%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO002-1 : TPTP v9.3.1. Released v1.0.0.
% 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 06:55:00 AM UTC 2026
% Result : Unsatisfiable 13.44s 2.14s
% Output : CNFRefutation 13.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 5
% Syntax : Number of formulae : 57 ( 57 unt; 0 def)
% Number of atoms : 57 ( 56 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 4 ( 1 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 : 192 ( 15 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] : multiply(multiply(VAR_0,VAR_1,VAR_2),VAR_3,multiply(VAR_0,VAR_1,VAR_4)) = multiply(VAR_0,VAR_1,multiply(VAR_2,VAR_3,VAR_4)),
file('theBenchmark.p',associativity) ).
cnf(c_1,plain,
multiply(multiply(A,B,C),D,multiply(A,B,E)) = multiply(A,B,multiply(C,D,E)),
inference(clausify,[status(thm)],[associativity]) ).
fof(ternary_multiply_1,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1,VAR_1) = VAR_1,
file('theBenchmark.p',ternary_multiply_1) ).
cnf(c_2,plain,
multiply(A,B,B) = B,
inference(clausify,[status(thm)],[ternary_multiply_1]) ).
fof(ternary_multiply_2,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_0,VAR_1) = VAR_0,
file('theBenchmark.p',ternary_multiply_2) ).
cnf(c_3,plain,
multiply(A,A,B) = A,
inference(clausify,[status(thm)],[ternary_multiply_2]) ).
fof(left_inverse,axiom,
! [VAR_0,VAR_1] : multiply(inverse(VAR_0),VAR_0,VAR_1) = VAR_1,
file('theBenchmark.p',left_inverse) ).
cnf(c_4,plain,
multiply(inverse(A),A,B) = B,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(prove_equation,axiom,
multiply(a,inverse(a),b) != b,
file('theBenchmark.p',prove_equation) ).
cnf(c_5,plain,
multiply(a,inverse(a),b) != b,
inference(clausify,[status(thm)],[prove_equation]) ).
cnf(c_6,plain,
multiply(multiply(A,B,multiply(C,D,E)),F,multiply(multiply(A,B,C),D,V6)) = multiply(multiply(A,B,C),D,multiply(multiply(A,B,E),F,V6)),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_8,plain,
multiply(A,B,multiply(C,A,D)) = multiply(C,A,multiply(A,B,D)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_9,plain,
multiply(multiply(A,B,C),D,B) = multiply(A,B,multiply(C,D,B)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_3685,plain,
multiply(A,B,multiply(A,A,C)) = multiply(A,A,multiply(D,B,C)),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_3686,plain,
multiply(A,B,A) = multiply(A,A,multiply(D,B,C)),
inference(paramod,[status(thm)],[c_3,c_3685]) ).
cnf(c_11,plain,
multiply(A,B,A) = A,
inference(paramod,[status(thm)],[c_3,c_3686]) ).
cnf(c_3687,plain,
multiply(A,B,C) = multiply(A,B,multiply(C,multiply(A,B,C),D)),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_12,plain,
multiply(A,B,multiply(C,multiply(A,B,C),D)) = multiply(A,B,C),
inference(copy,[status(thm)],[c_3687]) ).
cnf(c_3688,plain,
multiply(A,B,multiply(multiply(A,A,C),D,E)) = multiply(multiply(A,A,C),D,multiply(multiply(A,A,F),B,E)),
inference(paramod,[status(thm)],[c_3,c_6]) ).
cnf(c_3689,plain,
multiply(A,B,multiply(A,D,E)) = multiply(multiply(A,A,C),D,multiply(multiply(A,A,F),B,E)),
inference(paramod,[status(thm)],[c_3,c_3688]) ).
cnf(c_3690,plain,
multiply(A,B,multiply(A,D,E)) = multiply(A,D,multiply(multiply(A,A,F),B,E)),
inference(paramod,[status(thm)],[c_3,c_3689]) ).
