TSTP Solution File: GRP609-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP609-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 11:19:49 EDT 2022
% Result : Unsatisfiable 0.75s 1.05s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP609-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n027.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 : Tue Jun 14 13:36:03 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.75/1.05 ============================== Prover9 ===============================
% 0.75/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.75/1.05 Process 32407 was started by sandbox on n027.cluster.edu,
% 0.75/1.05 Tue Jun 14 13:36:04 2022
% 0.75/1.05 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_32254_n027.cluster.edu".
% 0.75/1.05 ============================== end of head ===========================
% 0.75/1.05
% 0.75/1.05 ============================== INPUT =================================
% 0.75/1.05
% 0.75/1.05 % Reading from file /tmp/Prover9_32254_n027.cluster.edu
% 0.75/1.05
% 0.75/1.05 set(prolog_style_variables).
% 0.75/1.05 set(auto2).
% 0.75/1.05 % set(auto2) -> set(auto).
% 0.75/1.05 % set(auto) -> set(auto_inference).
% 0.75/1.05 % set(auto) -> set(auto_setup).
% 0.75/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.75/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.75/1.05 % set(auto) -> set(auto_limits).
% 0.75/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.75/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.75/1.05 % set(auto) -> set(auto_denials).
% 0.75/1.05 % set(auto) -> set(auto_process).
% 0.75/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.75/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.75/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.75/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.75/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.75/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.75/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.75/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.75/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.75/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.75/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.75/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.75/1.05 % set(auto2) -> assign(stats, some).
% 0.75/1.05 % set(auto2) -> clear(echo_input).
% 0.75/1.05 % set(auto2) -> set(quiet).
% 0.75/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.75/1.05 % set(auto2) -> clear(print_given).
% 0.75/1.05 assign(lrs_ticks,-1).
% 0.75/1.05 assign(sos_limit,10000).
% 0.75/1.05 assign(order,kbo).
% 0.75/1.05 set(lex_order_vars).
% 0.75/1.05 clear(print_given).
% 0.75/1.05
% 0.75/1.05 % formulas(sos). % not echoed (3 formulas)
% 0.75/1.05
% 0.75/1.05 ============================== end of input ==========================
% 0.75/1.05
% 0.75/1.05 % From the command line: assign(max_seconds, 300).
% 0.75/1.05
% 0.75/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.75/1.05
% 0.75/1.05 % Formulas that are not ordinary clauses:
% 0.75/1.05
% 0.75/1.05 ============================== end of process non-clausal formulas ===
% 0.75/1.05
% 0.75/1.05 ============================== PROCESS INITIAL CLAUSES ===============
% 0.75/1.05
% 0.75/1.05 ============================== PREDICATE ELIMINATION =================
% 0.75/1.05
% 0.75/1.05 ============================== end predicate elimination =============
% 0.75/1.05
% 0.75/1.05 Auto_denials:
% 0.75/1.05 % copying label prove_these_axioms_1 to answer in negative clause
% 0.75/1.05
% 0.75/1.05 Term ordering decisions:
% 0.75/1.05
% 0.75/1.05 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.75/1.05 Function symbol KB weights: a1=1. b1=1. double_divide=1. multiply=1. inverse=0.
% 0.75/1.05
% 0.75/1.05 ============================== end of process initial clauses ========
% 0.75/1.05
% 0.75/1.05 ============================== CLAUSES FOR SEARCH ====================
% 0.75/1.05
% 0.75/1.05 ============================== end of clauses for search =============
% 0.75/1.05
% 0.75/1.05 ============================== SEARCH ================================
% 0.75/1.05
% 0.75/1.05 % Starting search at 0.01 seconds.
% 0.75/1.05
% 0.75/1.05 ============================== PROOF =================================
% 0.75/1.05 % SZS status Unsatisfiable
% 0.75/1.05 % SZS output start Refutation
% 0.75/1.05
% 0.75/1.05 % Proof 1 at 0.05 (+ 0.00) seconds: prove_these_axioms_1.
% 0.75/1.05 % Length of proof is 55.
% 0.75/1.05 % Level of proof is 20.
% 0.75/1.05 % Maximum clause weight is 27.000.
% 0.75/1.05 % Given clauses 20.
% 0.75/1.05
% 0.75/1.05 1 multiply(A,B) = inverse(double_divide(B,A)) # label(multiply) # label(axiom). [assumption].
