%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU360+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 : Tue Sep 29 12:48:32 PM UTC 2026
% Result : Theorem 2.77s 1.28s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 10
% Syntax : Number of formulae : 95 ( 7 unt; 0 def)
% Number of atoms : 537 ( 0 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 766 ( 324 ~; 328 |; 84 &)
% ( 11 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 200 ( 178 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( rel_str(X0)
=> ( lower_bounded_relstr(X0)
<=> ? [X1] :
( element(X1,the_carrier(X0))
& relstr_element_smaller(X0,the_carrier(X0),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_yellow_0) ).
fof(f4,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1,X2] :
( element(X2,the_carrier(X0))
=> ( relstr_element_smaller(X0,X1,X2)
<=> ! [X3] :
( element(X3,the_carrier(X0))
=> ( in(X3,X1)
=> related(X0,X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_lattice3) ).
fof(f6,axiom,
! [X0] :
( rel_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
fof(f13,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f19,axiom,
! [X0] :
( ( antisymmetric_relstr(X0)
& rel_str(X0) )
=> ! [X1] :
( ex_sup_of_relstr_set(X0,X1)
<=> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_set_smaller(X0,X1,X2)
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_set_smaller(X0,X1,X3)
=> related(X0,X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_yellow_0) ).
fof(f20,axiom,
! [X0] :
( ( antisymmetric_relstr(X0)
& rel_str(X0) )
=> ! [X1] :
( ex_inf_of_relstr_set(X0,X1)
<=> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_element_smaller(X0,X1,X2)
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_element_smaller(X0,X1,X3)
=> related(X0,X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_yellow_0) ).
fof(f21,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f22,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f23,conjecture,
! [X0] :
( ( ~ empty_carrier(X0)
& antisymmetric_relstr(X0)
& lower_bounded_relstr(X0)
& rel_str(X0) )
=> ( ex_sup_of_relstr_set(X0,empty_set)
& ex_inf_of_relstr_set(X0,the_carrier(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_yellow_0) ).
fof(f24,negated_conjecture,
~ ! [X0] :
( ( ~ empty_carrier(X0)
& antisymmetric_relstr(X0)
& lower_bounded_relstr(X0)
& rel_str(X0) )
=> ( ex_sup_of_relstr_set(X0,empty_set)
& ex_inf_of_relstr_set(X0,the_carrier(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f26,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ( relstr_set_smaller(X0,empty_set,X1)
& relstr_element_smaller(X0,empty_set,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_yellow_0) ).
fof(f29,plain,
? [X0] :
( ( ~ ex_sup_of_relstr_set(X0,empty_set)
| ~ ex_inf_of_relstr_set(X0,the_carrier(X0)) )
& ~ empty_carrier(X0)
& antisymmetric_relstr(X0)
& lower_bounded_relstr(X0)
& rel_str(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f30,plain,
? [X0] :
( ( ~ ex_sup_of_relstr_set(X0,empty_set)
| ~ ex_inf_of_relstr_set(X0,the_carrier(X0)) )
& ~ empty_carrier(X0)
& antisymmetric_relstr(X0)
& lower_bounded_relstr(X0)
& rel_str(X0) ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
! [X0] :
( ( lower_bounded_relstr(X0)
<=> ? [X1] :
( element(X1,the_carrier(X0))
& relstr_element_smaller(X0,the_carrier(X0),X1) ) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f32,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f33,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
! [X0] :
( ! [X1] :
( ex_sup_of_relstr_set(X0,X1)
<=> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_set_smaller(X0,X1,X2)
& ! [X3] :
( related(X0,X2,X3)
| ~ relstr_set_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) ) ) )
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f35,plain,
! [X0] :
( ! [X1] :
( ex_sup_of_relstr_set(X0,X1)
<=> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_set_smaller(X0,X1,X2)
& ! [X3] :
( related(X0,X2,X3)
| ~ relstr_set_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) ) ) )
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0] :
( ! [X1] :
( ex_inf_of_relstr_set(X0,X1)
<=> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_element_smaller(X0,X1,X2)
