%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG007-4 : 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 : n002.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 08:26:18 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 21 unt; 0 def)
% Number of atoms : 21 ( 20 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_additive_inverse,axiom,
! [VAR_0] : add(additive_inverse(VAR_0),VAR_0) = additive_identity,
file('theBenchmark.p',left_additive_inverse) ).
cnf(c_2,plain,
add(additive_inverse(A),A) = additive_identity,
inference(clausify,[status(thm)],[left_additive_inverse]) ).
fof(additive_inverse_additive_inverse,axiom,
! [VAR_0] : additive_inverse(additive_inverse(VAR_0)) = VAR_0,
file('theBenchmark.p',additive_inverse_additive_inverse) ).
cnf(c_6,plain,
additive_inverse(additive_inverse(A)) = A,
inference(clausify,[status(thm)],[additive_inverse_additive_inverse]) ).
fof(multiply_additive_inverse1,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,additive_inverse(VAR_1)) = additive_inverse(multiply(VAR_0,VAR_1)),
file('theBenchmark.p',multiply_additive_inverse1) ).
cnf(c_10,plain,
multiply(A,additive_inverse(B)) = additive_inverse(multiply(A,B)),
inference(clausify,[status(thm)],[multiply_additive_inverse1]) ).
fof(multiply_additive_inverse2,axiom,
! [VAR_0,VAR_1] : multiply(additive_inverse(VAR_0),VAR_1) = additive_inverse(multiply(VAR_0,VAR_1)),
file('theBenchmark.p',multiply_additive_inverse2) ).
cnf(c_11,plain,
multiply(additive_inverse(A),B) = additive_inverse(multiply(A,B)),
inference(clausify,[status(thm)],[multiply_additive_inverse2]) ).
fof(commutative_addition,axiom,
! [VAR_0,VAR_1] : add(VAR_0,VAR_1) = add(VAR_1,VAR_0),
file('theBenchmark.p',commutative_addition) ).
cnf(c_13,plain,
add(A,B) = add(B,A),
inference(clausify,[status(thm)],[commutative_addition]) ).
fof(boolean_ring,axiom,
! [VAR_0] : multiply(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',boolean_ring) ).
cnf(c_15,plain,
multiply(A,A) = A,
inference(clausify,[status(thm)],[boolean_ring]) ).
fof(prove_inverse,axiom,
add(a,a) != additive_identity,
file('theBenchmark.p',prove_inverse) ).
cnf(c_16,plain,
add(a,a) != additive_identity,
inference(clausify,[status(thm)],[prove_inverse]) ).
cnf(c_17,plain,
add(A,additive_inverse(A)) = additive_identity,
inference(paramod,[status(thm)],[c_13,c_2]) ).
cnf(c_28,plain,
additive_inverse(A) = additive_inverse(multiply(additive_inverse(A),A)),
inference(paramod,[status(thm)],[c_15,c_10]) ).
cnf(c_29,plain,
additive_inverse(A) = additive_inverse(additive_inverse(multiply(A,A))),
inference(paramod,[status(thm)],[c_11,c_28]) ).
cnf(c_30,plain,
additive_inverse(A) = additive_inverse(additive_inverse(A)),
inference(paramod,[status(thm)],[c_15,c_29]) ).
cnf(c_23,plain,
additive_inverse(A) = A,
inference(paramod,[status(thm)],[c_6,c_30]) ).
cnf(c_26,plain,
add(A,A) = additive_identity,
inference(paramod,[status(thm)],[c_23,c_17]) ).
cnf(c_27,plain,
$false,
inference(resolve,[status(thm)],[c_26,c_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG007-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 05:47:05 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 959098 was started by sandbox2 on n002,
% 0.10/0.38 % Sat Sep 26 05:47:05 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.40
% 0.10/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.40
% 0.10/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.10/0.40 % Length of proof is 11.
% 0.10/0.40 % Level of proof is 3.
% 0.10/0.40 % Maximum clause weight is 9.000.
% 0.10/0.40 % Given clauses 14.
% 0.10/0.40
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------