%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO069-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:55:13 AM UTC 2026
% Result : Unsatisfiable 0.13s 5.57s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 2
% Syntax : Number of formulae : 48 ( 48 unt; 0 def)
% Number of atoms : 48 ( 47 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-3 aty)
% Number of variables : 241 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] : multiply(multiply(VAR_0,inverse(VAR_0),VAR_1),inverse(multiply(multiply(VAR_2,VAR_3,VAR_4),VAR_5,multiply(VAR_2,VAR_3,VAR_6))),multiply(VAR_3,multiply(VAR_6,VAR_5,VAR_4),VAR_2)) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
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,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(prove_tba_axioms_3,axiom,
multiply(a,b,inverse(b)) != a,
file('theBenchmark.p',prove_tba_axioms_3) ).
cnf(c_2,plain,
multiply(a,b,inverse(b)) != a,
inference(clausify,[status(thm)],[prove_tba_axioms_3]) ).
cnf(c_3,plain,
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),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
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,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_10,plain,
multiply(inverse(A),multiply(B,inverse(multiply(A,inverse(A),C)),C),A) = B,
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_20,plain,
multiply(A,multiply(B,inverse(multiply(C,A,D)),D),C) = multiply(A,multiply(B,inverse(multiply(C,A,E)),E),C),
inference(paramod,[status(thm)],[c_3,c_3]) ).
cnf(c_28,plain,
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,
inference(paramod,[status(thm)],[c_10,c_1]) ).
cnf(c_569,plain,
multiply(A,inverse(multiply(multiply(B,C,D),E,multiply(B,C,F))),multiply(C,multiply(F,E,D),B)) = multiply(multiply(A,inverse(multiply(V6,inverse(V6),V7)),V7),multiply(V6,inverse(multiply(inverse(V6),multiply(A,inverse(multiply(V6,inverse(V6),V7)),V7),V8)),V8),inverse(V6)),
inference(paramod,[status(thm)],[c_10,c_3]) ).
cnf(c_30,plain,
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)),
inference(copy,[status(thm)],[c_569]) ).
cnf(c_42,plain,
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,
inference(paramod,[status(thm)],[c_20,c_1]) ).
cnf(c_570,plain,
multiply(multiply(A,inverse(multiply(B,inverse(B),C)),C),multiply(D,inverse(A),B),inverse(B)) = 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)),
inference(paramod,[status(thm)],[c_10,c_20]) ).
cnf(c_49,plain,
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)),
inference(copy,[status(thm)],[c_570]) ).
cnf(c_51,plain,
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)),
inference(paramod,[status(thm)],[c_49,c_30]) ).
cnf(c_64,plain,
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,
inference(paramod,[status(thm)],[c_42,c_10]) ).
cnf(c_94,plain,
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(E,multiply(V6,inverse(multiply(D,E,V7)),V7),D)),
inference(paramod,[status(thm)],[c_20,c_51]) ).
cnf(c_571,plain,
multiply(multiply(A,inverse(A),B),inverse(multiply(inverse(C),multiply(multiply(D,inverse(D),multiply(E,inverse(E),F)),inverse(multiply(C,inverse(C),V6)),V6),C)),multiply(inverse(D),F,D)) = B,
inference(paramod,[status(thm)],[c_28,c_6]) ).
cnf(c_107,plain,
multiply(multiply(A,inverse(A),B),inverse(multiply(C,inverse(C),multiply(D,inverse(D),E))),multiply(inverse(C),E,C)) = B,
inference(paramod,[status(thm)],[c_10,c_571]) ).
cnf(c_572,plain,
multiply(multiply(A,inverse(A),B),inverse(multiply(multiply(C,D,E),F,multiply(C,D,V6))),multiply(D,multiply(V6,F,E),C)) = multiply(inverse(V7),B,V7),
inference(paramod,[status(thm)],[c_107,c_1]) ).
cnf(c_573,plain,
B = multiply(inverse(V7),B,V7),
inference(paramod,[status(thm)],[c_1,c_572]) ).
cnf(c_127,plain,
multiply(inverse(A),B,A) = B,
inference(copy,[status(thm)],[c_573]) ).
cnf(c_574,plain,
multiply(inverse(multiply(A,inverse(A),multiply(B,inverse(B),C))),multiply(D,inverse(multiply(B,inverse(B),C)),multiply(inverse(A),C,A)),multiply(A,inverse(A),multiply(B,inverse(B),C))) = D,
inference(paramod,[status(thm)],[c_107,c_10]) ).
cnf(c_575,plain,
multiply(inverse(multiply(A,inverse(A),multiply(B,inverse(B),C))),multiply(D,inverse(multiply(B,inverse(B),C)),C),multiply(A,inverse(A),multiply(B,inverse(B),C))) = D,
inference(paramod,[status(thm)],[c_127,c_574]) ).
cnf(c_146,plain,
multiply(A,inverse(multiply(B,inverse(B),C)),C) = A,
inference(paramod,[status(thm)],[c_127,c_575]) ).
cnf(c_576,plain,
multiply(multiply(A,inverse(A),B),inverse(multiply(C,inverse(C),multiply(multiply(multiply(multiply(D,E,F),V6,multiply(D,E,V7)),inverse(multiply(V8,inverse(V8),V9)),V9),multiply(V8,inverse(multiply(multiply(D,E,F),V6,multiply(D,E,V7))),V8),inverse(V8)))),multiply(inverse(C),multiply(E,multiply(V7,V6,F),D),C)) = B,
inference(paramod,[status(thm)],[c_51,c_107]) ).
