TSTP Solution File: GRP104-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP104-1 : 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 11:17:10 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
% 0.10/0.13 % Problem : GRP104-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n019.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 05:15:09 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.75/1.03 ============================== Prover9 ===============================
% 0.75/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.75/1.03 Process 13518 was started by sandbox2 on n019.cluster.edu,
% 0.75/1.03 Tue Jun 14 05:15:10 2022
% 0.75/1.03 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_13365_n019.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_13365_n019.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).
% 0.75/1.04 % 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 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 (13).
% 0.75/1.04 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.
% 0.75/1.04
% 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 0.04 (+ 0.00) seconds: prove_these_axioms.
% 0.75/1.04 % Length of proof is 50.
% 0.75/1.04 % Level of proof is 18.
% 0.75/1.04 % Maximum clause weight is 51.000.
% 0.75/1.04 % Given clauses 43.
% 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 double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C # label(single_axiom) # label(axiom). [assumption].
% 0.75/1.04 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].
% 0.75/1.04 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)].
% 0.75/1.04 5 double_divide(A,inverse(double_divide(inverse(double_divide(B,inverse(C))),inverse(double_divide(inverse(double_divide(double_divide(A,D),inverse(B))),D))))) = C. [para(2(a,1),2(a,1,2,1,1,1,1))].
% 0.75/1.04 6 double_divide(inverse(double_divide(double_divide(double_divide(A,B),C),inverse(D))),C) = double_divide(A,inverse(double_divide(inverse(D),B))). [para(2(a,1),2(a,1,2,1,1,1)),flip(a)].
% 0.75/1.04 10 double_divide(inverse(double_divide(A,inverse(B))),inverse(A)) = B. [para(2(a,1),5(a,1,2,1))].
% 0.75/1.04 12 double_divide(A,inverse(double_divide(inverse(double_divide(B,inverse(C))),inverse(double_divide(inverse(double_divide(D,inverse(B))),inverse(double_divide(inverse(double_divide(E,inverse(D))),inverse(double_divide(inverse(double_divide(double_divide(A,F),inverse(E))),F))))))))) = C. [para(5(a,1),5(a,1,2,1,2,1,1,1,1))].
% 0.75/1.04 14 double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B) = double_divide(inverse(C),inverse(A)). [para(2(a,1),10(a,1,1,1)),flip(a)].
% 0.75/1.04 17 double_divide(inverse(double_divide(A,inverse(B))),inverse(double_divide(inverse(A),inverse(C)))) = double_divide(inverse(B),inverse(C)). [para(5(a,1),10(a,1,1,1)),rewrite([14(11)]),flip(a)].
% 0.75/1.04 18 double_divide(inverse(A),inverse(inverse(double_divide(B,inverse(A))))) = B. [para(10(a,1),10(a,1,1,1))].
% 0.75/1.04 19 double_divide(A,inverse(double_divide(inverse(B),inverse(A)))) = B. [back_rewrite(12),rewrite([14(14),17(14),17(11),17(8)])].
% 0.75/1.04 21 double_divide(inverse(A),inverse(double_divide(B,C))) = double_divide(B,inverse(double_divide(inverse(A),C))). [back_rewrite(6),rewrite([14(6)])].
% 0.75/1.04 22 double_divide(double_divide(inverse(A),inverse(inverse(B))),inverse(A)) = B. [para(19(a,1),19(a,1,2,1))].
% 0.75/1.04 23 inverse(double_divide(A,inverse(B))) = double_divide(inverse(A),inverse(inverse(B))). [para(18(a,1),10(a,1,1,1)),flip(a)].
% 0.75/1.04 25 double_divide(A,double_divide(inverse(inverse(B)),inverse(inverse(A)))) = B. [back_rewrite(19),rewrite([23(4)])].
% 0.75/1.04 26 double_divide(double_divide(inverse(A),inverse(inverse(B))),double_divide(inverse(inverse(A)),inverse(inverse(C)))) = double_divide(inverse(B),inverse(C)). [back_rewrite(17),rewrite([23(3),23(8)])].
% 0.75/1.04 28 double_divide(double_divide(inverse(double_divide(A,B)),inverse(inverse(C))),B) = double_divide(inverse(C),inverse(A)). [back_rewrite(14),rewrite([23(4)])].
