TSTP Solution File: BOO071-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO071-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 1.29s 1.56s
% Output : Refutation 1.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO071-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n024.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 19:04:06 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.29/1.56 ============================== Prover9 ===============================
% 1.29/1.56 Prover9 (32) version 2009-11A, November 2009.
% 1.29/1.56 Process 10589 was started by sandbox2 on n024.cluster.edu,
% 1.29/1.56 Wed Jun 1 19:04:06 2022
% 1.29/1.56 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_10435_n024.cluster.edu".
% 1.29/1.56 ============================== end of head ===========================
% 1.29/1.56
% 1.29/1.56 ============================== INPUT =================================
% 1.29/1.56
% 1.29/1.56 % Reading from file /tmp/Prover9_10435_n024.cluster.edu
% 1.29/1.56
% 1.29/1.56 set(prolog_style_variables).
% 1.29/1.56 set(auto2).
% 1.29/1.56 % set(auto2) -> set(auto).
% 1.29/1.56 % set(auto) -> set(auto_inference).
% 1.29/1.56 % set(auto) -> set(auto_setup).
% 1.29/1.56 % set(auto_setup) -> set(predicate_elim).
% 1.29/1.56 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.29/1.56 % set(auto) -> set(auto_limits).
% 1.29/1.56 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.29/1.56 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.29/1.56 % set(auto) -> set(auto_denials).
% 1.29/1.56 % set(auto) -> set(auto_process).
% 1.29/1.56 % set(auto2) -> assign(new_constants, 1).
% 1.29/1.56 % set(auto2) -> assign(fold_denial_max, 3).
% 1.29/1.56 % set(auto2) -> assign(max_weight, "200.000").
% 1.29/1.56 % set(auto2) -> assign(max_hours, 1).
% 1.29/1.56 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.29/1.56 % set(auto2) -> assign(max_seconds, 0).
% 1.29/1.56 % set(auto2) -> assign(max_minutes, 5).
% 1.29/1.56 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.29/1.56 % set(auto2) -> set(sort_initial_sos).
% 1.29/1.56 % set(auto2) -> assign(sos_limit, -1).
% 1.29/1.56 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.29/1.56 % set(auto2) -> assign(max_megs, 400).
% 1.29/1.56 % set(auto2) -> assign(stats, some).
% 1.29/1.56 % set(auto2) -> clear(echo_input).
% 1.29/1.56 % set(auto2) -> set(quiet).
% 1.29/1.56 % set(auto2) -> clear(print_initial_clauses).
% 1.29/1.56 % set(auto2) -> clear(print_given).
% 1.29/1.56 assign(lrs_ticks,-1).
% 1.29/1.56 assign(sos_limit,10000).
% 1.29/1.56 assign(order,kbo).
% 1.29/1.56 set(lex_order_vars).
% 1.29/1.56 clear(print_given).
% 1.29/1.56
% 1.29/1.56 % formulas(sos). % not echoed (2 formulas)
% 1.29/1.56
% 1.29/1.56 ============================== end of input ==========================
% 1.29/1.56
% 1.29/1.56 % From the command line: assign(max_seconds, 300).
% 1.29/1.56
% 1.29/1.56 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.29/1.56
% 1.29/1.56 % Formulas that are not ordinary clauses:
% 1.29/1.56
% 1.29/1.56 ============================== end of process non-clausal formulas ===
% 1.29/1.56
% 1.29/1.56 ============================== PROCESS INITIAL CLAUSES ===============
% 1.29/1.56
% 1.29/1.56 ============================== PREDICATE ELIMINATION =================
% 1.29/1.56
% 1.29/1.56 ============================== end predicate elimination =============
% 1.29/1.56
% 1.29/1.56 Auto_denials:
% 1.29/1.56 % copying label prove_tba_axioms_5 to answer in negative clause
% 1.29/1.56
% 1.29/1.56 Term ordering decisions:
% 1.29/1.56
% 1.29/1.56 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 1.29/1.56 Function symbol KB weights: a=1. b=1. multiply=1. inverse=0.
% 1.29/1.56
% 1.29/1.56 ============================== end of process initial clauses ========
% 1.29/1.56
% 1.29/1.56 ============================== CLAUSES FOR SEARCH ====================
% 1.29/1.56
% 1.29/1.56 ============================== end of clauses for search =============
% 1.29/1.56
% 1.29/1.56 ============================== SEARCH ================================
% 1.29/1.56
% 1.29/1.56 % Starting search at 0.01 seconds.
