TSTP Solution File: GRP061-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP061-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 11:17:00 EDT 2022
% Result : Unsatisfiable 2.33s 2.67s
% Output : Refutation 2.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : GRP061-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 02:21:43 EDT 2022
% 0.13/0.35 % CPUTime :
% 2.33/2.67 ============================== Prover9 ===============================
% 2.33/2.67 Prover9 (32) version 2009-11A, November 2009.
% 2.33/2.67 Process 2957 was started by sandbox2 on n018.cluster.edu,
% 2.33/2.67 Tue Jun 14 02:21:43 2022
% 2.33/2.67 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_2804_n018.cluster.edu".
% 2.33/2.67 ============================== end of head ===========================
% 2.33/2.67
% 2.33/2.67 ============================== INPUT =================================
% 2.33/2.67
% 2.33/2.67 % Reading from file /tmp/Prover9_2804_n018.cluster.edu
% 2.33/2.67
% 2.33/2.67 set(prolog_style_variables).
% 2.33/2.67 set(auto2).
% 2.33/2.67 % set(auto2) -> set(auto).
% 2.33/2.67 % set(auto) -> set(auto_inference).
% 2.33/2.67 % set(auto) -> set(auto_setup).
% 2.33/2.67 % set(auto_setup) -> set(predicate_elim).
% 2.33/2.67 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.33/2.67 % set(auto) -> set(auto_limits).
% 2.33/2.67 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.33/2.67 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.33/2.67 % set(auto) -> set(auto_denials).
% 2.33/2.67 % set(auto) -> set(auto_process).
% 2.33/2.67 % set(auto2) -> assign(new_constants, 1).
% 2.33/2.67 % set(auto2) -> assign(fold_denial_max, 3).
% 2.33/2.67 % set(auto2) -> assign(max_weight, "200.000").
% 2.33/2.67 % set(auto2) -> assign(max_hours, 1).
% 2.33/2.67 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.33/2.67 % set(auto2) -> assign(max_seconds, 0).
% 2.33/2.67 % set(auto2) -> assign(max_minutes, 5).
% 2.33/2.67 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.33/2.67 % set(auto2) -> set(sort_initial_sos).
% 2.33/2.67 % set(auto2) -> assign(sos_limit, -1).
% 2.33/2.67 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.33/2.67 % set(auto2) -> assign(max_megs, 400).
% 2.33/2.67 % set(auto2) -> assign(stats, some).
% 2.33/2.67 % set(auto2) -> clear(echo_input).
% 2.33/2.67 % set(auto2) -> set(quiet).
% 2.33/2.67 % set(auto2) -> clear(print_initial_clauses).
% 2.33/2.67 % set(auto2) -> clear(print_given).
% 2.33/2.67 assign(lrs_ticks,-1).
% 2.33/2.67 assign(sos_limit,10000).
% 2.33/2.67 assign(order,kbo).
% 2.33/2.67 set(lex_order_vars).
% 2.33/2.67 clear(print_given).
% 2.33/2.67
% 2.33/2.67 % formulas(sos). % not echoed (2 formulas)
% 2.33/2.67
% 2.33/2.67 ============================== end of input ==========================
% 2.33/2.67
% 2.33/2.67 % From the command line: assign(max_seconds, 300).
% 2.33/2.67
% 2.33/2.67 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.33/2.67
% 2.33/2.67 % Formulas that are not ordinary clauses:
% 2.33/2.67
% 2.33/2.67 ============================== end of process non-clausal formulas ===
% 2.33/2.67
% 2.33/2.67 ============================== PROCESS INITIAL CLAUSES ===============
% 2.33/2.67
% 2.33/2.67 ============================== PREDICATE ELIMINATION =================
% 2.33/2.67
% 2.33/2.67 ============================== end predicate elimination =============
% 2.33/2.67
% 2.33/2.67 Auto_denials:
% 2.33/2.67 % copying label prove_these_axioms to answer in negative clause
% 2.33/2.67
% 2.33/2.67 Term ordering decisions:
% 2.33/2.67
% 2.33/2.67 % Assigning unary symbol inverse kb_weight 0 and highest precedence (10).
% 2.33/2.67 Function symbol KB weights: a1=1. a2=1. a3=1. b1=1. b2=1. b3=1. c3=1. multiply=1. inverse=0.
