TSTP Solution File: BOO070-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO070-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 : Thu Jul 14 23:48:07 EDT 2022
% Result : Unsatisfiable 1.38s 1.65s
% Output : Refutation 1.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO070-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 1 21:48:42 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.38/1.65 ============================== Prover9 ===============================
% 1.38/1.65 Prover9 (32) version 2009-11A, November 2009.
% 1.38/1.65 Process 32312 was started by sandbox on n026.cluster.edu,
% 1.38/1.65 Wed Jun 1 21:48:42 2022
% 1.38/1.65 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_32158_n026.cluster.edu".
% 1.38/1.65 ============================== end of head ===========================
% 1.38/1.65
% 1.38/1.65 ============================== INPUT =================================
% 1.38/1.65
% 1.38/1.65 % Reading from file /tmp/Prover9_32158_n026.cluster.edu
% 1.38/1.65
% 1.38/1.65 set(prolog_style_variables).
% 1.38/1.65 set(auto2).
% 1.38/1.65 % set(auto2) -> set(auto).
% 1.38/1.65 % set(auto) -> set(auto_inference).
% 1.38/1.65 % set(auto) -> set(auto_setup).
% 1.38/1.65 % set(auto_setup) -> set(predicate_elim).
% 1.38/1.65 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.38/1.65 % set(auto) -> set(auto_limits).
% 1.38/1.65 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.38/1.65 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.38/1.65 % set(auto) -> set(auto_denials).
% 1.38/1.65 % set(auto) -> set(auto_process).
% 1.38/1.65 % set(auto2) -> assign(new_constants, 1).
% 1.38/1.65 % set(auto2) -> assign(fold_denial_max, 3).
% 1.38/1.65 % set(auto2) -> assign(max_weight, "200.000").
% 1.38/1.65 % set(auto2) -> assign(max_hours, 1).
% 1.38/1.65 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.38/1.65 % set(auto2) -> assign(max_seconds, 0).
% 1.38/1.65 % set(auto2) -> assign(max_minutes, 5).
% 1.38/1.65 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.38/1.65 % set(auto2) -> set(sort_initial_sos).
% 1.38/1.65 % set(auto2) -> assign(sos_limit, -1).
% 1.38/1.65 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.38/1.65 % set(auto2) -> assign(max_megs, 400).
% 1.38/1.65 % set(auto2) -> assign(stats, some).
% 1.38/1.65 % set(auto2) -> clear(echo_input).
% 1.38/1.65 % set(auto2) -> set(quiet).
% 1.38/1.65 % set(auto2) -> clear(print_initial_clauses).
% 1.38/1.65 % set(auto2) -> clear(print_given).
% 1.38/1.65 assign(lrs_ticks,-1).
% 1.38/1.65 assign(sos_limit,10000).
% 1.38/1.65 assign(order,kbo).
% 1.38/1.65 set(lex_order_vars).
% 1.38/1.65 clear(print_given).
% 1.38/1.65
% 1.38/1.65 % formulas(sos). % not echoed (2 formulas)
% 1.38/1.65
% 1.38/1.65 ============================== end of input ==========================
% 1.38/1.65
% 1.38/1.65 % From the command line: assign(max_seconds, 300).
% 1.38/1.65
% 1.38/1.65 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.38/1.65
% 1.38/1.65 % Formulas that are not ordinary clauses:
% 1.38/1.65
% 1.38/1.65 ============================== end of process non-clausal formulas ===
% 1.38/1.65
% 1.38/1.65 ============================== PROCESS INITIAL CLAUSES ===============
% 1.38/1.65
% 1.38/1.65 ============================== PREDICATE ELIMINATION =================
% 1.38/1.65
% 1.38/1.65 ============================== end predicate elimination =============
% 1.38/1.65
% 1.38/1.65 Auto_denials:
% 1.38/1.65 % copying label prove_tba_axioms_4 to answer in negative clause
% 1.38/1.65
% 1.38/1.65 Term ordering decisions:
% 1.38/1.65
% 1.38/1.65 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 1.38/1.65 Function symbol KB weights: a=1. b=1. multiply=1. inverse=0.
% 1.38/1.65
% 1.38/1.65 ============================== end of process initial clauses ========
% 1.38/1.65
% 1.38/1.65 ============================== CLAUSES FOR SEARCH ====================
% 1.38/1.65
% 1.38/1.65 ============================== end of clauses for search =============
% 1.38/1.65
% 1.38/1.65 ============================== SEARCH ================================
% 1.38/1.65
% 1.38/1.65 % Starting search at 0.01 seconds.
