TSTP Solution File: GRP441-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP441-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n003.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 11:19:06 EDT 2022
% Result : Unsatisfiable 3.50s 3.80s
% Output : Refutation 3.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP441-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jun 14 06:31:10 EDT 2022
% 0.14/0.34 % CPUTime :
% 3.50/3.80 ============================== Prover9 ===============================
% 3.50/3.80 Prover9 (32) version 2009-11A, November 2009.
% 3.50/3.80 Process 30484 was started by sandbox2 on n003.cluster.edu,
% 3.50/3.80 Tue Jun 14 06:31:10 2022
% 3.50/3.80 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_30331_n003.cluster.edu".
% 3.50/3.80 ============================== end of head ===========================
% 3.50/3.80
% 3.50/3.80 ============================== INPUT =================================
% 3.50/3.80
% 3.50/3.80 % Reading from file /tmp/Prover9_30331_n003.cluster.edu
% 3.50/3.80
% 3.50/3.80 set(prolog_style_variables).
% 3.50/3.80 set(auto2).
% 3.50/3.80 % set(auto2) -> set(auto).
% 3.50/3.80 % set(auto) -> set(auto_inference).
% 3.50/3.80 % set(auto) -> set(auto_setup).
% 3.50/3.80 % set(auto_setup) -> set(predicate_elim).
% 3.50/3.80 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.50/3.80 % set(auto) -> set(auto_limits).
% 3.50/3.80 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.50/3.80 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.50/3.80 % set(auto) -> set(auto_denials).
% 3.50/3.80 % set(auto) -> set(auto_process).
% 3.50/3.80 % set(auto2) -> assign(new_constants, 1).
% 3.50/3.80 % set(auto2) -> assign(fold_denial_max, 3).
% 3.50/3.80 % set(auto2) -> assign(max_weight, "200.000").
% 3.50/3.80 % set(auto2) -> assign(max_hours, 1).
% 3.50/3.80 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.50/3.80 % set(auto2) -> assign(max_seconds, 0).
% 3.50/3.80 % set(auto2) -> assign(max_minutes, 5).
% 3.50/3.80 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.50/3.80 % set(auto2) -> set(sort_initial_sos).
% 3.50/3.80 % set(auto2) -> assign(sos_limit, -1).
% 3.50/3.80 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.50/3.80 % set(auto2) -> assign(max_megs, 400).
% 3.50/3.80 % set(auto2) -> assign(stats, some).
% 3.50/3.80 % set(auto2) -> clear(echo_input).
% 3.50/3.80 % set(auto2) -> set(quiet).
% 3.50/3.80 % set(auto2) -> clear(print_initial_clauses).
% 3.50/3.80 % set(auto2) -> clear(print_given).
% 3.50/3.80 assign(lrs_ticks,-1).
% 3.50/3.80 assign(sos_limit,10000).
% 3.50/3.80 assign(order,kbo).
% 3.50/3.80 set(lex_order_vars).
% 3.50/3.80 clear(print_given).
% 3.50/3.80
% 3.50/3.80 % formulas(sos). % not echoed (2 formulas)
% 3.50/3.80
% 3.50/3.80 ============================== end of input ==========================
% 3.50/3.80
% 3.50/3.80 % From the command line: assign(max_seconds, 300).
% 3.50/3.80
% 3.50/3.80 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.50/3.80
% 3.50/3.80 % Formulas that are not ordinary clauses:
% 3.50/3.80
% 3.50/3.80 ============================== end of process non-clausal formulas ===
% 3.50/3.80
% 3.50/3.80 ============================== PROCESS INITIAL CLAUSES ===============
% 3.50/3.80
% 3.50/3.80 ============================== PREDICATE ELIMINATION =================
% 3.50/3.80
% 3.50/3.80 ============================== end predicate elimination =============
% 3.50/3.80
% 3.50/3.80 Auto_denials:
% 3.50/3.80 % copying label prove_these_axioms_3 to answer in negative clause
% 3.50/3.80
% 3.50/3.80 Term ordering decisions:
% 3.50/3.80
% 3.50/3.80 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 3.50/3.80 Function symbol KB weights: a3=1. b3=1. c3=1. multiply=1. inverse=0.
% 3.50/3.80
% 3.50/3.80 ============================== end of process initial clauses ========
% 3.50/3.80
% 3.50/3.80 ============================== CLAUSES FOR SEARCH ====================
% 3.50/3.80
% 3.50/3.80 ============================== end of clauses for search =============
% 3.50/3.80
% 3.50/3.80 ============================== SEARCH ================================
% 3.50/3.80
% 3.50/3.80 % Starting search at 0.01 seconds.