cnf(c_577,plain,
multiply(multiply(A,inverse(A),B),inverse(multiply(C,inverse(C),multiply(multiply(multiply(D,E,F),V6,multiply(D,E,V7)),multiply(V8,inverse(multiply(multiply(D,E,F),V6,multiply(D,E,V7))),V8),inverse(V8)))),multiply(inverse(C),multiply(E,multiply(V7,V6,F),D),C)) = B,
inference(paramod,[status(thm)],[c_146,c_576]) ).
cnf(c_155,plain,
multiply(multiply(A,inverse(A),B),inverse(multiply(C,inverse(C),multiply(multiply(multiply(D,E,F),V6,multiply(D,E,V7)),multiply(V8,inverse(multiply(multiply(D,E,F),V6,multiply(D,E,V7))),V8),inverse(V8)))),multiply(E,multiply(V7,V6,F),D)) = B,
inference(paramod,[status(thm)],[c_127,c_577]) ).
cnf(c_578,plain,
multiply(multiply(A,inverse(A),B),inverse(multiply(C,inverse(C),inverse(inverse(D)))),multiply(inverse(multiply(D,inverse(D),multiply(C,inverse(C),inverse(inverse(D))))),D,multiply(D,inverse(D),multiply(C,inverse(C),inverse(inverse(D)))))) = B,
inference(paramod,[status(thm)],[c_107,c_107]) ).
cnf(c_164,plain,
multiply(multiply(A,inverse(A),B),inverse(multiply(C,inverse(C),inverse(inverse(D)))),D) = B,
inference(paramod,[status(thm)],[c_127,c_578]) ).
cnf(c_170,plain,
multiply(A,inverse(multiply(B,C,D)),multiply(C,multiply(D,inverse(multiply(B,C,E)),E),B)) = A,
inference(paramod,[status(thm)],[c_127,c_64]) ).
cnf(c_183,plain,
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(D,multiply(F,inverse(multiply(C,D,V6)),V6),C)),
inference(paramod,[status(thm)],[c_146,c_94]) ).
cnf(c_214,plain,
multiply(inverse(inverse(A)),inverse(multiply(multiply(B,C,D),E,multiply(B,C,F))),multiply(C,multiply(F,E,D),B)) = A,
inference(paramod,[status(thm)],[c_127,c_1]) ).
cnf(c_579,plain,
inverse(A) = inverse(multiply(B,inverse(B),A)),
inference(paramod,[status(thm)],[c_146,c_127]) ).
cnf(c_281,plain,
inverse(multiply(A,inverse(A),B)) = inverse(B),
inference(copy,[status(thm)],[c_579]) ).
cnf(c_282,plain,
multiply(A,inverse(inverse(inverse(B))),B) = A,
inference(paramod,[status(thm)],[c_127,c_146]) ).
cnf(c_580,plain,
multiply(A,inverse(multiply(B,inverse(B),C)),C) = A,
inference(paramod,[status(thm)],[c_146,c_146]) ).
cnf(c_283,plain,
multiply(A,inverse(B),B) = A,
inference(paramod,[status(thm)],[c_281,c_580]) ).
cnf(c_581,plain,
multiply(A,multiply(B,inverse(A),B),inverse(B)) = multiply(A,inverse(multiply(C,D,F)),multiply(D,multiply(F,inverse(multiply(C,D,V6)),V6),C)),
inference(paramod,[status(thm)],[c_281,c_183]) ).
cnf(c_323,plain,
multiply(A,multiply(B,inverse(A),B),inverse(B)) = A,
inference(paramod,[status(thm)],[c_170,c_581]) ).
cnf(c_582,plain,
multiply(multiply(A,inverse(A),B),inverse(inverse(inverse(D))),D) = B,
inference(paramod,[status(thm)],[c_281,c_164]) ).
cnf(c_331,plain,
multiply(A,inverse(A),B) = B,
inference(paramod,[status(thm)],[c_282,c_582]) ).
cnf(c_583,plain,
multiply(B,inverse(multiply(C,inverse(C),multiply(multiply(multiply(D,E,F),V6,multiply(D,E,V7)),multiply(V8,inverse(multiply(multiply(D,E,F),V6,multiply(D,E,V7))),V8),inverse(V8)))),multiply(E,multiply(V7,V6,F),D)) = B,
inference(paramod,[status(thm)],[c_331,c_155]) ).
cnf(c_584,plain,
multiply(B,inverse(multiply(C,inverse(C),multiply(multiply(D,E,F),V6,multiply(D,E,V7)))),multiply(E,multiply(V7,V6,F),D)) = B,
inference(paramod,[status(thm)],[c_323,c_583]) ).
cnf(c_335,plain,
multiply(A,inverse(multiply(multiply(B,C,D),E,multiply(B,C,F))),multiply(C,multiply(F,E,D),B)) = A,
inference(paramod,[status(thm)],[c_331,c_584]) ).
cnf(c_429,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_335,c_214]) ).
cnf(c_567,plain,
multiply(A,B,inverse(B)) = A,
inference(paramod,[status(thm)],[c_429,c_283]) ).
cnf(c_568,plain,
$false,
inference(resolve,[status(thm)],[c_567,c_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO069-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n026.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sat Sep 26 22:45:48 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.37 % Process 2129478 was started by sandbox2 on n026,
% 0.09/5.37 % Sat Sep 26 22:45:48 2026
% 0.09/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.37
% 0.09/5.37 % From the command line: assign(max_seconds, 300).
% 0.13/5.57
% 0.13/5.57 % SZS status Unsatisfiable for theBenchmark
% 0.13/5.57
% 0.13/5.57 % Proof 1 at 0.17 (+ 0.02) seconds.
% 0.13/5.57 % Length of proof is 30.
% 0.13/5.57 % Level of proof is 12.
% 0.13/5.57 % Maximum clause weight is 95.000.
% 0.13/5.57 % Given clauses 26.
% 0.13/5.57
% 0.13/5.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------