TSTP Solution File: GRP111-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP111-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 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 : Sat Jul 16 11:17:12 EDT 2022
% Result : Unsatisfiable 0.72s 1.06s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP111-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 00:48:54 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.72/1.06 ============================== Prover9 ===============================
% 0.72/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.72/1.06 Process 31267 was started by sandbox2 on n019.cluster.edu,
% 0.72/1.06 Tue Jun 14 00:48:55 2022
% 0.72/1.06 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_31114_n019.cluster.edu".
% 0.72/1.06 ============================== end of head ===========================
% 0.72/1.06
% 0.72/1.06 ============================== INPUT =================================
% 0.72/1.06
% 0.72/1.06 % Reading from file /tmp/Prover9_31114_n019.cluster.edu
% 0.72/1.06
% 0.72/1.06 set(prolog_style_variables).
% 0.72/1.06 set(auto2).
% 0.72/1.06 % set(auto2) -> set(auto).
% 0.72/1.06 % set(auto) -> set(auto_inference).
% 0.72/1.06 % set(auto) -> set(auto_setup).
% 0.72/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.72/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.72/1.06 % set(auto) -> set(auto_limits).
% 0.72/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.72/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.72/1.06 % set(auto) -> set(auto_denials).
% 0.72/1.06 % set(auto) -> set(auto_process).
% 0.72/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.72/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.72/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.72/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.72/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.72/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.72/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.72/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.72/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.72/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.72/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.72/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.72/1.06 % set(auto2) -> assign(stats, some).
% 0.72/1.06 % set(auto2) -> clear(echo_input).
% 0.72/1.06 % set(auto2) -> set(quiet).
% 0.72/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.72/1.06 % set(auto2) -> clear(print_given).
% 0.72/1.06 assign(lrs_ticks,-1).
% 0.72/1.06 assign(sos_limit,10000).
% 0.72/1.06 assign(order,kbo).
% 0.72/1.06 set(lex_order_vars).
% 0.72/1.06 clear(print_given).
% 0.72/1.06
% 0.72/1.06 % formulas(sos). % not echoed (3 formulas)
% 0.72/1.06
% 0.72/1.06 ============================== end of input ==========================
% 0.72/1.06
% 0.72/1.06 % From the command line: assign(max_seconds, 300).
% 0.72/1.06
% 0.72/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.72/1.06
% 0.72/1.06 % Formulas that are not ordinary clauses:
% 0.72/1.06
% 0.72/1.06 ============================== end of process non-clausal formulas ===
% 0.72/1.06
% 0.72/1.06 ============================== PROCESS INITIAL CLAUSES ===============
% 0.72/1.06
% 0.72/1.06 ============================== PREDICATE ELIMINATION =================
% 0.72/1.06
% 0.72/1.06 ============================== end predicate elimination =============
% 0.72/1.06
% 0.72/1.06 Auto_denials:
% 0.72/1.06 % copying label prove_these_axioms to answer in negative clause
% 0.72/1.06
% 0.72/1.06 Term ordering decisions:
% 0.72/1.06
% 0.72/1.06 % Assigning unary symbol inverse kb_weight 0 and highest precedence (13).
% 0.72/1.06 Function symbol KB weights: a1=1. a2=1. a3=1. a4=1. b1=1. b2=1. b3=1. b4=1. c3=1. double_divide=1. multiply=1. inverse=0.
% 0.72/1.06
% 0.72/1.06 ============================== end of process initial clauses ========
% 0.72/1.06
% 0.72/1.06 ============================== CLAUSES FOR SEARCH ====================
% 0.72/1.06
% 0.72/1.06 ============================== end of clauses for search =============
% 0.72/1.06
% 0.72/1.06 ============================== SEARCH ================================
% 0.72/1.06
% 0.72/1.06 % Starting search at 0.01 seconds.
% 0.72/1.06
% 0.72/1.06 ============================== PROOF =================================
% 0.72/1.06 % SZS status Unsatisfiable
% 0.72/1.06 % SZS output start Refutation
% 0.72/1.06
% 0.72/1.06 % Proof 1 at 0.09 (+ 0.01) seconds: prove_these_axioms.
% 0.72/1.06 % Length of proof is 46.
% 0.72/1.06 % Level of proof is 19.
% 0.72/1.06 % Maximum clause weight is 45.000.
% 0.72/1.06 % Given clauses 50.
% 0.72/1.06
% 0.72/1.06 1 multiply(A,B) = inverse(double_divide(B,A)) # label(multiply) # label(axiom). [assumption].
% 0.72/1.06 2 double_divide(inverse(double_divide(inverse(double_divide(A,inverse(B))),C)),double_divide(A,C)) = B # label(single_axiom) # label(axiom). [assumption].
