TSTP Solution File: GRP083-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP083-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 11:17:05 EDT 2022
% Result : Unsatisfiable 1.10s 1.39s
% Output : Refutation 1.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP083-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n017.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
% 0.17/0.33 % WCLimit : 600
% 0.17/0.33 % DateTime : Tue Jun 14 02:43:38 EDT 2022
% 0.17/0.33 % CPUTime :
% 1.10/1.39 ============================== Prover9 ===============================
% 1.10/1.39 Prover9 (32) version 2009-11A, November 2009.
% 1.10/1.39 Process 818 was started by sandbox on n017.cluster.edu,
% 1.10/1.39 Tue Jun 14 02:43:39 2022
% 1.10/1.39 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_631_n017.cluster.edu".
% 1.10/1.39 ============================== end of head ===========================
% 1.10/1.39
% 1.10/1.39 ============================== INPUT =================================
% 1.10/1.39
% 1.10/1.39 % Reading from file /tmp/Prover9_631_n017.cluster.edu
% 1.10/1.39
% 1.10/1.39 set(prolog_style_variables).
% 1.10/1.39 set(auto2).
% 1.10/1.39 % set(auto2) -> set(auto).
% 1.10/1.39 % set(auto) -> set(auto_inference).
% 1.10/1.39 % set(auto) -> set(auto_setup).
% 1.10/1.39 % set(auto_setup) -> set(predicate_elim).
% 1.10/1.39 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.10/1.39 % set(auto) -> set(auto_limits).
% 1.10/1.39 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.10/1.39 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.10/1.39 % set(auto) -> set(auto_denials).
% 1.10/1.39 % set(auto) -> set(auto_process).
% 1.10/1.39 % set(auto2) -> assign(new_constants, 1).
% 1.10/1.39 % set(auto2) -> assign(fold_denial_max, 3).
% 1.10/1.39 % set(auto2) -> assign(max_weight, "200.000").
% 1.10/1.39 % set(auto2) -> assign(max_hours, 1).
% 1.10/1.39 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.10/1.39 % set(auto2) -> assign(max_seconds, 0).
% 1.10/1.39 % set(auto2) -> assign(max_minutes, 5).
% 1.10/1.39 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.10/1.39 % set(auto2) -> set(sort_initial_sos).
% 1.10/1.39 % set(auto2) -> assign(sos_limit, -1).
% 1.10/1.39 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.10/1.39 % set(auto2) -> assign(max_megs, 400).
% 1.10/1.39 % set(auto2) -> assign(stats, some).
% 1.10/1.39 % set(auto2) -> clear(echo_input).
% 1.10/1.39 % set(auto2) -> set(quiet).
% 1.10/1.39 % set(auto2) -> clear(print_initial_clauses).
% 1.10/1.39 % set(auto2) -> clear(print_given).
% 1.10/1.39 assign(lrs_ticks,-1).
% 1.10/1.39 assign(sos_limit,10000).
% 1.10/1.39 assign(order,kbo).
% 1.10/1.39 set(lex_order_vars).
% 1.10/1.39 clear(print_given).
% 1.10/1.39
% 1.10/1.39 % formulas(sos). % not echoed (3 formulas)
% 1.10/1.39
% 1.10/1.39 ============================== end of input ==========================
% 1.10/1.39
% 1.10/1.39 % From the command line: assign(max_seconds, 300).
% 1.10/1.39
% 1.10/1.39 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.10/1.39
% 1.10/1.39 % Formulas that are not ordinary clauses:
% 1.10/1.39
% 1.10/1.39 ============================== end of process non-clausal formulas ===
% 1.10/1.39
% 1.10/1.39 ============================== PROCESS INITIAL CLAUSES ===============
% 1.10/1.39
% 1.10/1.39 ============================== PREDICATE ELIMINATION =================
% 1.10/1.39
% 1.10/1.39 ============================== end predicate elimination =============
% 1.10/1.39
% 1.10/1.39 Auto_denials:
% 1.10/1.39 % copying label prove_these_axioms to answer in negative clause
% 1.10/1.39
% 1.10/1.39 Term ordering decisions:
% 1.10/1.39
% 1.10/1.39 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 1.10/1.39 Function symbol KB weights: a1=1. a2=1. a3=1. b1=1. b2=1. b3=1. c3=1. double_divide=1. multiply=1. inverse=0.