cnf(c_24,plain,
multiply(A,B,multiply(A,C,D)) = multiply(A,C,multiply(A,B,D)),
inference(paramod,[status(thm)],[c_3,c_3690]) ).
cnf(c_30,plain,
multiply(multiply(A,B,C),D,A) = multiply(A,B,multiply(C,D,A)),
inference(paramod,[status(thm)],[c_11,c_1]) ).
cnf(c_43,plain,
multiply(A,B,multiply(C,A,B)) = multiply(C,A,B),
inference(paramod,[status(thm)],[c_2,c_8]) ).
cnf(c_3691,plain,
multiply(multiply(multiply(A,B,C),C,A),B,C) = multiply(A,B,C),
inference(paramod,[status(thm)],[c_11,c_9]) ).
cnf(c_3692,plain,
multiply(multiply(A,B,multiply(C,C,A)),B,C) = multiply(A,B,C),
inference(paramod,[status(thm)],[c_30,c_3691]) ).
cnf(c_89,plain,
multiply(multiply(A,B,C),B,C) = multiply(A,B,C),
inference(paramod,[status(thm)],[c_3,c_3692]) ).
cnf(c_3693,plain,
multiply(multiply(A,B,C),D,B) = multiply(multiply(A,B,C),B,multiply(C,D,B)),
inference(paramod,[status(thm)],[c_89,c_9]) ).
cnf(c_3694,plain,
multiply(A,B,multiply(C,D,B)) = multiply(multiply(A,B,C),B,multiply(C,D,B)),
inference(paramod,[status(thm)],[c_9,c_3693]) ).
cnf(c_166,plain,
multiply(multiply(A,B,C),B,multiply(C,D,B)) = multiply(A,B,multiply(C,D,B)),
inference(copy,[status(thm)],[c_3694]) ).
cnf(c_3695,plain,
multiply(A,B,multiply(C,multiply(A,B,C),B)) = multiply(C,multiply(A,B,C),multiply(multiply(A,B,C),B,B)),
inference(paramod,[status(thm)],[c_166,c_8]) ).
cnf(c_3696,plain,
multiply(A,B,C) = multiply(C,multiply(A,B,C),multiply(multiply(A,B,C),B,B)),
inference(paramod,[status(thm)],[c_12,c_3695]) ).
cnf(c_3697,plain,
multiply(A,B,C) = multiply(C,multiply(A,B,C),B),
inference(paramod,[status(thm)],[c_2,c_3696]) ).
cnf(c_234,plain,
multiply(A,multiply(B,C,A),C) = multiply(B,C,A),
inference(copy,[status(thm)],[c_3697]) ).
cnf(c_3698,plain,
multiply(A,B,multiply(C,multiply(A,B,C),B)) = multiply(C,multiply(A,B,C),B),
inference(paramod,[status(thm)],[c_166,c_43]) ).
cnf(c_3699,plain,
multiply(A,B,multiply(A,B,C)) = multiply(C,multiply(A,B,C),B),
inference(paramod,[status(thm)],[c_234,c_3698]) ).
cnf(c_238,plain,
multiply(A,B,multiply(A,B,C)) = multiply(A,B,C),
inference(paramod,[status(thm)],[c_234,c_3699]) ).
cnf(c_3700,plain,
multiply(A,B,multiply(C,D,A)) = multiply(A,multiply(C,D,A),multiply(A,B,D)),
inference(paramod,[status(thm)],[c_234,c_24]) ).
cnf(c_276,plain,
multiply(A,multiply(B,C,A),multiply(A,D,C)) = multiply(A,D,multiply(B,C,A)),
inference(copy,[status(thm)],[c_3700]) ).
cnf(c_3701,plain,
multiply(multiply(A,B,C),D,C) = multiply(C,multiply(A,B,C),multiply(B,D,C)),
inference(paramod,[status(thm)],[c_234,c_30]) ).
cnf(c_278,plain,
multiply(A,multiply(B,C,A),multiply(C,D,A)) = multiply(multiply(B,C,A),D,A),
inference(copy,[status(thm)],[c_3701]) ).