% 2.33/2.67
% 2.33/2.67 ============================== end of process initial clauses ========
% 2.33/2.67
% 2.33/2.67 ============================== CLAUSES FOR SEARCH ====================
% 2.33/2.67
% 2.33/2.67 ============================== end of clauses for search =============
% 2.33/2.67
% 2.33/2.67 ============================== SEARCH ================================
% 2.33/2.67
% 2.33/2.67 % Starting search at 0.01 seconds.
% 2.33/2.67
% 2.33/2.67 ============================== PROOF =================================
% 2.33/2.67 % SZS status Unsatisfiable
% 2.33/2.67 % SZS output start Refutation
% 2.33/2.67
% 2.33/2.67 % Proof 1 at 1.69 (+ 0.02) seconds: prove_these_axioms.
% 2.33/2.67 % Length of proof is 103.
% 2.33/2.67 % Level of proof is 34.
% 2.33/2.67 % Maximum clause weight is 59.000.
% 2.33/2.67 % Given clauses 59.
% 2.33/2.67
% 2.33/2.67 1 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(D,multiply(A,C))))))) = D # label(single_axiom) # label(axiom). [assumption].
% 2.33/2.67 2 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].
% 2.33/2.67 3 multiply(inverse(b1),b1) != multiply(inverse(a1),a1) | multiply(multiply(inverse(b2),b2),a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms). [copy(2),flip(a)].
% 2.33/2.67 4 inverse(multiply(A,multiply(multiply(B,multiply(C,multiply(multiply(inverse(C),D),inverse(multiply(E,multiply(B,D)))))),multiply(multiply(E,F),inverse(multiply(V6,multiply(A,F))))))) = V6. [para(1(a,1),1(a,1,1,2,2,1,1))].
% 2.33/2.67 5 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(multiply(inverse(A),C),inverse(multiply(D,multiply(E,C))))),D)))) = E. [para(1(a,1),1(a,1,1,2,2,2))].
% 2.33/2.67 7 inverse(multiply(multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(D,multiply(A,C)))))),multiply(E,multiply(multiply(inverse(E),multiply(multiply(D,F),inverse(multiply(V6,multiply(V7,F))))),V6)))) = V7. [para(4(a,1),1(a,1,1,2,2,2))].
% 2.33/2.67 9 inverse(multiply(A,multiply(multiply(B,multiply(C,multiply(multiply(inverse(C),D),inverse(multiply(E,multiply(B,D)))))),multiply(multiply(E,multiply(multiply(inverse(A),F),inverse(multiply(V6,multiply(V7,F))))),V6)))) = V7. [para(1(a,1),4(a,1,1,2,2,2))].
% 2.33/2.67 12 inverse(multiply(multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(D,multiply(A,C)))))),multiply(multiply(E,multiply(F,multiply(multiply(inverse(F),V6),inverse(multiply(V7,multiply(E,V6)))))),multiply(multiply(V7,multiply(multiply(D,V8),inverse(multiply(V9,multiply(V10,V8))))),V9)))) = V10. [para(4(a,1),4(a,1,1,2,2,2))].
% 2.33/2.67 13 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(multiply(inverse(A),multiply(multiply(inverse(C),D),inverse(multiply(E,multiply(F,D))))),E)),F)))) = C. [para(5(a,1),1(a,1,1,2,2,2))].
% 2.33/2.67 19 multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(D,multiply(A,C)))))) = inverse(multiply(E,multiply(F,multiply(multiply(inverse(F),multiply(multiply(inverse(E),multiply(multiply(D,V6),inverse(multiply(V7,multiply(V8,V6))))),V7)),V8)))). [para(4(a,1),5(a,1,1,2,2,1,2,2)),flip(a)].
% 2.33/2.67 20 inverse(multiply(A,multiply(multiply(B,multiply(C,multiply(multiply(inverse(C),multiply(multiply(inverse(B),D),inverse(multiply(E,multiply(F,D))))),E))),multiply(multiply(F,multiply(multiply(inverse(A),V6),inverse(multiply(V7,multiply(V8,V6))))),V7)))) = V8. [para(5(a,1),5(a,1,1,2,2,1,1))].
% 2.33/2.67 541 multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(inverse(D),multiply(A,C)))))) = D. [para(19(a,2),13(a,1))].
