%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP010-1 : 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 : n016.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 07:26:09 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.56s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 15 unt; 0 def)
% Number of atoms : 49 ( 4 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 49 ( 26 ~; 23 |; 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; 3 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 20 !; 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(left_inverse,axiom,
! [VAR_0] : product(inverse(VAR_0),VAR_0,identity),
file('theBenchmark.p',left_inverse) ).
cnf(c_3,plain,
product(inverse(A),A,identity),
inference(clausify,[status(thm)],[left_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(associativity2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( product(VAR_2,VAR_3,VAR_5)
| ~ product(VAR_0,VAR_4,VAR_5)
| ~ product(VAR_1,VAR_3,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity2) ).
cnf(c_8,plain,
( product(C,D,F)
| ~ product(A,E,F)
| ~ product(B,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[associativity2]) ).
fof(a_multiply_b_is_identity,axiom,
product(a,b,identity),
file('theBenchmark.p',a_multiply_b_is_identity) ).
cnf(c_9,plain,
product(a,b,identity),
inference(clausify,[status(thm)],[a_multiply_b_is_identity]) ).
fof(prove_b_multiply_a_is_identity,axiom,
~ product(b,a,identity),
file('theBenchmark.p',prove_b_multiply_a_is_identity) ).
cnf(c_10,plain,
~ product(b,a,identity),
inference(clausify,[status(thm)],[prove_b_multiply_a_is_identity]) ).
cnf(c_48,plain,
( multiply(A,B) = C
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_14,plain,
multiply(identity,A) = A,
inference(resolve,[status(thm)],[c_48,c_1]) ).
cnf(c_49,plain,
( product(inverse(A),C,D)
| ~ product(identity,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_7,c_3]) ).
cnf(c_50,plain,
( product(inverse(a),identity,A)
| ~ product(identity,b,A) ),
inference(resolve,[status(thm)],[c_49,c_9]) ).
cnf(c_51,plain,
product(inverse(a),identity,multiply(identity,b)),
inference(resolve,[status(thm)],[c_50,c_5]) ).
cnf(c_40,plain,
product(inverse(a),identity,b),
inference(paramod,[status(thm)],[c_14,c_51]) ).
cnf(c_52,plain,
( product(B,C,D)
| ~ product(A,C,D)
| ~ product(A,identity,B) ),
inference(resolve,[status(thm)],[c_8,c_1]) ).
cnf(c_53,plain,
( product(B,A,identity)
| ~ product(inverse(A),identity,B) ),
inference(resolve,[status(thm)],[c_52,c_3]) ).
cnf(c_46,plain,
~ product(inverse(a),identity,b),
inference(resolve,[status(thm)],[c_53,c_10]) ).
cnf(c_47,plain,
$false,
inference(resolve,[status(thm)],[c_46,c_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.54 % Computer : n016.cluster.edu
% 0.10/0.54 % Model : x86_64 x86_64
% 0.10/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.54 % Memory : 8046.5625MB
% 0.10/0.54 % OS : Linux 6.8.0-71-generic
% 0.10/0.54 % CPULimit : 300
% 0.10/0.54 % WCLimit : 300
% 0.10/0.54 % DateTime : Fri Sep 25 14:21:01 UTC 2026
% 0.10/0.54 % CPUTime :
% 0.10/0.55 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.55 % Process 2571587 was started by sandbox on n016,
% 0.10/0.55 % Fri Sep 25 14:21:01 2026
% 0.10/0.55 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.55
% 0.10/0.55 % From the command line: assign(max_seconds, 300).
% 0.13/0.56
% 0.13/0.56 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.56
% 0.13/0.56 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.56 % Length of proof is 12.
% 0.13/0.56 % Level of proof is 3.
% 0.13/0.56 % Maximum clause weight is 16.000.
% 0.13/0.56 % Given clauses 10.
% 0.13/0.56
% 0.13/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------