% 0.72/1.06 3 multiply(inverse(a1),a1) != multiply(inverse(b1),b1) | multiply(multiply(inverse(b2),b2),a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) | multiply(a4,b4) != multiply(b4,a4) # label(prove_these_axioms) # label(negated_conjecture) # answer(prove_these_axioms). [assumption].
% 0.72/1.06 4 inverse(double_divide(b1,inverse(b1))) != inverse(double_divide(a1,inverse(a1))) | inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2 | inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))) | inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) # answer(prove_these_axioms). [copy(3),rewrite([1(4),1(9),1(15),1(18),1(24),1(27),1(32),1(34),1(39),1(43)]),flip(a),flip(c)].
% 0.72/1.06 5 double_divide(inverse(A),double_divide(inverse(double_divide(B,inverse(A))),double_divide(B,inverse(C)))) = C. [para(2(a,1),2(a,1,1,1))].
% 0.72/1.06 6 double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(A,inverse(B))),C)),inverse(D))),double_divide(A,C))),B) = D. [para(2(a,1),2(a,1,2))].
% 0.72/1.06 22 double_divide(inverse(double_divide(inverse(A),inverse(B))),A) = B. [para(6(a,1),6(a,1,1,1,1,1)),rewrite([2(9)])].
% 0.72/1.06 23 double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(A,inverse(B))),C)),inverse(D))),double_divide(A,C))),inverse(E))),B)),inverse(F))),D)),E) = F. [para(6(a,1),6(a,1,1,1,2))].
% 0.72/1.06 25 double_divide(inverse(A),double_divide(inverse(B),B)) = A. [para(22(a,1),2(a,1,1,1))].
% 0.72/1.06 35 double_divide(inverse(A),double_divide(inverse(inverse(B)),inverse(A))) = B. [para(22(a,1),22(a,1,1,1))].
% 0.72/1.06 40 double_divide(inverse(double_divide(inverse(A),A)),inverse(B)) = B. [para(25(a,1),22(a,1))].
% 0.72/1.06 63 double_divide(inverse(A),double_divide(inverse(A),B)) = B. [para(40(a,1),5(a,1,2,1,1)),rewrite([40(7)])].
% 0.72/1.06 75 double_divide(inverse(A),A) = double_divide(inverse(B),B). [para(25(a,1),63(a,1,2))].
% 0.72/1.06 76 double_divide(inverse(double_divide(inverse(A),A)),B) = inverse(B). [para(40(a,1),63(a,1,2))].
% 0.72/1.06 93 double_divide(inverse(A),A) = c_0. [new_symbol(75)].
% 0.72/1.06 96 double_divide(inverse(c_0),inverse(A)) = A. [back_rewrite(40),rewrite([93(2)])].
% 0.72/1.06 97 double_divide(inverse(c_0),A) = inverse(A). [back_rewrite(76),rewrite([93(2)])].
% 0.72/1.06 101 double_divide(inverse(A),c_0) = A. [back_rewrite(25),rewrite([93(3)])].
% 0.72/1.06 102 inverse(inverse(A)) = A. [back_rewrite(96),rewrite([97(4)])].
% 0.72/1.06 114 double_divide(inverse(A),double_divide(B,inverse(A))) = B. [back_rewrite(35),rewrite([102(3)])].
% 0.72/1.06 130 double_divide(inverse(double_divide(inverse(A),B)),A) = inverse(B). [para(102(a,1),22(a,1,1,1,2))].
% 0.72/1.06 131 double_divide(A,double_divide(A,B)) = B. [para(102(a,1),63(a,1,1)),rewrite([102(2)])].
% 0.72/1.06 132 double_divide(A,inverse(A)) = c_0. [para(102(a,1),93(a,1,1))].
% 0.72/1.06 133 inverse(double_divide(a2,inverse(c_0))) != a2 | inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))) | inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) # answer(prove_these_axioms). [back_rewrite(4),rewrite([132(4),132(6),132(10)]),xx(a)].
% 0.72/1.06 141 double_divide(A,c_0) = inverse(A). [para(102(a,1),101(a,1,1))].
% 0.72/1.06 143 inverse(c_0) = c_0. [para(97(a,1),93(a,1))].
% 0.72/1.06 144 inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))) | inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) # answer(prove_these_axioms). [back_rewrite(133),rewrite([143(3),141(3),102(3)]),xx(a)].
% 0.72/1.06 145 double_divide(c_0,A) = inverse(A). [back_rewrite(97),rewrite([143(2)])].
