%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU170+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 6.15s 1.34s
% Output : Proof 6.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 64 ( 11 unt; 0 def)
% Number of atoms : 190 ( 20 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 200 ( 74 ~; 79 |; 34 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 113 ( 3 sgn 54 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f2_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)],[f2]) ).
fof(f2_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_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,[sk1])],[f2_nnf]) ).
cnf(c6,plain,
( in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2)
| X2 != set_difference(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p61,plain,
( in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_difference(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c6]) ).
fof(f12,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,subset_complement(A,B)) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(f12_nnf,plain,
! [A,B] :
( subset_complement(A,subset_complement(A,B)) = B
| ~ element(B,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [B,A] :
( subset_complement(A,subset_complement(A,B)) = B
| ~ element(B,powerset(A)) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c22,plain,
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
fof(f22,conjecture,
! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,powerset(A))
=> ( disjoint(B,C)
<=> subset(B,subset_complement(A,C)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_subset_1) ).
fof(f22_neg,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,powerset(A))
=> ( disjoint(B,C)
<=> subset(B,subset_complement(A,C)) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f22_nnf,plain,
? [A,B] :
( ? [C] :
( ( ( subset(B,subset_complement(A,C))
& ~ disjoint(B,C) )
| ( ~ subset(B,subset_complement(A,C))
& disjoint(B,C) ) )
& element(C,powerset(A)) )
& element(B,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f22_neg]) ).
fof(f22_sk,plain,
( ( ( subset(sk9,subset_complement(sk8,sk10))
& ~ disjoint(sk9,sk10) )
| ( ~ subset(sk9,subset_complement(sk8,sk10))
& disjoint(sk9,sk10) ) )
& element(sk10,powerset(sk8))
& element(sk9,powerset(sk8)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8,sk9,sk10])],[f22_nnf]) ).
cnf(c36,plain,
element(sk9,powerset(sk8)),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p164,plain,
subset_complement(sk8,set_difference(sk8,sk9)) = sk9,
inference(resolution,[status(thm)],[c22,c36]) ).
fof(f6,axiom,
! [A,B] :
( element(B,powerset(A))
=> element(subset_complement(A,B),powerset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f6_nnf,plain,
! [A,B] :
( element(subset_complement(A,B),powerset(A))
| ~ element(B,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [B,A] :
( element(subset_complement(A,B),powerset(A))
| ~ element(B,powerset(A)) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c16,plain,
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p151,plain,
element(set_difference(sk8,sk9),powerset(sk8)),
inference(resolution,[status(thm)],[c16,c36]) ).
fof(f3,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
fof(f3_nnf,plain,
! [A,B] :
( subset_complement(A,B) = set_difference(A,B)
| ~ element(B,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B,A] :
( subset_complement(A,B) = set_difference(A,B)
| ~ element(B,powerset(A)) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c13,plain,
( subset_complement(X0,X1) = set_difference(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p156,plain,
subset_complement(sk8,set_difference(sk8,sk9)) = set_difference(sk8,set_difference(sk8,sk9)),
inference(resolution,[status(thm)],[p151,c13]) ).
cnf(p165,plain,
sk9 = set_difference(sk8,set_difference(sk8,sk9)),
inference(demodulation,[status(thm)],[p164,p156]) ).
cnf(c4,plain,
( in(X3,X0)
| ~ in(X3,X2)
| X2 != set_difference(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p185,plain,
( in(X0,sk8)
| ~ in(X0,sk9) ),
inference(resolution,[status(thm)],[p165,c4]) ).
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f1_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)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk0(A,B),B)
& in(sk0(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f1_nnf]) ).
cnf(c2,plain,
( in(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p195,plain,
( subset(sk9,X0)
| in(sk0(sk9,X0),sk8) ),
inference(resolution,[status(thm)],[p185,c2]) ).
cnf(p282,plain,
( subset(sk9,X0)
| in(sk0(sk9,X0),X1)
| in(sk0(sk9,X0),set_difference(sk8,X1)) ),
inference(resolution,[status(thm)],[p61,p195]) ).
cnf(c3,plain,
( ~ in(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p403,plain,
( subset(sk9,set_difference(sk8,X0))
| subset(sk9,set_difference(sk8,X0))
| in(sk0(sk9,set_difference(sk8,X0)),X0) ),
inference(resolution,[status(thm)],[p282,c3]) ).