& ! [X3] :
( related(X0,X3,X2)
| ~ relstr_element_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) ) ) )
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f37,plain,
! [X0] :
( ! [X1] :
( ex_inf_of_relstr_set(X0,X1)
<=> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_element_smaller(X0,X1,X2)
& ! [X3] :
( related(X0,X3,X2)
| ~ relstr_element_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) ) ) )
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
! [X0] :
( one_sorted_str(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f39,plain,
! [X0] :
( ! [X1,X2] :
( ( relstr_element_smaller(X0,X1,X2)
<=> ! [X3] :
( related(X0,X2,X3)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f40,plain,
! [X0] :
( ! [X1,X2] :
( ( relstr_element_smaller(X0,X1,X2)
<=> ! [X3] :
( related(X0,X2,X3)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
! [X0] :
( ! [X1] :
( ( relstr_set_smaller(X0,empty_set,X1)
& relstr_element_smaller(X0,empty_set,X1) )
| ~ element(X1,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f43,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f44,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f47,plain,
( ( ~ ex_sup_of_relstr_set(sK0,empty_set)
| ~ ex_inf_of_relstr_set(sK0,the_carrier(sK0)) )
& ~ empty_carrier(sK0)
& antisymmetric_relstr(sK0)
& lower_bounded_relstr(sK0)
& rel_str(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f30]) ).
fof(f49,plain,
! [X0] :
( ( ( lower_bounded_relstr(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ~ relstr_element_smaller(X0,the_carrier(X0),X1) ) )
& ( ? [X1] :
( element(X1,the_carrier(X0))
& relstr_element_smaller(X0,the_carrier(X0),X1) )
| ~ lower_bounded_relstr(X0) ) )
| ~ rel_str(X0) ),
inference(nnf_transformation,[],[f31]) ).
fof(f50,plain,
! [X0] :
( ( ( lower_bounded_relstr(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ~ relstr_element_smaller(X0,the_carrier(X0),X1) ) )
& ( ? [X2] :
( element(X2,the_carrier(X0))
& relstr_element_smaller(X0,the_carrier(X0),X2) )
| ~ lower_bounded_relstr(X0) ) )
| ~ rel_str(X0) ),
inference(rectify,[],[f49]) ).
fof(f51,plain,
! [X0] :
( ( ( lower_bounded_relstr(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ~ relstr_element_smaller(X0,the_carrier(X0),X1) ) )
& ( ( element(sK2(X0),the_carrier(X0))
& relstr_element_smaller(X0,the_carrier(X0),sK2(X0)) )
| ~ lower_bounded_relstr(X0) ) )
| ~ rel_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0))],[f50]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( ( ex_sup_of_relstr_set(X0,X1)
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ? [X3] :
( ~ related(X0,X2,X3)
& relstr_set_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) ) ) )
& ( ? [X2] :
( element(X2,the_carrier(X0))
& relstr_set_smaller(X0,X1,X2)
& ! [X3] :
( related(X0,X2,X3)
| ~ relstr_set_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) ) )
| ~ ex_sup_of_relstr_set(X0,X1) ) )
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0) ),
inference(nnf_transformation,[],[f35]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( ( ex_sup_of_relstr_set(X0,X1)
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ? [X3] :
( ~ related(X0,X2,X3)
& relstr_set_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) ) ) )
& ( ? [X4] :
( element(X4,the_carrier(X0))
& relstr_set_smaller(X0,X1,X4)
& ! [X5] :
( related(X0,X4,X5)
| ~ relstr_set_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0)) ) )
| ~ ex_sup_of_relstr_set(X0,X1) ) )
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0) ),
inference(rectify,[],[f53]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ( ex_sup_of_relstr_set(X0,X1)
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ( ~ related(X0,X2,sK4(X0,X1,X2))
& relstr_set_smaller(X0,X1,sK4(X0,X1,X2))
& element(sK4(X0,X1,X2),the_carrier(X0)) ) ) )
& ( ( element(sK5(X0,X1),the_carrier(X0))
& relstr_set_smaller(X0,X1,sK5(X0,X1))
& ! [X5] :
( related(X0,sK5(X0,X1),X5)
| ~ relstr_set_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0)) ) )
| ~ ex_sup_of_relstr_set(X0,X1) ) )
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X3,sK4(X0,X1,X2)),skolemize(X4,sK5(X0,X1))],[f54]) ).
