%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP012-3 : 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 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 33 ( 19 unt; 0 def)
% Number of atoms : 60 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 59 ( 32 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 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 : 77 ( 0 sgn 22 !; 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_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(prove_inverse_of_product_is_product_of_inverses,axiom,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
file('theBenchmark.p',prove_inverse_of_product_is_product_of_inverses) ).
cnf(c_9,plain,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
inference(clausify,[status(thm)],[prove_inverse_of_product_is_product_of_inverses]) ).
cnf(c_44,plain,
( multiply(A,B) = C
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_12,plain,
multiply(A,identity) = A,
inference(resolve,[status(thm)],[c_44,c_2]) ).
cnf(c_45,plain,
( product(multiply(D,A),B,E)
| ~ product(D,C,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_8,c_5]) ).
cnf(c_46,plain,
( product(multiply(A,C),inverse(C),B)
| ~ product(A,identity,B) ),
inference(resolve,[status(thm)],[c_45,c_4]) ).
cnf(c_47,plain,
product(multiply(A,B),inverse(B),multiply(A,identity)),
inference(resolve,[status(thm)],[c_46,c_5]) ).
cnf(c_25,plain,
product(multiply(A,B),inverse(B),A),
inference(paramod,[status(thm)],[c_12,c_47]) ).
cnf(c_48,plain,
( C = multiply(A,B)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_31,plain,
~ product(inverse(b),inverse(a),inverse(multiply(a,b))),
inference(resolve,[status(thm)],[c_48,c_9]) ).
cnf(c_49,plain,
( product(C,inverse(B),D)
| ~ product(A,identity,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_8,c_4]) ).
cnf(c_50,plain,
( product(C,inverse(B),A)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_49,c_2]) ).
cnf(c_36,plain,
~ product(inverse(multiply(a,b)),a,inverse(b)),
inference(resolve,[status(thm)],[c_50,c_31]) ).
cnf(c_51,plain,
( product(inverse(A),C,D)
| ~ product(identity,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_7,c_3]) ).
cnf(c_52,plain,
( product(inverse(A),C,B)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_51,c_1]) ).
cnf(c_42,plain,
~ product(multiply(a,b),inverse(b),a),
inference(resolve,[status(thm)],[c_52,c_36]) ).
cnf(c_43,plain,
$false,
inference(resolve,[status(thm)],[c_42,c_25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP012-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n004.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 14:16:24 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3344165 was started by sandbox2 on n004,
% 0.08/0.36 % Fri Sep 25 14:16:24 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.08/0.38
% 0.08/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.38
% 0.08/0.38 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.08/0.38 % Length of proof is 15.
% 0.08/0.38 % Level of proof is 4.
% 0.08/0.38 % Maximum clause weight is 16.000.
% 0.08/0.38 % Given clauses 12.
% 0.08/0.38
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------