%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET597+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 : Fri Sep 25 02:43:33 PM UTC 2026
% Result : Theorem 54.14s 8.24s
% Output : Proof 54.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 55 ( 19 unt; 0 def)
% Number of atoms : 145 ( 40 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 149 ( 59 ~; 60 |; 24 &)
% ( 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 : 56 ( 2 sgn 37 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,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('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th56) ).
fof(f8_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(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [B,C,D] :
( ( ! [E] :
( subset(B,E)
| ~ subset(D,E)
| ~ subset(C,E) )
& subset(D,B)
& subset(C,B)
& B != union(C,D) )
| ( ( ? [E] :
( ~ subset(B,E)
& subset(D,E)
& subset(C,E) )
| ~ subset(D,B)
| ~ subset(C,B) )
& B = union(C,D) ) ),
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
! [E] :
( ( ( subset(sk2,E)
| ~ subset(sk4,E)
| ~ subset(sk3,E) )
& subset(sk4,sk2)
& subset(sk3,sk2)
& sk2 != union(sk3,sk4) )
| ( ( ( ~ subset(sk2,sk5)
& subset(sk4,sk5)
& subset(sk3,sk5) )
| ~ subset(sk4,sk2)
| ~ subset(sk3,sk2) )
& sk2 = union(sk3,sk4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4,sk5])],[f8_nnf]) ).
cnf(c22,plain,
( subset(sk2,X3)
| ~ subset(sk4,X3)
| ~ subset(sk3,X3)
| sk2 = union(sk3,sk4) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f0,axiom,
! [B,C] : subset(B,union(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_of_union) ).
fof(f0_nnf,plain,
! [B,C] : subset(B,union(B,C)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C] : subset(B,union(B,C)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
subset(X0,union(X0,X1)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p240,plain,
( subset(sk2,union(sk3,X0))
| ~ subset(sk4,union(sk3,X0))
| sk2 = union(sk3,sk4) ),
inference(resolution,[status(thm)],[c22,c0]) ).
fof(f5,axiom,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f5_nnf,plain,
! [B,C] : union(B,C) = union(C,B),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [B,C] : union(B,C) = union(C,B),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c11,plain,
union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p38,plain,
subset(X0,union(X1,X0)),
inference(superposition,[status(thm)],[c11,c0]) ).
cnf(p1046,plain,
( subset(sk2,union(sk3,sk4))
| sk2 = union(sk3,sk4) ),
inference(resolution,[status(thm)],[p240,p38]) ).
cnf(c20,plain,
( subset(sk3,sk2)
| sk2 = union(sk3,sk4) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p46,plain,
( subset(sk3,sk2)
| subset(sk3,sk2) ),
inference(superposition,[status(thm)],[c20,c0]) ).
cnf(p53,plain,
subset(sk3,sk2),
inference(factoring,[status(thm)],[p46]) ).
fof(f1,axiom,
! [B,C,D] :
( ( subset(D,C)
& subset(B,C) )
=> subset(union(B,D),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_subset) ).
fof(f1_nnf,plain,
! [B,C,D] :
( subset(union(B,D),C)
| ~ subset(D,C)
| ~ subset(B,C) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C,D] :
( subset(union(B,D),C)
| ~ subset(D,C)
| ~ subset(B,C) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( subset(union(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p54,plain,
( subset(union(sk3,X0),sk2)
| ~ subset(X0,sk2) ),
inference(resolution,[status(thm)],[p53,c1]) ).
cnf(c21,plain,
( subset(sk4,sk2)
| sk2 = union(sk3,sk4) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p60,plain,
( subset(sk4,sk2)
| subset(sk4,sk2) ),
inference(superposition,[status(thm)],[c21,p38]) ).
cnf(p65,plain,
subset(sk4,sk2),
inference(factoring,[status(thm)],[p60]) ).
cnf(p153,plain,
subset(union(sk3,sk4),sk2),
inference(resolution,[status(thm)],[p54,p65]) ).
