%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU360+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 : n007.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 02:51:50 PM UTC 2026
% Result : Theorem 5.36s 1.21s
% Output : Proof 5.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 104 ( 15 unt; 0 def)
% Number of atoms : 395 ( 5 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 471 ( 180 ~; 211 |; 57 &)
% ( 4 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 136 ( 0 sgn 62 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [A] :
( ( rel_str(A)
& antisymmetric_relstr(A) )
=> ! [B] :
( ex_inf_of_relstr_set(A,B)
<=> ? [C] :
( ! [D] :
( element(D,the_carrier(A))
=> ( relstr_element_smaller(A,B,D)
=> related(A,D,C) ) )
& relstr_element_smaller(A,B,C)
& element(C,the_carrier(A)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_yellow_0) ).
fof(f19_nnf,plain,
! [A] :
( ! [B] :
( ( ! [C] :
( ? [D] :
( ~ related(A,D,C)
& relstr_element_smaller(A,B,D)
& element(D,the_carrier(A)) )
| ~ relstr_element_smaller(A,B,C)
| ~ element(C,the_carrier(A)) )
| ex_inf_of_relstr_set(A,B) )
& ( ? [C] :
( ! [D] :
( related(A,D,C)
| ~ relstr_element_smaller(A,B,D)
| ~ element(D,the_carrier(A)) )
& relstr_element_smaller(A,B,C)
& element(C,the_carrier(A)) )
| ~ ex_inf_of_relstr_set(A,B) ) )
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A,B,D,C] :
( ( ( ( ~ related(A,sk12(A,B,C),C)
& relstr_element_smaller(A,B,sk12(A,B,C))
& element(sk12(A,B,C),the_carrier(A)) )
| ~ relstr_element_smaller(A,B,C)
| ~ element(C,the_carrier(A))
| ex_inf_of_relstr_set(A,B) )
& ( ( ( related(A,D,sk11(A,B))
| ~ relstr_element_smaller(A,B,D)
| ~ element(D,the_carrier(A)) )
& relstr_element_smaller(A,B,sk11(A,B))
& element(sk11(A,B),the_carrier(A)) )
| ~ ex_inf_of_relstr_set(A,B) ) )
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11,sk12])],[f19_nnf]) ).
cnf(c34,plain,
( element(sk12(X0,X1,X2),the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ex_inf_of_relstr_set(X0,X1)
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
fof(f22,conjecture,
! [A] :
( ( rel_str(A)
& lower_bounded_relstr(A)
& antisymmetric_relstr(A)
& ~ empty_carrier(A) )
=> ( ex_inf_of_relstr_set(A,the_carrier(A))
& ex_sup_of_relstr_set(A,empty_set) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_yellow_0) ).
fof(f22_neg,negated_conjecture,
~ ! [A] :
( ( rel_str(A)
& lower_bounded_relstr(A)
& antisymmetric_relstr(A)
& ~ empty_carrier(A) )
=> ( ex_inf_of_relstr_set(A,the_carrier(A))
& ex_sup_of_relstr_set(A,empty_set) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f22_nnf,plain,
? [A] :
( ( ~ ex_inf_of_relstr_set(A,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,empty_set) )
& rel_str(A)
& lower_bounded_relstr(A)
& antisymmetric_relstr(A)
& ~ empty_carrier(A) ),
inference(nnf_transformation,[status(thm)],[f22_neg]) ).
fof(f22_sk,plain,
( ( ~ ex_inf_of_relstr_set(sk13,the_carrier(sk13))
| ~ ex_sup_of_relstr_set(sk13,empty_set) )
& rel_str(sk13)
& lower_bounded_relstr(sk13)
& antisymmetric_relstr(sk13)
& ~ empty_carrier(sk13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13])],[f22_nnf]) ).
cnf(c40,plain,
antisymmetric_relstr(sk13),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p108,plain,
( element(sk12(sk13,X0,X1),the_carrier(sk13))
| ~ relstr_element_smaller(sk13,X0,X1)
| ~ element(X1,the_carrier(sk13))
| ex_inf_of_relstr_set(sk13,X0)
| ~ rel_str(sk13) ),
inference(resolution,[status(thm)],[c34,c40]) ).