% 1.10/1.39
% 1.10/1.39 ============================== end of process initial clauses ========
% 1.10/1.39
% 1.10/1.39 ============================== CLAUSES FOR SEARCH ====================
% 1.10/1.39
% 1.10/1.39 ============================== end of clauses for search =============
% 1.10/1.39
% 1.10/1.39 ============================== SEARCH ================================
% 1.10/1.39
% 1.10/1.39 % Starting search at 0.01 seconds.
% 1.10/1.39
% 1.10/1.39 ============================== PROOF =================================
% 1.10/1.39 % SZS status Unsatisfiable
% 1.10/1.39 % SZS output start Refutation
% 1.10/1.39
% 1.10/1.39 % Proof 1 at 0.41 (+ 0.01) seconds: prove_these_axioms.
% 1.10/1.39 % Length of proof is 98.
% 1.10/1.39 % Level of proof is 29.
% 1.10/1.39 % Maximum clause weight is 62.000.
% 1.10/1.39 % Given clauses 30.
% 1.10/1.39
% 1.10/1.39 1 multiply(A,B) = inverse(double_divide(B,A)) # label(multiply) # label(axiom). [assumption].
% 1.10/1.39 2 double_divide(double_divide(A,inverse(double_divide(B,C))),double_divide(inverse(B),inverse(double_divide(D,double_divide(A,D))))) = C # label(single_axiom) # label(axiom). [assumption].
% 1.10/1.39 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)) # label(prove_these_axioms) # label(negated_conjecture) # answer(prove_these_axioms). [assumption].
% 1.10/1.39 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)))) # answer(prove_these_axioms). [copy(3),rewrite([1(4),1(9),1(15),1(18),1(24),1(27),1(32),1(34)]),flip(a),flip(c)].
% 1.10/1.39 5 double_divide(inverse(A),inverse(double_divide(B,double_divide(C,B)))) = double_divide(double_divide(D,inverse(E)),double_divide(inverse(double_divide(C,inverse(double_divide(A,E)))),inverse(double_divide(F,double_divide(D,F))))). [para(2(a,1),2(a,1,1,2,1)),flip(a)].
% 1.10/1.39 6 double_divide(double_divide(double_divide(A,inverse(double_divide(B,C))),inverse(double_divide(D,E))),double_divide(inverse(D),inverse(double_divide(double_divide(inverse(B),inverse(double_divide(F,double_divide(A,F)))),C)))) = E. [para(2(a,1),2(a,1,2,2,1,2))].
% 1.10/1.39 7 inverse(double_divide(inverse(A),inverse(double_divide(B,double_divide(C,B))))) = inverse(double_divide(double_divide(D,inverse(E)),double_divide(inverse(double_divide(C,inverse(double_divide(A,E)))),inverse(double_divide(F,double_divide(D,F)))))). [para(5(a,1),1(a,2,1)),rewrite([1(5)])].
% 1.10/1.39 9 double_divide(double_divide(double_divide(A,inverse(B)),double_divide(inverse(double_divide(C,inverse(double_divide(D,B)))),inverse(double_divide(E,double_divide(A,E))))),double_divide(inverse(F),inverse(double_divide(V6,double_divide(inverse(D),V6))))) = double_divide(C,F). [para(5(a,1),2(a,1,1))].
% 1.10/1.39 10 double_divide(double_divide(inverse(A),inverse(double_divide(B,C))),double_divide(inverse(B),inverse(double_divide(inverse(double_divide(D,double_divide(E,D))),double_divide(double_divide(F,inverse(V6)),double_divide(inverse(double_divide(E,inverse(double_divide(A,V6)))),inverse(double_divide(V7,double_divide(F,V7))))))))) = C. [para(5(a,1),2(a,1,2,2,1,2))].
% 1.10/1.39 11 double_divide(double_divide(A,inverse(double_divide(B,C))),double_divide(double_divide(D,inverse(E)),double_divide(inverse(double_divide(A,inverse(double_divide(B,E)))),inverse(double_divide(F,double_divide(D,F)))))) = C. [para(5(a,1),2(a,1,2))].
% 1.10/1.39 18 double_divide(inverse(A),inverse(double_divide(B,double_divide(C,B)))) = double_divide(D,double_divide(C,inverse(double_divide(A,double_divide(E,double_divide(D,E)))))). [para(5(a,1),5(a,2,1)),rewrite([9(28)])].
% 1.10/1.39 26 double_divide(inverse(A),inverse(double_divide(B,double_divide(C,B)))) = double_divide(inverse(A),inverse(double_divide(D,double_divide(C,D)))). [para(5(a,2),5(a,2))].
% 1.10/1.39 28 inverse(double_divide(A,double_divide(B,A))) = inverse(double_divide(C,double_divide(B,C))). [para(26(a,1),2(a,1,1,2,1)),rewrite([2(14)])].