% 0.75/1.05 2 inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C))) = B # label(single_axiom) # label(axiom). [assumption].
% 0.75/1.05 3 multiply(inverse(a1),a1) != multiply(inverse(b1),b1) # label(prove_these_axioms_1) # label(negated_conjecture) # answer(prove_these_axioms_1). [assumption].
% 0.75/1.05 4 inverse(double_divide(b1,inverse(b1))) != inverse(double_divide(a1,inverse(a1))) # answer(prove_these_axioms_1). [copy(3),rewrite([1(4),1(9)]),flip(a)].
% 0.75/1.05 5 inverse(double_divide(inverse(double_divide(A,B)),double_divide(inverse(double_divide(inverse(double_divide(C,A)),D)),B))) = double_divide(C,D). [para(2(a,1),2(a,1,1,1,1,1))].
% 0.75/1.05 6 inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),double_divide(B,C)))) = C. [para(2(a,1),2(a,1,1,1))].
% 0.75/1.05 7 inverse(double_divide(inverse(double_divide(double_divide(A,B),C)),double_divide(inverse(double_divide(D,E)),C))) = double_divide(inverse(double_divide(inverse(double_divide(A,D)),B)),E). [para(5(a,1),2(a,1,1,1,1,1))].
% 0.75/1.05 8 inverse(double_divide(double_divide(A,B),double_divide(C,double_divide(inverse(double_divide(inverse(double_divide(A,C)),B)),D)))) = D. [para(5(a,1),2(a,1,1,1))].
% 0.75/1.05 12 inverse(double_divide(inverse(double_divide(A,B)),double_divide(double_divide(C,D),B))) = double_divide(E,double_divide(inverse(double_divide(inverse(double_divide(C,E)),D)),A)). [para(5(a,1),5(a,1,1,2,1))].
% 0.75/1.05 16 double_divide(A,inverse(double_divide(B,double_divide(inverse(double_divide(A,B)),C)))) = C. [para(6(a,1),5(a,1)),flip(a)].
% 0.75/1.05 19 inverse(double_divide(inverse(double_divide(inverse(A),B)),double_divide(C,B))) = inverse(double_divide(D,double_divide(inverse(double_divide(C,D)),A))). [para(16(a,1),2(a,1,1,1,1,1,1))].
% 0.75/1.05 20 inverse(double_divide(inverse(A),double_divide(B,inverse(double_divide(C,double_divide(inverse(double_divide(inverse(double_divide(B,D)),C)),A)))))) = D. [para(16(a,1),2(a,1,1,1,1))].
% 0.75/1.05 25 inverse(double_divide(inverse(double_divide(A,B)),double_divide(inverse(C),B))) = double_divide(D,inverse(double_divide(E,double_divide(inverse(double_divide(inverse(double_divide(D,A)),E)),C)))). [para(16(a,1),5(a,1,1,2,1,1))].
% 0.75/1.05 28 double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(double_divide(B,C)))) = C. [para(5(a,1),16(a,1,2))].
% 0.75/1.05 33 inverse(double_divide(A,double_divide(inverse(double_divide(inverse(double_divide(B,C)),A)),D))) = double_divide(B,inverse(double_divide(C,D))). [para(16(a,1),16(a,1,2,1,2)),flip(a)].
% 0.75/1.05 35 inverse(double_divide(inverse(double_divide(A,B)),double_divide(inverse(C),B))) = double_divide(D,double_divide(D,inverse(double_divide(A,C)))). [back_rewrite(25),rewrite([33(13)])].
% 0.75/1.05 36 inverse(double_divide(inverse(A),double_divide(B,double_divide(B,inverse(double_divide(C,A)))))) = C. [back_rewrite(20),rewrite([33(8)])].
% 0.75/1.05 37 inverse(double_divide(inverse(double_divide(inverse(A),B)),double_divide(inverse(double_divide(C,D)),B))) = double_divide(C,inverse(double_divide(D,A))). [para(28(a,1),2(a,1,1,1,1,1,1))].
% 0.75/1.05 46 double_divide(A,double_divide(B,inverse(double_divide(double_divide(inverse(double_divide(C,B)),double_divide(C,A)),D)))) = D. [para(6(a,1),28(a,1,1))].
% 0.75/1.05 50 inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),C))) = double_divide(inverse(double_divide(D,B)),double_divide(D,inverse(C))). [para(16(a,1),28(a,1,2,2,1)),flip(a)].