cnf(p1315,plain,
( subset(sk9,set_difference(sk8,X0))
| in(sk0(sk9,set_difference(sk8,X0)),X0) ),
inference(factoring,[status(thm)],[p403]) ).
fof(f21,axiom,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f21_nnf,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,B)
| ~ in(C,A) ) )
& ( ? [C] :
( in(C,B)
& in(C,A) )
| disjoint(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A,B,C] :
( ( ~ disjoint(A,B)
| ~ in(C,B)
| ~ in(C,A) )
& ( ( in(sk7(A,B),B)
& in(sk7(A,B),A) )
| disjoint(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7])],[f21_nnf]) ).
cnf(c35,plain,
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p229,plain,
( subset(X0,X1)
| ~ disjoint(X0,X2)
| ~ in(sk0(X0,X1),X2) ),
inference(resolution,[status(thm)],[c35,c2]) ).
cnf(p1327,plain,
( subset(sk9,set_difference(sk8,X0))
| ~ disjoint(sk9,X0)
| subset(sk9,set_difference(sk8,X0)) ),
inference(resolution,[status(thm)],[p1315,p229]) ).
cnf(p1363,plain,
( ~ disjoint(sk9,X0)
| subset(sk9,set_difference(sk8,X0)) ),
inference(factoring,[status(thm)],[p1327]) ).
cnf(c37,plain,
element(sk10,powerset(sk8)),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p111,plain,
subset_complement(sk8,sk10) = set_difference(sk8,sk10),
inference(resolution,[status(thm)],[c13,c37]) ).
cnf(c1,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(c39,plain,
( subset(sk9,subset_complement(sk8,sk10))
| disjoint(sk9,sk10) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p47,plain,
( disjoint(sk9,sk10)
| in(X0,subset_complement(sk8,sk10))
| ~ in(X0,sk9) ),
inference(resolution,[status(thm)],[c1,c39]) ).
cnf(p114,plain,
( disjoint(sk9,sk10)
| in(X0,set_difference(sk8,sk10))
| ~ in(X0,sk9) ),
inference(demodulation,[status(thm)],[p111,p47]) ).
cnf(c33,plain,
( in(sk7(X0,X1),X0)
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p289,plain,
( disjoint(sk9,X0)
| disjoint(sk9,sk10)
| in(sk7(sk9,X0),set_difference(sk8,sk10)) ),
inference(resolution,[status(thm)],[p114,c33]) ).
cnf(p369,plain,
( disjoint(sk9,sk10)
| in(sk7(sk9,sk10),set_difference(sk8,sk10)) ),
inference(factoring,[status(thm)],[p289]) ).
cnf(c5,plain,
( ~ in(X3,X1)
| ~ in(X3,X2)
| X2 != set_difference(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p54,plain,
( ~ in(X0,X2)
| ~ in(X0,set_difference(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c5]) ).
cnf(p379,plain,
( ~ in(sk7(sk9,sk10),sk10)
| disjoint(sk9,sk10) ),
inference(resolution,[status(thm)],[p369,p54]) ).
cnf(c34,plain,
( in(sk7(X0,X1),X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p382,plain,
( disjoint(sk9,sk10)
| disjoint(sk9,sk10) ),
inference(resolution,[status(thm)],[p379,c34]) ).
cnf(p383,plain,
disjoint(sk9,sk10),
inference(factoring,[status(thm)],[p382]) ).
cnf(p1364,plain,
subset(sk9,set_difference(sk8,sk10)),
inference(resolution,[status(thm)],[p1363,p383]) ).
cnf(c40,plain,
( ~ disjoint(sk9,sk10)
| ~ subset(sk9,subset_complement(sk8,sk10)) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p113,plain,
( ~ disjoint(sk9,sk10)
| ~ subset(sk9,set_difference(sk8,sk10)) ),
inference(demodulation,[status(thm)],[p111,c40]) ).
cnf(p1373,plain,
~ disjoint(sk9,sk10),
inference(resolution,[status(thm)],[p1364,p113]) ).
cnf(p1374,plain,
$false,
inference(resolution,[status(thm)],[p1373,p383]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU170+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 13:01:58 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.15/1.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.15/1.34 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------