%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU265+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 : n001.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 02:51:32 PM UTC 2026
% Result : Theorem 8.28s 1.91s
% Output : Proof 8.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 17
% Syntax : Number of formulae : 123 ( 21 unt; 0 def)
% Number of atoms : 323 ( 61 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 312 ( 112 ~; 149 |; 31 &)
% ( 6 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-3 aty)
% Number of variables : 204 ( 9 sgn 129 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f31,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f31_nnf,plain,
! [A,B] :
( A = B
| ? [C] :
( ( in(C,B)
& ~ in(C,A) )
| ( ~ in(C,B)
& in(C,A) ) ) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [A,B] :
( A = B
| ( in(sk13(A,B),B)
& ~ in(sk13(A,B),A) )
| ( ~ in(sk13(A,B),B)
& in(sk13(A,B),A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13])],[f31_nnf]) ).
cnf(c45,plain,
( X0 = X1
| in(sk13(X0,X1),X1)
| in(sk13(X0,X1),X0) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
fof(f24,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> relation_dom_as_subset(A,B,C) = relation_dom(C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
fof(f24_nnf,plain,
! [A,B,C] :
( relation_dom_as_subset(A,B,C) = relation_dom(C)
| ~ relation_of2(C,A,B) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [C,A,B] :
( relation_dom_as_subset(A,B,C) = relation_dom(C)
| ~ relation_of2(C,A,B) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c29,plain,
( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
fof(f25,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f25_nnf,plain,
! [A,B,C] :
( ( ~ relation_of2(C,A,B)
| relation_of2_as_subset(C,A,B) )
& ( relation_of2(C,A,B)
| ~ relation_of2_as_subset(C,A,B) ) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [C,A,B] :
( ( ~ relation_of2(C,A,B)
| relation_of2_as_subset(C,A,B) )
& ( relation_of2(C,A,B)
| ~ relation_of2_as_subset(C,A,B) ) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c30,plain,
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
fof(f29,conjecture,
! [A,B,C] :
( relation_of2_as_subset(C,B,A)
=> ( ! [D] :
~ ( ! [E] : ~ in(ordered_pair(D,E),C)
& in(D,B) )
<=> relation_dom_as_subset(B,A,C) = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_relset_1) ).
fof(f29_neg,negated_conjecture,
~ ! [A,B,C] :
( relation_of2_as_subset(C,B,A)
=> ( ! [D] :
~ ( ! [E] : ~ in(ordered_pair(D,E),C)
& in(D,B) )
<=> relation_dom_as_subset(B,A,C) = B ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f29_nnf,plain,
? [A,B,C] :
( ( ( relation_dom_as_subset(B,A,C) = B
& ? [D] :
( ! [E] : ~ in(ordered_pair(D,E),C)
& in(D,B) ) )
| ( relation_dom_as_subset(B,A,C) != B
& ! [D] :
( ? [E] : in(ordered_pair(D,E),C)
| ~ in(D,B) ) ) )
& relation_of2_as_subset(C,B,A) ),
inference(nnf_transformation,[status(thm)],[f29_neg]) ).
fof(f29_sk,plain,
! [D,E] :
( ( ( relation_dom_as_subset(sk9,sk8,sk10) = sk9
& ~ in(ordered_pair(sk12,E),sk10)
& in(sk12,sk9) )
| ( relation_dom_as_subset(sk9,sk8,sk10) != sk9
& ( in(ordered_pair(D,sk11(D)),sk10)
| ~ in(D,sk9) ) ) )
& relation_of2_as_subset(sk10,sk9,sk8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8,sk9,sk10,sk11,sk12])],[f29_nnf]) ).
cnf(c36,plain,
relation_of2_as_subset(sk10,sk9,sk8),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p72,plain,
relation_of2(sk10,sk9,sk8),
inference(resolution,[status(thm)],[c30,c36]) ).
cnf(p102,plain,
relation_dom_as_subset(sk9,sk8,sk10) = relation_dom(sk10),
inference(resolution,[status(thm)],[c29,p72]) ).
cnf(c39,plain,
( relation_dom_as_subset(sk9,sk8,sk10) = sk9
| in(ordered_pair(X3,sk11(X3)),sk10)
| ~ in(X3,sk9) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p103,plain,
( relation_dom(sk10) = sk9
| in(ordered_pair(X0,sk11(X0)),sk10)
| ~ in(X0,sk9) ),
inference(demodulation,[status(thm)],[p102,c39]) ).