% 1.10/1.39 64 double_divide(inverse(double_divide(double_divide(A,inverse(double_divide(B,C))),A)),inverse(double_divide(D,double_divide(inverse(B),D)))) = C. [para(18(a,2),2(a,1))].
% 1.10/1.39 72 double_divide(inverse(A),inverse(double_divide(B,double_divide(C,B)))) = double_divide(double_divide(D,inverse(E)),double_divide(F,double_divide(D,inverse(double_divide(double_divide(C,inverse(double_divide(A,E))),double_divide(V6,double_divide(F,V6))))))). [para(18(a,1),5(a,2,2))].
% 1.10/1.39 77 double_divide(inverse(double_divide(A,B)),inverse(double_divide(C,double_divide(inverse(D),C)))) = double_divide(A,double_divide(double_divide(E,inverse(F)),double_divide(inverse(double_divide(B,inverse(double_divide(D,F)))),inverse(double_divide(V6,double_divide(E,V6)))))). [para(5(a,1),18(a,2,2))].
% 1.10/1.39 89 double_divide(inverse(A),inverse(double_divide(inverse(double_divide(B,double_divide(C,B))),double_divide(D,double_divide(C,inverse(double_divide(E,double_divide(F,double_divide(D,F))))))))) = double_divide(V6,double_divide(inverse(E),inverse(double_divide(A,double_divide(V7,double_divide(V6,V7)))))). [para(18(a,1),18(a,1,2,1,2))].
% 1.10/1.39 92 double_divide(inverse(double_divide(A,B)),inverse(double_divide(C,double_divide(inverse(D),C)))) = double_divide(A,double_divide(E,double_divide(B,inverse(double_divide(D,double_divide(F,double_divide(E,F))))))). [para(18(a,1),18(a,2,2))].
% 1.10/1.39 138 double_divide(double_divide(inverse(A),inverse(double_divide(double_divide(double_divide(B,inverse(double_divide(A,C))),B),D))),C) = D. [para(64(a,1),2(a,1,2))].
% 1.10/1.39 145 inverse(double_divide(A,double_divide(B,A))) = double_divide(inverse(double_divide(double_divide(C,inverse(double_divide(double_divide(D,inverse(E)),double_divide(inverse(double_divide(B,inverse(double_divide(F,E)))),inverse(double_divide(V6,double_divide(D,V6))))))),C)),inverse(double_divide(V7,double_divide(inverse(inverse(F)),V7)))). [para(5(a,1),64(a,1,1,1,1,2,1)),flip(a)].
% 1.10/1.39 164 double_divide(inverse(double_divide(double_divide(A,inverse(double_divide(inverse(B),inverse(double_divide(C,double_divide(D,C)))))),A)),inverse(double_divide(E,double_divide(inverse(F),E)))) = double_divide(D,inverse(double_divide(B,double_divide(V6,double_divide(F,V6))))). [para(18(a,2),64(a,1,1,1,1,2,1))].
% 1.10/1.39 191 inverse(double_divide(A,double_divide(double_divide(inverse(B),inverse(double_divide(double_divide(double_divide(C,inverse(double_divide(B,D))),C),E))),A))) = inverse(double_divide(D,E)). [para(138(a,1),28(a,1,1,2)),flip(a)].
% 1.10/1.39 195 double_divide(A,double_divide(double_divide(inverse(B),inverse(double_divide(double_divide(double_divide(C,inverse(double_divide(B,D))),C),E))),inverse(double_divide(F,double_divide(V6,double_divide(A,V6)))))) = double_divide(inverse(F),inverse(double_divide(D,E))). [para(138(a,1),18(a,1,2,1,2)),flip(a)].
% 1.10/1.39 198 double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,double_divide(B,double_divide(C,B)))),D))) = double_divide(C,D). [para(138(a,1),18(a,2,2)),rewrite([191(16)])].
% 1.10/1.39 207 double_divide(A,double_divide(inverse(B),inverse(double_divide(inverse(double_divide(B,C)),A)))) = C. [para(138(a,1),6(a,1,1)),rewrite([64(13)])].
% 1.10/1.39 230 double_divide(inverse(double_divide(A,double_divide(B,A))),double_divide(inverse(C),inverse(double_divide(inverse(double_divide(C,D)),inverse(double_divide(E,double_divide(B,E))))))) = D. [para(26(a,1),207(a,1,2,2,1))].