cnf(c42,plain,
rel_str(sk13),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p218,plain,
( element(sk12(sk13,X0,X1),the_carrier(sk13))
| ~ relstr_element_smaller(sk13,X0,X1)
| ~ element(X1,the_carrier(sk13))
| ex_inf_of_relstr_set(sk13,X0) ),
inference(resolution,[status(thm)],[p108,c42]) ).
fof(f2,axiom,
! [A] :
( rel_str(A)
=> ( lower_bounded_relstr(A)
<=> ? [B] :
( relstr_element_smaller(A,the_carrier(A),B)
& element(B,the_carrier(A)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_yellow_0) ).
fof(f2_nnf,plain,
! [A] :
( ( ( ! [B] :
( ~ relstr_element_smaller(A,the_carrier(A),B)
| ~ element(B,the_carrier(A)) )
| lower_bounded_relstr(A) )
& ( ? [B] :
( relstr_element_smaller(A,the_carrier(A),B)
& element(B,the_carrier(A)) )
| ~ lower_bounded_relstr(A) ) )
| ~ rel_str(A) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( ( ( ~ relstr_element_smaller(A,the_carrier(A),B)
| ~ element(B,the_carrier(A))
| lower_bounded_relstr(A) )
& ( ( relstr_element_smaller(A,the_carrier(A),sk0(A))
& element(sk0(A),the_carrier(A)) )
| ~ lower_bounded_relstr(A) ) )
| ~ rel_str(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f2_nnf]) ).
cnf(c2,plain,
( element(sk0(X0),the_carrier(X0))
| ~ lower_bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p54,plain,
( element(sk0(sk13),the_carrier(sk13))
| ~ lower_bounded_relstr(sk13) ),
inference(resolution,[status(thm)],[c42,c2]) ).
cnf(c41,plain,
lower_bounded_relstr(sk13),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p65,plain,
element(sk0(sk13),the_carrier(sk13)),
inference(resolution,[status(thm)],[p54,c41]) ).
cnf(p293,plain,
( element(sk12(sk13,X0,sk0(sk13)),the_carrier(sk13))
| ~ relstr_element_smaller(sk13,X0,sk0(sk13))
| ex_inf_of_relstr_set(sk13,X0) ),
inference(resolution,[status(thm)],[p218,p65]) ).
cnf(c3,plain,
( relstr_element_smaller(X0,the_carrier(X0),sk0(X0))
| ~ lower_bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p55,plain,
( relstr_element_smaller(sk13,the_carrier(sk13),sk0(sk13))
| ~ lower_bounded_relstr(sk13) ),
inference(resolution,[status(thm)],[c42,c3]) ).
cnf(p76,plain,
relstr_element_smaller(sk13,the_carrier(sk13),sk0(sk13)),
inference(resolution,[status(thm)],[p55,c41]) ).
cnf(p309,plain,
( element(sk12(sk13,the_carrier(sk13),sk0(sk13)),the_carrier(sk13))
| ex_inf_of_relstr_set(sk13,the_carrier(sk13)) ),
inference(resolution,[status(thm)],[p293,p76]) ).
fof(f3,axiom,
! [A] :
( rel_str(A)
=> ! [B,C] :
( element(C,the_carrier(A))
=> ( relstr_element_smaller(A,B,C)
<=> ! [D] :
( element(D,the_carrier(A))
=> ( in(D,B)
=> related(A,C,D) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_lattice3) ).
fof(f3_nnf,plain,
! [A] :
( ! [B,C] :
( ( ( ? [D] :
( ~ related(A,C,D)
& in(D,B)
& element(D,the_carrier(A)) )
| relstr_element_smaller(A,B,C) )
& ( ! [D] :
( related(A,C,D)
| ~ in(D,B)
| ~ element(D,the_carrier(A)) )
| ~ relstr_element_smaller(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ rel_str(A) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,C,B,D] :
( ( ( ( ~ related(A,C,sk1(A,B,C))
& in(sk1(A,B,C),B)
& element(sk1(A,B,C),the_carrier(A)) )
| relstr_element_smaller(A,B,C) )
& ( related(A,C,D)
| ~ in(D,B)
| ~ element(D,the_carrier(A))
| ~ relstr_element_smaller(A,B,C) ) )
| ~ element(C,the_carrier(A))
| ~ rel_str(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f3_nnf]) ).
