%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG023-7 : 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 08:26:22 AM UTC 2026
% Result : Unsatisfiable 0.14s 10.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 16 unt; 0 def)
% Number of atoms : 16 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 19 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(right_additive_inverse,axiom,
! [VAR_0] : add(VAR_0,additive_inverse(VAR_0)) = additive_identity,
file('theBenchmark.p',right_additive_inverse) ).
cnf(c_6,plain,
add(A,additive_inverse(A)) = additive_identity,
inference(clausify,[status(thm)],[right_additive_inverse]) ).
fof(commutativity_for_addition,axiom,
! [VAR_0,VAR_1] : add(VAR_0,VAR_1) = add(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_for_addition) ).
cnf(c_10,plain,
add(A,B) = add(B,A),
inference(clausify,[status(thm)],[commutativity_for_addition]) ).
fof(left_alternative,axiom,
! [VAR_0,VAR_1] : multiply(multiply(VAR_0,VAR_0),VAR_1) = multiply(VAR_0,multiply(VAR_0,VAR_1)),
file('theBenchmark.p',left_alternative) ).
cnf(c_14,plain,
multiply(multiply(A,A),B) = multiply(A,multiply(A,B)),
inference(clausify,[status(thm)],[left_alternative]) ).
fof(associator,axiom,
! [VAR_0,VAR_1,VAR_2] : associator(VAR_0,VAR_1,VAR_2) = add(multiply(multiply(VAR_0,VAR_1),VAR_2),additive_inverse(multiply(VAR_0,multiply(VAR_1,VAR_2)))),
file('theBenchmark.p',associator) ).
cnf(c_15,plain,
associator(A,B,C) = add(multiply(multiply(A,B),C),additive_inverse(multiply(A,multiply(B,C)))),
inference(clausify,[status(thm)],[associator]) ).
cnf(c_16,plain,
associator(A,B,C) = add(additive_inverse(multiply(A,multiply(B,C))),multiply(multiply(A,B),C)),
inference(paramod,[status(thm)],[c_10,c_15]) ).
fof(prove_left_alternative,axiom,
associator(x,x,y) != additive_identity,
file('theBenchmark.p',prove_left_alternative) ).
cnf(c_26,plain,
associator(x,x,y) != additive_identity,
inference(clausify,[status(thm)],[prove_left_alternative]) ).
cnf(c_28,plain,
add(additive_inverse(multiply(x,multiply(x,y))),multiply(multiply(x,x),y)) != additive_identity,
inference(paramod,[status(thm)],[c_16,c_26]) ).
cnf(c_29,plain,
add(additive_inverse(multiply(x,multiply(x,y))),multiply(x,multiply(x,y))) != additive_identity,
inference(paramod,[status(thm)],[c_14,c_28]) ).
cnf(c_30,plain,
add(multiply(x,multiply(x,y)),additive_inverse(multiply(x,multiply(x,y)))) != additive_identity,
inference(paramod,[status(thm)],[c_10,c_29]) ).
cnf(c_31,plain,
additive_identity != additive_identity,
inference(paramod,[status(thm)],[c_6,c_30]) ).
cnf(c_27,plain,
$false,
inference(copy,[status(thm)],[c_31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG023-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/10.39 % Computer : n002.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Sat Sep 26 05:49:48 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.11/10.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/10.39 % Process 964112 was started by sandbox2 on n002,
% 0.11/10.39 % Sat Sep 26 05:49:48 2026
% 0.11/10.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/10.40
% 0.11/10.40 % From the command line: assign(max_seconds, 300).
% 0.14/10.41
% 0.14/10.41 % SZS status Unsatisfiable for theBenchmark
% 0.14/10.41
% 0.14/10.41 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/10.41 % Length of proof is 7.
% 0.14/10.41 % Level of proof is 2.
% 0.14/10.41 % Maximum clause weight is 17.000.
% 0.14/10.41 % Given clauses 0.
% 0.14/10.41
% 0.14/10.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------