%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP702-10 : 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 : n001.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 07:31:15 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 16 unt; 0 def)
% Number of atoms : 16 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f08,axiom,
! [VAR_0,VAR_1] : mult(op_c,mult(VAR_0,VAR_1)) = mult(mult(op_c,VAR_0),VAR_1),
file('theBenchmark.p',f08) ).
cnf(c_9,plain,
mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
inference(clausify,[status(thm)],[f08]) ).
cnf(c_10,plain,
mult(mult(op_c,A),B) = mult(op_c,mult(A,B)),
inference(copy,[status(thm)],[c_9]) ).
fof(f11,axiom,
! [VAR_0] : op_d = ld(VAR_0,mult(op_c,VAR_0)),
file('theBenchmark.p',f11) ).
cnf(c_15,plain,
op_d = ld(A,mult(op_c,A)),
inference(clausify,[status(thm)],[f11]) ).
cnf(c_16,plain,
ld(A,mult(op_c,A)) = op_d,
inference(copy,[status(thm)],[c_15]) ).
fof(goal,axiom,
mult(op_d,mult(x0,x1)) != mult(mult(op_d,x0),x1),
file('theBenchmark.p',goal) ).
cnf(c_21,plain,
mult(op_d,mult(x0,x1)) != mult(mult(op_d,x0),x1),
inference(clausify,[status(thm)],[goal]) ).
cnf(c_22,plain,
mult(mult(op_d,x0),x1) != mult(op_d,mult(x0,x1)),
inference(copy,[status(thm)],[c_21]) ).
cnf(c_64,plain,
op_d = op_c,
inference(paramod,[status(thm)],[c_16,c_2]) ).
cnf(c_68,plain,
mult(mult(op_c,x0),x1) != mult(op_d,mult(x0,x1)),
inference(paramod,[status(thm)],[c_64,c_22]) ).
cnf(c_69,plain,
mult(op_c,mult(x0,x1)) != mult(op_d,mult(x0,x1)),
inference(paramod,[status(thm)],[c_10,c_68]) ).
cnf(c_70,plain,
mult(op_c,mult(x0,x1)) != mult(op_c,mult(x0,x1)),
inference(paramod,[status(thm)],[c_64,c_69]) ).
cnf(c_67,plain,
$false,
inference(copy,[status(thm)],[c_70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP702-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 15:44:11 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 3713519 was started by sandbox on n001,
% 0.09/0.38 % Fri Sep 25 15:44:11 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.39
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/0.39 % Length of proof is 9.
% 0.09/0.39 % Level of proof is 3.
% 0.09/0.39 % Maximum clause weight is 11.000.
% 0.09/0.39 % Given clauses 11.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------