cnf(p135,plain,
( relation_dom(sk10) = sk9
| in(ordered_pair(sk13(X0,sk9),sk11(sk13(X0,sk9))),sk10)
| X0 = sk9
| in(sk13(X0,sk9),X0) ),
inference(resolution,[status(thm)],[c45,p103]) ).
fof(f28,axiom,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_rng(C))
& in(A,relation_dom(C)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f28_nnf,plain,
! [A,B,C] :
( ( in(B,relation_rng(C))
& in(A,relation_dom(C)) )
| ~ in(ordered_pair(A,B),C)
| ~ relation(C) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [C,A,B] :
( ( in(B,relation_rng(C))
& in(A,relation_dom(C)) )
| ~ in(ordered_pair(A,B),C)
| ~ relation(C) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c34,plain,
( in(X0,relation_dom(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
fof(f16,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> element(C,powerset(cartesian_product2(A,B))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f16_nnf,plain,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
| ~ relation_of2_as_subset(C,A,B) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [C,A,B] :
( element(C,powerset(cartesian_product2(A,B)))
| ~ relation_of2_as_subset(C,A,B) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c21,plain,
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p88,plain,
element(sk10,powerset(cartesian_product2(sk9,sk8))),
inference(resolution,[status(thm)],[c21,c36]) ).
fof(f1,axiom,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f1_nnf,plain,
! [A,B,C] :
( relation(C)
| ~ element(C,powerset(cartesian_product2(A,B))) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [C,A,B] :
( relation(C)
| ~ element(C,powerset(cartesian_product2(A,B))) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p91,plain,
relation(sk10),
inference(resolution,[status(thm)],[p88,c1]) ).
cnf(p114,plain,
( in(X0,relation_dom(sk10))
| ~ in(ordered_pair(X0,X1),sk10) ),
inference(resolution,[status(thm)],[c34,p91]) ).
cnf(p488,plain,
( in(sk13(X0,sk9),relation_dom(sk10))
| relation_dom(sk10) = sk9
| X0 = sk9
| in(sk13(X0,sk9),X0) ),
inference(resolution,[status(thm)],[p135,p114]) ).
cnf(p1744,plain,
( relation_dom(sk10) = sk9
| relation_dom(sk10) = sk9
| in(sk13(relation_dom(sk10),sk9),relation_dom(sk10)) ),
inference(factoring,[status(thm)],[p488]) ).
cnf(p1759,plain,
( relation_dom(sk10) = sk9
| in(sk13(relation_dom(sk10),sk9),relation_dom(sk10)) ),
inference(factoring,[status(thm)],[p1744]) ).
fof(f33,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f33_nnf,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c50,plain,
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(p168,plain,
( X0 = X2
| in(sk13(X0,X2),X2)
| element(sk13(X0,X2),X1)
| ~ element(X0,powerset(X1)) ),
inference(resolution,[status(thm)],[c50,c45]) ).
fof(f12,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> element(relation_dom_as_subset(A,B,C),powerset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_1) ).
fof(f12_nnf,plain,
! [A,B,C] :
( element(relation_dom_as_subset(A,B,C),powerset(A))
| ~ relation_of2(C,A,B) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [C,A,B] :
( element(relation_dom_as_subset(A,B,C),powerset(A))
| ~ relation_of2(C,A,B) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c17,plain,
( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p83,plain,
element(relation_dom_as_subset(sk9,sk8,sk10),powerset(sk9)),
inference(resolution,[status(thm)],[c17,p72]) ).
cnf(p106,plain,
element(relation_dom(sk10),powerset(sk9)),
inference(demodulation,[status(thm)],[p102,p83]) ).
cnf(p577,plain,
( relation_dom(sk10) = X0
| in(sk13(relation_dom(sk10),X0),X0)
| element(sk13(relation_dom(sk10),X0),sk9) ),
inference(resolution,[status(thm)],[p168,p106]) ).
fof(f27,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f27_nnf,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c33,plain,
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p712,plain,
( element(sk13(relation_dom(sk10),X0),X0)
| relation_dom(sk10) = X0
| element(sk13(relation_dom(sk10),X0),sk9) ),
inference(resolution,[status(thm)],[p577,c33]) ).
cnf(p820,plain,
( relation_dom(sk10) = sk9
| element(sk13(relation_dom(sk10),sk9),sk9) ),
inference(factoring,[status(thm)],[p712]) ).