% 0.75/1.04 31 double_divide(inverse(b1),inverse(inverse(b1))) != double_divide(inverse(a1),inverse(inverse(a1))) | inverse(double_divide(a2,double_divide(inverse(b2),inverse(inverse(b2))))) != a2 | inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != double_divide(inverse(c3),inverse(inverse(double_divide(b3,a3)))) | inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) # answer(prove_these_axioms). [back_rewrite(4),rewrite([23(5),23(11),23(19),23(38)])].
% 0.75/1.04 44 inverse(double_divide(A,double_divide(inverse(B),inverse(inverse(C))))) = double_divide(inverse(A),double_divide(inverse(inverse(B)),inverse(inverse(inverse(C))))). [para(23(a,1),23(a,1,1,2)),rewrite([23(10),23(12)])].
% 0.75/1.04 46 double_divide(inverse(b1),inverse(inverse(b1))) != double_divide(inverse(a1),inverse(inverse(a1))) | double_divide(inverse(a2),double_divide(inverse(inverse(b2)),inverse(inverse(inverse(b2))))) != a2 | inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != double_divide(inverse(c3),inverse(inverse(double_divide(b3,a3)))) | inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) # answer(prove_these_axioms). [back_rewrite(31),rewrite([44(22)])].
% 0.75/1.04 48 double_divide(double_divide(inverse(A),inverse(inverse(B))),inverse(C)) = double_divide(inverse(B),double_divide(inverse(inverse(C)),inverse(inverse(inverse(A))))). [para(22(a,1),28(a,1,1,1,1)),rewrite([23(12)])].
% 0.75/1.04 49 double_divide(inverse(A),double_divide(inverse(inverse(double_divide(inverse(B),C))),inverse(inverse(inverse(double_divide(D,C)))))) = double_divide(inverse(B),double_divide(inverse(inverse(A)),inverse(inverse(D)))). [para(28(a,1),21(a,1,2,1)),rewrite([23(5),48(16)]),flip(a)].
% 0.75/1.04 59 double_divide(inverse(A),double_divide(inverse(inverse(B)),inverse(inverse(inverse(B))))) = A. [back_rewrite(22),rewrite([48(6)])].
% 0.75/1.04 61 double_divide(inverse(b1),inverse(inverse(b1))) != double_divide(inverse(a1),inverse(inverse(a1))) | inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != double_divide(inverse(c3),inverse(inverse(double_divide(b3,a3)))) | inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) # answer(prove_these_axioms). [back_rewrite(46),rewrite([59(24)]),xx(b)].
% 0.75/1.04 63 double_divide(inverse(A),B) = double_divide(B,inverse(A)). [para(59(a,1),21(a,2,2,1)),rewrite([44(9),59(11)])].
% 0.75/1.04 64 double_divide(double_divide(inverse(A),inverse(inverse(B))),double_divide(inverse(inverse(C)),inverse(inverse(inverse(C))))) = double_divide(A,inverse(B)). [para(23(a,1),59(a,1,1))].
% 0.75/1.04 65 double_divide(inverse(A),inverse(inverse(B))) = double_divide(B,inverse(A)). [para(59(a,1),28(a,1,1,1,1)),rewrite([64(11)]),flip(a)].
% 0.75/1.04 69 double_divide(A,double_divide(inverse(inverse(A)),inverse(inverse(B)))) = B. [back_rewrite(25),rewrite([63(5,R)])].
% 0.75/1.04 70 double_divide(inverse(b1),inverse(inverse(b1))) != double_divide(inverse(a1),inverse(inverse(a1))) | double_divide(inverse(c3),inverse(inverse(double_divide(b3,a3)))) != double_divide(inverse(a3),inverse(inverse(double_divide(c3,b3)))) | inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) # answer(prove_these_axioms). [back_rewrite(61),rewrite([63(19),23(20)]),flip(b)].
% 0.75/1.04 73 double_divide(inverse(A),double_divide(inverse(inverse(B)),double_divide(inverse(inverse(inverse(inverse(C)))),inverse(inverse(inverse(inverse(double_divide(D,C)))))))) = double_divide(inverse(B),double_divide(inverse(inverse(A)),inverse(inverse(D)))). [back_rewrite(49),rewrite([63(3),23(4),23(6),48(12),63(13,R)])].
% 0.75/1.04 88 double_divide(inverse(A),double_divide(inverse(B),inverse(inverse(B)))) = A. [para(65(a,1),59(a,1,2))].