fof(f56,plain,
! [X0] :
( ! [X1] :
( ( ex_inf_of_relstr_set(X0,X1)
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ? [X3] :
( ~ related(X0,X3,X2)
& relstr_element_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) ) ) )
& ( ? [X2] :
( element(X2,the_carrier(X0))
& relstr_element_smaller(X0,X1,X2)
& ! [X3] :
( related(X0,X3,X2)
| ~ relstr_element_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) ) )
| ~ ex_inf_of_relstr_set(X0,X1) ) )
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0) ),
inference(nnf_transformation,[],[f37]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ( ex_inf_of_relstr_set(X0,X1)
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ? [X3] :
( ~ related(X0,X3,X2)
& relstr_element_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) ) ) )
& ( ? [X4] :
( element(X4,the_carrier(X0))
& relstr_element_smaller(X0,X1,X4)
& ! [X5] :
( related(X0,X5,X4)
| ~ relstr_element_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0)) ) )
| ~ ex_inf_of_relstr_set(X0,X1) ) )
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0) ),
inference(rectify,[],[f56]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( ( ex_inf_of_relstr_set(X0,X1)
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ( ~ related(X0,sK6(X0,X1,X2),X2)
& relstr_element_smaller(X0,X1,sK6(X0,X1,X2))
& element(sK6(X0,X1,X2),the_carrier(X0)) ) ) )
& ( ( element(sK7(X0,X1),the_carrier(X0))
& relstr_element_smaller(X0,X1,sK7(X0,X1))
& ! [X5] :
( related(X0,X5,sK7(X0,X1))
| ~ relstr_element_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0)) ) )
| ~ ex_inf_of_relstr_set(X0,X1) ) )
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X3,sK6(X0,X1,X2)),skolemize(X4,sK7(X0,X1))],[f57]) ).
fof(f63,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relstr_element_smaller(X0,X1,X2)
| ? [X3] :
( ~ related(X0,X2,X3)
& in(X3,X1)
& element(X3,the_carrier(X0)) ) )
& ( ! [X3] :
( 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(nnf_transformation,[],[f40]) ).
fof(f64,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relstr_element_smaller(X0,X1,X2)
| ? [X3] :
( ~ related(X0,X2,X3)
& in(X3,X1)
& element(X3,the_carrier(X0)) ) )
& ( ! [X4] :
( related(X0,X2,X4)
| ~ in(X4,X1)
| ~ element(X4,the_carrier(X0)) )
| ~ relstr_element_smaller(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(rectify,[],[f63]) ).
fof(f65,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relstr_element_smaller(X0,X1,X2)
| ( ~ related(X0,X2,sK12(X0,X1,X2))
& in(sK12(X0,X1,X2),X1)
& element(sK12(X0,X1,X2),the_carrier(X0)) ) )
& ( ! [X4] :
( related(X0,X2,X4)
| ~ in(X4,X1)
| ~ element(X4,the_carrier(X0)) )
| ~ relstr_element_smaller(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X3,sK12(X0,X1,X2))],[f64]) ).
fof(f66,plain,
rel_str(sK0),
inference(cnf_transformation,[],[f47]) ).
fof(f67,plain,
lower_bounded_relstr(sK0),
inference(cnf_transformation,[],[f47]) ).
fof(f68,plain,
antisymmetric_relstr(sK0),
inference(cnf_transformation,[],[f47]) ).
fof(f69,plain,
~ empty_carrier(sK0),
inference(cnf_transformation,[],[f47]) ).
fof(f70,plain,
( ~ ex_inf_of_relstr_set(sK0,the_carrier(sK0))
| ~ ex_sup_of_relstr_set(sK0,empty_set) ),
inference(cnf_transformation,[],[f47]) ).
