%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET598+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 08:36:34 AM UTC 2026
% Result : Theorem 0.22s 0.52s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 47 ( 14 unt; 0 def)
% Number of atoms : 152 ( 39 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 172 ( 67 ~; 76 |; 23 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 39 ( 2 sgn 20 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_is_subset,axiom,
! [B,C] : subset(intersection(B,C),B),
file('theBenchmark.p',intersection_is_subset) ).
fof(intersection_of_subsets,axiom,
! [B,C,D] :
( ( subset(B,D)
& subset(B,C) )
=> subset(B,intersection(C,D)) ),
file('theBenchmark.p',intersection_of_subsets) ).
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('theBenchmark.p',equal_defn) ).
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('theBenchmark.p',commutativity_of_intersection) ).
fof(prove_th57,conjecture,
! [B,C,D] :
( B = intersection(C,D)
<=> ( ! [E] :
( ( subset(E,D)
& subset(E,C) )
=> subset(E,B) )
& subset(B,D)
& subset(B,C) ) ),
file('theBenchmark.p',prove_th57) ).
fof(prove_th57_neg,negated_conjecture,
~ ! [B,C,D] :
( B = intersection(C,D)
<=> ( ! [E] :
( ( subset(E,D)
& subset(E,C) )
=> subset(E,B) )
& subset(B,D)
& subset(B,C) ) ),
inference(assume_negation,[status(cth)],[prove_th57]) ).
cnf(c_10,plain,
subset(intersection(A,B),A),
inference(clausify,[status(thm)],[intersection_is_subset]) ).
cnf(c_11,plain,
( subset(A,intersection(B,C))
| ~ subset(A,C)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[intersection_of_subsets]) ).
cnf(c_20,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(clausify,[status(thm)],[equal_defn]) ).
cnf(c_21,plain,
intersection(A,B) = intersection(B,A),
inference(clausify,[status(thm)],[commutativity_of_intersection]) ).
fof(nnf_9,plain,
? [B,C,D] :
( ( ? [E] :
( ~ subset(E,B)
& subset(E,D)
& subset(E,C) )
| ~ subset(B,D)
| ~ subset(B,C)
| intersection(C,D) != B )
& ( ( ! [X0] :
( subset(X0,B)
| ~ subset(X0,D)
| ~ subset(X0,C) )
& subset(B,D)
& subset(B,C) )
| intersection(C,D) = B ) ),
inference(fof_nnf,[status(thm)],[prove_th57_neg]) ).
fof(sk_prove_th57_neg_sk,plain,
( ( ( ~ subset(sK3,sK2)
& subset(sK3,sK1)
& subset(sK3,sK0) )
| ~ subset(sK2,sK1)
| ~ subset(sK2,sK0)
| intersection(sK0,sK1) != sK2 )
& ( ( ! [X0] :
( subset(X0,sK2)
| ~ subset(X0,sK1)
| ~ subset(X0,sK0) )
& subset(sK2,sK1)
& subset(sK2,sK0) )
| intersection(sK0,sK1) = sK2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(B,sK2),skolemize(C,sK0),skolemize(D,sK1),skolemize(E,sK3)],[nnf_9]) ).
fof(sk_prove_th57_neg,plain,
( ( ~ subset(sK3,sK2)
| ~ subset(sK2,sK1)
| ~ subset(sK2,sK0)
| intersection(sK0,sK1) != sK2 )
& ( subset(sK3,sK1)
| ~ subset(sK2,sK1)
| ~ subset(sK2,sK0)
| intersection(sK0,sK1) != sK2 )
& ( subset(sK3,sK0)
| ~ subset(sK2,sK1)
| ~ subset(sK2,sK0)
| intersection(sK0,sK1) != sK2 )
& ! [VAR_0] :
( subset(VAR_0,sK2)
| ~ subset(VAR_0,sK1)
| ~ subset(VAR_0,sK0)
| intersection(sK0,sK1) = sK2 )
& ( subset(sK2,sK1)
| intersection(sK0,sK1) = sK2 )
& ( subset(sK2,sK0)
| intersection(sK0,sK1) = sK2 ) ),
inference(cnf_transformation,[status(thm)],[sk_prove_th57_neg_sk]) ).
