TSTP Solution File: GRP610-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP610-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.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 11:19:50 EDT 2022
% Result : Unsatisfiable 0.75s 1.04s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GRP610-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n020.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 08:00:05 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.75/1.04 ============================== Prover9 ===============================
% 0.75/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.75/1.04 Process 5628 was started by sandbox on n020.cluster.edu,
% 0.75/1.04 Mon Jun 13 08:00:05 2022
% 0.75/1.04 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_5475_n020.cluster.edu".
% 0.75/1.04 ============================== end of head ===========================
% 0.75/1.04
% 0.75/1.04 ============================== INPUT =================================
% 0.75/1.04
% 0.75/1.04 % Reading from file /tmp/Prover9_5475_n020.cluster.edu
% 0.75/1.04
% 0.75/1.04 set(prolog_style_variables).
% 0.75/1.04 set(auto2).
% 0.75/1.04 % set(auto2) -> set(auto).
% 0.75/1.04 % set(auto) -> set(auto_inference).
% 0.75/1.04 % set(auto) -> set(auto_setup).
% 0.75/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.75/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.75/1.04 % set(auto) -> set(auto_limits).
% 0.75/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.75/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.75/1.04 % set(auto) -> set(auto_denials).
% 0.75/1.04 % set(auto) -> set(auto_process).
% 0.75/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.75/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.75/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.75/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.75/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.75/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.75/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.75/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.75/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.75/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.75/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.75/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.75/1.04 % set(auto2) -> assign(stats, some).
% 0.75/1.04 % set(auto2) -> clear(echo_input).
% 0.75/1.04 % set(auto2) -> set(quiet).
% 0.75/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.75/1.04 % set(auto2) -> clear(print_given).
% 0.75/1.04 assign(lrs_ticks,-1).
% 0.75/1.04 assign(sos_limit,10000).
% 0.75/1.04 assign(order,kbo).
% 0.75/1.04 set(lex_order_vars).
% 0.75/1.04 clear(print_given).
% 0.75/1.04
% 0.75/1.04 % formulas(sos). % not echoed (3 formulas)
% 0.75/1.04
% 0.75/1.04 ============================== end of input ==========================
% 0.75/1.04
% 0.75/1.04 % From the command line: assign(max_seconds, 300).
% 0.75/1.04
% 0.75/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.75/1.04
% 0.75/1.04 % Formulas that are not ordinary clauses:
% 0.75/1.04
% 0.75/1.04 ============================== end of process non-clausal formulas ===
% 0.75/1.04
% 0.75/1.04 ============================== PROCESS INITIAL CLAUSES ===============
% 0.75/1.04
% 0.75/1.04 ============================== PREDICATE ELIMINATION =================
% 0.75/1.04
% 0.75/1.04 ============================== end predicate elimination =============
% 0.75/1.04
% 0.75/1.04 Auto_denials:
% 0.75/1.04 % copying label prove_these_axioms_2 to answer in negative clause
% 0.75/1.04
% 0.75/1.04 Term ordering decisions:
% 0.75/1.04
% 0.75/1.04 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.75/1.04 Function symbol KB weights: a2=1. b2=1. double_divide=1. multiply=1. inverse=0.
% 0.75/1.04
% 0.75/1.04 ============================== end of process initial clauses ========
% 0.75/1.04
% 0.75/1.04 ============================== CLAUSES FOR SEARCH ====================
% 0.75/1.04
% 0.75/1.04 ============================== end of clauses for search =============
% 0.75/1.04
% 0.75/1.04 ============================== SEARCH ================================
% 0.75/1.04
% 0.75/1.04 % Starting search at 0.01 seconds.
% 0.75/1.04
% 0.75/1.04 ============================== PROOF =================================
% 0.75/1.04 % SZS status Unsatisfiable
% 0.75/1.04 % SZS output start Refutation
% 0.75/1.04
% 0.75/1.04 % Proof 1 at 0.02 (+ 0.00) seconds: prove_these_axioms_2.
% 0.75/1.04 % Length of proof is 48.
% 0.75/1.04 % Level of proof is 18.
% 0.75/1.04 % Maximum clause weight is 30.000.
% 0.75/1.04 % Given clauses 14.
% 0.75/1.04
% 0.75/1.04 1 multiply(A,B) = inverse(double_divide(B,A)) # label(multiply) # label(axiom). [assumption].
% 0.75/1.04 2 inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C))) = B # label(single_axiom) # label(axiom). [assumption].
% 0.75/1.04 3 multiply(multiply(inverse(b2),b2),a2) != a2 # label(prove_these_axioms_2) # label(negated_conjecture) # answer(prove_these_axioms_2). [assumption].
% 0.75/1.04 4 inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2 # answer(prove_these_axioms_2). [copy(3),rewrite([1(4),1(7)])].
% 0.75/1.04 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))].
% 0.75/1.04 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))].
% 0.75/1.04 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))].
% 0.75/1.04 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))].
% 0.75/1.04 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)].
% 0.75/1.04 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))].
% 0.75/1.04 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))].