cnf(c5,plain,
( related(X0,X2,X3)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p61,plain,
( related(sk13,X0,X2)
| ~ in(X2,X1)
| ~ element(X2,the_carrier(sk13))
| ~ relstr_element_smaller(sk13,X1,X0)
| ~ element(X0,the_carrier(sk13)) ),
inference(resolution,[status(thm)],[c5,c42]) ).
cnf(p333,plain,
( related(sk13,sk12(sk13,the_carrier(sk13),sk0(sk13)),X1)
| ~ in(X1,X0)
| ~ element(X1,the_carrier(sk13))
| ~ relstr_element_smaller(sk13,X0,sk12(sk13,the_carrier(sk13),sk0(sk13)))
| ex_inf_of_relstr_set(sk13,the_carrier(sk13)) ),
inference(resolution,[status(thm)],[p309,p61]) ).
cnf(c35,plain,
( relstr_element_smaller(X0,X1,sk12(X0,X1,X2))
| ~ relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ex_inf_of_relstr_set(X0,X1)
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p118,plain,
( relstr_element_smaller(sk13,X0,sk12(sk13,X0,X1))
| ~ relstr_element_smaller(sk13,X0,X1)
| ~ element(X1,the_carrier(sk13))
| ex_inf_of_relstr_set(sk13,X0)
| ~ rel_str(sk13) ),
inference(resolution,[status(thm)],[c35,c40]) ).
cnf(p225,plain,
( relstr_element_smaller(sk13,X0,sk12(sk13,X0,X1))
| ~ relstr_element_smaller(sk13,X0,X1)
| ~ element(X1,the_carrier(sk13))
| ex_inf_of_relstr_set(sk13,X0) ),
inference(resolution,[status(thm)],[p118,c42]) ).
cnf(p380,plain,
( relstr_element_smaller(sk13,X0,sk12(sk13,X0,sk0(sk13)))
| ~ relstr_element_smaller(sk13,X0,sk0(sk13))
| ex_inf_of_relstr_set(sk13,X0) ),
inference(resolution,[status(thm)],[p225,p65]) ).
cnf(p390,plain,
( relstr_element_smaller(sk13,the_carrier(sk13),sk12(sk13,the_carrier(sk13),sk0(sk13)))
| ex_inf_of_relstr_set(sk13,the_carrier(sk13)) ),
inference(resolution,[status(thm)],[p380,p76]) ).
cnf(p1495,plain,
( ex_inf_of_relstr_set(sk13,the_carrier(sk13))
| related(sk13,sk12(sk13,the_carrier(sk13),sk0(sk13)),X0)
| ~ in(X0,the_carrier(sk13))
| ~ element(X0,the_carrier(sk13))
| ex_inf_of_relstr_set(sk13,the_carrier(sk13)) ),
inference(resolution,[status(thm)],[p333,p390]) ).
cnf(p1541,plain,
( related(sk13,sk12(sk13,the_carrier(sk13),sk0(sk13)),X0)
| ~ in(X0,the_carrier(sk13))
| ~ element(X0,the_carrier(sk13))
| ex_inf_of_relstr_set(sk13,the_carrier(sk13)) ),
inference(factoring,[status(thm)],[p1495]) ).
cnf(p1544,plain,
( related(sk13,sk12(sk13,the_carrier(sk13),sk0(sk13)),sk0(sk13))
| ~ in(sk0(sk13),the_carrier(sk13))
| ex_inf_of_relstr_set(sk13,the_carrier(sk13)) ),
inference(resolution,[status(thm)],[p1541,p65]) ).
fof(f21,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f21_nnf,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c38,plain,
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p78,plain,
( in(sk0(sk13),the_carrier(sk13))
| empty(the_carrier(sk13)) ),
inference(resolution,[status(thm)],[c38,p65]) ).
cnf(p1586,plain,
( empty(the_carrier(sk13))
| related(sk13,sk12(sk13,the_carrier(sk13),sk0(sk13)),sk0(sk13))
| ex_inf_of_relstr_set(sk13,the_carrier(sk13)) ),
inference(resolution,[status(thm)],[p1544,p78]) ).
