%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET597+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 : n013.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 0.12s 0.41s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 14 unt; 0 def)
% Number of atoms : 155 ( 42 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 174 ( 67 ~; 78 |; 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(subset_of_union,axiom,
! [B,C] : subset(B,union(B,C)),
file('theBenchmark.p',subset_of_union) ).
fof(union_subset,axiom,
! [B,C,D] :
( ( subset(D,C)
& subset(B,C) )
=> subset(union(B,D),C) ),
file('theBenchmark.p',union_subset) ).
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('theBenchmark.p',equal_defn) ).
fof(commutativity_of_union,axiom,
! [B,C] : union(B,C) = union(C,B),
file('theBenchmark.p',commutativity_of_union) ).
fof(prove_th56,conjecture,
! [B,C,D] :
( B = union(C,D)
<=> ( ! [E] :
( ( subset(D,E)
& subset(C,E) )
=> subset(B,E) )
& subset(D,B)
& subset(C,B) ) ),
file('theBenchmark.p',prove_th56) ).
fof(prove_th56_neg,negated_conjecture,
~ ! [B,C,D] :
( B = union(C,D)
<=> ( ! [E] :
( ( subset(D,E)
& subset(C,E) )
=> subset(B,E) )
& subset(D,B)
& subset(C,B) ) ),
inference(assume_negation,[status(cth)],[prove_th56]) ).
cnf(c_10,plain,
subset(A,union(A,B)),
inference(clausify,[status(thm)],[subset_of_union]) ).
cnf(c_11,plain,
( subset(union(A,C),B)
| ~ subset(C,B)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[union_subset]) ).
cnf(c_20,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(clausify,[status(thm)],[equal_defn]) ).
cnf(c_21,plain,
union(A,B) = union(B,A),
inference(clausify,[status(thm)],[commutativity_of_union]) ).
fof(nnf_9,plain,
? [B,C,D] :
( ( ? [E] :
( ~ subset(B,E)
& subset(D,E)
& subset(C,E) )
| ~ subset(D,B)
| ~ subset(C,B)
| union(C,D) != B )
& ( ( ! [X0] :
( subset(B,X0)
| ~ subset(D,X0)
| ~ subset(C,X0) )
& subset(D,B)
& subset(C,B) )
| union(C,D) = B ) ),
inference(fof_nnf,[status(thm)],[prove_th56_neg]) ).
fof(sk_prove_th56_neg_sk,plain,
( ( ( ~ subset(sK2,sK3)
& subset(sK1,sK3)
& subset(sK0,sK3) )
| ~ subset(sK1,sK2)
| ~ subset(sK0,sK2)
| union(sK0,sK1) != sK2 )
& ( ( ! [X0] :
( subset(sK2,X0)
| ~ subset(sK1,X0)
| ~ subset(sK0,X0) )
& subset(sK1,sK2)
& subset(sK0,sK2) )
| union(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_th56_neg,plain,
( ( ~ subset(sK2,sK3)
| ~ subset(sK1,sK2)
| ~ subset(sK0,sK2)
| union(sK0,sK1) != sK2 )
& ( subset(sK1,sK3)
| ~ subset(sK1,sK2)
| ~ subset(sK0,sK2)
| union(sK0,sK1) != sK2 )
& ( subset(sK0,sK3)
| ~ subset(sK1,sK2)
| ~ subset(sK0,sK2)
| union(sK0,sK1) != sK2 )
& ! [VAR_0] :
( subset(sK2,VAR_0)
| ~ subset(sK1,VAR_0)
| ~ subset(sK0,VAR_0)
| union(sK0,sK1) = sK2 )
& ( subset(sK1,sK2)
| union(sK0,sK1) = sK2 )
& ( subset(sK0,sK2)
| union(sK0,sK1) = sK2 ) ),
inference(cnf_transformation,[status(thm)],[sk_prove_th56_neg_sk]) ).
cnf(c_27,negated_conjecture,
( subset(sK0,sK2)
| union(sK0,sK1) = sK2 ),
inference(split_conjunct,[status(thm)],[sk_prove_th56_neg]) ).
cnf(c_28,negated_conjecture,
( subset(sK1,sK2)
| union(sK0,sK1) = sK2 ),
inference(split_conjunct,[status(thm)],[sk_prove_th56_neg]) ).
cnf(c_29,negated_conjecture,
( subset(sK2,A)
| ~ subset(sK1,A)
| ~ subset(sK0,A)
| union(sK0,sK1) = sK2 ),
inference(split_conjunct,[status(thm)],[sk_prove_th56_neg]) ).
cnf(c_30,negated_conjecture,
( subset(sK0,sK3)
| ~ subset(sK1,sK2)
| ~ subset(sK0,sK2)
| union(sK0,sK1) != sK2 ),
inference(split_conjunct,[status(thm)],[sk_prove_th56_neg]) ).
cnf(c_31,negated_conjecture,
( subset(sK1,sK3)
| ~ subset(sK1,sK2)
| ~ subset(sK0,sK2)
| union(sK0,sK1) != sK2 ),
inference(split_conjunct,[status(thm)],[sk_prove_th56_neg]) ).
cnf(c_32,negated_conjecture,
( ~ subset(sK2,sK3)
| ~ subset(sK1,sK2)
| ~ subset(sK0,sK2)
| union(sK0,sK1) != sK2 ),
inference(split_conjunct,[status(thm)],[sk_prove_th56_neg]) ).
cnf(c_45,plain,
subset(A,union(B,A)),
inference(paramod,[status(thm)],[c_21,c_10]) ).
cnf(c_263,negated_conjecture,
( union(sK0,sK1) = sK2
| subset(union(sK0,A),sK2)
| ~ subset(A,sK2) ),
inference(resolve,[status(thm)],[c_11,c_27]) ).