% 2.33/2.67 677 inverse(multiply(A,multiply(B,multiply(C,inverse(multiply(D,multiply(A,multiply(E,multiply(multiply(inverse(E),F),inverse(multiply(inverse(C),multiply(inverse(B),F)))))))))))) = D. [para(541(a,1),1(a,1,1,2,2,1))].
% 2.33/2.67 692 multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(multiply(inverse(A),multiply(multiply(inverse(inverse(C)),D),inverse(multiply(E,multiply(F,D))))),E)),F))) = C. [para(5(a,1),541(a,1,2,2,2))].
% 2.33/2.67 1281 inverse(multiply(inverse(A),multiply(A,multiply(B,inverse(multiply(C,B)))))) = C. [para(19(a,1),677(a,1,1,2,2,2,1,2)),rewrite([13(16)])].
% 2.33/2.67 1399 multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(C,inverse(multiply(D,C)))),D))) = A. [para(1281(a,1),19(a,1,2,2,2)),rewrite([13(23)])].
% 2.33/2.67 1401 multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(D,multiply(A,C)))))) = inverse(multiply(multiply(inverse(E),multiply(E,multiply(F,inverse(multiply(V6,F))))),multiply(V7,multiply(multiply(inverse(V7),multiply(multiply(V6,multiply(multiply(D,V8),inverse(multiply(V9,multiply(V10,V8))))),V9)),V10)))). [para(1281(a,1),19(a,2,1,2,2,1,2,1,1))].
% 2.33/2.67 1428 inverse(multiply(A,multiply(B,multiply(inverse(B),inverse(multiply(C,A)))))) = C. [para(1281(a,1),677(a,1,1,2,2,2,1,2,2,2,2)),rewrite([1399(9)])].
% 2.33/2.67 1432 inverse(multiply(inverse(A),multiply(A,multiply(multiply(B,multiply(C,inverse(multiply(D,C)))),D)))) = inverse(B). [para(1281(a,1),1281(a,1,1,2,2,2))].
% 2.33/2.67 1683 multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(inverse(A),inverse(multiply(C,inverse(D))))),C))) = D. [para(1428(a,1),541(a,1,2,2,2))].
% 2.33/2.67 1710 inverse(multiply(inverse(A),multiply(A,multiply(multiply(B,multiply(inverse(B),inverse(multiply(C,D)))),C)))) = D. [para(1428(a,1),1281(a,1,1,2,2,2))].
% 2.33/2.67 1721 inverse(multiply(multiply(A,multiply(inverse(A),inverse(multiply(B,C)))),multiply(D,multiply(inverse(D),B)))) = C. [para(1428(a,1),1428(a,1,1,2,2,2))].
% 2.33/2.67 1792 multiply(A,multiply(B,multiply(inverse(B),inverse(multiply(inverse(C),A))))) = C. [para(1399(a,1),541(a,1,2,2,1)),rewrite([1399(10)])].
% 2.33/2.67 1825 multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(multiply(C,multiply(inverse(C),inverse(multiply(D,E)))),D)),E))) = A. [para(1428(a,1),1399(a,1,2,2,1,2,2))].
% 2.33/2.67 1942 multiply(multiply(A,multiply(B,inverse(multiply(C,B)))),multiply(D,multiply(inverse(D),C))) = A. [para(1281(a,1),1792(a,1,2,2,2))].
% 2.33/2.67 1953 multiply(multiply(A,multiply(inverse(A),inverse(multiply(B,inverse(C))))),multiply(D,multiply(inverse(D),B))) = C. [para(1428(a,1),1792(a,1,2,2,2))].
% 2.33/2.67 2094 multiply(multiply(A,multiply(B,inverse(multiply(multiply(inverse(inverse(C)),inverse(multiply(inverse(D),C))),B)))),D) = A. [para(1792(a,1),1942(a,1,2))].
% 2.33/2.67 2305 multiply(inverse(A),multiply(A,multiply(multiply(B,multiply(C,inverse(multiply(D,C)))),D))) = B. [para(1432(a,1),13(a,1,1,2,2,1,2,1,2,1,1)),rewrite([13(15)]),flip(a)].
% 2.33/2.67 3014 multiply(A,multiply(multiply(inverse(A),B),inverse(multiply(C,multiply(D,B))))) = inverse(multiply(inverse(E),multiply(E,multiply(multiply(F,multiply(inverse(F),C)),D)))). [para(1(a,1),1710(a,1,1,2,2,1,2,2)),flip(a)].