cnf(c36,plain,
( ~ related(X0,sk12(X0,X1,X2),X2)
| ~ relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ex_inf_of_relstr_set(X0,X1)
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p126,plain,
( ~ related(sk13,sk12(sk13,X0,X1),X1)
| ~ relstr_element_smaller(sk13,X0,X1)
| ~ element(X1,the_carrier(sk13))
| ex_inf_of_relstr_set(sk13,X0)
| ~ rel_str(sk13) ),
inference(resolution,[status(thm)],[c36,c40]) ).
cnf(p248,plain,
( ~ related(sk13,sk12(sk13,X0,X1),X1)
| ~ relstr_element_smaller(sk13,X0,X1)
| ~ element(X1,the_carrier(sk13))
| ex_inf_of_relstr_set(sk13,X0) ),
inference(resolution,[status(thm)],[p126,c42]) ).
cnf(p393,plain,
( ~ related(sk13,sk12(sk13,X0,sk0(sk13)),sk0(sk13))
| ~ relstr_element_smaller(sk13,X0,sk0(sk13))
| ex_inf_of_relstr_set(sk13,X0) ),
inference(resolution,[status(thm)],[p248,p65]) ).
cnf(p403,plain,
( ~ related(sk13,sk12(sk13,the_carrier(sk13),sk0(sk13)),sk0(sk13))
| ex_inf_of_relstr_set(sk13,the_carrier(sk13)) ),
inference(resolution,[status(thm)],[p393,p76]) ).
cnf(p1587,plain,
( ex_inf_of_relstr_set(sk13,the_carrier(sk13))
| empty(the_carrier(sk13))
| ex_inf_of_relstr_set(sk13,the_carrier(sk13)) ),
inference(resolution,[status(thm)],[p1586,p403]) ).
cnf(p1588,plain,
( empty(the_carrier(sk13))
| ex_inf_of_relstr_set(sk13,the_carrier(sk13)) ),
inference(factoring,[status(thm)],[p1587]) ).
fof(f18,axiom,
! [A] :
( ( rel_str(A)
& antisymmetric_relstr(A) )
=> ! [B] :
( ex_sup_of_relstr_set(A,B)
<=> ? [C] :
( ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,B,D)
=> related(A,C,D) ) )
& relstr_set_smaller(A,B,C)
& element(C,the_carrier(A)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_yellow_0) ).
fof(f18_nnf,plain,
! [A] :
( ! [B] :
( ( ! [C] :
( ? [D] :
( ~ related(A,C,D)
& relstr_set_smaller(A,B,D)
& element(D,the_carrier(A)) )
| ~ relstr_set_smaller(A,B,C)
| ~ element(C,the_carrier(A)) )
| ex_sup_of_relstr_set(A,B) )
& ( ? [C] :
( ! [D] :
( related(A,C,D)
| ~ relstr_set_smaller(A,B,D)
| ~ element(D,the_carrier(A)) )
& relstr_set_smaller(A,B,C)
& element(C,the_carrier(A)) )
| ~ ex_sup_of_relstr_set(A,B) ) )
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A,B,D,C] :
( ( ( ( ~ related(A,C,sk10(A,B,C))
& relstr_set_smaller(A,B,sk10(A,B,C))
& element(sk10(A,B,C),the_carrier(A)) )
| ~ relstr_set_smaller(A,B,C)
| ~ element(C,the_carrier(A))
| ex_sup_of_relstr_set(A,B) )
& ( ( ( related(A,sk9(A,B),D)
| ~ relstr_set_smaller(A,B,D)
| ~ element(D,the_carrier(A)) )
& relstr_set_smaller(A,B,sk9(A,B))
& element(sk9(A,B),the_carrier(A)) )
| ~ ex_sup_of_relstr_set(A,B) ) )
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9,sk10])],[f18_nnf]) ).
cnf(c28,plain,
( element(sk10(X0,X1,X2),the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ex_sup_of_relstr_set(X0,X1)
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p88,plain,
( element(sk10(sk13,X0,X1),the_carrier(sk13))
| ~ relstr_set_smaller(sk13,X0,X1)
| ~ element(X1,the_carrier(sk13))
| ex_sup_of_relstr_set(sk13,X0)
| ~ rel_str(sk13) ),
inference(resolution,[status(thm)],[c28,c40]) ).
