%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP665-12 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 07:31:07 AM UTC 2026
% Result : Unsatisfiable 0.05s 5.40s
% Output : CNFRefutation 0.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 26 unt; 0 def)
% Number of atoms : 26 ( 25 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f01,axiom,
! [VAR_0,VAR_1] : mult(VAR_0,ld(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',f01) ).
cnf(c_1,plain,
mult(A,ld(A,B)) = B,
inference(clausify,[status(thm)],[f01]) ).
fof(f02,axiom,
! [VAR_0,VAR_1] : ld(VAR_0,mult(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',f02) ).
cnf(c_2,plain,
ld(A,mult(A,B)) = B,
inference(clausify,[status(thm)],[f02]) ).
fof(f03,axiom,
! [VAR_0,VAR_1] : mult(rd(VAR_0,VAR_1),VAR_1) = VAR_0,
file('theBenchmark.p',f03) ).
cnf(c_3,plain,
mult(rd(A,B),B) = A,
inference(clausify,[status(thm)],[f03]) ).
fof(f07,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(VAR_0,mult(VAR_1,VAR_2)) = mult(rd(mult(VAR_0,VAR_1),VAR_0),mult(VAR_0,VAR_2)),
file('theBenchmark.p',f07) ).
cnf(c_7,plain,
mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)),
inference(clausify,[status(thm)],[f07]) ).
cnf(c_8,plain,
mult(rd(mult(A,B),A),mult(A,C)) = mult(A,mult(B,C)),
inference(copy,[status(thm)],[c_7]) ).
fof(f09,axiom,
! [VAR_0] : mult(op_c,VAR_0) = mult(VAR_0,op_c),
file('theBenchmark.p',f09) ).
cnf(c_11,plain,
mult(op_c,A) = mult(A,op_c),
inference(clausify,[status(thm)],[f09]) ).
fof(goal,axiom,
mult(mult(x0,x1),op_c) != mult(x0,mult(x1,op_c)),
file('theBenchmark.p',goal) ).
cnf(c_12,plain,
mult(mult(x0,x1),op_c) != mult(x0,mult(x1,op_c)),
inference(clausify,[status(thm)],[goal]) ).
cnf(c_69,plain,
mult(op_c,mult(x0,x1)) != mult(x0,mult(x1,op_c)),
inference(paramod,[status(thm)],[c_11,c_12]) ).
cnf(c_70,plain,
mult(op_c,mult(x0,x1)) != mult(x0,mult(op_c,x1)),
inference(paramod,[status(thm)],[c_11,c_69]) ).
cnf(c_13,plain,
mult(x0,mult(op_c,x1)) != mult(op_c,mult(x0,x1)),
inference(copy,[status(thm)],[c_70]) ).
cnf(c_20,plain,
mult(rd(A,B),mult(B,C)) = mult(B,mult(ld(B,A),C)),
inference(paramod,[status(thm)],[c_1,c_8]) ).
cnf(c_43,plain,
ld(op_c,mult(A,op_c)) = A,
inference(paramod,[status(thm)],[c_11,c_2]) ).
cnf(c_71,plain,
ld(op_c,A) = rd(A,op_c),
inference(paramod,[status(thm)],[c_3,c_43]) ).
cnf(c_52,plain,
rd(A,op_c) = ld(op_c,A),
inference(copy,[status(thm)],[c_71]) ).
cnf(c_72,plain,
mult(rd(mult(A,op_c),op_c),mult(op_c,B)) = mult(op_c,mult(A,B)),
inference(paramod,[status(thm)],[c_43,c_20]) ).
cnf(c_73,plain,
mult(ld(op_c,mult(A,op_c)),mult(op_c,B)) = mult(op_c,mult(A,B)),
inference(paramod,[status(thm)],[c_52,c_72]) ).
cnf(c_74,plain,
mult(A,mult(op_c,B)) = mult(op_c,mult(A,B)),
inference(paramod,[status(thm)],[c_43,c_73]) ).
cnf(c_67,plain,
mult(op_c,mult(A,B)) = mult(A,mult(op_c,B)),
inference(copy,[status(thm)],[c_74]) ).
cnf(c_75,plain,
mult(op_c,mult(x0,x1)) != mult(x0,mult(op_c,x1)),
inference(copy,[status(thm)],[c_13]) ).
cnf(c_68,plain,
$false,
inference(resolve,[status(thm)],[c_67,c_75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP665-12 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/5.34 % Computer : n014.cluster.edu
% 0.05/5.34 % Model : x86_64 x86_64
% 0.05/5.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/5.34 % Memory : 8046.5625MB
% 0.05/5.34 % OS : Linux 6.8.0-71-generic
% 0.05/5.35 % CPULimit : 300
% 0.05/5.35 % WCLimit : 300
% 0.05/5.35 % DateTime : Fri Sep 25 15:33:23 UTC 2026
% 0.05/5.35 % CPUTime :
% 0.05/5.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.05/5.35 % Process 572472 was started by sandbox on n014,
% 0.05/5.35 % Fri Sep 25 15:33:23 2026
% 0.05/5.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.05/5.36
% 0.05/5.36 % From the command line: assign(max_seconds, 300).
% 0.05/5.40
% 0.05/5.40 % SZS status Unsatisfiable for theBenchmark
% 0.05/5.40
% 0.05/5.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.05/5.40 % Length of proof is 13.
% 0.05/5.40 % Level of proof is 4.
% 0.05/5.40 % Maximum clause weight is 15.000.
% 0.05/5.40 % Given clauses 21.
% 0.05/5.40
% 0.05/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------