fof(f73,plain,
! [X0] :
( relstr_element_smaller(X0,the_carrier(X0),sK2(X0))
| ~ lower_bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f74,plain,
! [X0] :
( element(sK2(X0),the_carrier(X0))
| ~ lower_bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f78,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f82,plain,
! [X2,X0,X1] :
( element(sK4(X0,X1,X2),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ex_sup_of_relstr_set(X0,X1)
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f84,plain,
! [X2,X0,X1] :
( ~ related(X0,X2,sK4(X0,X1,X2))
| ~ element(X2,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ex_sup_of_relstr_set(X0,X1)
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f88,plain,
! [X2,X0,X1] :
( element(sK6(X0,X1,X2),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ex_inf_of_relstr_set(X0,X1)
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f89,plain,
! [X2,X0,X1] :
( relstr_element_smaller(X0,X1,sK6(X0,X1,X2))
| ~ element(X2,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ex_inf_of_relstr_set(X0,X1)
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f90,plain,
! [X2,X0,X1] :
( ~ related(X0,sK6(X0,X1,X2),X2)
| ~ element(X2,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ex_inf_of_relstr_set(X0,X1)
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f95,plain,
! [X0] :
( one_sorted_str(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f96,plain,
! [X2,X0,X1,X4] :
( related(X0,X2,X4)
| ~ in(X4,X1)
| ~ element(X4,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f101,plain,
! [X0,X1] :
( relstr_set_smaller(X0,empty_set,X1)
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f103,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f104,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f154,plain,
! [X2,X3,X0,X1] :
( ~ element(X0,the_carrier(X1))
| ~ relstr_set_smaller(X1,X2,X0)
| ex_sup_of_relstr_set(X1,X2)
| ~ antisymmetric_relstr(X1)
| ~ rel_str(X1)
| ~ in(sK4(X1,X2,X0),X3)
| ~ element(sK4(X1,X2,X0),the_carrier(X1))
| ~ relstr_element_smaller(X1,X3,X0)
| ~ element(X0,the_carrier(X1))
| ~ rel_str(X1) ),
inference(resolution,[],[f84,f96]) ).
fof(f155,plain,
! [X2,X3,X0,X1] :
( ~ element(X0,the_carrier(X1))
| ~ relstr_set_smaller(X1,X2,X0)
| ex_sup_of_relstr_set(X1,X2)
| ~ antisymmetric_relstr(X1)
| ~ rel_str(X1)
| ~ in(sK4(X1,X2,X0),X3)
| ~ element(sK4(X1,X2,X0),the_carrier(X1))
| ~ relstr_element_smaller(X1,X3,X0) ),
inference(duplicate_literal_removal,[],[f154]) ).
fof(f157,plain,
! [X2,X3,X0,X1] :
( ~ in(sK4(X1,X2,X0),X3)
| ~ relstr_set_smaller(X1,X2,X0)
| ex_sup_of_relstr_set(X1,X2)
| ~ antisymmetric_relstr(X1)
| ~ rel_str(X1)
| ~ element(X0,the_carrier(X1))
| ~ relstr_element_smaller(X1,X3,X0) ),
inference(forward_subsumption_resolution,[],[f155,f82]) ).
fof(f172,plain,
! [X2,X3,X0,X1] :
( ~ element(X0,the_carrier(X1))
| ~ relstr_element_smaller(X1,X2,X0)
| ex_inf_of_relstr_set(X1,X2)
| ~ antisymmetric_relstr(X1)
| ~ rel_str(X1)
| ~ in(X0,X3)
| ~ element(X0,the_carrier(X1))
| ~ relstr_element_smaller(X1,X3,sK6(X1,X2,X0))
| ~ element(sK6(X1,X2,X0),the_carrier(X1))
| ~ rel_str(X1) ),
inference(resolution,[],[f90,f96]) ).
fof(f173,plain,
! [X2,X3,X0,X1] :
( ~ element(X0,the_carrier(X1))
| ~ relstr_element_smaller(X1,X2,X0)
| ex_inf_of_relstr_set(X1,X2)
| ~ antisymmetric_relstr(X1)
| ~ rel_str(X1)
| ~ in(X0,X3)
| ~ relstr_element_smaller(X1,X3,sK6(X1,X2,X0))
| ~ element(sK6(X1,X2,X0),the_carrier(X1)) ),
inference(duplicate_literal_removal,[],[f172]) ).