% 1.38/1.65
% 1.38/1.65 ============================== PROOF =================================
% 1.38/1.65 % SZS status Unsatisfiable
% 1.38/1.65 % SZS output start Refutation
% 1.38/1.65
% 1.38/1.65 % Proof 1 at 0.58 (+ 0.01) seconds: prove_tba_axioms_4.
% 1.38/1.65 % Length of proof is 48.
% 1.38/1.65 % Level of proof is 16.
% 1.38/1.65 % Maximum clause weight is 93.000.
% 1.38/1.65 % Given clauses 33.
% 1.38/1.65
% 1.38/1.65 1 multiply(multiply(A,inverse(A),B),inverse(multiply(multiply(C,D,E),F,multiply(C,D,V6))),multiply(D,multiply(V6,F,E),C)) = B # label(single_axiom) # label(axiom). [assumption].
% 1.38/1.65 2 multiply(a,a,b) != a # label(prove_tba_axioms_4) # label(negated_conjecture) # answer(prove_tba_axioms_4). [assumption].
% 1.38/1.65 3 multiply(multiply(A,B,C),inverse(multiply(multiply(D,E,F),V6,multiply(D,E,V7))),multiply(E,multiply(V7,V6,F),D)) = multiply(B,multiply(C,inverse(multiply(A,B,V8)),V8),A). [para(1(a,1),1(a,1,1))].
% 1.38/1.65 6 multiply(multiply(A,inverse(A),B),inverse(multiply(multiply(C,D,multiply(E,multiply(F,V6,V7),V8)),inverse(multiply(multiply(V8,E,V7),V6,multiply(V8,E,F))),multiply(C,D,multiply(V9,inverse(V9),V10)))),multiply(D,V10,C)) = B. [para(1(a,1),1(a,1,3,2))].
% 1.38/1.65 12 multiply(inverse(A),multiply(B,inverse(multiply(A,inverse(A),C)),C),A) = B. [para(3(a,1),1(a,1))].
% 1.38/1.65 28 multiply(A,multiply(B,inverse(multiply(C,A,D)),D),C) = multiply(A,multiply(B,inverse(multiply(C,A,E)),E),C). [para(3(a,1),3(a,1))].
% 1.38/1.65 40 multiply(multiply(A,inverse(A),B),inverse(multiply(multiply(C,D,E),multiply(F,inverse(multiply(E,inverse(E),V6)),V6),multiply(C,D,inverse(E)))),multiply(D,F,C)) = B. [para(12(a,1),1(a,1,3,2))].
% 1.38/1.65 41 multiply(multiply(A,inverse(A),B),inverse(multiply(multiply(C,inverse(C),D),inverse(multiply(C,inverse(C),D)),multiply(C,inverse(C),E))),E) = B. [para(12(a,1),1(a,1,3))].
% 1.38/1.65 43 multiply(multiply(A,inverse(multiply(B,inverse(B),C)),C),multiply(B,inverse(multiply(inverse(B),multiply(A,inverse(multiply(B,inverse(B),C)),C),D)),D),inverse(B)) = multiply(A,inverse(multiply(multiply(E,F,V6),V7,multiply(E,F,V8))),multiply(F,multiply(V8,V7,V6),E)). [para(12(a,1),3(a,1,1)),flip(a)].
% 1.38/1.65 47 multiply(multiply(A,B,C),inverse(multiply(multiply(D,inverse(D),E),inverse(multiply(D,inverse(D),E)),multiply(D,inverse(D),F))),F) = multiply(B,multiply(C,inverse(multiply(A,B,V6)),V6),A). [para(12(a,1),3(a,1,3))].
% 1.38/1.65 54 multiply(multiply(A,inverse(A),B),inverse(multiply(multiply(C,D,E),inverse(multiply(C,D,E)),multiply(C,D,F))),multiply(D,multiply(F,inverse(multiply(C,D,V6)),V6),C)) = B. [para(28(a,1),1(a,1,3))].