cnf(p191,plain,
( element(sk10(sk13,X0,X1),the_carrier(sk13))
| ~ relstr_set_smaller(sk13,X0,X1)
| ~ element(X1,the_carrier(sk13))
| ex_sup_of_relstr_set(sk13,X0) ),
inference(resolution,[status(thm)],[p88,c42]) ).
cnf(p227,plain,
( element(sk10(sk13,X0,sk0(sk13)),the_carrier(sk13))
| ~ relstr_set_smaller(sk13,X0,sk0(sk13))
| ex_sup_of_relstr_set(sk13,X0) ),
inference(resolution,[status(thm)],[p191,p65]) ).
fof(f24,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> ( relstr_element_smaller(A,empty_set,B)
& relstr_set_smaller(A,empty_set,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_yellow_0) ).
fof(f24_nnf,plain,
! [A] :
( ! [B] :
( ( relstr_element_smaller(A,empty_set,B)
& relstr_set_smaller(A,empty_set,B) )
| ~ element(B,the_carrier(A)) )
| ~ rel_str(A) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [A,B] :
( ( relstr_element_smaller(A,empty_set,B)
& relstr_set_smaller(A,empty_set,B) )
| ~ element(B,the_carrier(A))
| ~ rel_str(A) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c45,plain,
( relstr_set_smaller(X0,empty_set,X1)
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p83,plain,
( relstr_set_smaller(sk13,empty_set,X0)
| ~ element(X0,the_carrier(sk13)) ),
inference(resolution,[status(thm)],[c45,c42]) ).
cnf(p87,plain,
relstr_set_smaller(sk13,empty_set,sk0(sk13)),
inference(resolution,[status(thm)],[p83,p65]) ).
cnf(p232,plain,
( element(sk10(sk13,empty_set,sk0(sk13)),the_carrier(sk13))
| ex_sup_of_relstr_set(sk13,empty_set) ),
inference(resolution,[status(thm)],[p227,p87]) ).
cnf(p164,plain,
( related(sk13,sk0(sk13),X1)
| ~ in(X1,X0)
| ~ element(X1,the_carrier(sk13))
| ~ relstr_element_smaller(sk13,X0,sk0(sk13)) ),
inference(resolution,[status(thm)],[p61,p65]) ).
cnf(p206,plain,
( related(sk13,sk0(sk13),X0)
| ~ in(X0,the_carrier(sk13))
| ~ element(X0,the_carrier(sk13)) ),
inference(resolution,[status(thm)],[p164,p76]) ).
cnf(p242,plain,
( related(sk13,sk0(sk13),sk10(sk13,empty_set,sk0(sk13)))
| ~ in(sk10(sk13,empty_set,sk0(sk13)),the_carrier(sk13))
| ex_sup_of_relstr_set(sk13,empty_set) ),
inference(resolution,[status(thm)],[p232,p206]) ).
cnf(p233,plain,
( in(sk10(sk13,empty_set,sk0(sk13)),the_carrier(sk13))
| empty(the_carrier(sk13))
| ex_sup_of_relstr_set(sk13,empty_set) ),
inference(resolution,[status(thm)],[p232,c38]) ).
cnf(p436,plain,
( empty(the_carrier(sk13))
| ex_sup_of_relstr_set(sk13,empty_set)
| related(sk13,sk0(sk13),sk10(sk13,empty_set,sk0(sk13)))
| ex_sup_of_relstr_set(sk13,empty_set) ),
inference(resolution,[status(thm)],[p242,p233]) ).
cnf(p454,plain,
( empty(the_carrier(sk13))
| related(sk13,sk0(sk13),sk10(sk13,empty_set,sk0(sk13)))
| ex_sup_of_relstr_set(sk13,empty_set) ),
inference(factoring,[status(thm)],[p436]) ).