% 1.10/1.39 233 double_divide(A,double_divide(inverse(B),inverse(double_divide(inverse(double_divide(C,double_divide(D,C))),A)))) = double_divide(D,B). [para(28(a,1),207(a,1,2,2,1,1))].
% 1.10/1.39 269 double_divide(A,inverse(double_divide(B,double_divide(C,B)))) = double_divide(A,inverse(double_divide(D,double_divide(C,D)))). [para(26(a,1),198(a,1,2,1)),rewrite([198(11)])].
% 1.10/1.39 272 double_divide(inverse(double_divide(A,B)),inverse(double_divide(inverse(double_divide(C,double_divide(B,C))),D))) = double_divide(A,D). [para(28(a,1),198(a,1,2,1,1))].
% 1.10/1.39 275 double_divide(inverse(A),inverse(double_divide(inverse(double_divide(inverse(double_divide(B,double_divide(C,double_divide(D,C)))),E)),double_divide(D,E)))) = double_divide(F,double_divide(inverse(B),inverse(double_divide(A,double_divide(V6,double_divide(F,V6)))))). [para(198(a,1),18(a,1,2,1,2))].
% 1.10/1.39 290 double_divide(inverse(double_divide(double_divide(A,double_divide(B,A)),inverse(double_divide(C,D)))),inverse(D)) = double_divide(B,inverse(double_divide(E,double_divide(inverse(C),E)))). [para(64(a,1),198(a,1,2,1))].
% 1.10/1.39 297 double_divide(A,double_divide(B,A)) = double_divide(C,double_divide(B,C)). [para(198(a,1),207(a,1,2))].
% 1.10/1.39 376 double_divide(double_divide(inverse(double_divide(A,inverse(double_divide(B,C)))),inverse(double_divide(D,double_divide(E,D)))),double_divide(inverse(B),inverse(double_divide(F,double_divide(A,F))))) = double_divide(V6,double_divide(double_divide(E,inverse(C)),V6)). [para(5(a,2),297(a,1,2))].
% 1.10/1.39 392 double_divide(double_divide(A,B),double_divide(C,double_divide(A,C))) = double_divide(D,double_divide(B,D)). [para(297(a,1),297(a,1,2))].
% 1.10/1.39 443 double_divide(double_divide(A,double_divide(inverse(B),inverse(double_divide(double_divide(double_divide(C,inverse(double_divide(B,D))),C),E)))),double_divide(F,double_divide(A,F))) = double_divide(D,E). [para(138(a,1),392(a,2,2))].
% 1.10/1.39 445 double_divide(A,double_divide(double_divide(inverse(B),inverse(double_divide(inverse(double_divide(B,C)),D))),A)) = double_divide(C,double_divide(E,double_divide(D,E))). [para(207(a,1),392(a,1,1)),flip(a)].
% 1.10/1.39 491 double_divide(A,inverse(double_divide(inverse(double_divide(inverse(double_divide(B,double_divide(C,double_divide(D,C)))),E)),double_divide(D,E)))) = double_divide(A,inverse(double_divide(F,double_divide(inverse(B),F)))). [para(198(a,1),269(a,1,2,1,2))].
% 1.10/1.39 698 double_divide(double_divide(A,inverse(double_divide(B,double_divide(C,B)))),double_divide(double_divide(D,inverse(E)),double_divide(inverse(double_divide(A,inverse(double_divide(F,E)))),inverse(double_divide(V6,double_divide(D,V6)))))) = double_divide(C,F). [para(5(a,1),233(a,1,2))].
% 1.10/1.39 705 double_divide(double_divide(A,inverse(double_divide(B,double_divide(C,B)))),double_divide(D,double_divide(A,inverse(double_divide(E,double_divide(F,double_divide(D,F))))))) = double_divide(C,E). [para(18(a,1),233(a,1,2))].
% 1.10/1.39 729 double_divide(A,double_divide(inverse(B),inverse(double_divide(C,double_divide(D,C))))) = double_divide(A,double_divide(double_divide(E,inverse(F)),double_divide(inverse(double_divide(D,inverse(double_divide(B,F)))),inverse(double_divide(V6,double_divide(E,V6)))))). [para(7(a,1),233(a,1,2,1)),rewrite([233(19)]),flip(a)].
% 1.10/1.39 731 double_divide(double_divide(A,B),double_divide(C,double_divide(D,C))) = double_divide(E,double_divide(double_divide(inverse(B),inverse(double_divide(inverse(double_divide(F,double_divide(A,F))),D))),E)). [para(233(a,1),392(a,1,1))].
