%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET935+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 02:44:20 PM UTC 2026
% Result : Theorem 15.94s 2.49s
% Output : Proof 15.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 20 unt; 0 def)
% Number of atoms : 158 ( 34 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 159 ( 56 ~; 64 |; 31 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 96 ( 5 sgn 54 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,conjecture,
! [A,B] :
( set_union2(powerset(A),powerset(B)) = powerset(set_union2(A,B))
=> inclusion_comparable(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_zfmisc_1) ).
fof(f15_neg,negated_conjecture,
~ ! [A,B] :
( set_union2(powerset(A),powerset(B)) = powerset(set_union2(A,B))
=> inclusion_comparable(A,B) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f15_nnf,plain,
? [A,B] :
( ~ inclusion_comparable(A,B)
& set_union2(powerset(A),powerset(B)) = powerset(set_union2(A,B)) ),
inference(nnf_transformation,[status(thm)],[f15_neg]) ).
fof(f15_sk,plain,
( ~ inclusion_comparable(sk4,sk5)
& set_union2(powerset(sk4),powerset(sk5)) = powerset(set_union2(sk4,sk5)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5])],[f15_nnf]) ).
cnf(c32,plain,
set_union2(powerset(sk4),powerset(sk5)) = powerset(set_union2(sk4,sk5)),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
fof(f4,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f4_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)],[f4]) ).
fof(f4_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])],[f4_nnf]) ).
cnf(c11,plain,
( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2)
| X2 != set_union2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p75,plain,
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c11]) ).
cnf(p253,plain,
( in(X0,powerset(sk5))
| in(X0,powerset(sk4))
| ~ in(X0,powerset(set_union2(sk4,sk5))) ),
inference(superposition,[status(thm)],[c32,p75]) ).
fof(f3,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f3_nnf,plain,
! [A,B] :
( ( ? [C] :
( ( subset(C,A)
& ~ in(C,B) )
| ( ~ subset(C,A)
& in(C,B) ) )
| B = powerset(A) )
& ( ! [C] :
( ( ~ subset(C,A)
| in(C,B) )
& ( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B,A,C] :
( ( ( subset(sk0(A,B),A)
& ~ in(sk0(A,B),B) )
| ( ~ subset(sk0(A,B),A)
& in(sk0(A,B),B) )
| B = powerset(A) )
& ( ( ( ~ subset(C,A)
| in(C,B) )
& ( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f3_nnf]) ).
cnf(c6,plain,
( ~ subset(X2,X0)
| in(X2,X1)
| X1 != powerset(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p44,plain,
( ~ subset(X0,X1)
| in(X0,powerset(X1)) ),
inference(equality_resolution,[status(thm)],[c6]) ).
fof(f11,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f11_nnf,plain,
! [A,B] : subset(A,A),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A] : subset(A,A),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c28,plain,
subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p46,plain,
in(X0,powerset(X0)),
inference(resolution,[status(thm)],[p44,c28]) ).
cnf(p1034,plain,
( in(set_union2(sk4,sk5),powerset(sk5))
| in(set_union2(sk4,sk5),powerset(sk4)) ),
inference(resolution,[status(thm)],[p253,p46]) ).
cnf(c5,plain,
( subset(X2,X0)
| ~ in(X2,X1)
| X1 != powerset(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p43,plain,
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(equality_resolution,[status(thm)],[c5]) ).
cnf(p1081,plain,
( subset(set_union2(sk4,sk5),sk5)
| in(set_union2(sk4,sk5),powerset(sk4)) ),
inference(resolution,[status(thm)],[p1034,p43]) ).
cnf(p1085,plain,
( subset(set_union2(sk4,sk5),sk4)
| subset(set_union2(sk4,sk5),sk5) ),
inference(resolution,[status(thm)],[p1081,p43]) ).
fof(f2,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f2_nnf,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c4,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f1,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f1_nnf,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f14,axiom,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f14_nnf,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c31,plain,
subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p35,plain,
subset(X0,set_union2(X1,X0)),
inference(superposition,[status(thm)],[c1,c31]) ).
cnf(p40,plain,
( ~ subset(set_union2(X1,X0),X0)
| X0 = set_union2(X1,X0) ),
inference(resolution,[status(thm)],[c4,p35]) ).
cnf(p1090,plain,
( sk5 = set_union2(sk4,sk5)
| subset(set_union2(sk4,sk5),sk4) ),
inference(resolution,[status(thm)],[p1085,p40]) ).
cnf(p39,plain,
( ~ subset(set_union2(X0,X1),X0)
| X0 = set_union2(X0,X1) ),
inference(resolution,[status(thm)],[c4,c31]) ).
cnf(p1093,plain,
( sk4 = set_union2(sk4,sk5)
| sk5 = set_union2(sk4,sk5) ),
inference(resolution,[status(thm)],[p1090,p39]) ).
cnf(p1130,plain,
( subset(sk4,sk5)
| sk4 = set_union2(sk4,sk5) ),
inference(superposition,[status(thm)],[p1093,c31]) ).
fof(f5,axiom,
! [A,B] :
( inclusion_comparable(A,B)
<=> ( subset(B,A)
| subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_xboole_0) ).
fof(f5_nnf,plain,
! [A,B] :
( ( ( ~ subset(B,A)
& ~ subset(A,B) )
| inclusion_comparable(A,B) )
& ( subset(B,A)
| subset(A,B)
| ~ inclusion_comparable(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B] :
( ( ( ~ subset(B,A)
& ~ subset(A,B) )
| inclusion_comparable(A,B) )
& ( subset(B,A)
| subset(A,B)
| ~ inclusion_comparable(A,B) ) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c22,plain,
( ~ subset(X1,X0)
| inclusion_comparable(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p42,plain,
inclusion_comparable(set_union2(X0,X1),X1),
inference(resolution,[status(thm)],[c22,p35]) ).
cnf(p1286,plain,
( inclusion_comparable(sk4,sk5)
| subset(sk4,sk5) ),
inference(superposition,[status(thm)],[p1130,p42]) ).
cnf(c33,plain,
~ inclusion_comparable(sk4,sk5),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p1474,plain,
subset(sk4,sk5),
inference(resolution,[status(thm)],[p1286,c33]) ).
cnf(c21,plain,
( ~ subset(X0,X1)
| inclusion_comparable(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p1475,plain,
inclusion_comparable(sk4,sk5),
inference(resolution,[status(thm)],[p1474,c21]) ).
cnf(p1479,plain,
$false,
inference(resolution,[status(thm)],[p1475,c33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET935+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.38 % Computer : n003.cluster.edu
% 0.08/0.38 % Model : x86_64 x86_64
% 0.08/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.38 % Memory : 8046.5625MB
% 0.08/0.38 % OS : Linux 6.8.0-71-generic
% 0.08/0.38 % CPULimit : 300
% 0.08/0.38 % WCLimit : 300
% 0.08/0.38 % DateTime : Thu Sep 24 12:26:21 UTC 2026
% 0.08/0.38 % CPUTime :
% 0.08/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 15.94/2.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.94/2.49 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------