%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET025-9 : 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 : n010.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 08:35:24 AM UTC 2026
% Result : Unsatisfiable 31.77s 10.22s
% Output : CNFRefutation 31.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 13 unt; 0 def)
% Number of atoms : 23 ( 10 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 15 ( 2 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_predicate_is_small,axiom,
~ little_set(a),
file('theBenchmark.p',prove_predicate_is_small) ).
cnf(c_64,plain,
~ little_set(a),
inference(clausify,[status(thm)],[prove_predicate_is_small]) ).
fof(an_ordered_pair_predicate,axiom,
ordered_pair_predicate(a),
file('theBenchmark.p',an_ordered_pair_predicate) ).
cnf(c_65,plain,
ordered_pair_predicate(a),
inference(clausify,[status(thm)],[an_ordered_pair_predicate]) ).
fof(ordered_pair_predicate3,axiom,
! [VAR_0] :
( VAR_0 = ordered_pair(f2(VAR_0),f3(VAR_0))
| ~ ordered_pair_predicate(VAR_0) ),
file('theBenchmark.p',ordered_pair_predicate3) ).
cnf(c_180,plain,
( A = ordered_pair(f2(A),f3(A))
| ~ ordered_pair_predicate(A) ),
inference(clausify,[status(thm)],[ordered_pair_predicate3]) ).
cnf(c_181,plain,
( ordered_pair(f2(A),f3(A)) = A
| ~ ordered_pair_predicate(A) ),
inference(copy,[status(thm)],[c_180]) ).
fof(ordered_pair,axiom,
! [VAR_0,VAR_1] : ordered_pair(VAR_0,VAR_1) = non_ordered_pair(singleton_set(VAR_0),non_ordered_pair(VAR_0,VAR_1)),
file('theBenchmark.p',ordered_pair) ).
cnf(c_184,plain,
ordered_pair(A,B) = non_ordered_pair(singleton_set(A),non_ordered_pair(A,B)),
inference(clausify,[status(thm)],[ordered_pair]) ).
fof(singleton_set,axiom,
! [VAR_0] : singleton_set(VAR_0) = non_ordered_pair(VAR_0,VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_185,plain,
singleton_set(A) = non_ordered_pair(A,A),
inference(clausify,[status(thm)],[singleton_set]) ).
fof(non_ordered_pair4,axiom,
! [VAR_0,VAR_1] : little_set(non_ordered_pair(VAR_0,VAR_1)),
file('theBenchmark.p',non_ordered_pair4) ).
cnf(c_186,plain,
little_set(non_ordered_pair(A,B)),
inference(clausify,[status(thm)],[non_ordered_pair4]) ).
cnf(c_24674,plain,
( non_ordered_pair(singleton_set(f2(A)),non_ordered_pair(f2(A),f3(A))) = A
| ~ ordered_pair_predicate(A) ),
inference(paramod,[status(thm)],[c_184,c_181]) ).
cnf(c_301,plain,
( non_ordered_pair(non_ordered_pair(f2(A),f2(A)),non_ordered_pair(f2(A),f3(A))) = A
| ~ ordered_pair_predicate(A) ),
inference(paramod,[status(thm)],[c_185,c_24674]) ).
cnf(c_671,plain,
non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f3(a))) = a,
inference(resolve,[status(thm)],[c_301,c_65]) ).
cnf(c_24675,plain,
little_set(a),
inference(paramod,[status(thm)],[c_671,c_186]) ).
cnf(c_24673,plain,
$false,
inference(resolve,[status(thm)],[c_64,c_24675]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET025-9 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/5.63 % Computer : n010.cluster.edu
% 0.15/5.63 % Model : x86_64 x86_64
% 0.15/5.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.63 % Memory : 8046.5625MB
% 0.15/5.63 % OS : Linux 6.8.0-71-generic
% 0.15/5.63 % CPULimit : 300
% 0.15/5.63 % WCLimit : 300
% 0.15/5.63 % DateTime : Sat Sep 26 06:54:36 UTC 2026
% 0.15/5.63 % CPUTime :
% 0.15/5.63 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/5.63 % Process 2728873 was started by sandbox2 on n010,
% 0.15/5.63 % Sat Sep 26 06:54:36 2026
% 0.15/5.63 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/5.64
% 0.15/5.64 % From the command line: assign(max_seconds, 300).
% 31.77/10.22
% 31.77/10.22 % given #500 (T,wt=5): 5769 intersection(A,empty_set) = empty_set. [resolve(418,a,124,a)].
% 31.77/10.22
% 31.77/10.22 % given #1000 (T,wt=7): 6580 member(powerset(powerset(f23(infinity,infinity))),universal_set). [resolve(3114,a,123,b)].
% 31.77/10.22
% 31.77/10.22 % given #1500 (T,wt=7): 22819 member(f23(universal_set,powerset(A)),powerset(A)). [resolve(919,a,2807,a)].
% 31.77/10.22
% 31.77/10.22 % SZS status Unsatisfiable for theBenchmark
% 31.77/10.22
% 31.77/10.22 % Proof 1 at 3.58 (+ 0.93) seconds.
% 31.77/10.22 % Length of proof is 10.
% 31.77/10.22 % Level of proof is 4.
% 31.77/10.22 % Maximum clause weight is 15.000.
% 31.77/10.22 % Given clauses 1659.
% 31.77/10.22
% 31.77/10.22 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------