fof(f175,plain,
! [X2,X3,X0,X1] :
( ~ relstr_element_smaller(X1,X3,sK6(X1,X2,X0))
| ~ relstr_element_smaller(X1,X2,X0)
| ex_inf_of_relstr_set(X1,X2)
| ~ antisymmetric_relstr(X1)
| ~ rel_str(X1)
| ~ in(X0,X3)
| ~ element(X0,the_carrier(X1)) ),
inference(forward_subsumption_resolution,[],[f173,f88]) ).
fof(f179,plain,
! [X2,X3,X0,X1] :
( ~ element(sK4(X0,X1,X2),X3)
| ex_sup_of_relstr_set(X0,X1)
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ relstr_element_smaller(X0,X3,X2)
| empty(X3)
| ~ relstr_set_smaller(X0,X1,X2) ),
inference(resolution,[],[f157,f103]) ).
fof(f195,plain,
! [X2,X0,X1] :
( ~ relstr_element_smaller(X0,X1,X2)
| ex_inf_of_relstr_set(X0,X1)
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0)
| ~ in(X2,X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ex_inf_of_relstr_set(X0,X1)
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0) ),
inference(resolution,[],[f175,f89]) ).
fof(f198,plain,
! [X2,X0,X1] :
( ~ relstr_element_smaller(X0,X1,X2)
| ex_inf_of_relstr_set(X0,X1)
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0)
| ~ in(X2,X1)
| ~ element(X2,the_carrier(X0)) ),
inference(duplicate_literal_removal,[],[f195]) ).
fof(f209,plain,
! [X0] :
( ex_inf_of_relstr_set(X0,the_carrier(X0))
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0)
| ~ in(sK2(X0),the_carrier(X0))
| ~ element(sK2(X0),the_carrier(X0))
| ~ lower_bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(resolution,[],[f198,f73]) ).
fof(f220,plain,
! [X0] :
( ex_inf_of_relstr_set(X0,the_carrier(X0))
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0)
| ~ in(sK2(X0),the_carrier(X0))
| ~ element(sK2(X0),the_carrier(X0))
| ~ lower_bounded_relstr(X0) ),
inference(duplicate_literal_removal,[],[f209]) ).
fof(f223,plain,
! [X0] :
( ~ in(sK2(X0),the_carrier(X0))
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0)
| ex_inf_of_relstr_set(X0,the_carrier(X0))
| ~ lower_bounded_relstr(X0) ),
inference(forward_subsumption_resolution,[],[f220,f104]) ).
fof(f291,plain,
! [X0] :
( ~ antisymmetric_relstr(X0)
| ~ rel_str(X0)
| ex_inf_of_relstr_set(X0,the_carrier(X0))
| ~ lower_bounded_relstr(X0)
| empty(the_carrier(X0))
| ~ element(sK2(X0),the_carrier(X0)) ),
inference(resolution,[],[f223,f103]) ).
fof(f292,plain,
! [X0] :
( ex_inf_of_relstr_set(X0,the_carrier(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ lower_bounded_relstr(X0)
| empty(the_carrier(X0)) ),
inference(forward_subsumption_resolution,[],[f291,f74]) ).
fof(f293,plain,
( ~ rel_str(sK0)
| ~ antisymmetric_relstr(sK0)
| ~ lower_bounded_relstr(sK0)
| empty(the_carrier(sK0))
| ~ ex_sup_of_relstr_set(sK0,empty_set) ),
inference(resolution,[],[f292,f70]) ).
fof(f296,plain,
( ~ antisymmetric_relstr(sK0)
| ~ lower_bounded_relstr(sK0)
| empty(the_carrier(sK0))
| ~ ex_sup_of_relstr_set(sK0,empty_set) ),
inference(forward_subsumption_resolution,[],[f293,f66]) ).
fof(f297,plain,
( ~ lower_bounded_relstr(sK0)
| empty(the_carrier(sK0))
| ~ ex_sup_of_relstr_set(sK0,empty_set) ),
inference(forward_subsumption_resolution,[],[f296,f68]) ).