% 3.50/3.80
% 3.50/3.80 ============================== PROOF =================================
% 3.50/3.80 % SZS status Unsatisfiable
% 3.50/3.80 % SZS output start Refutation
% 3.50/3.80
% 3.50/3.80 % Proof 1 at 2.74 (+ 0.02) seconds: prove_these_axioms_3.
% 3.50/3.80 % Length of proof is 100.
% 3.50/3.80 % Level of proof is 34.
% 3.50/3.80 % Maximum clause weight is 59.000.
% 3.50/3.80 % Given clauses 58.
% 3.50/3.80
% 3.50/3.80 1 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(D,multiply(A,C))))))) = D # label(single_axiom) # label(axiom). [assumption].
% 3.50/3.80 2 multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # label(prove_these_axioms_3) # label(negated_conjecture) # answer(prove_these_axioms_3). [assumption].
% 3.50/3.80 3 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))].
% 3.50/3.80 4 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))].
% 3.50/3.80 6 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(3(a,1),1(a,1,1,2,2,2))].
% 3.50/3.80 8 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),3(a,1,1,2,2,2))].
% 3.50/3.80 11 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(3(a,1),3(a,1,1,2,2,2))].
% 3.50/3.80 12 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(4(a,1),1(a,1,1,2,2,2))].
% 3.50/3.80 18 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(3(a,1),4(a,1,1,2,2,1,2,2)),flip(a)].
% 3.50/3.80 19 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(4(a,1),4(a,1,1,2,2,1,1))].
% 3.50/3.80 540 multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(inverse(D),multiply(A,C)))))) = D. [para(18(a,2),12(a,1))].
% 3.50/3.80 676 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(540(a,1),1(a,1,1,2,2,1))].
% 3.50/3.80 691 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(4(a,1),540(a,1,2,2,2))].
% 3.50/3.80 1280 inverse(multiply(inverse(A),multiply(A,multiply(B,inverse(multiply(C,B)))))) = C. [para(18(a,1),676(a,1,1,2,2,2,1,2)),rewrite([12(16)])].
% 3.50/3.80 1398 multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(C,inverse(multiply(D,C)))),D))) = A. [para(1280(a,1),18(a,1,2,2,2)),rewrite([12(23)])].
% 3.50/3.80 1400 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(1280(a,1),18(a,2,1,2,2,1,2,1,1))].
% 3.50/3.80 1427 inverse(multiply(A,multiply(B,multiply(inverse(B),inverse(multiply(C,A)))))) = C. [para(1280(a,1),676(a,1,1,2,2,2,1,2,2,2,2)),rewrite([1398(9)])].
% 3.50/3.80 1431 inverse(multiply(inverse(A),multiply(A,multiply(multiply(B,multiply(C,inverse(multiply(D,C)))),D)))) = inverse(B). [para(1280(a,1),1280(a,1,1,2,2,2))].
% 3.50/3.80 1682 multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(inverse(A),inverse(multiply(C,inverse(D))))),C))) = D. [para(1427(a,1),540(a,1,2,2,2))].
% 3.50/3.80 1709 inverse(multiply(inverse(A),multiply(A,multiply(multiply(B,multiply(inverse(B),inverse(multiply(C,D)))),C)))) = D. [para(1427(a,1),1280(a,1,1,2,2,2))].
% 3.50/3.80 1720 inverse(multiply(multiply(A,multiply(inverse(A),inverse(multiply(B,C)))),multiply(D,multiply(inverse(D),B)))) = C. [para(1427(a,1),1427(a,1,1,2,2,2))].
% 3.50/3.80 1791 multiply(A,multiply(B,multiply(inverse(B),inverse(multiply(inverse(C),A))))) = C. [para(1398(a,1),540(a,1,2,2,1)),rewrite([1398(10)])].
% 3.50/3.80 1824 multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(multiply(C,multiply(inverse(C),inverse(multiply(D,E)))),D)),E))) = A. [para(1427(a,1),1398(a,1,2,2,1,2,2))].
% 3.50/3.80 1941 multiply(multiply(A,multiply(B,inverse(multiply(C,B)))),multiply(D,multiply(inverse(D),C))) = A. [para(1280(a,1),1791(a,1,2,2,2))].
% 3.50/3.80 1952 multiply(multiply(A,multiply(inverse(A),inverse(multiply(B,inverse(C))))),multiply(D,multiply(inverse(D),B))) = C. [para(1427(a,1),1791(a,1,2,2,2))].
