%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP022-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 07:26:17 AM UTC 2026
% Result : Unsatisfiable 0.03s 10.35s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 15 unt; 0 def)
% Number of atoms : 38 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 33 ( 18 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 15 !; 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(right_inverse,axiom,
! [VAR_0] : product(VAR_0,inverse(VAR_0),identity),
file('theBenchmark.p',right_inverse) ).
cnf(c_4,plain,
product(A,inverse(A),identity),
inference(clausify,[status(thm)],[right_inverse]) ).
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(prove_inverse_of_inverse_is_original,axiom,
inverse(inverse(a)) != a,
file('theBenchmark.p',prove_inverse_of_inverse_is_original) ).
cnf(c_9,plain,
inverse(inverse(a)) != a,
inference(clausify,[status(thm)],[prove_inverse_of_inverse_is_original]) ).
cnf(c_33,plain,
( multiply(A,B) = C
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_13,plain,
multiply(identity,A) = A,
inference(resolve,[status(thm)],[c_33,c_1]) ).
cnf(c_34,plain,
( product(A,C,D)
| ~ product(identity,B,D)
| ~ product(inverse(A),B,C) ),
inference(resolve,[status(thm)],[c_7,c_4]) ).
cnf(c_35,plain,
( product(A,identity,B)
| ~ product(identity,inverse(inverse(A)),B) ),
inference(resolve,[status(thm)],[c_34,c_4]) ).
cnf(c_36,plain,
product(A,identity,multiply(identity,inverse(inverse(A)))),
inference(resolve,[status(thm)],[c_35,c_5]) ).
cnf(c_20,plain,
product(A,identity,inverse(inverse(A))),
inference(paramod,[status(thm)],[c_13,c_36]) ).
cnf(c_37,plain,
( B = A
| ~ product(A,identity,B) ),
inference(resolve,[status(thm)],[c_6,c_2]) ).
cnf(c_31,plain,
~ product(a,identity,inverse(inverse(a))),
inference(resolve,[status(thm)],[c_37,c_9]) ).
cnf(c_32,plain,
$false,
inference(resolve,[status(thm)],[c_31,c_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP022-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/10.33 % Computer : n012.cluster.edu
% 0.03/10.33 % Model : x86_64 x86_64
% 0.03/10.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/10.33 % Memory : 8046.5625MB
% 0.03/10.33 % OS : Linux 6.8.0-71-generic
% 0.03/10.33 % CPULimit : 300
% 0.03/10.33 % WCLimit : 300
% 0.03/10.33 % DateTime : Fri Sep 25 14:17:06 UTC 2026
% 0.03/10.33 % CPUTime :
% 0.03/10.33 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/10.33 % Process 2271958 was started by sandbox2 on n012,
% 0.03/10.33 % Fri Sep 25 14:17:06 2026
% 0.03/10.33 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/10.33
% 0.03/10.33 % From the command line: assign(max_seconds, 300).
% 0.03/10.35
% 0.03/10.35 % SZS status Unsatisfiable for theBenchmark
% 0.03/10.35
% 0.03/10.35 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.03/10.35 % Length of proof is 11.
% 0.03/10.35 % Level of proof is 3.
% 0.03/10.35 % Maximum clause weight is 16.000.
% 0.03/10.35 % Given clauses 9.
% 0.03/10.35
% 0.03/10.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------