%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM004-1 : 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 : n009.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 08:16:01 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 12 unt; 0 def)
% Number of atoms : 30 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 15 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity,axiom,
! [VAR_0] : equalish(VAR_0,VAR_0),
file('theBenchmark.p',reflexivity) ).
cnf(c_1,plain,
equalish(A,A),
inference(clausify,[status(thm)],[reflexivity]) ).
fof(transitivity,axiom,
! [VAR_0,VAR_1,VAR_2] :
( equalish(VAR_0,VAR_2)
| ~ equalish(VAR_1,VAR_2)
| ~ equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity) ).
cnf(c_2,plain,
( equalish(A,C)
| ~ equalish(B,C)
| ~ equalish(A,B) ),
inference(clausify,[status(thm)],[transitivity]) ).
fof(commutativity_of_addition,axiom,
! [VAR_0,VAR_1] : equalish(add(VAR_0,VAR_1),add(VAR_1,VAR_0)),
file('theBenchmark.p',commutativity_of_addition) ).
cnf(c_3,plain,
equalish(add(A,B),add(B,A)),
inference(clausify,[status(thm)],[commutativity_of_addition]) ).
fof(commutativity2,axiom,
! [VAR_0,VAR_1,VAR_2] : equalish(subtract(add(VAR_0,VAR_1),VAR_2),add(subtract(VAR_0,VAR_2),VAR_1)),
file('theBenchmark.p',commutativity2) ).
cnf(c_8,plain,
equalish(subtract(add(A,B),C),add(subtract(A,C),B)),
inference(clausify,[status(thm)],[commutativity2]) ).
fof(subtract_substitution1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_2,subtract(VAR_1,VAR_3))
| ~ equalish(VAR_2,subtract(VAR_0,VAR_3))
| ~ equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',subtract_substitution1) ).
cnf(c_11,plain,
( equalish(C,subtract(B,D))
| ~ equalish(C,subtract(A,D))
| ~ equalish(A,B) ),
inference(clausify,[status(thm)],[subtract_substitution1]) ).
fof(prove_equation,axiom,
~ equalish(subtract(add(a,b),c),add(a,subtract(b,c))),
file('theBenchmark.p',prove_equation) ).
cnf(c_13,plain,
~ equalish(subtract(add(a,b),c),add(a,subtract(b,c))),
inference(clausify,[status(thm)],[prove_equation]) ).
cnf(c_183,plain,
( equalish(A,subtract(add(C,B),D))
| ~ equalish(A,subtract(add(B,C),D)) ),
inference(resolve,[status(thm)],[c_11,c_3]) ).
cnf(c_107,plain,
equalish(subtract(add(A,B),C),subtract(add(B,A),C)),
inference(resolve,[status(thm)],[c_183,c_1]) ).
cnf(c_184,plain,
( equalish(A,add(C,B))
| ~ equalish(A,add(B,C)) ),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_138,plain,
~ equalish(subtract(add(a,b),c),add(subtract(b,c),a)),
inference(resolve,[status(thm)],[c_184,c_13]) ).
cnf(c_185,plain,
( equalish(A,add(subtract(B,D),C))
| ~ equalish(A,subtract(add(B,C),D)) ),
inference(resolve,[status(thm)],[c_2,c_8]) ).
cnf(c_181,plain,
~ equalish(subtract(add(a,b),c),subtract(add(b,a),c)),
inference(resolve,[status(thm)],[c_185,c_138]) ).
cnf(c_182,plain,
$false,
inference(resolve,[status(thm)],[c_181,c_107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM004-1 : 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 : n009.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 01:51:59 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3106600 was started by sandbox2 on n009,
% 0.10/0.37 % Sat Sep 26 01:51:59 2026
% 0.10/0.37 % 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 (+ 0.01) seconds.
% 0.10/0.40 % Length of proof is 10.
% 0.10/0.40 % Level of proof is 3.
% 0.10/0.40 % Maximum clause weight is 13.000.
% 0.10/0.40 % Given clauses 15.
% 0.10/0.40
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------