% 3.50/3.80 2093 multiply(multiply(A,multiply(B,inverse(multiply(multiply(inverse(inverse(C)),inverse(multiply(inverse(D),C))),B)))),D) = A. [para(1791(a,1),1941(a,1,2))].
% 3.50/3.80 2304 multiply(inverse(A),multiply(A,multiply(multiply(B,multiply(C,inverse(multiply(D,C)))),D))) = B. [para(1431(a,1),12(a,1,1,2,2,1,2,1,2,1,1)),rewrite([12(15)]),flip(a)].
% 3.50/3.80 3013 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),1709(a,1,1,2,2,1,2,2)),flip(a)].
% 3.50/3.80 3045 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(6(a,1),1709(a,1,1,2,2,1,2,2)),flip(a)].
% 3.50/3.80 3098 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(1709(a,1),18(a,2,1,2,2,1,2,1,1))].
% 3.50/3.80 3122 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(1709(a,1),691(a,1,2,2,1,2,1,1))].
% 3.50/3.80 3183 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(1709(a,1),1709(a,1,1,2,2,1,2,2)),flip(a)].
% 3.50/3.80 3241 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(8(a,1),1720(a,1,1,1,2,2)),flip(a)].
% 3.50/3.80 3331 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(11(a,1),1720(a,1,1,1,2,2)),flip(a)].
% 3.50/3.80 3681 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(2093(a,1),1280(a,1,1,2,2,2,1)),flip(a)].
% 3.50/3.80 3739 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(2093(a,1),1709(a,1,1,2,2,1,2,2,1))].
% 3.50/3.80 4295 multiply(A,multiply(B,multiply(inverse(B),multiply(multiply(C,multiply(inverse(C),inverse(D))),D)))) = A. [para(1398(a,1),1824(a,1,2,2,1,2,1,2,2,1)),rewrite([1398(15)])].
% 3.50/3.80 4326 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(1824(a,1),1709(a,1,1,2,2,1,2,2,1)),flip(a)].
% 3.50/3.80 4339 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(1824(a,1),2093(a,1,1,2,2,1,1,2,1))].
% 3.50/3.80 4482 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(4295(a,1),1791(a,1,2,2,2,1))].
% 3.50/3.80 4486 multiply(A,multiply(B,inverse(multiply(multiply(multiply(C,multiply(inverse(C),inverse(D))),D),B)))) = A. [para(4295(a,1),1941(a,1))].
% 3.50/3.80 4515 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(4295(a,1),1720(a,1,1,1,2,2,1)),flip(a)].
% 3.50/3.80 4524 multiply(A,multiply(inverse(A),inverse(multiply(multiply(multiply(B,multiply(inverse(B),inverse(C))),C),inverse(D))))) = D. [para(4295(a,1),1952(a,1))].
% 3.50/3.80 4540 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(4295(a,1),4295(a,1,2,2,2))].
% 3.50/3.80 4542 multiply(multiply(A,multiply(inverse(A),inverse(B))),B) = inverse(multiply(inverse(C),C)). [para(4486(a,1),1(a,1,1,2)),flip(a)].
% 3.50/3.80 4669 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(4486(a,1),1280(a,1,1,2,2,2,1))].
% 3.50/3.80 4704 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(4486(a,1),2304(a,1,2,2))].
% 3.50/3.80 4720 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(4486(a,1),1709(a,1,1,2,2,1,2,2,1)),flip(a)].
% 3.50/3.80 4724 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(4486(a,1),1720(a,1,1,1,2,2,1)),flip(a)].
% 3.50/3.80 4725 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(4486(a,1),1720(a,1,1,2,2))].
% 3.50/3.80 4754 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(4295(a,1),4486(a,1,2,2,1))].
% 3.50/3.80 4933 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(1941(a,1),19(a,1,1,2,2,1,2,2,1,2)),flip(a)].
% 3.50/3.80 4993 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(1952(a,1),19(a,1,1,2,2,1,2,2,1,2)),flip(a)].
% 3.50/3.80 5291 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(4542(a,1),2304(a,1,2,2,1))].
% 3.50/3.80 5292 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(4542(a,1),2304(a,1,2))].
% 3.50/3.80 5301 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(4542(a,1),1682(a,1,2,2,1,2,2,1))].
% 3.50/3.80 5328 multiply(inverse(A),A) = inverse(inverse(multiply(inverse(B),B))). [para(4542(a,1),1720(a,1,1)),flip(a)].
% 3.50/3.80 5369 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(4542(a,1),4295(a,1)),flip(a)].
% 3.50/3.80 5398 multiply(inverse(A),A) = c_0. [new_symbol(5328)].
