%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM341+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 08:16:28 AM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 4 unt; 0 def)
% Number of atoms : 27 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 9 ~; 8 |; 2 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 35 ( 3 sgn 3 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(minus_entry_point,axiom,
! [X,Y,Z] :
( sum(Y,Z,X)
<=> difference(X,Y,Z) ),
file('theBenchmark.p',minus_entry_point) ).
fof(add_same_as_subtract,conjecture,
? [X,Y,Z] :
( sum(X,Y,Z)
<=> ( difference(Z,X,Y)
& difference(Z,Y,X) ) ),
file('theBenchmark.p',add_same_as_subtract) ).
fof(add_same_as_subtract_neg,negated_conjecture,
~ ? [X,Y,Z] :
( sum(X,Y,Z)
<=> ( difference(Z,X,Y)
& difference(Z,Y,X) ) ),
inference(assume_negation,[status(cth)],[add_same_as_subtract]) ).
cnf(c_328,plain,
( difference(C,A,B)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[minus_entry_point]) ).
cnf(c_329,plain,
( ~ difference(C,A,B)
| sum(A,B,C) ),
inference(clausify,[status(thm)],[minus_entry_point]) ).
cnf(c_435,negated_conjecture,
( difference(C,B,A)
| sum(A,B,C) ),
inference(clausify,[status(thm)],[add_same_as_subtract_neg]) ).
cnf(c_437,negated_conjecture,
( ~ difference(C,A,B)
| ~ difference(C,B,A)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[add_same_as_subtract_neg]) ).
cnf(c_460,plain,
( ~ difference(B,A,A)
| ~ sum(A,A,B) ),
inference(factor,[status(thm)],[c_437]) ).
cnf(c_489,plain,
( difference(A,C,B)
| difference(A,B,C) ),
inference(resolve,[status(thm)],[c_435,c_328]) ).
cnf(c_491,plain,
( sum(B,A,C)
| sum(A,B,C) ),
inference(resolve,[status(thm)],[c_435,c_329]) ).
cnf(c_492,plain,
difference(A,B,B),
inference(factor,[status(thm)],[c_489]) ).
cnf(c_493,plain,
sum(A,A,B),
inference(factor,[status(thm)],[c_491]) ).
cnf(c_495,plain,
~ difference(A,B,B),
inference(resolve,[status(thm)],[c_493,c_460]) ).
cnf(c_494,plain,
$false,
inference(resolve,[status(thm)],[c_492,c_495]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM341+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n020.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 02:29:33 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 412827 was started by sandbox on n020,
% 0.08/0.36 % Sat Sep 26 02:29:33 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SInE: 149 to sos, 252 to usable, of 401 axioms (tolerance 2.00, depth 0 fixpoint).
% 0.13/0.42
% 0.13/0.42 % SZS status Theorem for theBenchmark
% 0.13/0.42
% 0.13/0.42 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.13/0.42 % Length of proof is 12.
% 0.13/0.42 % Level of proof is 4.
% 0.13/0.42 % Maximum clause weight is 17.000.
% 0.13/0.42 % Given clauses 8.
% 0.13/0.42
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------