% 0.75/1.04 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))].
% 0.75/1.04 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)].
% 0.75/1.04 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)])].
% 0.75/1.04 36 inverse(double_divide(inverse(A),double_divide(B,double_divide(B,inverse(double_divide(C,A)))))) = C. [back_rewrite(20),rewrite([33(8)])].
% 0.75/1.04 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))].
% 0.75/1.04 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)].
% 0.75/1.04 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))].
% 0.75/1.04 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)].
% 0.75/1.04 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))].
% 0.75/1.04 79 inverse(double_divide(inverse(double_divide(double_divide(A,B),C)),double_divide(inverse(D),C))) = double_divide(inverse(double_divide(inverse(double_divide(A,E)),B)),inverse(double_divide(F,double_divide(inverse(double_divide(E,F)),D)))). [para(16(a,1),7(a,1,1,2,1,1))].
% 0.75/1.04 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)])].
% 0.75/1.04 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))].
% 0.75/1.04 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)])].
% 0.75/1.04 103 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))].
% 0.75/1.04 115 double_divide(inverse(inverse(double_divide(A,double_divide(B,A)))),C) = double_divide(B,C). [back_rewrite(71),rewrite([90(6),87(6)])].
% 0.75/1.04 133 double_divide(inverse(inverse(A)),B) = double_divide(A,B). [para(28(a,1),115(a,1,1,1,1))].
% 0.75/1.04 135 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)].
% 0.75/1.04 140 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)])].
% 0.75/1.04 149 inverse(inverse(A)) = A. [para(133(a,1),36(a,1,1,2,2,2,1)),rewrite([36(7)]),flip(a)].
% 0.75/1.04 153 double_divide(A,double_divide(B,A)) = B. [back_rewrite(135),rewrite([149(4)])].
% 0.75/1.04 159 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)].
% 0.75/1.04 167 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)])].
% 0.75/1.04 171 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))].
% 0.75/1.04 172 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)].
% 0.75/1.04 174 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)].
% 0.75/1.04 179 double_divide(inverse(double_divide(A,B)),double_divide(inverse(C),B)) = double_divide(A,C). [back_rewrite(171),rewrite([172(10),174(5)])].
% 0.75/1.04 191 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)])].
% 0.75/1.04 196 inverse(double_divide(a2,double_divide(inverse(b2),b2))) != a2 # answer(prove_these_axioms_2). [back_rewrite(4),rewrite([174(6)])].
% 0.75/1.04 198 double_divide(A,double_divide(inverse(double_divide(B,A)),C)) = inverse(double_divide(B,C)). [back_rewrite(159),rewrite([179(8)])].
% 0.75/1.04 202 double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(B,D)) = inverse(double_divide(double_divide(A,C),D)). [back_rewrite(79),rewrite([179(6),198(11),149(10)]),flip(a)].
% 0.75/1.04 204 double_divide(A,double_divide(A,inverse(double_divide(B,C)))) = inverse(double_divide(B,C)). [back_rewrite(35),rewrite([179(5)]),flip(a)].
% 0.75/1.04 223 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)].
% 0.75/1.04 226 double_divide(inverse(double_divide(A,B)),C) = double_divide(A,inverse(double_divide(B,C))). [back_rewrite(33),rewrite([198(6),149(5)])].
% 0.75/1.04 240 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)].
% 0.75/1.04 251 double_divide(A,B) = double_divide(B,A). [back_rewrite(223),rewrite([226(5),240(5),149(2)])].
% 0.75/1.04 256 inverse(double_divide(A,double_divide(B,C))) = double_divide(C,double_divide(A,inverse(B))). [back_rewrite(202),rewrite([251(3),174(4),191(5),251(4),240(4),251(2),174(3),251(2),251(5)]),flip(a)].
% 0.75/1.04 294 $F # answer(prove_these_axioms_2). [back_rewrite(196),rewrite([251(5),256(7),153(7)]),xx(a)].
% 0.75/1.04
% 0.75/1.04 % SZS output end Refutation
% 0.75/1.04 ============================== end of proof ==========================
% 0.75/1.04
% 0.75/1.04 ============================== STATISTICS ============================
% 0.75/1.04
% 0.75/1.04 Given=14. Generated=549. Kept=292. proofs=1.
% 0.75/1.04 Usable=2. Sos=10. Demods=44. Limbo=43, Disabled=240. Hints=0.
% 0.75/1.04 Megabytes=0.32.
% 0.75/1.04 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.75/1.04
% 0.75/1.04 ============================== end of statistics =====================
% 0.75/1.04
% 0.75/1.04 ============================== end of search =========================
% 0.75/1.04
% 0.75/1.04 THEOREM PROVED
% 0.75/1.04 % SZS status Unsatisfiable
% 0.75/1.04
% 0.75/1.04 Exiting with 1 proof.
% 0.75/1.04
% 0.75/1.04 Process 5628 exit (max_proofs) Mon Jun 13 08:00:05 2022
% 0.75/1.04 Prover9 interrupted
%------------------------------------------------------------------------------