%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP012-2 : 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 : n004.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 07:26:10 AM UTC 2026
% Result : Unsatisfiable 0.10s 5.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 19 unt; 0 def)
% Number of atoms : 58 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 57 ( 31 ~; 26 |; 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 : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 57 ( 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(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(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(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_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_c,axiom,
product(a,b,c),
file('theBenchmark.p',a_multiply_b_is_c) ).
cnf(c_9,plain,
product(a,b,c),
inference(clausify,[status(thm)],[a_multiply_b_is_c]) ).
fof(inverse_b_multiply_inverse_a_is_d,axiom,
product(inverse(b),inverse(a),d),
file('theBenchmark.p',inverse_b_multiply_inverse_a_is_d) ).
cnf(c_10,plain,
product(inverse(b),inverse(a),d),
inference(clausify,[status(thm)],[inverse_b_multiply_inverse_a_is_d]) ).
fof(prove_c_inverse_equals_d,axiom,
inverse(c) != d,
file('theBenchmark.p',prove_c_inverse_equals_d) ).
cnf(c_11,plain,
inverse(c) != d,
inference(clausify,[status(thm)],[prove_c_inverse_equals_d]) ).
cnf(c_161,plain,
( product(inverse(A),C,D)
| ~ product(identity,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_7,c_3]) ).
cnf(c_162,plain,
( product(inverse(a),c,A)
| ~ product(identity,b,A) ),
inference(resolve,[status(thm)],[c_161,c_9]) ).
cnf(c_103,plain,
product(inverse(a),c,b),
inference(resolve,[status(thm)],[c_162,c_1]) ).
cnf(c_163,plain,
( B = A
| ~ product(A,identity,B) ),
inference(resolve,[status(thm)],[c_6,c_2]) ).
cnf(c_141,plain,
~ product(d,identity,inverse(c)),
inference(resolve,[status(thm)],[c_163,c_11]) ).
cnf(c_164,plain,
( product(A,identity,D)
| ~ product(C,inverse(B),D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_7,c_4]) ).
cnf(c_165,plain,
( product(A,identity,inverse(B))
| ~ product(A,B,identity) ),
inference(resolve,[status(thm)],[c_164,c_1]) ).
cnf(c_149,plain,
~ product(d,c,identity),
inference(resolve,[status(thm)],[c_165,c_141]) ).
cnf(c_166,plain,
( product(d,A,C)
| ~ product(inverse(b),B,C)
| ~ product(inverse(a),A,B) ),
inference(resolve,[status(thm)],[c_8,c_10]) ).
cnf(c_167,plain,
( product(d,A,identity)
| ~ product(inverse(a),A,b) ),
inference(resolve,[status(thm)],[c_166,c_3]) ).
cnf(c_168,plain,
~ product(inverse(a),c,b),
inference(resolve,[status(thm)],[c_167,c_149]) ).
cnf(c_160,plain,
$false,
inference(resolve,[status(thm)],[c_103,c_168]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP012-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n004.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Fri Sep 25 14:16:13 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 3343400 was started by sandbox2 on n004,
% 0.10/5.38 % Fri Sep 25 14:16:13 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/5.38
% 0.10/5.38 % From the command line: assign(max_seconds, 300).
% 0.10/5.39
% 0.10/5.39 % SZS status Unsatisfiable for theBenchmark
% 0.10/5.39
% 0.10/5.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/5.39 % Length of proof is 14.
% 0.10/5.39 % Level of proof is 3.
% 0.10/5.39 % Maximum clause weight is 21.000.
% 0.10/5.39 % Given clauses 15.
% 0.10/5.39
% 0.10/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------