% 3.50/3.80 5417 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(5369),rewrite([5398(14)])].
% 3.50/3.80 5450 inverse(inverse(c_0)) = c_0. [back_rewrite(5328),rewrite([5398(2),5398(3)]),flip(a)].
% 3.50/3.80 5473 multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(inverse(A),c_0)),multiply(C,multiply(inverse(C),inverse(inverse(D))))))) = D. [back_rewrite(5301),rewrite([5398(4),5450(5)])].
% 3.50/3.80 5480 multiply(inverse(multiply(A,multiply(inverse(A),inverse(multiply(multiply(B,multiply(C,inverse(multiply(D,C)))),D))))),inverse(c_0)) = B. [back_rewrite(5292),rewrite([5398(12)])].
% 3.50/3.80 5481 multiply(inverse(A),multiply(A,multiply(inverse(c_0),B))) = multiply(C,multiply(inverse(C),inverse(multiply(D,inverse(multiply(B,D)))))). [back_rewrite(5291),rewrite([5398(3)])].
% 3.50/3.80 5687 multiply(multiply(A,multiply(inverse(A),inverse(B))),B) = inverse(c_0). [back_rewrite(4542),rewrite([5398(7)])].
% 3.50/3.80 5693 multiply(A,multiply(B,multiply(inverse(B),multiply(C,multiply(inverse(C),inverse(multiply(D,multiply(inverse(D),inverse(c_0))))))))) = A. [back_rewrite(4540),rewrite([5687(8)])].
% 3.50/3.80 5704 multiply(A,multiply(inverse(A),inverse(multiply(B,multiply(inverse(B),inverse(c_0)))))) = inverse(c_0). [back_rewrite(5417),rewrite([5687(7)])].
% 3.50/3.80 5781 multiply(A,inverse(c_0)) = A. [back_rewrite(4754),rewrite([5687(6),5687(10),5450(8),5687(7)])].
% 3.50/3.80 5799 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(4725),rewrite([5687(6)])].
% 3.50/3.80 5800 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(4724),rewrite([5687(5)])].
% 3.50/3.80 5802 multiply(A,inverse(multiply(inverse(c_0),A))) = inverse(c_0). [back_rewrite(4720),rewrite([5687(5),5687(11),5781(9),5398(7)])].
% 3.50/3.80 5813 multiply(inverse(A),multiply(A,B)) = B. [back_rewrite(4704),rewrite([5687(6),5802(6),5802(6),5781(4)])].
% 3.50/3.80 5832 inverse(multiply(inverse(c_0),inverse(A))) = A. [back_rewrite(4669),rewrite([5687(6),5802(6),5813(7)])].
% 3.50/3.80 5929 multiply(A,multiply(inverse(A),B)) = B. [back_rewrite(4524),rewrite([5687(6),5832(6)])].
% 3.50/3.80 5935 inverse(c_0) = c_0. [back_rewrite(4515),rewrite([5929(5),5398(3),5929(4),5929(5),5929(5),5398(3)]),flip(a)].
% 3.50/3.80 5950 multiply(c_0,inverse(inverse(A))) = A. [back_rewrite(4482),rewrite([5929(5),5398(3),5929(4),5929(6)])].
% 3.50/3.80 6032 multiply(A,multiply(multiply(inverse(A),multiply(inverse(multiply(B,C)),B)),C)) = c_0. [back_rewrite(4326),rewrite([5929(6),5929(12),5398(10),5813(11),5935(9)])].
% 3.50/3.80 6033 multiply(A,c_0) = A. [back_rewrite(4295),rewrite([5929(5),5398(3),5929(4)])].
% 3.50/3.80 6036 multiply(A,inverse(multiply(B,inverse(B)))) = A. [back_rewrite(5693),rewrite([5935(5),6033(5),5929(7),5929(6)])].
% 3.50/3.80 6041 multiply(multiply(A,multiply(B,inverse(multiply(C,B)))),C) = A. [back_rewrite(4339),rewrite([5929(6),6032(7),5935(2),5935(2),5950(4)])].
% 3.50/3.80 6085 multiply(A,inverse(A)) = c_0. [back_rewrite(5704),rewrite([5935(4),6033(4),6036(5),5935(4)])].
% 3.50/3.80 6123 inverse(inverse(A)) = A. [back_rewrite(5480),rewrite([6041(6),5929(4),5935(4),6033(4)])].
% 3.50/3.80 6133 multiply(A,inverse(multiply(c_0,A))) = c_0. [back_rewrite(5800),rewrite([5935(2),5929(8),5929(8),5398(6),5935(6)])].
