%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET605+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 : n001.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 02:43:34 PM UTC 2026
% Result : Theorem 2.54s 1.40s
% Output : Proof 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 12 unt; 0 def)
% Number of atoms : 24 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 5 |; 2 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 2 sgn 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C] :
( difference(B,C) = empty_set
<=> subset(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_empty_set) ).
fof(f1_nnf,plain,
! [B,C] :
( ( ~ subset(B,C)
| difference(B,C) = empty_set )
& ( subset(B,C)
| difference(B,C) != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C] :
( ( ~ subset(B,C)
| difference(B,C) = empty_set )
& ( subset(B,C)
| difference(B,C) != empty_set ) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c2,plain,
( ~ subset(X0,X1)
| difference(X0,X1) = empty_set ),
inference(cnf_transformation,[status(esa)],[f1_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(p27,plain,
difference(X0,union(X0,X1)) = empty_set,
inference(resolution,[status(thm)],[c2,c0]) ).
fof(f11,conjecture,
! [B,C] : difference(B,union(B,C)) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th76) ).
fof(f11_neg,negated_conjecture,
~ ! [B,C] : difference(B,union(B,C)) = empty_set,
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
? [B,C] : difference(B,union(B,C)) != empty_set,
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
difference(sk3,union(sk3,sk4)) != empty_set,
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f11_nnf]) ).
cnf(c26,plain,
difference(sk3,union(sk3,sk4)) != empty_set,
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p28,plain,
empty_set != empty_set,
inference(demodulation,[status(thm)],[p27,c26]) ).
cnf(p64,plain,
$false,
inference(equality_resolution,[status(thm)],[p28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET605+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 11:31:22 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.54/1.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.54/1.40 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------