% 1.10/1.39 849 double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,C)))),inverse(double_divide(D,double_divide(inverse(inverse(double_divide(E,double_divide(C,E)))),D)))) = B. [para(272(a,1),64(a,1,1,1,1))].
% 1.10/1.39 861 double_divide(A,double_divide(inverse(B),inverse(double_divide(inverse(double_divide(B,C)),inverse(double_divide(D,double_divide(E,D))))))) = double_divide(inverse(double_divide(A,E)),inverse(C)). [para(207(a,1),272(a,1,2,1)),flip(a)].
% 1.10/1.39 901 double_divide(inverse(double_divide(inverse(double_divide(A,double_divide(B,A))),B)),inverse(C)) = C. [back_rewrite(230),rewrite([861(13)])].
% 1.10/1.39 950 double_divide(double_divide(double_divide(inverse(A),inverse(B)),C),double_divide(inverse(D),inverse(double_divide(E,double_divide(inverse(F),E))))) = double_divide(double_divide(inverse(double_divide(F,B)),inverse(double_divide(A,C))),D). [para(64(a,1),9(a,1,1,2))].
% 1.10/1.39 1055 double_divide(inverse(A),double_divide(inverse(inverse(double_divide(B,double_divide(C,B)))),inverse(A))) = C. [para(901(a,1),207(a,1,2,2,1))].
% 1.10/1.39 1196 double_divide(inverse(double_divide(A,double_divide(B,A))),double_divide(C,double_divide(B,inverse(double_divide(inverse(double_divide(D,double_divide(E,D))),double_divide(F,double_divide(C,F))))))) = E. [para(18(a,1),1055(a,1,2))].
% 1.10/1.39 1221 double_divide(A,double_divide(inverse(inverse(double_divide(B,double_divide(C,B)))),A)) = C. [para(1055(a,1),297(a,1)),flip(a)].
% 1.10/1.39 1264 double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,C)))),inverse(C)) = B. [back_rewrite(849),rewrite([1221(11)])].
% 1.10/1.39 1279 double_divide(A,double_divide(inverse(inverse(double_divide(inverse(double_divide(B,double_divide(C,B))),double_divide(D,double_divide(C,inverse(double_divide(E,double_divide(F,double_divide(D,F))))))))),A)) = inverse(E). [para(18(a,1),1221(a,1,2,1,1,1,2))].
% 1.10/1.39 1309 double_divide(A,double_divide(inverse(B),inverse(double_divide(inverse(double_divide(double_divide(inverse(inverse(double_divide(C,double_divide(D,C)))),E),D)),A)))) = double_divide(E,B). [para(1221(a,1),233(a,1,2,2,1,1,1,2))].
% 1.10/1.39 1317 double_divide(A,double_divide(inverse(inverse(double_divide(inverse(double_divide(inverse(double_divide(B,double_divide(C,B))),D)),double_divide(E,D)))),A)) = inverse(double_divide(E,C)). [para(272(a,1),1221(a,1,2,1,1,1,2))].
% 1.10/1.39 1321 inverse(double_divide(inverse(double_divide(A,double_divide(B,A))),B)) = double_divide(C,double_divide(inverse(inverse(double_divide(inverse(D),D))),C)). [para(901(a,1),1221(a,1,2,1,1,1,2)),flip(a)].
% 1.10/1.39 1324 double_divide(A,double_divide(inverse(inverse(double_divide(double_divide(inverse(inverse(double_divide(B,double_divide(C,B)))),D),C))),A)) = D. [para(1221(a,1),1221(a,1,2,1,1,1,2))].
% 1.10/1.39 1340 double_divide(inverse(double_divide(A,inverse(double_divide(B,C)))),inverse(double_divide(D,double_divide(E,D)))) = double_divide(double_divide(inverse(F),inverse(double_divide(inverse(B),inverse(double_divide(V6,double_divide(A,V6)))))),double_divide(inverse(double_divide(E,inverse(C))),inverse(double_divide(inverse(double_divide(V7,double_divide(V8,V7))),double_divide(double_divide(V9,inverse(V10)),double_divide(inverse(double_divide(V8,inverse(double_divide(F,V10)))),inverse(double_divide(V11,double_divide(V9,V11))))))))). [para(5(a,2),10(a,1,1,2,1)),flip(a)].