% 0.75/1.05 58 inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,B))) = double_divide(D,double_divide(E,double_divide(E,inverse(double_divide(C,double_divide(D,A)))))). [para(36(a,1),5(a,1,1,2,1))].
% 0.75/1.05 63 double_divide(inverse(double_divide(A,inverse(B))),inverse(double_divide(C,B))) = double_divide(A,C). [para(36(a,1),16(a,1,2)),flip(a)].
% 0.75/1.05 71 double_divide(inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C)),D) = double_divide(B,D). [para(7(a,1),5(a,1))].
% 0.75/1.05 87 double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C)))) = inverse(double_divide(C,B)). [para(63(a,1),2(a,1,1,1,1,1,1)),rewrite([37(10)])].
% 0.75/1.05 90 double_divide(inverse(double_divide(A,inverse(double_divide(B,C)))),D) = double_divide(A,inverse(double_divide(inverse(double_divide(B,D)),C))). [para(2(a,1),63(a,1,2))].
% 0.75/1.05 92 double_divide(inverse(double_divide(A,B)),inverse(double_divide(C,double_divide(B,D)))) = double_divide(inverse(double_divide(A,inverse(D))),C). [para(63(a,1),5(a,1,1,2,1,1,1,1)),rewrite([37(11)])].
% 0.75/1.05 103 inverse(double_divide(inverse(inverse(double_divide(A,B))),double_divide(C,double_divide(C,inverse(double_divide(D,A)))))) = inverse(double_divide(D,inverse(B))). [para(63(a,1),36(a,1,1,2,2,2,1))].
% 0.75/1.05 115 double_divide(inverse(inverse(double_divide(A,double_divide(B,A)))),C) = double_divide(B,C). [back_rewrite(71),rewrite([90(6),87(6)])].
% 0.75/1.05 133 double_divide(inverse(inverse(A)),B) = double_divide(A,B). [para(28(a,1),115(a,1,1,1,1))].
% 0.75/1.05 135 inverse(inverse(double_divide(A,double_divide(B,A)))) = B. [para(115(a,1),36(a,1,1,2,2,2,1)),rewrite([36(7)]),flip(a)].
% 0.75/1.05 140 inverse(double_divide(double_divide(A,B),double_divide(C,double_divide(C,inverse(double_divide(D,A)))))) = inverse(double_divide(D,inverse(B))). [back_rewrite(103),rewrite([133(8)])].
% 0.75/1.05 149 inverse(inverse(A)) = A. [para(133(a,1),36(a,1,1,2,2,2,1)),rewrite([36(7)]),flip(a)].
% 0.75/1.05 153 double_divide(A,double_divide(B,A)) = B. [back_rewrite(135),rewrite([149(4)])].
% 0.75/1.05 159 double_divide(inverse(double_divide(A,B)),double_divide(inverse(double_divide(inverse(double_divide(C,A)),D)),B)) = inverse(double_divide(C,D)). [para(5(a,1),149(a,1,1)),flip(a)].
% 0.75/1.05 167 inverse(double_divide(double_divide(A,B),double_divide(C,D))) = double_divide(inverse(double_divide(A,C)),inverse(double_divide(B,D))). [para(16(a,1),8(a,1,1,2,2)),rewrite([33(13)])].
% 0.75/1.05 171 double_divide(inverse(double_divide(A,B)),inverse(double_divide(C,double_divide(double_divide(D,E),double_divide(F,double_divide(inverse(double_divide(inverse(double_divide(D,F)),E)),B)))))) = double_divide(A,C). [para(8(a,1),63(a,1,1,1,2))].
% 0.75/1.05 172 double_divide(double_divide(A,B),double_divide(C,double_divide(inverse(double_divide(inverse(double_divide(A,C)),B)),D))) = inverse(D). [para(8(a,1),149(a,1,1)),flip(a)].
% 0.75/1.05 174 inverse(double_divide(A,inverse(B))) = double_divide(inverse(A),B). [back_rewrite(140),rewrite([167(7),92(8),149(3),153(2)]),flip(a)].
% 0.75/1.05 179 double_divide(inverse(double_divide(A,B)),double_divide(inverse(C),B)) = double_divide(A,C). [back_rewrite(171),rewrite([172(10),174(5)])].
