%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP012-4 : 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 07:26:10 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 23 unt; 0 def)
% Number of atoms : 23 ( 22 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : multiply(identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
multiply(identity,A) = A,
inference(clausify,[status(thm)],[left_identity]) ).
fof(left_inverse,axiom,
! [VAR_0] : multiply(inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_2,plain,
multiply(inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity) ).
cnf(c_3,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity]) ).
fof(right_identity,axiom,
! [VAR_0] : multiply(VAR_0,identity) = VAR_0,
file('theBenchmark.p',right_identity) ).
cnf(c_4,plain,
multiply(A,identity) = A,
inference(clausify,[status(thm)],[right_identity]) ).
fof(right_inverse,axiom,
! [VAR_0] : multiply(VAR_0,inverse(VAR_0)) = identity,
file('theBenchmark.p',right_inverse) ).
cnf(c_5,plain,
multiply(A,inverse(A)) = identity,
inference(clausify,[status(thm)],[right_inverse]) ).
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_6,plain,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
inference(clausify,[status(thm)],[prove_inverse_of_product_is_product_of_inverses]) ).
cnf(c_27,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_28,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_27]) ).
cnf(c_7,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_28]) ).
cnf(c_29,plain,
identity = multiply(A,multiply(B,inverse(multiply(A,B)))),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_10,plain,
multiply(A,multiply(B,inverse(multiply(A,B)))) = identity,
inference(copy,[status(thm)],[c_29]) ).
cnf(c_30,plain,
multiply(inverse(A),identity) = multiply(B,inverse(multiply(A,B))),
inference(paramod,[status(thm)],[c_10,c_7]) ).
cnf(c_31,plain,
inverse(A) = multiply(B,inverse(multiply(A,B))),
inference(paramod,[status(thm)],[c_4,c_30]) ).
cnf(c_15,plain,
multiply(A,inverse(multiply(B,A))) = inverse(B),
inference(copy,[status(thm)],[c_31]) ).
cnf(c_32,plain,
multiply(inverse(A),inverse(B)) = inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_15,c_7]) ).
cnf(c_25,plain,
inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_26,plain,
$false,
inference(resolve,[status(thm)],[c_25,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP012-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 14:11:49 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2446503 was started by sandbox on n017,
% 0.09/0.37 % Fri Sep 25 14:11:49 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.39
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.39 % Length of proof is 11.
% 0.09/0.39 % Level of proof is 4.
% 0.09/0.39 % Maximum clause weight is 11.000.
% 0.09/0.39 % Given clauses 13.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------