% 1.10/1.39 1370 inverse(double_divide(A,double_divide(inverse(B),A))) = double_divide(double_divide(inverse(C),inverse(D)),double_divide(inverse(inverse(double_divide(double_divide(E,inverse(double_divide(B,D))),E))),inverse(double_divide(inverse(double_divide(F,double_divide(V6,F))),double_divide(double_divide(V7,inverse(V8)),double_divide(inverse(double_divide(V6,inverse(double_divide(C,V8)))),inverse(double_divide(V9,double_divide(V7,V9))))))))). [para(64(a,1),10(a,1,1,2,1)),flip(a)].
% 1.10/1.39 1445 inverse(double_divide(inverse(double_divide(A,double_divide(B,A))),C)) = double_divide(double_divide(inverse(D),inverse(double_divide(E,C))),double_divide(inverse(inverse(double_divide(E,B))),inverse(double_divide(inverse(double_divide(F,double_divide(V6,F))),double_divide(double_divide(V7,inverse(V8)),double_divide(inverse(double_divide(V6,inverse(double_divide(D,V8)))),inverse(double_divide(V9,double_divide(V7,V9))))))))). [para(272(a,1),10(a,1,1,2,1)),flip(a)].
% 1.10/1.39 1541 double_divide(inverse(double_divide(double_divide(A,double_divide(B,A)),inverse(double_divide(C,D)))),inverse(D)) = double_divide(B,C). [para(297(a,1),1264(a,1,1,1,1))].
% 1.10/1.39 1588 double_divide(A,inverse(double_divide(B,double_divide(inverse(C),B)))) = double_divide(A,C). [back_rewrite(290),rewrite([1541(8)]),flip(a)].
% 1.10/1.39 1680 double_divide(double_divide(inverse(double_divide(A,B)),inverse(double_divide(C,D))),E) = double_divide(double_divide(double_divide(inverse(C),inverse(B)),D),double_divide(inverse(E),A)). [back_rewrite(950),rewrite([1588(10)]),flip(a)].
% 1.10/1.39 1728 double_divide(A,inverse(double_divide(inverse(double_divide(inverse(double_divide(B,double_divide(C,double_divide(D,C)))),E)),double_divide(D,E)))) = double_divide(A,B). [back_rewrite(491),rewrite([1588(15)])].
% 1.10/1.39 1761 double_divide(inverse(double_divide(double_divide(A,inverse(double_divide(inverse(B),inverse(double_divide(C,double_divide(D,C)))))),A)),E) = double_divide(D,inverse(double_divide(B,double_divide(F,double_divide(E,F))))). [back_rewrite(164),rewrite([1588(14)])].
% 1.10/1.39 1771 inverse(double_divide(A,double_divide(B,A))) = double_divide(inverse(double_divide(double_divide(C,inverse(double_divide(double_divide(D,inverse(E)),double_divide(inverse(double_divide(B,inverse(double_divide(F,E)))),inverse(double_divide(V6,double_divide(D,V6))))))),C)),inverse(F)). [back_rewrite(145),rewrite([1588(24)])].
% 1.10/1.39 1778 double_divide(A,double_divide(B,double_divide(C,inverse(double_divide(D,double_divide(E,double_divide(B,E))))))) = double_divide(inverse(double_divide(A,C)),D). [back_rewrite(92),rewrite([1588(7)]),flip(a)].
% 1.10/1.39 1780 double_divide(A,double_divide(double_divide(B,inverse(C)),double_divide(inverse(double_divide(D,inverse(double_divide(E,C)))),inverse(double_divide(F,double_divide(B,F)))))) = double_divide(inverse(double_divide(A,D)),E). [back_rewrite(77),rewrite([1588(7)]),flip(a)].
% 1.10/1.39 1846 double_divide(double_divide(double_divide(inverse(A),inverse(inverse(double_divide(B,C)))),double_divide(D,A)),double_divide(inverse(double_divide(inverse(B),inverse(double_divide(E,double_divide(F,E))))),F)) = double_divide(V6,double_divide(double_divide(D,inverse(C)),V6)). [back_rewrite(376),rewrite([1680(14)])].
% 1.10/1.39 1888 double_divide(A,double_divide(inverse(B),inverse(double_divide(C,double_divide(D,double_divide(A,D)))))) = double_divide(inverse(C),B). [back_rewrite(275),rewrite([1728(11)]),flip(a)].
% 1.10/1.39 1899 double_divide(inverse(A),inverse(double_divide(inverse(double_divide(inverse(double_divide(B,double_divide(C,B))),C)),D))) = double_divide(inverse(A),D). [back_rewrite(89),rewrite([1778(11),1888(16)])].
% 1.10/1.39 1918 inverse(double_divide(inverse(double_divide(A,double_divide(B,A))),C)) = double_divide(double_divide(inverse(D),inverse(double_divide(E,C))),double_divide(inverse(inverse(double_divide(E,B))),D)). [back_rewrite(1445),rewrite([1780(27),1899(20)])].
