%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU124+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 02:51:00 PM UTC 2026
% Result : Theorem 25.21s 4.18s
% Output : Proof 25.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 7 unt; 0 def)
% Number of atoms : 67 ( 6 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 76 ( 28 ~; 28 |; 16 &)
% ( 3 <=>; 1 =>; 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 : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 47 ( 4 sgn 25 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f5_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_union2(A,B) )
& ( ! [D] :
( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [C,A,B,D] :
( ( ( ( in(sk1(A,B,C),B)
| in(sk1(A,B,C),A) )
& ~ in(sk1(A,B,C),C) )
| ( ~ in(sk1(A,B,C),B)
& ~ in(sk1(A,B,C),A)
& in(sk1(A,B,C),C) )
| C = set_union2(A,B) )
& ( ( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f5_nnf]) ).
cnf(c9,plain,
( ~ in(X3,X0)
| in(X3,X2)
| X2 != set_union2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p69,plain,
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c9]) ).
fof(f6,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f6_nnf,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk2(A,B),B)
& in(sk2(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f6_nnf]) ).
cnf(c18,plain,
( in(sk2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p115,plain,
( subset(X0,X1)
| in(sk2(X0,X1),set_union2(X0,X2)) ),
inference(resolution,[status(thm)],[p69,c18]) ).
cnf(c19,plain,
( ~ in(sk2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p259,plain,
( subset(X0,set_union2(X0,X1))
| subset(X0,set_union2(X0,X1)) ),
inference(resolution,[status(thm)],[p115,c19]) ).
cnf(p489,plain,
subset(X0,set_union2(X0,X1)),
inference(factoring,[status(thm)],[p259]) ).
fof(f29,conjecture,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f29_neg,negated_conjecture,
~ ! [A,B] : subset(A,set_union2(A,B)),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f29_nnf,plain,
? [A,B] : ~ subset(A,set_union2(A,B)),
inference(nnf_transformation,[status(thm)],[f29_neg]) ).
fof(f29_sk,plain,
~ subset(sk8,set_union2(sk8,sk9)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8,sk9])],[f29_nnf]) ).
cnf(c54,plain,
~ subset(sk8,set_union2(sk8,sk9)),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p490,plain,
$false,
inference(resolution,[status(thm)],[p489,c54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU124+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n015.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Thu Sep 24 12:52:55 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 25.21/4.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.21/4.18 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------