cnf(c_27,negated_conjecture,
( subset(sK2,sK0)
| intersection(sK0,sK1) = sK2 ),
inference(split_conjunct,[status(thm)],[sk_prove_th57_neg]) ).
cnf(c_28,negated_conjecture,
( subset(sK2,sK1)
| intersection(sK0,sK1) = sK2 ),
inference(split_conjunct,[status(thm)],[sk_prove_th57_neg]) ).
cnf(c_29,negated_conjecture,
( subset(A,sK2)
| ~ subset(A,sK1)
| ~ subset(A,sK0)
| intersection(sK0,sK1) = sK2 ),
inference(split_conjunct,[status(thm)],[sk_prove_th57_neg]) ).
cnf(c_30,negated_conjecture,
( subset(sK3,sK0)
| ~ subset(sK2,sK1)
| ~ subset(sK2,sK0)
| intersection(sK0,sK1) != sK2 ),
inference(split_conjunct,[status(thm)],[sk_prove_th57_neg]) ).
cnf(c_31,negated_conjecture,
( subset(sK3,sK1)
| ~ subset(sK2,sK1)
| ~ subset(sK2,sK0)
| intersection(sK0,sK1) != sK2 ),
inference(split_conjunct,[status(thm)],[sk_prove_th57_neg]) ).
cnf(c_32,negated_conjecture,
( ~ subset(sK3,sK2)
| ~ subset(sK2,sK1)
| ~ subset(sK2,sK0)
| intersection(sK0,sK1) != sK2 ),
inference(split_conjunct,[status(thm)],[sk_prove_th57_neg]) ).
cnf(c_46,plain,
subset(intersection(A,B),B),
inference(paramod,[status(thm)],[c_21,c_10]) ).
cnf(c_220,negated_conjecture,
( intersection(sK0,sK1) = sK2
| subset(sK2,intersection(sK0,A))
| ~ subset(sK2,A) ),
inference(resolve,[status(thm)],[c_11,c_27]) ).
cnf(c_221,negated_conjecture,
( intersection(sK0,sK1) = sK2
| intersection(sK0,sK1) = sK2
| subset(sK2,intersection(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_220,c_28]) ).
cnf(c_103,negated_conjecture,
( intersection(sK0,sK1) = sK2
| subset(sK2,intersection(sK0,sK1)) ),
inference(copy,[status(thm)],[c_221]) ).
cnf(c_222,negated_conjecture,
( subset(intersection(sK0,A),sK2)
| ~ subset(intersection(sK0,A),sK1)
| intersection(sK0,sK1) = sK2 ),
inference(resolve,[status(thm)],[c_29,c_10]) ).
cnf(c_115,negated_conjecture,
( subset(intersection(sK0,sK1),sK2)
| intersection(sK0,sK1) = sK2 ),
inference(resolve,[status(thm)],[c_222,c_46]) ).
cnf(c_223,plain,
( intersection(sK0,sK1) = sK2
| ~ subset(intersection(sK0,sK1),sK2)
| intersection(sK0,sK1) = sK2 ),
inference(resolve,[status(thm)],[c_20,c_103]) ).
cnf(c_224,plain,
( intersection(sK0,sK1) = sK2
| intersection(sK0,sK1) = sK2
| intersection(sK0,sK1) = sK2 ),
inference(resolve,[status(thm)],[c_223,c_115]) ).
cnf(c_225,plain,
( intersection(sK0,sK1) = sK2
| intersection(sK0,sK1) = sK2 ),
inference(copy,[status(thm)],[c_224]) ).