% 1.10/1.39 1942 inverse(double_divide(A,double_divide(inverse(B),A))) = double_divide(double_divide(inverse(C),inverse(D)),double_divide(inverse(inverse(double_divide(double_divide(E,inverse(double_divide(B,D))),E))),C)). [back_rewrite(1370),rewrite([1780(28),1899(21)])].
% 1.10/1.39 1952 double_divide(inverse(double_divide(A,inverse(double_divide(B,C)))),inverse(double_divide(D,double_divide(E,D)))) = double_divide(double_divide(inverse(F),inverse(double_divide(inverse(B),inverse(double_divide(V6,double_divide(A,V6)))))),double_divide(inverse(double_divide(E,inverse(C))),F)). [back_rewrite(1340),rewrite([1780(34),1899(27)])].
% 1.10/1.39 1958 double_divide(A,double_divide(inverse(inverse(double_divide(inverse(double_divide(inverse(double_divide(B,double_divide(C,B))),C)),D))),A)) = inverse(D). [back_rewrite(1279),rewrite([1778(10)])].
% 1.10/1.39 1959 double_divide(A,double_divide(B,A)) = B. [back_rewrite(1196),rewrite([1778(13),901(9)])].
% 1.10/1.39 1965 double_divide(double_divide(A,inverse(B)),double_divide(C,double_divide(A,inverse(double_divide(D,C))))) = double_divide(B,D). [back_rewrite(705),rewrite([1959(2),1959(4)])].
% 1.10/1.39 1978 double_divide(A,double_divide(B,inverse(double_divide(C,A)))) = double_divide(inverse(C),inverse(B)). [back_rewrite(72),rewrite([1959(3),1959(10),1965(13)]),flip(a)].
% 1.10/1.39 2022 double_divide(A,double_divide(double_divide(B,inverse(C)),double_divide(inverse(double_divide(D,inverse(double_divide(E,C)))),inverse(B)))) = double_divide(A,double_divide(inverse(E),inverse(D))). [back_rewrite(729),rewrite([1959(3),1959(12)]),flip(a)].
% 1.10/1.39 2023 double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))) = double_divide(B,C). [back_rewrite(698),rewrite([1959(2),1959(10),2022(12)])].
% 1.10/1.39 2028 double_divide(double_divide(A,B),A) = B. [back_rewrite(11),rewrite([1959(11),2023(12),1978(7),2023(7)])].
% 1.10/1.39 2048 inverse(inverse(double_divide(double_divide(inverse(inverse(A)),B),A))) = B. [back_rewrite(1324),rewrite([1959(2),1959(8)])].
% 1.10/1.39 2056 double_divide(A,inverse(inverse(B))) = double_divide(A,B). [back_rewrite(1309),rewrite([1959(3),1978(10),2048(6)])].
% 1.10/1.39 2061 double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,B)),C))) = double_divide(B,C). [back_rewrite(443),rewrite([2028(5),1959(9),2028(8)])].
% 1.10/1.39 2067 double_divide(double_divide(A,B),C) = double_divide(inverse(B),inverse(double_divide(inverse(A),C))). [back_rewrite(731),rewrite([1959(3),1959(5),1959(9)])].
% 1.10/1.39 2072 double_divide(inverse(inverse(A)),B) = double_divide(A,B). [back_rewrite(445),rewrite([2061(6),2067(2),1978(6),2056(5),1959(5)])].
% 1.10/1.39 2077 double_divide(A,double_divide(inverse(B),inverse(double_divide(inverse(C),inverse(double_divide(D,A)))))) = double_divide(inverse(D),inverse(double_divide(C,B))). [back_rewrite(195),rewrite([2028(5),2061(6),1959(3),2067(4)])].
% 1.10/1.39 2081 double_divide(inverse(A),inverse(double_divide(A,B))) = inverse(B). [back_rewrite(1958),rewrite([1959(2),2072(7),2067(5),2072(6),2067(4),2072(5),2077(8)])].
% 1.10/1.39 2086 double_divide(inverse(double_divide(A,inverse(double_divide(B,C)))),inverse(D)) = double_divide(A,inverse(double_divide(B,double_divide(D,inverse(C))))). [back_rewrite(1952),rewrite([1959(6),1959(10),2067(17),2072(18),1959(16),2056(16),2072(14),2067(12),2072(13),2072(13)])].
