%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU167+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 08:45:17 AM UTC 2026
% Result : Theorem 36.77s 5.74s
% Output : CNFRefutation 36.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 7 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 26 ( 9 ~; 5 |; 8 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 14 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t118_zfmisc_1,axiom,
! [A,B,C] :
( subset(A,B)
=> ( subset(cartesian_product2(C,A),cartesian_product2(C,B))
& subset(cartesian_product2(A,C),cartesian_product2(B,C)) ) ),
file('theBenchmark.p',t118_zfmisc_1) ).
fof(t1_xboole_1,axiom,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('theBenchmark.p',t1_xboole_1) ).
fof(t119_zfmisc_1,conjecture,
! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('theBenchmark.p',t119_zfmisc_1) ).
fof(t119_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
inference(assume_negation,[status(cth)],[t119_zfmisc_1]) ).
cnf(c_197,plain,
( subset(cartesian_product2(A,C),cartesian_product2(B,C))
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t118_zfmisc_1]) ).
cnf(c_198,plain,
( subset(cartesian_product2(C,A),cartesian_product2(C,B))
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t118_zfmisc_1]) ).
cnf(c_203,plain,
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t1_xboole_1]) ).
fof(nnf_95,plain,
? [A,B,C,D] :
( ~ subset(cartesian_product2(A,C),cartesian_product2(B,D))
& subset(C,D)
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[t119_zfmisc_1_neg]) ).
fof(sk_t119_zfmisc_1_neg,plain,
( ~ subset(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK3))
& subset(sK2,sK3)
& subset(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2),skolemize(D,sK3)],[nnf_95]) ).
cnf(c_254,negated_conjecture,
subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t119_zfmisc_1_neg]) ).
cnf(c_255,negated_conjecture,
subset(sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_t119_zfmisc_1_neg]) ).
cnf(c_256,negated_conjecture,
~ subset(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK3)),
inference(split_conjunct,[status(thm)],[sk_t119_zfmisc_1_neg]) ).
cnf(c_1268,plain,
subset(cartesian_product2(sK0,A),cartesian_product2(sK1,A)),
inference(resolve,[status(thm)],[c_254,c_197]) ).
cnf(c_1282,plain,
subset(cartesian_product2(A,sK2),cartesian_product2(A,sK3)),
inference(resolve,[status(thm)],[c_255,c_198]) ).
cnf(c_4004,plain,
( subset(A,cartesian_product2(sK1,B))
| ~ subset(A,cartesian_product2(sK0,B)) ),
inference(resolve,[status(thm)],[c_1268,c_203]) ).
cnf(c_19001,plain,
subset(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK3)),
inference(resolve,[status(thm)],[c_4004,c_1282]) ).
cnf(c_19000,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_256,c_19001]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU167+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 08:43:46 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 2674435 was started by sandbox2 on n014,
% 0.10/0.36 % Sat Sep 26 08:43:46 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.40
% 0.14/0.40 % From the command line: assign(max_seconds, 300).
% 36.77/5.74
% 36.77/5.74 % given #500 (F,wt=23): 5022 -disjoint(unordered_pair(A,set_difference(B,C)),powerset(B)). [resolve(3113,a,3163,a)].
% 36.77/5.74
% 36.77/5.74 % given #1000 (T,wt=19): 4325 -subset(A,powerset(empty_set)) | subset(A,unordered_pair(empty_set,B)). [resolve(4294,a,203,b)].
% 36.77/5.74
% 36.77/5.74 % given #1500 (F,wt=45): 15955 set_difference(A,powerset(set_union2(B,C))) != unordered_pair(set_difference(set_difference(set_difference(B,C),C),C),D). [para(99(a,1),11760(a,1,2,1))].
% 36.77/5.74
% 36.77/5.74 % given #2000 (T,wt=19): 18122 c3 = empty_set | subset(f19(c4,c3),union(c4)). [resolve(18056,b,182,a)].
% 36.77/5.74
% 36.77/5.74 % SZS status Theorem for theBenchmark
% 36.77/5.74
% 36.77/5.74 % Proof 1 at 3.85 (+ 1.40) seconds.
% 36.77/5.74 % Length of proof is 13.
% 36.77/5.74 % Level of proof is 4.
% 36.77/5.74 % Maximum clause weight is 20.000.
% 36.77/5.74 % Given clauses 2231.
% 36.77/5.74
% 36.77/5.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------