%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP671-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 07:31:09 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 15 unt; 0 def)
% Number of atoms : 15 ( 14 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c05,axiom,
! [VAR_0] : mult(VAR_0,unit) = VAR_0,
file('theBenchmark.p',c05) ).
cnf(c_5,plain,
mult(A,unit) = A,
inference(clausify,[status(thm)],[c05]) ).
fof(c06,axiom,
! [VAR_0] : mult(unit,VAR_0) = VAR_0,
file('theBenchmark.p',c06) ).
cnf(c_6,plain,
mult(unit,A) = A,
inference(clausify,[status(thm)],[c06]) ).
fof(c09,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(mult(VAR_0,VAR_1),mult(VAR_2,mult(VAR_0,VAR_1))) = mult(mult(mult(VAR_0,mult(VAR_1,VAR_2)),VAR_0),VAR_1),
file('theBenchmark.p',c09) ).
cnf(c_9,plain,
mult(mult(A,B),mult(C,mult(A,B))) = mult(mult(mult(A,mult(B,C)),A),B),
inference(clausify,[status(thm)],[c09]) ).
cnf(c_10,plain,
mult(mult(mult(A,mult(B,C)),A),B) = mult(mult(A,B),mult(C,mult(A,B))),
inference(copy,[status(thm)],[c_9]) ).
fof(goals,axiom,
mult(mult(a,b),a) != mult(a,mult(b,a)),
file('theBenchmark.p',goals) ).
cnf(c_11,plain,
mult(mult(a,b),a) != mult(a,mult(b,a)),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_41,plain,
mult(mult(A,unit),mult(B,mult(A,unit))) = mult(mult(A,mult(unit,B)),A),
inference(paramod,[status(thm)],[c_10,c_5]) ).
cnf(c_42,plain,
mult(A,mult(B,mult(A,unit))) = mult(mult(A,mult(unit,B)),A),
inference(paramod,[status(thm)],[c_5,c_41]) ).
cnf(c_43,plain,
mult(A,mult(B,A)) = mult(mult(A,mult(unit,B)),A),
inference(paramod,[status(thm)],[c_5,c_42]) ).
cnf(c_44,plain,
mult(A,mult(B,A)) = mult(mult(A,B),A),
inference(paramod,[status(thm)],[c_6,c_43]) ).
cnf(c_39,plain,
mult(mult(A,B),A) = mult(A,mult(B,A)),
inference(copy,[status(thm)],[c_44]) ).
cnf(c_40,plain,
$false,
inference(resolve,[status(thm)],[c_39,c_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP671-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n010.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 15:35:14 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 1122588 was started by sandbox on n010,
% 0.08/0.35 % Fri Sep 25 15:35:14 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 0.12/0.36
% 0.12/0.36 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.36
% 0.12/0.36 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.36 % Length of proof is 7.
% 0.12/0.36 % Level of proof is 3.
% 0.12/0.36 % Maximum clause weight is 19.000.
% 0.12/0.36 % Given clauses 9.
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------