cnf(c_3702,plain,
multiply(A,multiply(B,inverse(C),A),A) = multiply(multiply(B,inverse(C),A),C,A),
inference(paramod,[status(thm)],[c_4,c_278]) ).
cnf(c_3703,plain,
A = multiply(multiply(B,inverse(C),A),C,A),
inference(paramod,[status(thm)],[c_11,c_3702]) ).
cnf(c_419,plain,
multiply(multiply(A,inverse(B),C),B,C) = C,
inference(copy,[status(thm)],[c_3703]) ).
cnf(c_3704,plain,
multiply(A,multiply(B,multiply(A,C,B),A),multiply(A,C,multiply(A,C,B))) = multiply(A,C,B),
inference(paramod,[status(thm)],[c_12,c_276]) ).
cnf(c_3705,plain,
multiply(A,multiply(B,multiply(A,C,B),A),multiply(A,C,B)) = multiply(A,C,B),
inference(paramod,[status(thm)],[c_238,c_3704]) ).
cnf(c_534,plain,
multiply(A,multiply(B,C,A),B) = multiply(B,C,A),
inference(paramod,[status(thm)],[c_234,c_3705]) ).
cnf(c_3706,plain,
multiply(A,B,multiply(C,D,A)) = multiply(A,multiply(C,D,A),multiply(A,B,C)),
inference(paramod,[status(thm)],[c_534,c_24]) ).
cnf(c_555,plain,
multiply(A,multiply(B,C,A),multiply(A,D,B)) = multiply(A,D,multiply(B,C,A)),
inference(copy,[status(thm)],[c_3706]) ).
cnf(c_3707,plain,
multiply(multiply(A,B,C),D,C) = multiply(C,multiply(A,B,C),multiply(A,D,C)),
inference(paramod,[status(thm)],[c_534,c_30]) ).
cnf(c_557,plain,
multiply(A,multiply(B,C,A),multiply(B,D,A)) = multiply(multiply(B,C,A),D,A),
inference(copy,[status(thm)],[c_3707]) ).
cnf(c_3708,plain,
multiply(A,multiply(B,C,A),multiply(B,D,A)) = multiply(A,multiply(B,D,A),multiply(B,C,A)),
inference(paramod,[status(thm)],[c_534,c_555]) ).
cnf(c_3709,plain,
multiply(multiply(B,C,A),D,A) = multiply(A,multiply(B,D,A),multiply(B,C,A)),
inference(paramod,[status(thm)],[c_557,c_3708]) ).
cnf(c_3222,plain,
multiply(multiply(A,B,C),D,C) = multiply(multiply(A,D,C),B,C),
inference(paramod,[status(thm)],[c_557,c_3709]) ).
cnf(c_3554,plain,
multiply(multiply(A,B,C),inverse(B),C) = C,
inference(paramod,[status(thm)],[c_3222,c_419]) ).
cnf(c_3683,plain,
multiply(A,inverse(A),B) = B,
inference(paramod,[status(thm)],[c_3,c_3554]) ).
cnf(c_3684,plain,
$false,
inference(resolve,[status(thm)],[c_3683,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n026.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Sat Sep 26 22:35:41 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 2101376 was started by sandbox2 on n026,
% 0.11/0.36 % Sat Sep 26 22:35:41 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.36
% 0.11/0.36 % From the command line: assign(max_seconds, 300).
% 13.44/2.14
% 13.44/2.14 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 13.44/2.14
% 13.44/2.14 % SZS status Unsatisfiable for theBenchmark
% 13.44/2.14
% 13.44/2.14 % Proof 1 at 1.51 (+ 0.22) seconds.
% 13.44/2.14 % Length of proof is 27.
% 13.44/2.14 % Level of proof is 12.
% 13.44/2.14 % Maximum clause weight is 50.000.
% 13.44/2.14 % Given clauses 64.
% 13.44/2.14
% 13.44/2.14 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------