% 2.33/2.67 3046 multiply(A,multiply(multiply(inverse(A),multiply(multiply(B,C),inverse(multiply(D,multiply(E,C))))),D)) = inverse(multiply(inverse(F),multiply(F,multiply(multiply(V6,multiply(inverse(V6),E)),multiply(V7,multiply(V8,multiply(multiply(inverse(V8),V9),inverse(multiply(B,multiply(V7,V9)))))))))). [para(7(a,1),1710(a,1,1,2,2,1,2,2)),flip(a)].
% 2.33/2.67 3099 multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(D,multiply(A,C)))))) = inverse(multiply(multiply(inverse(E),multiply(E,multiply(multiply(F,multiply(inverse(F),inverse(multiply(V6,V7)))),V6))),multiply(V8,multiply(multiply(inverse(V8),multiply(multiply(V7,multiply(multiply(D,V9),inverse(multiply(V10,multiply(V11,V9))))),V10)),V11)))). [para(1710(a,1),19(a,2,1,2,2,1,2,1,1))].
% 2.33/2.67 3123 multiply(multiply(inverse(A),multiply(A,multiply(multiply(B,multiply(inverse(B),inverse(multiply(C,D)))),C))),multiply(E,multiply(multiply(inverse(E),multiply(multiply(D,multiply(multiply(inverse(inverse(F)),V6),inverse(multiply(V7,multiply(V8,V6))))),V7)),V8))) = F. [para(1710(a,1),692(a,1,2,2,1,2,1,1))].
% 2.33/2.67 3184 multiply(A,multiply(multiply(B,multiply(inverse(B),inverse(multiply(C,D)))),C)) = inverse(multiply(inverse(E),multiply(E,multiply(multiply(F,multiply(inverse(F),D)),inverse(A))))). [para(1710(a,1),1710(a,1,1,2,2,1,2,2)),flip(a)].
% 2.33/2.67 3242 multiply(multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(D,multiply(A,C)))))),multiply(multiply(D,multiply(multiply(inverse(E),F),inverse(multiply(V6,multiply(V7,F))))),V6)) = inverse(multiply(multiply(V8,multiply(inverse(V8),V7)),multiply(V9,multiply(inverse(V9),E)))). [para(9(a,1),1721(a,1,1,1,2,2)),flip(a)].
% 2.33/2.67 3332 multiply(multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(D,multiply(A,C)))))),multiply(multiply(D,multiply(multiply(E,F),inverse(multiply(V6,multiply(V7,F))))),V6)) = inverse(multiply(multiply(V8,multiply(inverse(V8),V7)),multiply(V9,multiply(inverse(V9),multiply(V10,multiply(V11,multiply(multiply(inverse(V11),V12),inverse(multiply(E,multiply(V10,V12)))))))))). [para(12(a,1),1721(a,1,1,1,2,2)),flip(a)].
% 2.33/2.67 3682 multiply(A,multiply(B,inverse(multiply(multiply(inverse(inverse(C)),inverse(multiply(inverse(D),C))),B)))) = inverse(multiply(inverse(E),multiply(E,multiply(D,inverse(A))))). [para(2094(a,1),1281(a,1,1,2,2,2,1)),flip(a)].
% 2.33/2.67 3740 inverse(multiply(inverse(A),multiply(A,multiply(multiply(B,multiply(inverse(B),inverse(C))),multiply(C,multiply(D,inverse(multiply(multiply(inverse(inverse(E)),inverse(multiply(inverse(F),E))),D)))))))) = F. [para(2094(a,1),1710(a,1,1,2,2,1,2,2,1))].
% 2.33/2.67 4296 multiply(A,multiply(B,multiply(inverse(B),multiply(multiply(C,multiply(inverse(C),inverse(D))),D)))) = A. [para(1399(a,1),1825(a,1,2,2,1,2,1,2,2,1)),rewrite([1399(15)])].
% 2.33/2.67 4327 multiply(A,multiply(multiply(inverse(A),multiply(multiply(B,multiply(inverse(B),inverse(multiply(C,D)))),C)),D)) = inverse(multiply(inverse(E),multiply(E,multiply(multiply(F,multiply(inverse(F),inverse(V6))),V6)))). [para(1825(a,1),1710(a,1,1,2,2,1,2,2,1)),flip(a)].