fof(f30,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f30_nnf,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c43,plain,
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(p835,plain,
( in(sk13(relation_dom(sk10),sk9),sk9)
| empty(sk9)
| relation_dom(sk10) = sk9 ),
inference(resolution,[status(thm)],[p820,c43]) ).
cnf(c46,plain,
( X0 = X1
| ~ in(sk13(X0,X1),X0)
| ~ in(sk13(X0,X1),X1) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p840,plain,
( relation_dom(sk10) = sk9
| ~ in(sk13(relation_dom(sk10),sk9),relation_dom(sk10))
| empty(sk9)
| relation_dom(sk10) = sk9 ),
inference(resolution,[status(thm)],[p835,c46]) ).
cnf(p1181,plain,
( ~ in(sk13(relation_dom(sk10),sk9),relation_dom(sk10))
| empty(sk9)
| relation_dom(sk10) = sk9 ),
inference(factoring,[status(thm)],[p840]) ).
cnf(p1766,plain,
( empty(sk9)
| relation_dom(sk10) = sk9
| relation_dom(sk10) = sk9 ),
inference(resolution,[status(thm)],[p1759,p1181]) ).
cnf(p1768,plain,
( empty(sk9)
| relation_dom(sk10) = sk9 ),
inference(factoring,[status(thm)],[p1766]) ).
fof(f3,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f3_nnf,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] : in(ordered_pair(C,D),A)
& ~ in(C,B) )
| ( ! [D] : ~ in(ordered_pair(C,D),A)
& in(C,B) ) )
| B = relation_dom(A) )
& ( ! [C] :
( ( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C,D] :
( ( ( ( in(ordered_pair(sk1(A,B),sk2(A,B)),A)
& ~ in(sk1(A,B),B) )
| ( ~ in(ordered_pair(sk1(A,B),D),A)
& in(sk1(A,B),B) )
| B = relation_dom(A) )
& ( ( ( ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ( in(ordered_pair(C,sk0(A,B,C)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f3_nnf]) ).
cnf(c3,plain,
( in(ordered_pair(X2,sk0(X0,X1,X2)),X0)
| ~ in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p94,plain,
( in(ordered_pair(X1,sk0(sk10,X0,X1)),sk10)
| ~ in(X1,X0)
| X0 != relation_dom(sk10) ),
inference(resolution,[status(thm)],[p91,c3]) ).
cnf(p118,plain,
( in(ordered_pair(X0,sk0(sk10,relation_dom(sk10),X0)),sk10)
| ~ in(X0,relation_dom(sk10)) ),
inference(equality_resolution,[status(thm)],[p94]) ).
cnf(p1773,plain,
( in(ordered_pair(X0,sk0(sk10,relation_dom(sk10),X0)),sk10)
| ~ in(X0,sk9)
| empty(sk9) ),
inference(superposition,[status(thm)],[p1768,p118]) ).
cnf(c37,plain,
( in(sk12,sk9)
| in(ordered_pair(X3,sk11(X3)),sk10)
| ~ in(X3,sk9) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p127,plain,
( in(sk12,sk9)
| in(ordered_pair(sk13(X0,sk9),sk11(sk13(X0,sk9))),sk10)
| X0 = sk9
| in(sk13(X0,sk9),X0) ),
inference(resolution,[status(thm)],[c45,c37]) ).
cnf(p414,plain,
( in(sk13(X0,sk9),relation_dom(sk10))
| in(sk12,sk9)
| X0 = sk9
| in(sk13(X0,sk9),X0) ),
inference(resolution,[status(thm)],[p127,p114]) ).
cnf(p1144,plain,
( in(sk12,sk9)
| relation_dom(sk10) = sk9
| in(sk13(relation_dom(sk10),sk9),relation_dom(sk10)) ),
inference(factoring,[status(thm)],[p414]) ).
cnf(p1182,plain,
( in(sk12,sk9)
| relation_dom(sk10) = sk9
| empty(sk9)
| relation_dom(sk10) = sk9 ),
inference(resolution,[status(thm)],[p1181,p1144]) ).
cnf(p1183,plain,
( in(sk12,sk9)
| empty(sk9)
| relation_dom(sk10) = sk9 ),
inference(factoring,[status(thm)],[p1182]) ).