% 0.75/1.05 191 double_divide(double_divide(inverse(A),double_divide(B,C)),D) = double_divide(A,inverse(double_divide(inverse(double_divide(B,D)),C))). [back_rewrite(90),rewrite([174(4)])].
% 0.75/1.05 196 double_divide(inverse(b1),b1) != double_divide(inverse(a1),a1) # answer(prove_these_axioms_1). [back_rewrite(4),rewrite([174(5),174(9)])].
% 0.75/1.05 198 double_divide(A,double_divide(inverse(double_divide(B,A)),C)) = inverse(double_divide(B,C)). [back_rewrite(159),rewrite([179(8)])].
% 0.75/1.05 204 double_divide(A,double_divide(A,inverse(double_divide(B,C)))) = inverse(double_divide(B,C)). [back_rewrite(35),rewrite([179(5)]),flip(a)].
% 0.75/1.05 208 double_divide(A,inverse(double_divide(B,double_divide(inverse(double_divide(B,C)),A)))) = C. [back_rewrite(46),rewrite([191(5),174(7),198(7)])].
% 0.75/1.05 223 double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(C))) = double_divide(B,C). [back_rewrite(50),rewrite([198(4),149(3)]),flip(a)].
% 0.75/1.05 226 double_divide(inverse(double_divide(A,B)),C) = double_divide(A,inverse(double_divide(B,C))). [back_rewrite(33),rewrite([198(6),149(5)])].
% 0.75/1.05 230 inverse(double_divide(A,double_divide(B,inverse(double_divide(A,C))))) = double_divide(C,B). [back_rewrite(19),rewrite([226(5),153(3),174(4),149(2),226(4)]),flip(a)].
% 0.75/1.05 240 double_divide(A,inverse(double_divide(B,double_divide(A,C)))) = double_divide(inverse(C),B). [back_rewrite(58),rewrite([226(4),153(2),174(3),204(7)]),flip(a)].
% 0.75/1.05 242 double_divide(A,double_divide(B,double_divide(inverse(A),double_divide(C,D)))) = double_divide(inverse(C),double_divide(B,D)). [back_rewrite(12),rewrite([226(5),153(3),174(4),226(6),174(7),191(7),226(6),174(7)]),flip(a)].
% 0.75/1.05 251 double_divide(A,B) = double_divide(B,A). [back_rewrite(223),rewrite([226(5),240(5),149(2)])].
% 0.75/1.05 254 double_divide(A,double_divide(A,B)) = B. [back_rewrite(208),rewrite([251(3),230(5),251(1)])].
% 0.75/1.05 294 double_divide(b1,inverse(b1)) != double_divide(a1,inverse(a1)) # answer(prove_these_axioms_1). [back_rewrite(196),rewrite([251(4),251(8)])].
% 0.75/1.05 302 double_divide(A,double_divide(B,A)) = B. [para(254(a,1),251(a,1)),rewrite([251(1),251(2)]),flip(a)].
% 0.75/1.05 312 double_divide(A,inverse(A)) = double_divide(B,inverse(B)). [para(302(a,1),242(a,1,2)),rewrite([251(5),302(5),251(4)])].
% 0.75/1.05 313 $F # answer(prove_these_axioms_1). [resolve(312,a,294,a)].
% 0.75/1.05
% 0.75/1.05 % SZS output end Refutation
% 0.75/1.05 ============================== end of proof ==========================
% 0.75/1.05
% 0.75/1.05 ============================== STATISTICS ============================
% 0.75/1.05
% 0.75/1.05 Given=20. Generated=608. Kept=311. proofs=1.
% 0.75/1.05 Usable=7. Sos=40. Demods=39. Limbo=9, Disabled=257. Hints=0.
% 0.75/1.05 Megabytes=0.33.
% 0.75/1.05 User_CPU=0.05, System_CPU=0.00, Wall_clock=0.
% 0.75/1.05
% 0.75/1.05 ============================== end of statistics =====================
% 0.75/1.05
% 0.75/1.05 ============================== end of search =========================
% 0.75/1.05
% 0.75/1.05 THEOREM PROVED
% 0.75/1.05 % SZS status Unsatisfiable
% 0.75/1.05
% 0.75/1.05 Exiting with 1 proof.
% 0.75/1.05
% 0.75/1.05 Process 32407 exit (max_proofs) Tue Jun 14 13:36:04 2022
% 0.75/1.05 Prover9 interrupted
%------------------------------------------------------------------------------