% 2.33/2.67 4340 multiply(multiply(A,multiply(B,inverse(multiply(multiply(inverse(inverse(multiply(C,multiply(multiply(inverse(C),multiply(multiply(D,multiply(inverse(D),inverse(multiply(E,F)))),E)),F)))),inverse(inverse(V6))),B)))),V6) = A. [para(1825(a,1),2094(a,1,1,2,2,1,1,2,1))].
% 2.33/2.67 4483 multiply(multiply(A,multiply(inverse(A),multiply(multiply(B,multiply(inverse(B),inverse(C))),C))),multiply(D,multiply(inverse(D),inverse(inverse(E))))) = E. [para(4296(a,1),1792(a,1,2,2,2,1))].
% 2.33/2.67 4487 multiply(A,multiply(B,inverse(multiply(multiply(multiply(C,multiply(inverse(C),inverse(D))),D),B)))) = A. [para(4296(a,1),1942(a,1))].
% 2.33/2.67 4516 multiply(A,multiply(inverse(A),multiply(multiply(B,multiply(inverse(B),inverse(C))),C))) = inverse(multiply(multiply(D,multiply(inverse(D),inverse(E))),multiply(F,multiply(inverse(F),E)))). [para(4296(a,1),1721(a,1,1,1,2,2,1)),flip(a)].
% 2.33/2.67 4525 multiply(A,multiply(inverse(A),inverse(multiply(multiply(multiply(B,multiply(inverse(B),inverse(C))),C),inverse(D))))) = D. [para(4296(a,1),1953(a,1))].
% 2.33/2.67 4541 multiply(A,multiply(B,multiply(inverse(B),multiply(C,multiply(inverse(C),inverse(multiply(D,multiply(inverse(D),multiply(multiply(E,multiply(inverse(E),inverse(F))),F))))))))) = A. [para(4296(a,1),4296(a,1,2,2,2))].
% 2.33/2.67 4543 multiply(multiply(A,multiply(inverse(A),inverse(B))),B) = inverse(multiply(inverse(C),C)). [para(4487(a,1),1(a,1,1,2)),flip(a)].
% 2.33/2.67 4670 inverse(multiply(inverse(A),multiply(A,multiply(multiply(B,inverse(multiply(multiply(multiply(C,multiply(inverse(C),inverse(D))),D),B))),inverse(E))))) = E. [para(4487(a,1),1281(a,1,1,2,2,2,1))].
% 2.33/2.67 4705 multiply(inverse(A),multiply(A,multiply(B,multiply(C,inverse(multiply(multiply(D,inverse(multiply(multiply(multiply(E,multiply(inverse(E),inverse(F))),F),D))),C)))))) = B. [para(4487(a,1),2305(a,1,2,2))].
% 2.33/2.67 4721 multiply(A,inverse(multiply(multiply(multiply(B,multiply(inverse(B),inverse(C))),C),A))) = inverse(multiply(inverse(D),multiply(D,multiply(multiply(E,multiply(inverse(E),inverse(F))),F)))). [para(4487(a,1),1710(a,1,1,2,2,1,2,2,1)),flip(a)].
% 2.33/2.67 4725 multiply(A,inverse(multiply(multiply(multiply(B,multiply(inverse(B),inverse(C))),C),A))) = inverse(multiply(multiply(D,multiply(inverse(D),inverse(E))),multiply(F,multiply(inverse(F),E)))). [para(4487(a,1),1721(a,1,1,1,2,2,1)),flip(a)].
% 2.33/2.67 4726 inverse(multiply(multiply(A,multiply(inverse(A),inverse(multiply(multiply(B,inverse(multiply(multiply(multiply(C,multiply(inverse(C),inverse(D))),D),B))),E)))),multiply(F,inverse(F)))) = E. [para(4487(a,1),1721(a,1,1,2,2))].
% 2.33/2.67 4755 multiply(A,multiply(multiply(B,multiply(inverse(B),multiply(multiply(C,multiply(inverse(C),inverse(D))),D))),inverse(multiply(multiply(E,multiply(inverse(E),inverse(F))),F)))) = A. [para(4296(a,1),4487(a,1,2,2,1))].