cnf(c_264,negated_conjecture,
( union(sK0,sK1) = sK2
| union(sK0,sK1) = sK2
| subset(union(sK0,sK1),sK2) ),
inference(resolve,[status(thm)],[c_263,c_28]) ).
cnf(c_100,negated_conjecture,
( union(sK0,sK1) = sK2
| subset(union(sK0,sK1),sK2) ),
inference(copy,[status(thm)],[c_264]) ).
cnf(c_265,negated_conjecture,
( subset(sK2,union(sK0,A))
| ~ subset(sK1,union(sK0,A))
| union(sK0,sK1) = sK2 ),
inference(resolve,[status(thm)],[c_29,c_10]) ).
cnf(c_112,negated_conjecture,
( subset(sK2,union(sK0,sK1))
| union(sK0,sK1) = sK2 ),
inference(resolve,[status(thm)],[c_265,c_45]) ).
cnf(c_266,plain,
( union(sK0,sK1) = sK2
| ~ subset(sK2,union(sK0,sK1))
| sK2 = union(sK0,sK1) ),
inference(resolve,[status(thm)],[c_20,c_100]) ).
cnf(c_267,plain,
( union(sK0,sK1) = sK2
| union(sK0,sK1) = sK2
| sK2 = union(sK0,sK1) ),
inference(resolve,[status(thm)],[c_266,c_112]) ).
cnf(c_268,plain,
( union(sK0,sK1) = sK2
| union(sK0,sK1) = sK2
| union(sK0,sK1) = sK2 ),
inference(copy,[status(thm)],[c_267]) ).
cnf(c_269,plain,
( union(sK0,sK1) = sK2
| union(sK0,sK1) = sK2 ),
inference(copy,[status(thm)],[c_268]) ).
cnf(c_173,plain,
union(sK0,sK1) = sK2,
inference(copy,[status(thm)],[c_269]) ).
cnf(c_270,negated_conjecture,
( ~ subset(sK2,sK3)
| ~ subset(sK1,sK2)
| ~ subset(sK0,sK2)
| sK2 != sK2 ),
inference(paramod,[status(thm)],[c_173,c_32]) ).
cnf(c_174,negated_conjecture,
( ~ subset(sK2,sK3)
| ~ subset(sK1,sK2)
| ~ subset(sK0,sK2) ),
inference(copy,[status(thm)],[c_270]) ).
cnf(c_271,negated_conjecture,
( subset(sK1,sK3)
| ~ subset(sK1,sK2)
| ~ subset(sK0,sK2)
| sK2 != sK2 ),
inference(paramod,[status(thm)],[c_173,c_31]) ).
cnf(c_175,negated_conjecture,
( subset(sK1,sK3)
| ~ subset(sK1,sK2)
| ~ subset(sK0,sK2) ),
inference(copy,[status(thm)],[c_271]) ).
cnf(c_272,negated_conjecture,
( subset(sK0,sK3)
| ~ subset(sK1,sK2)
| ~ subset(sK0,sK2)
| sK2 != sK2 ),
inference(paramod,[status(thm)],[c_173,c_30]) ).
cnf(c_176,negated_conjecture,
( subset(sK0,sK3)
| ~ subset(sK1,sK2)
| ~ subset(sK0,sK2) ),
inference(copy,[status(thm)],[c_272]) ).
cnf(c_179,plain,
subset(sK0,sK2),
inference(paramod,[status(thm)],[c_173,c_10]) ).
cnf(c_182,plain,
subset(sK1,sK2),
inference(paramod,[status(thm)],[c_173,c_45]) ).
cnf(c_273,negated_conjecture,
( subset(sK0,sK3)
| ~ subset(sK1,sK2) ),
inference(resolve,[status(thm)],[c_179,c_176]) ).
cnf(c_186,negated_conjecture,
subset(sK0,sK3),
inference(resolve,[status(thm)],[c_182,c_273]) ).
cnf(c_274,negated_conjecture,
( subset(sK1,sK3)
| ~ subset(sK1,sK2) ),
inference(resolve,[status(thm)],[c_179,c_175]) ).
cnf(c_187,negated_conjecture,
subset(sK1,sK3),
inference(resolve,[status(thm)],[c_182,c_274]) ).
cnf(c_275,negated_conjecture,
( ~ subset(sK2,sK3)
| ~ subset(sK1,sK2) ),
inference(resolve,[status(thm)],[c_179,c_174]) ).
cnf(c_188,negated_conjecture,
~ subset(sK2,sK3),
inference(resolve,[status(thm)],[c_182,c_275]) ).
cnf(c_276,negated_conjecture,
( subset(union(sK0,A),sK3)
| ~ subset(A,sK3) ),
inference(resolve,[status(thm)],[c_11,c_186]) ).
cnf(c_277,negated_conjecture,
subset(union(sK0,sK1),sK3),
inference(resolve,[status(thm)],[c_276,c_187]) ).
cnf(c_278,negated_conjecture,
subset(sK2,sK3),
inference(paramod,[status(thm)],[c_173,c_277]) ).
cnf(c_262,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_188,c_278]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET597+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n013.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 26 07:57:36 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.34 % Process 2280538 was started by sandbox2 on n013,
% 0.07/0.34 % Sat Sep 26 07:57:36 2026
% 0.07/0.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.35
% 0.07/0.35 % From the command line: assign(max_seconds, 300).
% 0.12/0.41
% 0.12/0.41 % SZS status Theorem for theBenchmark
% 0.12/0.41
% 0.12/0.41 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.12/0.41 % Length of proof is 28.
% 0.12/0.41 % Level of proof is 7.
% 0.12/0.41 % Maximum clause weight is 24.000.
% 0.12/0.41 % Given clauses 54.
% 0.12/0.41
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------