% 0.72/1.06 149 double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(A,inverse(B))),C)),inverse(D))),double_divide(A,C))),inverse(E))),B)),F)),D)),E) = inverse(F). [para(102(a,1),23(a,1,1,1,1,1,2))].
% 0.72/1.06 153 inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(A,inverse(B))),C)),inverse(D))),double_divide(A,C))),inverse(E))),B)) = double_divide(D,E). [para(132(a,1),23(a,1,1,1,1,1)),rewrite([143(2),145(2),102(2)]),flip(a)].
% 0.72/1.06 159 double_divide(inverse(double_divide(inverse(double_divide(double_divide(A,B),C)),A)),B) = inverse(C). [back_rewrite(149),rewrite([153(16)])].
% 0.72/1.06 161 double_divide(A,double_divide(B,A)) = B. [para(102(a,1),114(a,1,1)),rewrite([102(2)])].
% 0.72/1.06 162 double_divide(inverse(A),B) = double_divide(B,inverse(A)). [para(114(a,1),131(a,1,2))].
% 0.72/1.06 164 double_divide(A,inverse(double_divide(B,inverse(double_divide(double_divide(B,A),C))))) = inverse(C). [back_rewrite(159),rewrite([162(4),162(6)])].
% 0.72/1.06 176 inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(a3,inverse(double_divide(c3,b3)))) | inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) # answer(prove_these_axioms). [back_rewrite(144),rewrite([162(6)]),flip(a)].
% 0.72/1.06 184 double_divide(A,inverse(double_divide(B,inverse(A)))) = inverse(B). [back_rewrite(130),rewrite([162(2),162(4)])].
% 0.72/1.06 216 double_divide(A,B) = double_divide(B,A). [para(161(a,1),131(a,1,2))].
% 0.72/1.06 227 inverse(double_divide(c3,inverse(double_divide(a3,b3)))) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))) # answer(prove_these_axioms). [back_rewrite(176),rewrite([216(4),216(11),216(18)]),xx(b)].
% 0.72/1.06 233 double_divide(A,inverse(double_divide(B,inverse(double_divide(C,double_divide(A,B)))))) = inverse(C). [back_rewrite(164),rewrite([216(1),216(2)])].
% 0.72/1.06 237 inverse(double_divide(A,inverse(B))) = double_divide(B,inverse(A)). [para(184(a,1),131(a,1,2)),flip(a)].
% 0.72/1.06 240 double_divide(A,double_divide(inverse(B),double_divide(C,double_divide(A,B)))) = inverse(C). [back_rewrite(233),rewrite([237(5),216(4)])].
% 0.72/1.06 246 double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(inverse(a3),double_divide(b3,c3)) # answer(prove_these_axioms). [back_rewrite(227),rewrite([237(7),216(6),237(13),216(12)])].
% 0.72/1.06 324 double_divide(inverse(A),double_divide(B,double_divide(C,A))) = double_divide(C,inverse(B)). [para(240(a,1),131(a,1,2)),flip(a)].
% 0.72/1.06 352 double_divide(inverse(A),double_divide(B,inverse(C))) = double_divide(C,double_divide(A,B)). [para(324(a,1),131(a,1,2)),rewrite([216(5)])].
% 0.72/1.06 389 double_divide(inverse(A),double_divide(B,C)) = double_divide(inverse(C),double_divide(A,B)). [para(102(a,1),352(a,1,2,2))].
% 0.72/1.06 390 $F # answer(prove_these_axioms). [resolve(389,a,246,a(flip))].
% 0.72/1.06
% 0.72/1.06 % SZS output end Refutation
% 0.72/1.06 ============================== end of proof ==========================
% 0.72/1.06
% 0.72/1.06 ============================== STATISTICS ============================
% 0.72/1.06
% 0.72/1.06 Given=50. Generated=1073. Kept=388. proofs=1.
% 0.72/1.06 Usable=18. Sos=63. Demods=73. Limbo=0, Disabled=309. Hints=0.
% 0.72/1.06 Megabytes=0.42.
% 0.72/1.06 User_CPU=0.09, System_CPU=0.01, Wall_clock=0.
% 0.72/1.06
% 0.72/1.06 ============================== end of statistics =====================
% 0.72/1.06
% 0.72/1.06 ============================== end of search =========================
% 0.72/1.06
% 0.72/1.06 THEOREM PROVED
% 0.72/1.06 % SZS status Unsatisfiable
% 0.72/1.06
% 0.72/1.06 Exiting with 1 proof.
% 0.72/1.06
% 0.72/1.06 Process 31267 exit (max_proofs) Tue Jun 14 00:48:55 2022
% 0.72/1.06 Prover9 interrupted
%------------------------------------------------------------------------------