%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP017-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 07:26:16 AM UTC 2026
% Result : Unsatisfiable 0.09s 5.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 18 unt; 0 def)
% Number of atoms : 41 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 34 ( 19 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : product(identity,VAR_0,VAR_0),
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
product(identity,A,A),
inference(clausify,[status(thm)],[left_identity]) ).
fof(right_identity,axiom,
! [VAR_0] : product(VAR_0,identity,VAR_0),
file('theBenchmark.p',right_identity) ).
cnf(c_2,plain,
product(A,identity,A),
inference(clausify,[status(thm)],[right_identity]) ).
fof(total_function1,axiom,
! [VAR_0,VAR_1] : product(VAR_0,VAR_1,multiply(VAR_0,VAR_1)),
file('theBenchmark.p',total_function1) ).
cnf(c_5,plain,
product(A,B,multiply(A,B)),
inference(clausify,[status(thm)],[total_function1]) ).
fof(total_function2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_2 = VAR_3
| ~ product(VAR_0,VAR_1,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',total_function2) ).
cnf(c_6,plain,
( C = D
| ~ product(A,B,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[total_function2]) ).
fof(associativity1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( product(VAR_0,VAR_4,VAR_5)
| ~ product(VAR_2,VAR_3,VAR_5)
| ~ product(VAR_1,VAR_3,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity1) ).
cnf(c_7,plain,
( product(A,E,F)
| ~ product(C,D,F)
| ~ product(B,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[associativity1]) ).
fof(b_times_a_is_identity,axiom,
product(b,a,identity),
file('theBenchmark.p',b_times_a_is_identity) ).
cnf(c_10,plain,
product(b,a,identity),
inference(clausify,[status(thm)],[b_times_a_is_identity]) ).
fof(a_times_c_is_identity,axiom,
product(a,c,identity),
file('theBenchmark.p',a_times_c_is_identity) ).
cnf(c_11,plain,
product(a,c,identity),
inference(clausify,[status(thm)],[a_times_c_is_identity]) ).
fof(prove_b_equals_c,axiom,
b != c,
file('theBenchmark.p',prove_b_equals_c) ).
cnf(c_13,plain,
b != c,
inference(clausify,[status(thm)],[prove_b_equals_c]) ).
cnf(c_14,plain,
c != b,
inference(copy,[status(thm)],[c_13]) ).
cnf(c_90,plain,
( multiply(A,B) = C
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_18,plain,
multiply(identity,A) = A,
inference(resolve,[status(thm)],[c_90,c_1]) ).
cnf(c_91,plain,
( product(b,B,C)
| ~ product(identity,A,C)
| ~ product(a,A,B) ),
inference(resolve,[status(thm)],[c_7,c_10]) ).
cnf(c_92,plain,
( product(b,identity,A)
| ~ product(identity,c,A) ),
inference(resolve,[status(thm)],[c_91,c_11]) ).
cnf(c_93,plain,
product(b,identity,multiply(identity,c)),
inference(resolve,[status(thm)],[c_92,c_5]) ).
cnf(c_68,plain,
product(b,identity,c),
inference(paramod,[status(thm)],[c_18,c_93]) ).
cnf(c_94,plain,
( B = A
| ~ product(A,identity,B) ),
inference(resolve,[status(thm)],[c_6,c_2]) ).
cnf(c_88,plain,
~ product(b,identity,c),
inference(resolve,[status(thm)],[c_94,c_14]) ).
cnf(c_89,plain,
$false,
inference(resolve,[status(thm)],[c_88,c_68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP017-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n017.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Fri Sep 25 14:12:08 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.37 % Process 2446887 was started by sandbox on n017,
% 0.09/5.37 % Fri Sep 25 14:12:08 2026
% 0.09/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/5.37
% 0.09/5.37 % From the command line: assign(max_seconds, 300).
% 0.09/5.38
% 0.09/5.38 % SZS status Unsatisfiable for theBenchmark
% 0.09/5.38
% 0.09/5.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/5.38 % Length of proof is 13.
% 0.09/5.38 % Level of proof is 3.
% 0.09/5.38 % Maximum clause weight is 18.000.
% 0.09/5.38 % Given clauses 13.
% 0.09/5.38
% 0.09/5.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------