fof(f4,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f4_nnf,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c10,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p166,plain,
( ~ subset(sk2,union(sk3,sk4))
| union(sk3,sk4) = sk2 ),
inference(resolution,[status(thm)],[p153,c10]) ).
cnf(p1439,plain,
( union(sk3,sk4) = sk2
| sk2 = union(sk3,sk4) ),
inference(resolution,[status(thm)],[p1046,p166]) ).
cnf(p1969,plain,
( sk2 = union(sk3,sk4)
| sk2 = union(sk3,sk4) ),
inference(superposition,[status(thm)],[p1439,c11]) ).
cnf(p2345,plain,
sk2 = union(sk3,sk4),
inference(factoring,[status(thm)],[p1969]) ).
cnf(p2347,plain,
union(sk3,sk4) = sk2,
inference(superposition,[status(thm)],[p2345,c11]) ).
cnf(c23,plain,
( sk2 != union(sk3,sk4)
| subset(sk3,sk5)
| ~ subset(sk4,sk2)
| ~ subset(sk3,sk2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p270,plain,
( sk2 != union(sk3,sk4)
| subset(sk3,sk5)
| ~ subset(sk4,sk2) ),
inference(resolution,[status(thm)],[c23,p53]) ).
cnf(p1048,plain,
( sk2 != union(sk3,sk4)
| subset(sk3,sk5) ),
inference(resolution,[status(thm)],[p270,p65]) ).
cnf(p2348,plain,
( sk2 != sk2
| subset(sk3,sk5) ),
inference(demodulation,[status(thm)],[p2347,p1048]) ).
cnf(p2365,plain,
subset(sk3,sk5),
inference(equality_resolution,[status(thm)],[p2348]) ).
cnf(p2366,plain,
( subset(union(sk3,X0),sk5)
| ~ subset(X0,sk5) ),
inference(resolution,[status(thm)],[p2365,c1]) ).
cnf(c27,plain,
( sk2 != union(sk3,sk4)
| subset(sk4,sk5)
| ~ subset(sk4,sk2)
| ~ subset(sk3,sk2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p315,plain,
( sk2 != union(sk3,sk4)
| subset(sk4,sk5)
| ~ subset(sk4,sk2) ),
inference(resolution,[status(thm)],[c27,p53]) ).
cnf(p1116,plain,
( sk2 != union(sk3,sk4)
| subset(sk4,sk5) ),
inference(resolution,[status(thm)],[p315,p65]) ).
cnf(p2351,plain,
( sk2 != sk2
| subset(sk4,sk5) ),
inference(demodulation,[status(thm)],[p2347,p1116]) ).
cnf(p2404,plain,
subset(sk4,sk5),
inference(equality_resolution,[status(thm)],[p2351]) ).
cnf(p2553,plain,
subset(sk2,sk5),
inference(resolution,[status(thm)],[p2366,p2404]) ).
cnf(c31,plain,
( sk2 != union(sk3,sk4)
| ~ subset(sk2,sk5)
| ~ subset(sk4,sk2)
| ~ subset(sk3,sk2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p363,plain,
( sk2 != union(sk3,sk4)
| ~ subset(sk2,sk5)
| ~ subset(sk4,sk2) ),
inference(resolution,[status(thm)],[c31,p53]) ).
cnf(p1133,plain,
( sk2 != union(sk3,sk4)
| ~ subset(sk2,sk5) ),
inference(resolution,[status(thm)],[p363,p65]) ).
cnf(p2352,plain,
( sk2 != sk2
| ~ subset(sk2,sk5) ),
inference(demodulation,[status(thm)],[p2347,p1133]) ).
cnf(p2449,plain,
~ subset(sk2,sk5),
inference(equality_resolution,[status(thm)],[p2352]) ).
cnf(p2558,plain,
$false,
inference(resolution,[status(thm)],[p2553,p2449]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET597+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n026.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 : Thu Sep 24 11:26:39 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 54.14/8.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 54.14/8.24 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------