cnf(c30,plain,
( ~ related(X0,X2,sk10(X0,X1,X2))
| ~ relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ex_sup_of_relstr_set(X0,X1)
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p96,plain,
( ~ related(sk13,X1,sk10(sk13,X0,X1))
| ~ relstr_set_smaller(sk13,X0,X1)
| ~ element(X1,the_carrier(sk13))
| ex_sup_of_relstr_set(sk13,X0)
| ~ rel_str(sk13) ),
inference(resolution,[status(thm)],[c30,c40]) ).
cnf(p203,plain,
( ~ related(sk13,X1,sk10(sk13,X0,X1))
| ~ relstr_set_smaller(sk13,X0,X1)
| ~ element(X1,the_carrier(sk13))
| ex_sup_of_relstr_set(sk13,X0) ),
inference(resolution,[status(thm)],[p96,c42]) ).
cnf(p284,plain,
( ~ related(sk13,sk0(sk13),sk10(sk13,X0,sk0(sk13)))
| ~ relstr_set_smaller(sk13,X0,sk0(sk13))
| ex_sup_of_relstr_set(sk13,X0) ),
inference(resolution,[status(thm)],[p203,p65]) ).
cnf(p291,plain,
( ~ related(sk13,sk0(sk13),sk10(sk13,empty_set,sk0(sk13)))
| ex_sup_of_relstr_set(sk13,empty_set) ),
inference(resolution,[status(thm)],[p284,p87]) ).
cnf(p455,plain,
( ex_sup_of_relstr_set(sk13,empty_set)
| empty(the_carrier(sk13))
| ex_sup_of_relstr_set(sk13,empty_set) ),
inference(resolution,[status(thm)],[p454,p291]) ).
cnf(p456,plain,
( empty(the_carrier(sk13))
| ex_sup_of_relstr_set(sk13,empty_set) ),
inference(factoring,[status(thm)],[p455]) ).
cnf(c43,plain,
( ~ ex_inf_of_relstr_set(sk13,the_carrier(sk13))
| ~ ex_sup_of_relstr_set(sk13,empty_set) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p457,plain,
( ~ ex_inf_of_relstr_set(sk13,the_carrier(sk13))
| empty(the_carrier(sk13)) ),
inference(resolution,[status(thm)],[p456,c43]) ).
cnf(p1593,plain,
( empty(the_carrier(sk13))
| empty(the_carrier(sk13)) ),
inference(resolution,[status(thm)],[p1588,p457]) ).
cnf(p1594,plain,
empty(the_carrier(sk13)),
inference(factoring,[status(thm)],[p1593]) ).
fof(f23,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f23_nnf,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c44,plain,
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p1596,plain,
the_carrier(sk13) = empty_set,
inference(resolution,[status(thm)],[p1594,c44]) ).
fof(f12,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ~ empty(the_carrier(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f12_nnf,plain,
! [A] :
( ~ empty(the_carrier(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A] :
( ~ empty(the_carrier(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c17,plain,
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
fof(f5,axiom,
! [A] :
( rel_str(A)
=> one_sorted_str(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
fof(f5_nnf,plain,
! [A] :
( one_sorted_str(A)
| ~ rel_str(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] :
( one_sorted_str(A)
| ~ rel_str(A) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c10,plain,
( one_sorted_str(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p58,plain,
one_sorted_str(sk13),
inference(resolution,[status(thm)],[c10,c42]) ).
cnf(p71,plain,
( ~ empty(the_carrier(sk13))
| empty_carrier(sk13) ),
inference(resolution,[status(thm)],[c17,p58]) ).
cnf(p1602,plain,
( ~ empty(empty_set)
| empty_carrier(sk13) ),
inference(demodulation,[status(thm)],[p1596,p71]) ).
fof(f13,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f13_nnf,plain,
empty(empty_set),
inference(nnf_transformation,[status(thm)],[f13]) ).
cnf(c18,plain,
empty(empty_set),
inference(cnf_transformation,[status(esa)],[f13_nnf]) ).
cnf(p1973,plain,
empty_carrier(sk13),
inference(resolution,[status(thm)],[p1602,c18]) ).
cnf(c39,plain,
~ empty_carrier(sk13),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p1974,plain,
$false,
inference(resolution,[status(thm)],[p1973,c39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU360+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 13:48:07 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.36/1.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.36/1.21 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------