%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU126+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 02:51:00 PM UTC 2026
% Result : Theorem 17.87s 17.89s
% Output : Proof 17.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 5 unt; 0 def)
% Number of atoms : 84 ( 20 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 91 ( 31 ~; 36 |; 18 &)
% ( 3 <=>; 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 : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 44 ( 0 sgn 25 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,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(f3_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)],[f3]) ).
fof(f3_sk,plain,
! [C,A,B,D] :
( ( ( ( in(sk0(A,B,C),B)
| in(sk0(A,B,C),A) )
& ~ in(sk0(A,B,C),C) )
| ( ~ in(sk0(A,B,C),B)
& ~ in(sk0(A,B,C),A)
& in(sk0(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,[sk0])],[f3_nnf]) ).
cnf(c9,plain,
( in(sk0(X0,X1,X2),X1)
| in(sk0(X0,X1,X2),X0)
| in(sk0(X0,X1,X2),X2)
| X2 = set_union2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p64,plain,
( in(sk0(X0,X1,X0),X1)
| in(sk0(X0,X1,X0),X0)
| X0 = set_union2(X0,X1) ),
inference(factoring,[status(thm)],[c9]) ).
fof(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f4_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)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk1(A,B),B)
& in(sk1(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f4_nnf]) ).
cnf(c14,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f14,conjecture,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f14_neg,negated_conjecture,
~ ! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f14_nnf,plain,
? [A,B] :
( set_union2(A,B) != B
& subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f14_neg]) ).
fof(f14_sk,plain,
( set_union2(sk4,sk5) != sk5
& subset(sk4,sk5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5])],[f14_nnf]) ).
cnf(c26,plain,
subset(sk4,sk5),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p51,plain,
( in(X0,sk5)
| ~ in(X0,sk4) ),
inference(resolution,[status(thm)],[c14,c26]) ).
cnf(p205,plain,
( in(sk0(X0,sk4,X0),sk5)
| in(sk0(X0,sk4,X0),X0)
| X0 = set_union2(X0,sk4) ),
inference(resolution,[status(thm)],[p64,p51]) ).
cnf(p1847,plain,
( in(sk0(sk5,sk4,sk5),sk5)
| sk5 = set_union2(sk4,sk5) ),
inference(factoring,[status(thm)],[p205]) ).
cnf(c10,plain,
( ~ in(sk0(X0,X1,X2),X2)
| ~ in(sk0(X0,X1,X2),X0)
| X2 = set_union2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p87,plain,
( ~ in(sk0(X0,X1,X0),X0)
| X0 = set_union2(X0,X1) ),
inference(factoring,[status(thm)],[c10]) ).
cnf(p1862,plain,
( sk5 = set_union2(sk4,sk5)
| sk5 = set_union2(sk4,sk5) ),
inference(resolution,[status(thm)],[p1847,p87]) ).
cnf(p1870,plain,
sk5 = set_union2(sk4,sk5),
inference(factoring,[status(thm)],[p1862]) ).
cnf(c27,plain,
set_union2(sk4,sk5) != sk5,
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p1871,plain,
sk5 != sk5,
inference(superposition,[status(thm)],[p1870,c27]) ).
cnf(p1882,plain,
$false,
inference(equality_resolution,[status(thm)],[p1871]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU126+1 : 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 : n011.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
% 0.07/15.43 % CPULimit : 300
% 0.07/15.43 % WCLimit : 300
% 0.07/15.43 % DateTime : Thu Sep 24 12:50:13 UTC 2026
% 0.07/15.43 % CPUTime :
% 0.07/15.43 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 17.87/17.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.87/17.89 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------