%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM002-1 : 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 : n019.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 08:16:00 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.36s
% Output : CNFRefutation 0.11s
% 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 : 44 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(commutativity1,axiom,
! [VAR_0,VAR_1,VAR_2] : equalish(add(subtract(VAR_0,VAR_1),VAR_2),subtract(add(VAR_0,VAR_2),VAR_1)),
file('theBenchmark.p',commutativity1) ).
cnf(c_7,plain,
equalish(add(subtract(A,B),C),subtract(add(A,C),B)),
inference(clausify,[status(thm)],[commutativity1]) ).
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(add(subtract(a,b),c),add(a,subtract(c,b))),
file('theBenchmark.p',prove_equation) ).
cnf(c_13,plain,
~ equalish(add(subtract(a,b),c),add(a,subtract(c,b))),
inference(clausify,[status(thm)],[prove_equation]) ).
cnf(c_187,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_108,plain,
equalish(add(subtract(A,B),C),subtract(add(C,A),B)),
inference(resolve,[status(thm)],[c_187,c_7]) ).
cnf(c_188,plain,
( equalish(A,add(C,B))
| ~ equalish(A,add(B,C)) ),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_142,plain,
~ equalish(add(subtract(a,b),c),add(subtract(c,b),a)),
inference(resolve,[status(thm)],[c_188,c_13]) ).
cnf(c_189,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_190,plain,
~ equalish(add(subtract(a,b),c),subtract(add(c,a),b)),
inference(resolve,[status(thm)],[c_189,c_142]) ).
cnf(c_186,plain,
$false,
inference(resolve,[status(thm)],[c_108,c_190]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n019.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 01:52:05 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 142728 was started by sandbox on n019,
% 0.08/0.35 % Sat Sep 26 01:52:05 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 0.11/0.36
% 0.11/0.36 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.36
% 0.11/0.36 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.36 % Length of proof is 9.
% 0.11/0.36 % Level of proof is 2.
% 0.11/0.36 % Maximum clause weight is 26.000.
% 0.11/0.36 % Given clauses 19.
% 0.11/0.36
% 0.11/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------