%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU172+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 02:51:13 PM UTC 2026
% Result : Theorem 0.13s 5.84s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 7 unt; 0 def)
% Number of atoms : 64 ( 11 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 71 ( 27 ~; 20 |; 19 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 37 ( 2 sgn 24 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f21_nnf,plain,
! [A,B,C] :
( ( ? [D] :
( ( ~ in(D,B)
& in(D,A)
& ~ in(D,C) )
| ( ( in(D,B)
| ~ in(D,A) )
& in(D,C) ) )
| C = set_difference(A,B) )
& ( ! [D] :
( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [C,A,B,D] :
( ( ( ~ in(sk8(A,B,C),B)
& in(sk8(A,B,C),A)
& ~ in(sk8(A,B,C),C) )
| ( ( in(sk8(A,B,C),B)
| ~ in(sk8(A,B,C),A) )
& in(sk8(A,B,C),C) )
| C = set_difference(A,B) )
& ( ( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8])],[f21_nnf]) ).
cnf(c26,plain,
( ~ in(X3,X1)
| ~ in(X3,X2)
| X2 != set_difference(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p83,plain,
( ~ in(X0,X2)
| ~ in(X0,set_difference(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c26]) ).
fof(f19,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
fof(f19_nnf,plain,
! [A,B] :
( subset_complement(A,B) = set_difference(A,B)
| ~ element(B,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [B,A] :
( subset_complement(A,B) = set_difference(A,B)
| ~ element(B,powerset(A)) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c21,plain,
( subset_complement(X0,X1) = set_difference(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
fof(f20,conjecture,
! [A,B,C] :
( element(C,powerset(A))
=> ~ ( in(B,C)
& in(B,subset_complement(A,C)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
fof(f20_neg,negated_conjecture,
~ ! [A,B,C] :
( element(C,powerset(A))
=> ~ ( in(B,C)
& in(B,subset_complement(A,C)) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f20_nnf,plain,
? [A,B,C] :
( in(B,C)
& in(B,subset_complement(A,C))
& element(C,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f20_neg]) ).
fof(f20_sk,plain,
( in(sk6,sk7)
& in(sk6,subset_complement(sk5,sk7))
& element(sk7,powerset(sk5)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5,sk6,sk7])],[f20_nnf]) ).
cnf(c22,plain,
element(sk7,powerset(sk5)),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p55,plain,
subset_complement(sk5,sk7) = set_difference(sk5,sk7),
inference(resolution,[status(thm)],[c21,c22]) ).
cnf(c23,plain,
in(sk6,subset_complement(sk5,sk7)),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p56,plain,
in(sk6,set_difference(sk5,sk7)),
inference(demodulation,[status(thm)],[p55,c23]) ).
cnf(p258,plain,
~ in(sk6,sk7),
inference(resolution,[status(thm)],[p83,p56]) ).
cnf(c24,plain,
in(sk6,sk7),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p266,plain,
$false,
inference(resolution,[status(thm)],[p258,c24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU172+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.38 % Computer : n011.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Thu Sep 24 13:03:04 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/5.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/5.84 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------