),rewrite([97(7)])].
% 0.75/1.03 124 multiply(inverse(b),inverse(inverse(c_0))) = a. [back_rewrite(9),rewrite([115(6),90(5)])].
% 0.75/1.03 133 multiply(multiply(A,B),inverse(B)) = A. [para(91(a,1),8(a,1,1,1,1)),rewrite([116(2),97(4)])].
% 0.75/1.03 189 multiply(a,inverse(inverse(b))) = inverse(inverse(c_0)). [para(124(a,1),89(a,1,1))].
% 0.75/1.03 192 inverse(inverse(A)) = A. [para(91(a,1),133(a,1,1)),rewrite([116(4)])].
% 0.75/1.03 199 multiply(a,b) = c_0. [back_rewrite(189),rewrite([192(4),192(6)])].
% 0.75/1.03 200 $F # answer(prove_these_axioms_4). [resolve(199,a,5,a)].
% 0.75/1.03
% 0.75/1.03 % SZS output end Refutation
% 0.75/1.03 ============================== end of proof ==========================
% 0.75/1.03
% 0.75/1.03 ============================== STATISTICS ============================
% 0.75/1.03
% 0.75/1.03 Given=23. Generated=325. Kept=198. proofs=1.
% 0.75/1.03 Usable=12. Sos=47. Demods=63. Limbo=8, Disabled=132. Hints=0.
% 0.75/1.03 Megabytes=0.19.
% 0.75/1.03 User_CPU=0.02, System_CPU=0.01, Wall_clock=0.
% 0.75/1.03
% 0.75/1.03 ============================== end of statistics =====================
% 0.75/1.03
% 0.75/1.03 ============================== end of search =========================
% 0.75/1.03
% 0.75/1.03 THEOREM PROVED
% 0.75/1.03 % SZS status Unsatisfiable
% 0.75/1.03
% 0.75/1.03 Exiting with 1 proof.
% 0.75/1.03
% 0.75/1.03 Process 8521 exit (max_proofs) Mon Jun 13 06:17:34 2022
% 0.75/1.03 Prover9 interrupted
%------------------------------------------------------------------------------