% 2.33/2.67 4934 multiply(A,multiply(B,inverse(multiply(C,B)))) = inverse(multiply(D,multiply(multiply(E,multiply(F,multiply(multiply(inverse(F),multiply(multiply(inverse(E),V6),inverse(multiply(V7,multiply(V8,V6))))),V7))),multiply(multiply(V8,multiply(multiply(inverse(D),multiply(V9,multiply(inverse(V9),C))),inverse(multiply(V10,A)))),V10)))). [para(1942(a,1),20(a,1,1,2,2,1,2,2,1,2)),flip(a)].
% 2.33/2.67 4994 multiply(A,multiply(inverse(A),inverse(multiply(B,inverse(C))))) = inverse(multiply(D,multiply(multiply(E,multiply(F,multiply(multiply(inverse(F),multiply(multiply(inverse(E),V6),inverse(multiply(V7,multiply(V8,V6))))),V7))),multiply(multiply(V8,multiply(multiply(inverse(D),multiply(V9,multiply(inverse(V9),B))),inverse(multiply(V10,C)))),V10)))). [para(1953(a,1),20(a,1,1,2,2,1,2,2,1,2)),flip(a)].
% 2.33/2.67 5292 multiply(inverse(A),multiply(A,multiply(inverse(multiply(inverse(B),B)),C))) = multiply(D,multiply(inverse(D),inverse(multiply(E,inverse(multiply(C,E)))))). [para(4543(a,1),2305(a,1,2,2,1))].
% 2.33/2.67 5293 multiply(inverse(multiply(A,multiply(inverse(A),inverse(multiply(multiply(B,multiply(C,inverse(multiply(D,C)))),D))))),inverse(multiply(inverse(E),E))) = B. [para(4543(a,1),2305(a,1,2))].
% 2.33/2.67 5302 multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(inverse(A),inverse(inverse(multiply(inverse(C),C))))),multiply(D,multiply(inverse(D),inverse(inverse(E))))))) = E. [para(4543(a,1),1683(a,1,2,2,1,2,2,1))].
% 2.33/2.67 5329 multiply(inverse(A),A) = inverse(inverse(multiply(inverse(B),B))). [para(4543(a,1),1721(a,1,1)),flip(a)].
% 2.33/2.67 5370 multiply(A,multiply(inverse(A),inverse(multiply(B,multiply(inverse(B),multiply(multiply(C,multiply(inverse(C),inverse(D))),D)))))) = inverse(multiply(inverse(E),E)). [para(4543(a,1),4296(a,1)),flip(a)].
% 2.33/2.67 5399 multiply(inverse(A),A) = c_0. [new_symbol(5329)].
% 2.33/2.67 5418 multiply(A,multiply(inverse(A),inverse(multiply(B,multiply(inverse(B),multiply(multiply(C,multiply(inverse(C),inverse(D))),D)))))) = inverse(c_0). [back_rewrite(5370),rewrite([5399(14)])].
% 2.33/2.67 5451 inverse(inverse(c_0)) = c_0. [back_rewrite(5329),rewrite([5399(2),5399(3)]),flip(a)].
% 2.33/2.67 5474 multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(inverse(A),c_0)),multiply(C,multiply(inverse(C),inverse(inverse(D))))))) = D. [back_rewrite(5302),rewrite([5399(4),5451(5)])].
% 2.33/2.67 5481 multiply(inverse(multiply(A,multiply(inverse(A),inverse(multiply(multiply(B,multiply(C,inverse(multiply(D,C)))),D))))),inverse(c_0)) = B. [back_rewrite(5293),rewrite([5399(12)])].
% 2.33/2.67 5482 multiply(inverse(A),multiply(A,multiply(inverse(c_0),B))) = multiply(C,multiply(inverse(C),inverse(multiply(D,inverse(multiply(B,D)))))). [back_rewrite(5292),rewrite([5399(3)])].
% 2.33/2.67 5688 multiply(multiply(A,multiply(inverse(A),inverse(B))),B) = inverse(c_0). [back_rewrite(4543),rewrite([5399(7)])].
% 2.33/2.67 5689 multiply(c_0,a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms). [back_rewrite(3),rewrite([5399(4),5399(5),5399(7)]),xx(a)].
% 2.33/2.67 5695 multiply(A,multiply(B,multiply(inverse(B),multiply(C,multiply(inverse(C),inverse(multiply(D,multiply(inverse(D),inverse(c_0))))))))) = A. [back_rewrite(4541),rewrite([5688(8)])].