% 0.75/1.04 96 double_divide(inverse(b1),inverse(inverse(b1))) != double_divide(inverse(a1),inverse(inverse(a1))) | double_divide(inverse(inverse(inverse(a3))),inverse(inverse(double_divide(c3,b3)))) != double_divide(inverse(c3),inverse(inverse(double_divide(b3,a3)))) | inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) # answer(prove_these_axioms). [para(65(a,2),70(b,2)),rewrite([63(31,R)]),flip(b)].
% 0.75/1.04 97 double_divide(inverse(A),inverse(inverse(inverse(B)))) = double_divide(inverse(A),inverse(B)). [para(65(a,2),63(a,1))].
% 0.75/1.04 111 double_divide(inverse(A),double_divide(inverse(inverse(B)),double_divide(inverse(inverse(inverse(inverse(C)))),inverse(inverse(double_divide(D,C)))))) = double_divide(inverse(B),double_divide(inverse(inverse(A)),inverse(inverse(D)))). [back_rewrite(73),rewrite([97(13)])].
% 0.75/1.04 125 double_divide(inverse(A),double_divide(inverse(A),inverse(inverse(B)))) = B. [para(69(a,1),63(a,1)),rewrite([63(6,R),97(6),63(4,R),63(6,R)]),flip(a)].
% 0.75/1.04 126 double_divide(A,double_divide(B,inverse(inverse(A)))) = B. [para(65(a,1),69(a,1,2))].
% 0.75/1.04 128 inverse(inverse(A)) = A. [para(126(a,1),26(a,1)),rewrite([23(8),97(9),63(7,R),125(8)])].
% 0.75/1.04 131 double_divide(A,double_divide(A,B)) = B. [para(63(a,2),126(a,1,2)),rewrite([128(2)])].
% 0.75/1.04 133 double_divide(A,double_divide(B,A)) = B. [back_rewrite(126),rewrite([128(2)])].
% 0.75/1.04 143 double_divide(inverse(A),double_divide(B,C)) = double_divide(inverse(B),double_divide(A,C)). [back_rewrite(111),rewrite([128(3),128(3),128(3),128(4),133(3),128(6),128(6)])].
% 0.75/1.04 150 double_divide(b1,inverse(b1)) != double_divide(a1,inverse(a1)) | double_divide(inverse(c3),double_divide(b3,a3)) != double_divide(inverse(a3),double_divide(c3,b3)) | inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) # answer(prove_these_axioms). [back_rewrite(96),rewrite([128(5),63(4),128(9),63(8),128(12),128(16),128(22)]),flip(b)].
% 0.75/1.04 153 double_divide(inverse(A),double_divide(B,inverse(B))) = A. [back_rewrite(88),rewrite([128(4),63(3)])].
% 0.75/1.04 159 double_divide(A,B) = double_divide(B,A). [para(128(a,1),63(a,1,1)),rewrite([128(3)])].
% 0.75/1.04 164 double_divide(b1,inverse(b1)) != double_divide(a1,inverse(a1)) | double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(inverse(a3),double_divide(b3,c3)) # answer(prove_these_axioms). [back_rewrite(150),rewrite([159(14),159(20),159(25)]),xx(c)].
% 0.75/1.04 171 double_divide(A,inverse(A)) = double_divide(B,inverse(B)). [para(153(a,1),131(a,1,2)),rewrite([159(2)])].
% 0.75/1.04 172 double_divide(A,inverse(A)) = c_0. [new_symbol(171)].
% 0.75/1.04 173 double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(inverse(a3),double_divide(b3,c3)) # answer(prove_these_axioms). [back_unit_del(164),rewrite([172(4),172(5)]),xx(a)].
% 0.75/1.04 195 double_divide(inverse(A),double_divide(B,C)) = double_divide(inverse(C),double_divide(A,B)). [para(159(a,1),143(a,1,2))].
% 0.75/1.04 196 $F # answer(prove_these_axioms). [resolve(195,a,173,a(flip))].
% 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=43. Generated=593. Kept=194. proofs=1.
% 0.75/1.04 Usable=14. Sos=20. Demods=26. Limbo=2, Disabled=160. Hints=0.
% 0.75/1.04 Megabytes=0.21.
% 0.75/1.04 User_CPU=0.04, 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 13518 exit (max_proofs) Tue Jun 14 05:15:10 2022
% 0.75/1.04 Prover9 interrupted
%------------------------------------------------------------------------------