% 1.38/1.65 65 multiply(multiply(A,inverse(multiply(B,inverse(B),C)),C),multiply(D,inverse(multiply(inverse(B),multiply(A,inverse(multiply(B,inverse(B),C)),C),E)),E),inverse(B)) = multiply(multiply(A,inverse(multiply(B,inverse(B),C)),C),multiply(D,inverse(A),B),inverse(B)). [para(12(a,1),28(a,1,2,2,1)),flip(a)].
% 1.38/1.65 68 multiply(multiply(A,inverse(multiply(B,inverse(B),C)),C),multiply(B,inverse(A),B),inverse(B)) = multiply(A,inverse(multiply(multiply(D,E,F),V6,multiply(D,E,V7))),multiply(E,multiply(V7,V6,F),D)). [back_rewrite(43),rewrite([65(14)])].
% 1.38/1.65 248 multiply(inverse(multiply(multiply(A,B,C),inverse(multiply(A,B,C)),multiply(A,B,D))),multiply(E,inverse(multiply(A,B,D)),multiply(B,multiply(D,inverse(multiply(A,B,F)),F),A)),multiply(multiply(A,B,C),inverse(multiply(A,B,C)),multiply(A,B,D))) = E. [para(54(a,1),12(a,1,2,2,1))].
% 1.38/1.65 356 multiply(multiply(multiply(inverse(A),inverse(A),A),multiply(inverse(A),inverse(multiply(A,inverse(A),B)),B),multiply(C,inverse(C),D)),inverse(multiply(multiply(E,inverse(E),F),inverse(multiply(E,inverse(E),F)),multiply(E,inverse(E),V6))),V6) = multiply(multiply(inverse(A),inverse(multiply(A,inverse(A),B)),B),D,multiply(inverse(A),inverse(A),A)). [para(40(a,1),47(a,2,2))].
% 1.38/1.65 612 multiply(multiply(A,inverse(A),B),inverse(multiply(C,inverse(C),C)),multiply(C,inverse(multiply(multiply(D,E,F),V6,multiply(D,E,V7))),multiply(E,multiply(V7,V6,F),D))) = B. [para(68(a,1),1(a,1,3)),rewrite([12(8),12(9)])].
% 1.38/1.65 646 multiply(multiply(A,inverse(multiply(B,inverse(B),C)),C),multiply(B,inverse(A),B),inverse(B)) = multiply(A,inverse(multiply(multiply(D,E,F),inverse(multiply(D,E,F)),multiply(D,E,V6))),multiply(multiply(D,E,V6),inverse(multiply(multiply(V7,V8,V9),V10,multiply(V7,V8,V11))),multiply(V8,multiply(V11,V10,V9),V7))). [para(3(a,2),68(a,2,3))].
% 1.38/1.65 714 multiply(multiply(multiply(multiply(multiply(A,B,C),D,multiply(A,B,E)),inverse(multiply(F,inverse(F),V6)),V6),multiply(F,inverse(multiply(multiply(A,B,C),D,multiply(A,B,E))),F),inverse(F)),inverse(multiply(multiply(V7,V8,V9),inverse(multiply(V7,V8,V9)),multiply(V7,V8,V10))),multiply(V8,multiply(V10,inverse(multiply(V7,V8,V11)),V11),V7)) = multiply(B,multiply(E,D,C),A). [para(68(a,2),54(a,1,1))].
% 1.38/1.65 718 multiply(multiply(A,inverse(A),B),inverse(multiply(multiply(C,inverse(multiply(multiply(D,E,F),V6,multiply(D,E,V7))),V8),inverse(multiply(C,inverse(multiply(multiply(D,E,F),V6,multiply(D,E,V7))),V8)),multiply(C,inverse(multiply(multiply(D,E,F),V6,multiply(D,E,V7))),V9))),multiply(inverse(multiply(multiply(D,E,F),V6,multiply(D,E,V7))),multiply(V9,inverse(multiply(multiply(C,inverse(multiply(V10,inverse(V10),V11)),V11),multiply(V10,inverse(C),V10),inverse(V10))),multiply(E,multiply(V7,V6,F),D)),C)) = B. [para(68(a,2),54(a,1,3,2,2,1))].
% 1.38/1.65 856 multiply(inverse(multiply(A,inverse(A),A)),multiply(B,inverse(A),multiply(A,inverse(multiply(multiply(C,D,E),F,multiply(C,D,V6))),multiply(D,multiply(V6,F,E),C))),multiply(A,inverse(A),A)) = B. [para(612(a,1),12(a,1,2,2,1))].