% 3.50/3.80 6134 multiply(c_0,A) = A. [back_rewrite(5799),rewrite([5935(3),6133(5),5929(6),6085(5),6033(5),6123(4)])].
% 3.50/3.80 6145 inverse(multiply(A,inverse(multiply(B,A)))) = B. [back_rewrite(5481),rewrite([5935(3),6134(3),5813(3),5929(7)]),flip(a)].
% 3.50/3.80 6172 multiply(A,inverse(multiply(inverse(B),A))) = B. [back_rewrite(3739),rewrite([5929(5),6123(4),5813(11),5813(10),6145(8)])].
% 3.50/3.80 6177 multiply(A,multiply(B,inverse(multiply(C,B)))) = inverse(multiply(C,inverse(A))). [back_rewrite(3681),rewrite([6123(2),6172(4),5813(9)])].
% 3.50/3.80 6189 multiply(A,multiply(inverse(multiply(B,C)),B)) = inverse(multiply(C,inverse(A))). [back_rewrite(3183),rewrite([5929(5),5929(8),5813(9)])].
% 3.50/3.80 6214 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(3122),rewrite([5929(6),6189(5),6123(8)])].
% 3.50/3.80 6227 multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(D,multiply(A,C)))))) = inverse(D). [back_rewrite(3098),rewrite([5929(14),6189(13),6214(25)])].
% 3.50/3.80 6252 multiply(A,multiply(multiply(inverse(A),multiply(multiply(B,C),inverse(multiply(D,multiply(E,C))))),D)) = inverse(multiply(E,inverse(B))). [back_rewrite(3045),rewrite([5929(13),6227(18),5813(14)])].
% 3.50/3.80 6266 multiply(A,multiply(multiply(inverse(A),B),inverse(multiply(C,multiply(D,B))))) = inverse(multiply(C,D)). [back_rewrite(3013),rewrite([5929(11),5813(11)])].
% 3.50/3.80 6293 multiply(A,inverse(multiply(B,A))) = inverse(B). [back_rewrite(1400),rewrite([6266(7),6177(8),6214(20)])].
% 3.50/3.80 6349 multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(A)),C))) = C. [back_rewrite(5473),rewrite([6033(4),6123(6),5929(6)])].
% 3.50/3.80 6353 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(4993),rewrite([5929(6),6252(13),6123(5),6293(6),5929(8)]),flip(a)].
% 3.50/3.80 6358 inverse(multiply(A,inverse(B))) = multiply(B,inverse(A)). [back_rewrite(4933),rewrite([6293(3),6252(12),6123(4),6293(5),5929(7),6353(13)]),flip(a)].
% 3.50/3.80 6448 multiply(inverse(A),multiply(multiply(A,multiply(multiply(B,C),inverse(multiply(D,multiply(E,C))))),D)) = multiply(B,inverse(E)). [back_rewrite(3331),rewrite([6266(7),6293(3),5929(12),6266(17),6293(13),5929(13),6358(12)])].
% 3.50/3.80 6467 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [back_rewrite(3241),rewrite([6266(7),6293(3),6448(10),5929(6),5929(6)]),flip(a)].
% 3.50/3.80 7081 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)). [para(5929(a,1),6349(a,1,2,2)),rewrite([6467(6),6123(4),6123(4)]),flip(a)].
% 3.50/3.80 7082 $F # answer(prove_these_axioms_3). [resolve(7081,a,2,a)].
% 3.50/3.80
% 3.50/3.80 % SZS output end Refutation
% 3.50/3.80 ============================== end of proof ==========================
% 3.50/3.80
% 3.50/3.80 ============================== STATISTICS ============================
% 3.50/3.80
% 3.50/3.80 Given=58. Generated=14195. Kept=7081. proofs=1.
% 3.50/3.80 Usable=14. Sos=451. Demods=466. Limbo=3, Disabled=6614. Hints=0.
% 3.50/3.80 Megabytes=16.39.
% 3.50/3.80 User_CPU=2.74, System_CPU=0.02, Wall_clock=3.
% 3.50/3.80
% 3.50/3.80 ============================== end of statistics =====================
% 3.50/3.80
% 3.50/3.80 ============================== end of search =========================
% 3.50/3.80
% 3.50/3.80 THEOREM PROVED
% 3.50/3.80 % SZS status Unsatisfiable
% 3.50/3.80
% 3.50/3.80 Exiting with 1 proof.
% 3.50/3.80
% 3.50/3.80 Process 30484 exit (max_proofs) Tue Jun 14 06:31:13 2022
% 3.50/3.80 Prover9 interrupted
%------------------------------------------------------------------------------