fof(f298,plain,
( empty(the_carrier(sK0))
| ~ ex_sup_of_relstr_set(sK0,empty_set) ),
inference(forward_subsumption_resolution,[],[f297,f67]) ).
fof(f304,plain,
( ~ ex_sup_of_relstr_set(sK0,empty_set)
| empty_carrier(sK0)
| ~ one_sorted_str(sK0) ),
inference(resolution,[],[f298,f78]) ).
fof(f305,plain,
( ~ ex_sup_of_relstr_set(sK0,empty_set)
| ~ one_sorted_str(sK0) ),
inference(forward_subsumption_resolution,[],[f304,f69]) ).
fof(f306,plain,
! [X2,X0,X1] :
( ex_sup_of_relstr_set(X0,X1)
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ relstr_element_smaller(X0,the_carrier(X0),X2)
| empty(the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ex_sup_of_relstr_set(X0,X1)
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0) ),
inference(resolution,[],[f179,f82]) ).
fof(f308,plain,
! [X2,X0,X1] :
( ~ relstr_element_smaller(X0,the_carrier(X0),X2)
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| ex_sup_of_relstr_set(X0,X1)
| empty(the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2) ),
inference(duplicate_literal_removal,[],[f306]) ).
fof(f379,plain,
! [X0,X1] :
( ~ antisymmetric_relstr(X0)
| ~ rel_str(X0)
| ~ element(sK2(X0),the_carrier(X0))
| ex_sup_of_relstr_set(X0,X1)
| empty(the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,sK2(X0))
| ~ lower_bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(resolution,[],[f308,f73]) ).
fof(f390,plain,
! [X0,X1] :
( ~ antisymmetric_relstr(X0)
| ~ rel_str(X0)
| ~ element(sK2(X0),the_carrier(X0))
| ex_sup_of_relstr_set(X0,X1)
| empty(the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,sK2(X0))
| ~ lower_bounded_relstr(X0) ),
inference(duplicate_literal_removal,[],[f379]) ).
fof(f394,plain,
! [X0,X1] :
( ~ relstr_set_smaller(X0,X1,sK2(X0))
| ~ rel_str(X0)
| ex_sup_of_relstr_set(X0,X1)
| empty(the_carrier(X0))
| ~ antisymmetric_relstr(X0)
| ~ lower_bounded_relstr(X0) ),
inference(forward_subsumption_resolution,[],[f390,f74]) ).
fof(f399,plain,
! [X0] :
( ~ rel_str(X0)
| ex_sup_of_relstr_set(X0,empty_set)
| empty(the_carrier(X0))
| ~ antisymmetric_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ element(sK2(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(resolution,[],[f394,f101]) ).
fof(f400,plain,
! [X0] :
( ~ rel_str(X0)
| ex_sup_of_relstr_set(X0,empty_set)
| empty(the_carrier(X0))
| ~ antisymmetric_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ element(sK2(X0),the_carrier(X0)) ),
inference(duplicate_literal_removal,[],[f399]) ).
fof(f401,plain,
! [X0] :
( ex_sup_of_relstr_set(X0,empty_set)
| ~ rel_str(X0)
| empty(the_carrier(X0))
| ~ antisymmetric_relstr(X0)
| ~ lower_bounded_relstr(X0) ),
inference(forward_subsumption_resolution,[],[f400,f74]) ).
fof(f403,plain,
( ~ rel_str(sK0)
| empty(the_carrier(sK0))
| ~ antisymmetric_relstr(sK0)
| ~ lower_bounded_relstr(sK0)
| ~ one_sorted_str(sK0) ),
inference(resolution,[],[f401,f305]) ).
fof(f405,plain,
( empty(the_carrier(sK0))
| ~ antisymmetric_relstr(sK0)
| ~ lower_bounded_relstr(sK0)
| ~ one_sorted_str(sK0) ),
inference(forward_subsumption_resolution,[],[f403,f66]) ).