% 2.33/2.67 5706 multiply(A,multiply(inverse(A),inverse(multiply(B,multiply(inverse(B),inverse(c_0)))))) = inverse(c_0). [back_rewrite(5418),rewrite([5688(7)])].
% 2.33/2.67 5783 multiply(A,inverse(c_0)) = A. [back_rewrite(4755),rewrite([5688(6),5688(10),5451(8),5688(7)])].
% 2.33/2.67 5801 inverse(multiply(multiply(A,multiply(inverse(A),inverse(multiply(multiply(B,inverse(multiply(inverse(c_0),B))),C)))),multiply(D,inverse(D)))) = C. [back_rewrite(4726),rewrite([5688(6)])].
% 2.33/2.67 5802 multiply(A,inverse(multiply(inverse(c_0),A))) = inverse(multiply(multiply(B,multiply(inverse(B),inverse(C))),multiply(D,multiply(inverse(D),C)))). [back_rewrite(4725),rewrite([5688(5)])].
% 2.33/2.67 5804 multiply(A,inverse(multiply(inverse(c_0),A))) = inverse(c_0). [back_rewrite(4721),rewrite([5688(5),5688(11),5783(9),5399(7)])].
% 2.33/2.67 5815 multiply(inverse(A),multiply(A,B)) = B. [back_rewrite(4705),rewrite([5688(6),5804(6),5804(6),5783(4)])].
% 2.33/2.67 5834 inverse(multiply(inverse(c_0),inverse(A))) = A. [back_rewrite(4670),rewrite([5688(6),5804(6),5815(7)])].
% 2.33/2.67 5931 multiply(A,multiply(inverse(A),B)) = B. [back_rewrite(4525),rewrite([5688(6),5834(6)])].
% 2.33/2.67 5937 inverse(c_0) = c_0. [back_rewrite(4516),rewrite([5931(5),5399(3),5931(4),5931(5),5931(5),5399(3)]),flip(a)].
% 2.33/2.67 5952 multiply(c_0,inverse(inverse(A))) = A. [back_rewrite(4483),rewrite([5931(5),5399(3),5931(4),5931(6)])].
% 2.33/2.67 6034 multiply(A,multiply(multiply(inverse(A),multiply(inverse(multiply(B,C)),B)),C)) = c_0. [back_rewrite(4327),rewrite([5931(6),5931(12),5399(10),5815(11),5937(9)])].
% 2.33/2.67 6035 multiply(A,c_0) = A. [back_rewrite(4296),rewrite([5931(5),5399(3),5931(4)])].
% 2.33/2.67 6038 multiply(A,inverse(multiply(B,inverse(B)))) = A. [back_rewrite(5695),rewrite([5937(5),6035(5),5931(7),5931(6)])].
% 2.33/2.67 6043 multiply(multiply(A,multiply(B,inverse(multiply(C,B)))),C) = A. [back_rewrite(4340),rewrite([5931(6),6034(7),5937(2),5937(2),5952(4)])].
% 2.33/2.67 6087 multiply(A,inverse(A)) = c_0. [back_rewrite(5706),rewrite([5937(4),6035(4),6038(5),5937(4)])].
% 2.33/2.67 6125 inverse(inverse(A)) = A. [back_rewrite(5481),rewrite([6043(6),5931(4),5937(4),6035(4)])].
% 2.33/2.67 6135 multiply(A,inverse(multiply(c_0,A))) = c_0. [back_rewrite(5802),rewrite([5937(2),5931(8),5931(8),5399(6),5937(6)])].
% 2.33/2.67 6136 multiply(c_0,A) = A. [back_rewrite(5801),rewrite([5937(3),6135(5),5931(6),6087(5),6035(5),6125(4)])].
% 2.33/2.67 6147 inverse(multiply(A,inverse(multiply(B,A)))) = B. [back_rewrite(5482),rewrite([5937(3),6136(3),5815(3),5931(7)]),flip(a)].
% 2.33/2.67 6174 multiply(A,inverse(multiply(inverse(B),A))) = B. [back_rewrite(3740),rewrite([5931(5),6125(4),5815(11),5815(10),6147(8)])].
% 2.33/2.67 6179 multiply(A,multiply(B,inverse(multiply(C,B)))) = inverse(multiply(C,inverse(A))). [back_rewrite(3682),rewrite([6125(2),6174(4),5815(9)])].