% 1.29/1.56
% 1.29/1.56 ============================== PROOF =================================
% 1.29/1.56 % SZS status Unsatisfiable
% 1.29/1.56 % SZS output start Refutation
% 1.29/1.56
% 1.29/1.56 % Proof 1 at 0.57 (+ 0.01) seconds: prove_tba_axioms_5.
% 1.29/1.56 % Length of proof is 36.
% 1.29/1.56 % Level of proof is 13.
% 1.29/1.56 % Maximum clause weight is 93.000.
% 1.29/1.56 % Given clauses 24.
% 1.29/1.56
% 1.29/1.56 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].
% 1.29/1.56 2 multiply(inverse(b),b,a) != a # label(prove_tba_axioms_5) # label(negated_conjecture) # answer(prove_tba_axioms_5). [assumption].
% 1.29/1.56 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))].
% 1.29/1.56 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))].
% 1.29/1.56 12 multiply(inverse(A),multiply(B,inverse(multiply(A,inverse(A),C)),C),A) = B. [para(3(a,1),1(a,1))].
% 1.29/1.56 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))].
% 1.29/1.56 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))].
% 1.29/1.56 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)].
% 1.29/1.56 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))].
% 1.29/1.56 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)].
% 1.29/1.56 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)])].
% 1.29/1.56 248 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))].
% 1.29/1.56 612 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)])].
% 1.29/1.56 646 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))].
% 1.29/1.56 714 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))].
% 1.29/1.56 718 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))].
% 1.29/1.56 856 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))].
% 1.29/1.56 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)])].
% 1.29/1.56 1197 multiply(inverse(A),B,A) = B. [para(1068(a,1),1(a,1,1)),rewrite([1(9)]),flip(a)].
% 1.29/1.56 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)])].
% 1.29/1.56 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)])].
% 1.29/1.56 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)])].
% 1.29/1.56 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)])].
% 1.29/1.56 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)])].
% 1.29/1.56 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)])].
% 1.29/1.56 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))].
% 1.29/1.56 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)].
% 1.29/1.56 1750 inverse(multiply(A,inverse(A),B)) = inverse(B). [para(1213(a,1),1197(a,1)),flip(a)].
% 1.29/1.56 1752 multiply(A,inverse(B),B) = A. [para(1213(a,1),1213(a,1,2,1)),rewrite([1750(3)])].
% 1.29/1.56 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)])].
% 1.29/1.56 1843 multiply(A,multiply(B,inverse(A),B),inverse(B)) = A. [back_rewrite(1583),rewrite([1750(10),1289(15)])].
% 1.29/1.56 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)])].
% 1.29/1.56 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)])].
% 1.29/1.56 1944 inverse(inverse(A)) = A. [back_rewrite(1709),rewrite([1851(8),1853(10),1851(10),1752(8),1752(6)])].
% 1.29/1.56 1977 multiply(inverse(A),A,B) = B. [para(1944(a,1),1853(a,1,2))].
% 1.29/1.56 1978 $F # answer(prove_tba_axioms_5). [resolve(1977,a,2,a)].
% 1.29/1.56
% 1.29/1.56 % SZS output end Refutation
% 1.29/1.56 ============================== end of proof ==========================
% 1.29/1.56
% 1.29/1.56 ============================== STATISTICS ============================
% 1.29/1.56
% 1.29/1.56 Given=24. Generated=3754. Kept=1977. proofs=1.
% 1.29/1.56 Usable=5. Sos=83. Demods=86. Limbo=0, Disabled=1890. Hints=0.
% 1.29/1.56 Megabytes=6.67.
% 1.29/1.56 User_CPU=0.57, System_CPU=0.01, Wall_clock=1.
% 1.29/1.56
% 1.29/1.56 ============================== end of statistics =====================
% 1.29/1.56
% 1.29/1.56 ============================== end of search =========================
% 1.29/1.56
% 1.29/1.56 THEOREM PROVED
% 1.29/1.56 % SZS status Unsatisfiable
% 1.29/1.56
% 1.29/1.56 Exiting with 1 proof.
% 1.29/1.56
% 1.29/1.56 Process 10589 exit (max_proofs) Wed Jun 1 19:04:07 2022
% 1.29/1.56 Prover9 interrupted
%------------------------------------------------------------------------------