%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP704-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 07:31:16 AM UTC 2026
% Result : Unsatisfiable 0.15s 5.48s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 23 unt; 0 def)
% Number of atoms : 23 ( 22 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 : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 8 !; 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(f05,axiom,
! [VAR_0] : mult(VAR_0,unit) = VAR_0,
file('theBenchmark.p',f05) ).
cnf(c_5,plain,
mult(A,unit) = A,
inference(clausify,[status(thm)],[f05]) ).
fof(f06,axiom,
! [VAR_0] : mult(unit,VAR_0) = VAR_0,
file('theBenchmark.p',f06) ).
cnf(c_6,plain,
mult(unit,A) = A,
inference(clausify,[status(thm)],[f06]) ).
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(f13,axiom,
! [VAR_0,VAR_1] : op_f = mult(VAR_0,mult(VAR_1,ld(mult(VAR_0,VAR_1),op_c))),
file('theBenchmark.p',f13) ).
cnf(c_19,plain,
op_f = mult(A,mult(B,ld(mult(A,B),op_c))),
inference(clausify,[status(thm)],[f13]) ).
cnf(c_20,plain,
mult(A,mult(B,ld(mult(A,B),op_c))) = op_f,
inference(copy,[status(thm)],[c_19]) ).
fof(goal,axiom,
mult(op_f,mult(x4,x5)) != mult(mult(op_f,x4),x5),
file('theBenchmark.p',goal) ).
cnf(c_21,plain,
mult(op_f,mult(x4,x5)) != mult(mult(op_f,x4),x5),
inference(clausify,[status(thm)],[goal]) ).
cnf(c_22,plain,
mult(mult(op_f,x4),x5) != mult(op_f,mult(x4,x5)),
inference(copy,[status(thm)],[c_21]) ).
cnf(c_97,plain,
mult(A,mult(unit,ld(A,op_c))) = op_f,
inference(paramod,[status(thm)],[c_5,c_20]) ).
cnf(c_98,plain,
mult(A,ld(A,op_c)) = op_f,
inference(paramod,[status(thm)],[c_6,c_97]) ).
cnf(c_99,plain,
op_c = op_f,
inference(paramod,[status(thm)],[c_1,c_98]) ).
cnf(c_89,plain,
op_f = op_c,
inference(copy,[status(thm)],[c_99]) ).
cnf(c_100,plain,
mult(mult(op_c,x4),x5) != mult(op_f,mult(x4,x5)),
inference(paramod,[status(thm)],[c_89,c_22]) ).
cnf(c_101,plain,
mult(op_c,mult(x4,x5)) != mult(op_f,mult(x4,x5)),
inference(paramod,[status(thm)],[c_10,c_100]) ).
cnf(c_102,plain,
mult(op_c,mult(x4,x5)) != mult(op_c,mult(x4,x5)),
inference(paramod,[status(thm)],[c_89,c_101]) ).
cnf(c_96,plain,
$false,
inference(copy,[status(thm)],[c_102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP704-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/5.44 % Computer : n007.cluster.edu
% 0.15/5.44 % Model : x86_64 x86_64
% 0.15/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.44 % Memory : 8046.5625MB
% 0.15/5.44 % OS : Linux 6.8.0-71-generic
% 0.15/5.44 % CPULimit : 300
% 0.15/5.44 % WCLimit : 300
% 0.15/5.44 % DateTime : Fri Sep 25 15:36:58 UTC 2026
% 0.15/5.44 % CPUTime :
% 0.15/5.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/5.44 % Process 1382617 was started by sandbox2 on n007,
% 0.15/5.44 % Fri Sep 25 15:36:58 2026
% 0.15/5.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/5.45
% 0.15/5.45 % From the command line: assign(max_seconds, 300).
% 0.15/5.48
% 0.15/5.48 % SZS status Unsatisfiable for theBenchmark
% 0.15/5.48
% 0.15/5.48 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.15/5.48 % Length of proof is 11.
% 0.15/5.48 % Level of proof is 3.
% 0.15/5.48 % Maximum clause weight is 11.000.
% 0.15/5.48 % Given clauses 13.
% 0.15/5.48
% 0.15/5.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------