cnf(c_166,plain,
intersection(sK0,sK1) = sK2,
inference(copy,[status(thm)],[c_225]) ).
cnf(c_226,negated_conjecture,
( ~ subset(sK3,sK2)
| ~ subset(sK2,sK1)
| ~ subset(sK2,sK0)
| sK2 != sK2 ),
inference(paramod,[status(thm)],[c_166,c_32]) ).
cnf(c_167,negated_conjecture,
( ~ subset(sK3,sK2)
| ~ subset(sK2,sK1)
| ~ subset(sK2,sK0) ),
inference(copy,[status(thm)],[c_226]) ).
cnf(c_227,negated_conjecture,
( subset(sK3,sK1)
| ~ subset(sK2,sK1)
| ~ subset(sK2,sK0)
| sK2 != sK2 ),
inference(paramod,[status(thm)],[c_166,c_31]) ).
cnf(c_168,negated_conjecture,
( subset(sK3,sK1)
| ~ subset(sK2,sK1)
| ~ subset(sK2,sK0) ),
inference(copy,[status(thm)],[c_227]) ).
cnf(c_228,negated_conjecture,
( subset(sK3,sK0)
| ~ subset(sK2,sK1)
| ~ subset(sK2,sK0)
| sK2 != sK2 ),
inference(paramod,[status(thm)],[c_166,c_30]) ).
cnf(c_169,negated_conjecture,
( subset(sK3,sK0)
| ~ subset(sK2,sK1)
| ~ subset(sK2,sK0) ),
inference(copy,[status(thm)],[c_228]) ).
cnf(c_171,plain,
subset(sK2,sK0),
inference(paramod,[status(thm)],[c_166,c_10]) ).
cnf(c_175,plain,
subset(sK2,sK1),
inference(paramod,[status(thm)],[c_166,c_46]) ).
cnf(c_229,negated_conjecture,
( subset(sK3,sK0)
| ~ subset(sK2,sK1) ),
inference(resolve,[status(thm)],[c_171,c_169]) ).
cnf(c_179,negated_conjecture,
subset(sK3,sK0),
inference(resolve,[status(thm)],[c_175,c_229]) ).
cnf(c_230,negated_conjecture,
( subset(sK3,sK1)
| ~ subset(sK2,sK1) ),
inference(resolve,[status(thm)],[c_171,c_168]) ).
cnf(c_180,negated_conjecture,
subset(sK3,sK1),
inference(resolve,[status(thm)],[c_175,c_230]) ).
cnf(c_231,negated_conjecture,
( ~ subset(sK3,sK2)
| ~ subset(sK2,sK1) ),
inference(resolve,[status(thm)],[c_171,c_167]) ).
cnf(c_181,negated_conjecture,
~ subset(sK3,sK2),
inference(resolve,[status(thm)],[c_175,c_231]) ).
cnf(c_232,negated_conjecture,
( subset(sK3,intersection(sK0,A))
| ~ subset(sK3,A) ),
inference(resolve,[status(thm)],[c_11,c_179]) ).
cnf(c_233,negated_conjecture,
subset(sK3,intersection(sK0,sK1)),
inference(resolve,[status(thm)],[c_232,c_180]) ).
cnf(c_234,negated_conjecture,
subset(sK3,sK2),
inference(paramod,[status(thm)],[c_166,c_233]) ).
cnf(c_219,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_181,c_234]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET598+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n017.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 07:54:03 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 213543 was started by sandbox2 on n017,
% 0.17/0.44 % Sat Sep 26 07:54:03 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 0.22/0.52
% 0.22/0.52 % SZS status Theorem for theBenchmark
% 0.22/0.52
% 0.22/0.52 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.22/0.52 % Length of proof is 28.
% 0.22/0.52 % Level of proof is 7.
% 0.22/0.52 % Maximum clause weight is 24.000.
% 0.22/0.52 % Given clauses 53.
% 0.22/0.52
% 0.22/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------