% 1.38/1.65 1068 multiply(multiply(A,inverse(A),B),inverse(multiply(C,inverse(C),multiply(D,inverse(D),E))),multiply(inverse(C),E,C)) = B. [para(41(a,1),6(a,1,2,1)),rewrite([12(12)])].
% 1.38/1.65 1197 multiply(inverse(A),B,A) = B. [para(1068(a,1),1(a,1,1)),rewrite([1(9)]),flip(a)].
% 1.38/1.65 1213 multiply(A,inverse(multiply(B,inverse(B),C)),C) = A. [para(1068(a,1),12(a,1,2,2,1)),rewrite([1197(10),1197(14)])].
% 1.38/1.65 1289 multiply(A,inverse(B),multiply(B,inverse(multiply(multiply(C,D,E),F,multiply(C,D,V6))),multiply(D,multiply(V6,F,E),C))) = A. [back_rewrite(856),rewrite([1197(15)])].
% 1.38/1.65 1306 multiply(multiply(inverse(A),inverse(A),multiply(B,inverse(B),C)),inverse(multiply(multiply(D,inverse(D),E),inverse(multiply(D,inverse(D),E)),multiply(D,inverse(D),F))),F) = multiply(inverse(A),C,inverse(A)). [back_rewrite(356),rewrite([1197(3),1213(6),1213(20),1197(19)])].
% 1.38/1.65 1308 multiply(A,inverse(multiply(B,C,D)),multiply(C,multiply(D,inverse(multiply(B,C,E)),E),B)) = A. [back_rewrite(248),rewrite([1197(19)])].
% 1.38/1.65 1529 multiply(multiply(A,inverse(A),B),inverse(multiply(multiply(C,inverse(multiply(multiply(D,E,F),V6,multiply(D,E,V7))),V8),inverse(multiply(C,inverse(multiply(multiply(D,E,F),V6,multiply(D,E,V7))),V8)),multiply(C,inverse(multiply(multiply(D,E,F),V6,multiply(D,E,V7))),V9))),multiply(inverse(multiply(multiply(D,E,F),V6,multiply(D,E,V7))),multiply(V9,inverse(multiply(C,multiply(V10,inverse(C),V10),inverse(V10))),multiply(E,multiply(V7,V6,F),D)),C)) = B. [back_rewrite(718),rewrite([1213(28)])].
% 1.38/1.65 1533 multiply(multiply(multiply(multiply(A,B,C),D,multiply(A,B,E)),multiply(F,inverse(multiply(multiply(A,B,C),D,multiply(A,B,E))),F),inverse(F)),inverse(multiply(multiply(V6,V7,V8),inverse(multiply(V6,V7,V8)),multiply(V6,V7,V9))),multiply(V7,multiply(V9,inverse(multiply(V6,V7,V10)),V10),V6)) = multiply(B,multiply(E,D,C),A). [back_rewrite(714),rewrite([1213(7)])].
% 1.38/1.65 1583 multiply(A,multiply(B,inverse(A),B),inverse(B)) = multiply(A,inverse(multiply(multiply(C,D,E),inverse(multiply(C,D,E)),multiply(C,D,F))),multiply(multiply(C,D,F),inverse(multiply(multiply(V6,V7,V8),V9,multiply(V6,V7,V10))),multiply(V7,multiply(V10,V9,V8),V6))). [back_rewrite(646),rewrite([1213(4)])].
% 1.38/1.65 1699 multiply(multiply(A,B,inverse(C)),inverse(multiply(multiply(D,E,F),V6,multiply(D,E,V7))),multiply(E,multiply(V7,V6,F),D)) = multiply(B,inverse(multiply(A,B,C)),A). [para(1197(a,1),3(a,2,2))].
% 1.38/1.65 1709 multiply(inverse(inverse(A)),inverse(multiply(multiply(B,C,multiply(D,multiply(E,F,V6),V7)),inverse(multiply(multiply(V7,D,V6),F,multiply(V7,D,E))),multiply(B,C,multiply(V8,inverse(V8),V9)))),multiply(C,V9,B)) = A. [para(1197(a,1),6(a,1,1))].
% 1.38/1.65 1727 multiply(inverse(multiply(A,inverse(A),B)),multiply(C,inverse(multiply(D,inverse(multiply(A,inverse(A),B)),E)),E),D) = multiply(inverse(multiply(A,inverse(A),B)),multiply(C,inverse(D),B),D). [para(1213(a,1),28(a,1,2,2,1)),flip(a)].