cnf(c40,plain,
( in(sk12,sk9)
| relation_dom_as_subset(sk9,sk8,sk10) != sk9 ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p104,plain,
( in(sk12,sk9)
| relation_dom(sk10) != sk9 ),
inference(demodulation,[status(thm)],[p102,c40]) ).
cnf(p1184,plain,
( in(sk12,sk9)
| in(sk12,sk9)
| empty(sk9) ),
inference(resolution,[status(thm)],[p1183,p104]) ).
cnf(p1252,plain,
( in(sk12,sk9)
| empty(sk9) ),
inference(factoring,[status(thm)],[p1184]) ).
cnf(p1880,plain,
( empty(sk9)
| in(ordered_pair(sk12,sk0(sk10,relation_dom(sk10),sk12)),sk10)
| empty(sk9) ),
inference(resolution,[status(thm)],[p1773,p1252]) ).
cnf(p1889,plain,
( in(ordered_pair(sk12,sk0(sk10,relation_dom(sk10),sk12)),sk10)
| empty(sk9) ),
inference(factoring,[status(thm)],[p1880]) ).
cnf(c41,plain,
( ~ in(ordered_pair(sk12,X4),sk10)
| relation_dom_as_subset(sk9,sk8,sk10) != sk9 ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p105,plain,
( ~ in(ordered_pair(sk12,X0),sk10)
| relation_dom(sk10) != sk9 ),
inference(demodulation,[status(thm)],[p102,c41]) ).
cnf(p1770,plain,
( ~ in(ordered_pair(sk12,X0),sk10)
| empty(sk9) ),
inference(resolution,[status(thm)],[p1768,p105]) ).
cnf(p1904,plain,
( empty(sk9)
| empty(sk9) ),
inference(resolution,[status(thm)],[p1889,p1770]) ).
cnf(p1906,plain,
empty(sk9),
inference(factoring,[status(thm)],[p1904]) ).
fof(f35,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f35_nnf,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(skolemisation,[status(esa)],[f35_nnf]) ).
cnf(c52,plain,
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p1907,plain,
sk9 = empty_set,
inference(resolution,[status(thm)],[p1906,c52]) ).
fof(f18,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f18_nnf,plain,
! [A] :
? [B] : element(B,A),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A] : element(sk4(A),A),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f18_nnf]) ).
cnf(c23,plain,
element(sk4(X0),X0),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p80,plain,
( in(sk4(X0),X0)
| empty(X0) ),
inference(resolution,[status(thm)],[c43,c23]) ).
fof(f34,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f34_nnf,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c51,plain,
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p288,plain,
( ~ empty(X1)
| ~ element(X0,powerset(X1))
| empty(X0) ),
inference(resolution,[status(thm)],[p80,c51]) ).
cnf(p1395,plain,
( ~ empty(sk9)
| empty(relation_dom(sk10)) ),
inference(resolution,[status(thm)],[p288,p106]) ).
cnf(p2252,plain,
( ~ empty(empty_set)
| empty(relation_dom(sk10)) ),
inference(demodulation,[status(thm)],[p1907,p1395]) ).
fof(f20,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f20_nnf,plain,
empty(empty_set),
inference(nnf_transformation,[status(thm)],[f20]) ).
cnf(c25,plain,
empty(empty_set),
inference(cnf_transformation,[status(esa)],[f20_nnf]) ).
cnf(p2457,plain,
empty(relation_dom(sk10)),
inference(resolution,[status(thm)],[p2252,c25]) ).
cnf(p2458,plain,
relation_dom(sk10) = empty_set,
inference(resolution,[status(thm)],[p2457,c52]) ).
cnf(p1918,plain,
( in(sk12,empty_set)
| relation_dom(sk10) != empty_set ),
inference(demodulation,[status(thm)],[p1907,p104]) ).
cnf(p2742,plain,
( in(sk12,empty_set)
| empty_set != empty_set ),
inference(demodulation,[status(thm)],[p2458,p1918]) ).
cnf(p2876,plain,
in(sk12,empty_set),
inference(equality_resolution,[status(thm)],[p2742]) ).
fof(f36,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f36_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f36]) ).
fof(f36_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f36_nnf]) ).
cnf(c53,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p2878,plain,
~ empty(empty_set),
inference(resolution,[status(thm)],[p2876,c53]) ).
cnf(p2882,plain,
$false,
inference(resolution,[status(thm)],[p2878,c25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU265+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 13:33:39 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.28/1.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.28/1.91 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------