% 2.33/2.67 6191 multiply(A,multiply(inverse(multiply(B,C)),B)) = inverse(multiply(C,inverse(A))). [back_rewrite(3184),rewrite([5931(5),5931(8),5815(9)])].
% 2.33/2.67 6216 multiply(multiply(inverse(A),inverse(multiply(B,inverse(A)))),multiply(C,multiply(multiply(inverse(C),multiply(multiply(B,multiply(multiply(D,E),inverse(multiply(F,multiply(V6,E))))),F)),V6))) = D. [back_rewrite(3123),rewrite([5931(6),6191(5),6125(8)])].
% 2.33/2.67 6229 multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(D,multiply(A,C)))))) = inverse(D). [back_rewrite(3099),rewrite([5931(14),6191(13),6216(25)])].
% 2.33/2.67 6254 multiply(A,multiply(multiply(inverse(A),multiply(multiply(B,C),inverse(multiply(D,multiply(E,C))))),D)) = inverse(multiply(E,inverse(B))). [back_rewrite(3046),rewrite([5931(13),6229(18),5815(14)])].
% 2.33/2.67 6268 multiply(A,multiply(multiply(inverse(A),B),inverse(multiply(C,multiply(D,B))))) = inverse(multiply(C,D)). [back_rewrite(3014),rewrite([5931(11),5815(11)])].
% 2.33/2.67 6295 multiply(A,inverse(multiply(B,A))) = inverse(B). [back_rewrite(1401),rewrite([6268(7),6179(8),6216(20)])].
% 2.33/2.67 6351 multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(A)),C))) = C. [back_rewrite(5474),rewrite([6035(4),6125(6),5931(6)])].
% 2.33/2.67 6355 inverse(multiply(A,multiply(inverse(B),multiply(multiply(B,multiply(multiply(inverse(A),C),inverse(multiply(D,E)))),D)))) = inverse(multiply(C,inverse(E))). [back_rewrite(4994),rewrite([5931(6),6254(13),6125(5),6295(6),5931(8)]),flip(a)].
% 2.33/2.67 6360 inverse(multiply(A,inverse(B))) = multiply(B,inverse(A)). [back_rewrite(4934),rewrite([6295(3),6254(12),6125(4),6295(5),5931(7),6355(13)]),flip(a)].
% 2.33/2.67 6450 multiply(inverse(A),multiply(multiply(A,multiply(multiply(B,C),inverse(multiply(D,multiply(E,C))))),D)) = multiply(B,inverse(E)). [back_rewrite(3332),rewrite([6268(7),6295(3),5931(12),6268(17),6295(13),5931(13),6360(12)])].
% 2.33/2.67 6469 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [back_rewrite(3242),rewrite([6268(7),6295(3),6450(10),5931(6),5931(6)]),flip(a)].
% 2.33/2.67 6846 multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms). [back_rewrite(5689),rewrite([6136(3)]),xx(a)].
% 2.33/2.67 7084 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)). [para(5931(a,1),6351(a,1,2,2)),rewrite([6469(6),6125(4),6125(4)]),flip(a)].
% 2.33/2.67 7085 $F # answer(prove_these_axioms). [resolve(7084,a,6846,a)].
% 2.33/2.67
% 2.33/2.67 % SZS output end Refutation
% 2.33/2.67 ============================== end of proof ==========================
% 2.33/2.67
% 2.33/2.67 ============================== STATISTICS ============================
% 2.33/2.67
% 2.33/2.67 Given=59. Generated=14197. Kept=7083. proofs=1.
% 2.33/2.67 Usable=14. Sos=451. Demods=466. Limbo=3, Disabled=6616. Hints=0.
% 2.33/2.67 Megabytes=16.41.
% 2.33/2.67 User_CPU=1.69, System_CPU=0.02, Wall_clock=2.
% 2.33/2.67
% 2.33/2.67 ============================== end of statistics =====================
% 2.33/2.67
% 2.33/2.67 ============================== end of search =========================
% 2.33/2.67
% 2.33/2.67 THEOREM PROVED
% 2.33/2.67 % SZS status Unsatisfiable
% 2.33/2.67
% 2.33/2.67 Exiting with 1 proof.
% 2.33/2.67
% 2.33/2.67 Process 2957 exit (max_proofs) Tue Jun 14 02:21:45 2022
% 2.33/2.67 Prover9 interrupted
%------------------------------------------------------------------------------