% 1.38/1.65 1750 inverse(multiply(A,inverse(A),B)) = inverse(B). [para(1213(a,1),1197(a,1)),flip(a)].
% 1.38/1.65 1752 multiply(A,inverse(B),B) = A. [para(1213(a,1),1213(a,1,2,1)),rewrite([1750(3)])].
% 1.38/1.65 1800 multiply(inverse(A),multiply(B,inverse(multiply(C,inverse(A),D)),D),C) = multiply(inverse(A),multiply(B,inverse(C),A),C). [back_rewrite(1727),rewrite([1750(3),1750(4),1750(9)])].
% 1.38/1.65 1843 multiply(A,multiply(B,inverse(A),B),inverse(B)) = A. [back_rewrite(1583),rewrite([1750(10),1289(15)])].
% 1.38/1.65 1851 multiply(multiply(A,B,C),D,multiply(A,B,E)) = multiply(B,multiply(E,D,C),A). [back_rewrite(1533),rewrite([1843(10),1750(9),1308(10)])].
% 1.38/1.65 1853 multiply(A,inverse(A),B) = B. [back_rewrite(1529),rewrite([1851(5),1851(9),1851(14),1851(16),1800(12),1851(14),1843(18),1752(20)])].
% 1.38/1.65 1892 multiply(inverse(A),inverse(A),B) = multiply(inverse(A),B,inverse(A)). [back_rewrite(1306),rewrite([1853(4),1853(5),1853(5),1853(6),1853(5),1752(5)])].
% 1.38/1.65 1944 inverse(inverse(A)) = A. [back_rewrite(1709),rewrite([1851(8),1853(10),1851(10),1752(8),1752(6)])].
% 1.38/1.65 1947 multiply(A,inverse(multiply(B,A,C)),B) = multiply(B,A,inverse(C)). [back_rewrite(1699),rewrite([1851(5),1752(8)]),flip(a)].
% 1.38/1.65 1975 multiply(A,B,inverse(B)) = A. [para(1944(a,1),1752(a,1,2))].
% 1.38/1.65 1982 multiply(A,B,C) = multiply(C,B,A). [para(1197(a,1),1851(a,2)),rewrite([1853(2),1853(2)])].
% 1.38/1.65 2028 multiply(inverse(A),B,inverse(A)) = multiply(B,inverse(A),inverse(A)). [back_rewrite(1892),rewrite([1982(3)]),flip(a)].
% 1.38/1.65 2043 multiply(A,B,A) = multiply(A,A,B). [para(1944(a,1),2028(a,1,1)),rewrite([1944(2),1944(3),1944(3),1982(2)])].
% 1.38/1.65 2053 multiply(A,B,B) = multiply(B,A,B). [para(2043(a,2),1982(a,2))].
% 1.38/1.65 2061 multiply(A,A,B) = A. [para(1975(a,1),1947(a,1,2,1)),rewrite([1752(2),1944(2),2053(1),2043(1)]),flip(a)].
% 1.38/1.65 2062 $F # answer(prove_tba_axioms_4). [resolve(2061,a,2,a)].
% 1.38/1.65
% 1.38/1.65 % SZS output end Refutation
% 1.38/1.65 ============================== end of proof ==========================
% 1.38/1.65
% 1.38/1.65 ============================== STATISTICS ============================
% 1.38/1.65
% 1.38/1.65 Given=33. Generated=3979. Kept=2061. proofs=1.
% 1.38/1.65 Usable=10. Sos=57. Demods=64. Limbo=4, Disabled=1991. Hints=0.
% 1.38/1.65 Megabytes=6.69.
% 1.38/1.65 User_CPU=0.58, System_CPU=0.01, Wall_clock=1.
% 1.38/1.65
% 1.38/1.65 ============================== end of statistics =====================
% 1.38/1.65
% 1.38/1.65 ============================== end of search =========================
% 1.38/1.65
% 1.38/1.65 THEOREM PROVED
% 1.38/1.65 % SZS status Unsatisfiable
% 1.38/1.65
% 1.38/1.65 Exiting with 1 proof.
% 1.38/1.65
% 1.38/1.65 Process 32312 exit (max_proofs) Wed Jun 1 21:48:43 2022
% 1.38/1.65 Prover9 interrupted
%------------------------------------------------------------------------------