fof(f406,plain,
( empty(the_carrier(sK0))
| ~ lower_bounded_relstr(sK0)
| ~ one_sorted_str(sK0) ),
inference(forward_subsumption_resolution,[],[f405,f68]) ).
fof(f407,plain,
( empty(the_carrier(sK0))
| ~ one_sorted_str(sK0) ),
inference(forward_subsumption_resolution,[],[f406,f67]) ).
fof(f409,plain,
( ~ one_sorted_str(sK0)
| empty_carrier(sK0)
| ~ one_sorted_str(sK0) ),
inference(resolution,[],[f407,f78]) ).
fof(f410,plain,
( ~ one_sorted_str(sK0)
| empty_carrier(sK0) ),
inference(duplicate_literal_removal,[],[f409]) ).
fof(f411,plain,
~ one_sorted_str(sK0),
inference(forward_subsumption_resolution,[],[f410,f69]) ).
fof(f412,plain,
~ rel_str(sK0),
inference(resolution,[],[f411,f95]) ).
fof(f413,plain,
$false,
inference(forward_subsumption_resolution,[],[f412,f66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU360+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n013.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Sep 28 04:53:51 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.77/1.28 % (810038)Detected formulas, will run a generic FOF schedule.
% 2.77/1.28 % (810049)dis-21_1_sil=8000:lcm=predicate:random_seed=3071513380:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.77/1.28 % (810047)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2148041898:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.77/1.28 % (810046)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=725084978:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.77/1.28 % (810048)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3424922997:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.77/1.28 % (810045)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1994437925:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.77/1.28 % (810044)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3906285207:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.77/1.28 % (810043)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=221920825:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.77/1.28 % (810049)Instruction limit reached!
% 2.77/1.28 % (810049)------------------------------
% 2.77/1.28 % (810049)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.28 % (810049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.28 % (810049)CaDiCaL version: 2.1.3
% 2.77/1.28 % (810049)Termination reason: Instruction limit
% 2.77/1.28 % (810049)Termination phase: Saturation
% 2.77/1.28 % (810049)Time elapsed: 0.031 s
% 2.77/1.28 % (810049)Peak memory usage: 89 MB
% 2.77/1.28 % (810049)Instructions burned: 135 (million)
% 2.77/1.28 % (810046)Refutation not found, incomplete strategy
% 2.77/1.28 % (810046)------------------------------
% 2.77/1.28 % (810046)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.28 % (810046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.28 % (810046)CaDiCaL version: 2.1.3
% 2.77/1.28 % (810046)Termination reason: Refutation not found, incomplete strategy
% 2.77/1.28 % (810046)Time elapsed: 0.002 s
% 2.77/1.28 % (810046)Peak memory usage: 88 MB
% 2.77/1.28 % (810046)Instructions burned: 2 (million)
% 2.77/1.28 % (810047)First to succeed.
% 2.77/1.28 % (810047)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-810038"
% 2.77/1.28 % (810048)Also succeeded, but the first one will report.
% 2.77/1.28 % (810057)lrs+10_1_sil=8000:sp=occurrence:random_seed=1294300981:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.77/1.28 % (810057)Also succeeded, but the first one will report.
% 2.77/1.28 % (810046)------------------------------
% 2.77/1.28 % (810046)------------------------------
% 2.77/1.28 % (810047)Refutation found. Thanks to Tanya!
% 2.77/1.28 % SZS status Theorem for theBenchmark
% 2.77/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.67/1.48 % (810047)------------------------------
% 3.67/1.48 % (810047)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.48 % (810047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.48 % (810047)CaDiCaL version: 2.1.3
% 3.67/1.48 % (810047)Termination reason: Refutation
% 3.67/1.48 % (810047)Time elapsed: 0.010 s
% 3.67/1.48 % (810047)Peak memory usage: 88 MB
% 3.67/1.48 % (810047)Instructions burned: 15 (million)
% 3.67/1.48 % (810047)------------------------------
% 3.67/1.48 % (810047)------------------------------
% 3.67/1.48 % (810038)Success in time 0.441 s
% 3.67/1.48 % Vampire exiting
%------------------------------------------------------------------------------