% 1.10/1.39 2087 inverse(inverse(A)) = A. [back_rewrite(1942),rewrite([1959(3),2028(9),2072(10),2067(9),2072(10),1959(8),2056(8),2072(6),1959(4)])].
% 1.10/1.39 2089 inverse(double_divide(inverse(A),B)) = double_divide(inverse(B),A). [back_rewrite(1918),rewrite([1959(2),2087(10),2067(9),2067(13),2087(6),2087(6),1978(10),2087(6),2087(6),2067(7),2081(8),2087(6)])].
% 1.10/1.39 2099 double_divide(A,double_divide(B,double_divide(inverse(A),C))) = double_divide(C,inverse(B)). [back_rewrite(1846),rewrite([2087(4),2067(5),2087(4),1959(4),1959(7),2089(8),2087(6),2028(6),2067(5),2087(2),2087(3),2028(2),2067(5),2087(4),2089(5)]),flip(a)].
% 1.10/1.39 2104 double_divide(inverse(double_divide(A,B)),C) = double_divide(A,double_divide(inverse(C),inverse(B))). [back_rewrite(1780),rewrite([1959(8),2086(8),1978(8)]),flip(a)].
% 1.10/1.39 2105 double_divide(A,double_divide(B,inverse(B))) = inverse(A). [back_rewrite(1771),rewrite([1959(2),1959(9),2104(9),2087(5),2087(6),2067(7),2087(3),2089(7),2104(6),2081(6),1978(5),2089(5),2087(3),2028(4),2104(5),2087(3)]),flip(a)].
% 1.10/1.39 2106 double_divide(A,inverse(double_divide(B,C))) = double_divide(A,double_divide(inverse(C),inverse(B))). [back_rewrite(1761),rewrite([1959(3),2089(4),2087(2),2028(3),2104(3),1959(6)]),flip(a)].
% 1.10/1.40 2111 double_divide(inverse(A),A) = double_divide(B,inverse(B)). [back_rewrite(1321),rewrite([1959(2),2089(3),2089(5),2089(5),2067(5),2087(5),2106(6),1959(7)])].
% 1.10/1.40 2112 inverse(double_divide(A,B)) = double_divide(inverse(B),inverse(A)). [back_rewrite(1317),rewrite([1959(2),2089(3),2067(4),2087(3),1959(3),2089(4),2087(2),2104(3),2099(5)]),flip(a)].
% 1.10/1.40 2128 double_divide(b1,inverse(b1)) != double_divide(a1,inverse(a1)) # answer(prove_these_axioms). [back_rewrite(4),rewrite([2112(5),2087(3),2112(9),2087(7),2112(15),2087(13),2105(15),2087(12),2112(16),2067(19),2087(15),2087(16),2112(17),2112(20),2112(18),2087(15),2087(16),2067(18),2112(20),2087(17),2087(18),2112(23),2112(26),2112(24),2087(21),2087(22),2067(24),2112(26),2087(23),2087(24)]),xx(b),xx(c)].
% 1.10/1.40 2130 double_divide(inverse(A),A) = c_0. [new_symbol(2111)].
% 1.10/1.40 2144 double_divide(A,inverse(A)) = c_0. [back_rewrite(2111),rewrite([2130(2)]),flip(a)].
% 1.10/1.40 2147 $F # answer(prove_these_axioms). [back_rewrite(2128),rewrite([2144(4),2144(5)]),xx(a)].
% 1.10/1.40
% 1.10/1.40 % SZS output end Refutation
% 1.10/1.40 ============================== end of proof ==========================
% 1.10/1.40
% 1.10/1.40 ============================== STATISTICS ============================
% 1.10/1.40
% 1.10/1.40 Given=30. Generated=4800. Kept=2145. proofs=1.
% 1.10/1.40 Usable=0. Sos=18. Demods=21. Limbo=3, Disabled=2127. Hints=0.
% 1.10/1.40 Megabytes=4.08.
% 1.10/1.40 User_CPU=0.41, System_CPU=0.01, Wall_clock=0.
% 1.10/1.40
% 1.10/1.40 ============================== end of statistics =====================
% 1.10/1.40
% 1.10/1.40 ============================== end of search =========================
% 1.10/1.40
% 1.10/1.40 THEOREM PROVED
% 1.10/1.40 % SZS status Unsatisfiable
% 1.10/1.40
% 1.10/1.40 Exiting with 1 proof.
% 1.10/1.40
% 1.10/1.40 Process 818 exit (max_proofs) Tue Jun 14 02:43:39 2022
% 1.10/1.40 Prover9 interrupted
%------------------------------------------------------------------------------