%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU206+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 12:52:22 PM UTC 2026
% Result : Theorem 1.65s 0.75s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 98 ( 20 unt; 3 def)
% Number of atoms : 360 ( 67 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 436 ( 174 ~; 198 |; 43 &)
% ( 14 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 4 con; 0-3 aty)
% Number of variables : 236 ( 209 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f6,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f7,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f8,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f9,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f37,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_image(X1,X0),relation_rng(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_relat_1) ).
fof(f38,conjecture,
! [X0] :
( relation(X0)
=> relation_image(X0,relation_dom(X0)) = relation_rng(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_relat_1) ).
fof(f39,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> relation_image(X0,relation_dom(X0)) = relation_rng(X0) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f51,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f52,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f62,plain,
! [X0,X1] :
( subset(relation_image(X1,X0),relation_rng(X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f63,plain,
? [X0] :
( relation_rng(X0) != relation_image(X0,relation_dom(X0))
& relation(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f75,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(ordered_pair(X4,X3),X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(ordered_pair(X4,X3),X0)
| ~ in(X4,X1) ) )
& ( ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) )
| ~ in(X3,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f51]) ).
fof(f76,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(ordered_pair(X4,X3),X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(ordered_pair(X5,X3),X0)
& in(X5,X1) )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(ordered_pair(X7,X6),X0)
| ~ in(X7,X1) ) )
& ( ? [X8] :
( in(ordered_pair(X8,X6),X0)
& in(X8,X1) )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(rectify,[],[f75]) ).
fof(f77,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ( ( ! [X4] :
( ~ in(ordered_pair(X4,sK0(X0,X1,X2)),X0)
| ~ in(X4,X1) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(ordered_pair(sK1(X0,X1,X2),sK0(X0,X1,X2)),X0)
& in(sK1(X0,X1,X2),X1) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(ordered_pair(X7,X6),X0)
| ~ in(X7,X1) ) )
& ( ( in(ordered_pair(sK2(X0,X1,X6),X6),X0)
& in(sK2(X0,X1,X6),X1) )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X5,sK1(X0,X1,X2)),skolemize(X8,sK2(X0,X1,X6))],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f79,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f78]) ).
fof(f80,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK3(X0,X1),X1)
& in(sK3(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f79]) ).
fof(f81,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f53]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f81]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK4(X0,X1),X3),X0)
| ~ in(sK4(X0,X1),X1) )
& ( in(ordered_pair(sK4(X0,X1),sK5(X0,X1)),X0)
| in(sK4(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK6(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X2,sK4(X0,X1)),skolemize(X4,sK5(X0,X1)),skolemize(X7,sK6(X0,X5))],[f82]) ).
fof(f84,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f54]) ).
fof(f85,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f84]) ).
fof(f86,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK7(X0,X1)),X0)
| ~ in(sK7(X0,X1),X1) )
& ( in(ordered_pair(sK8(X0,X1),sK7(X0,X1)),X0)
| in(sK7(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK9(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X2,sK7(X0,X1)),skolemize(X4,sK8(X0,X1)),skolemize(X7,sK9(X0,X5))],[f85]) ).
fof(f94,plain,
( relation_rng(sK17) != relation_image(sK17,relation_dom(sK17))
& relation(sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X0,sK17)],[f63]) ).
fof(f98,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f104,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(ordered_pair(X7,X6),X0)
| ~ in(X7,X1)
| relation_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f108,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f112,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f115,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK9(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f116,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X6,X5),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f117,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| in(ordered_pair(sK8(X0,X1),sK7(X0,X1)),X0)
| in(sK7(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f118,plain,
! [X3,X0,X1] :
( relation_rng(X0) = X1
| ~ in(ordered_pair(X3,sK7(X0,X1)),X0)
| ~ in(sK7(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f119,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f145,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_image(X1,X0),relation_rng(X1)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f146,plain,
relation(sK17),
inference(cnf_transformation,[],[f94]) ).
fof(f147,plain,
relation_rng(sK17) != relation_image(sK17,relation_dom(sK17)),
inference(cnf_transformation,[],[f94]) ).
fof(f159,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(unordered_pair(unordered_pair(X7,X6),singleton(X7)),X0)
| ~ in(X7,X1)
| relation_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f104,f119]) ).
fof(f163,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f112,f119]) ).
fof(f165,plain,
! [X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X3,sK7(X0,X1)),singleton(X3)),X0)
| relation_rng(X0) = X1
| ~ in(sK7(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f118,f119]) ).
fof(f166,plain,
! [X0,X1] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK8(X0,X1),sK7(X0,X1)),singleton(sK8(X0,X1))),X0)
| in(sK7(X0,X1),X1)
| relation_rng(X0) = X1 ),
inference(definition_unfolding,[],[f117,f119]) ).
fof(f167,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f116,f119]) ).
fof(f168,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(sK9(X0,X5),X5),singleton(sK9(X0,X5))),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f115,f119]) ).
fof(f172,plain,
! [X0,X1,X6,X7] :
( ~ in(unordered_pair(unordered_pair(X7,X6),singleton(X7)),X0)
| in(X6,relation_image(X0,X1))
| ~ in(X7,X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f159]) ).
fof(f175,plain,
! [X0,X6,X5] :
( ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f163]) ).
fof(f177,plain,
! [X0,X6,X5] :
( ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f167]) ).
fof(f178,plain,
! [X0,X5] :
( ~ in(X5,relation_rng(X0))
| in(unordered_pair(unordered_pair(sK9(X0,X5),X5),singleton(sK9(X0,X5))),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f168]) ).
fof(f179,definition,
sF18 = relation_rng(sK17),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f180,plain,
relation_rng(sK17) = sF18,
inference(reorient_equations,[],[f179]) ).
fof(f181,definition,
sF19 = relation_dom(sK17),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f182,plain,
relation_dom(sK17) = sF19,
inference(reorient_equations,[],[f181]) ).
fof(f183,definition,
sF20 = relation_image(sK17,sF19),
introduced(definition,[new_symbols(definition,[sF20])],[function_definition]) ).
fof(f184,plain,
relation_image(sK17,sF19) = sF20,
inference(reorient_equations,[],[f183]) ).
fof(f185,plain,
sF18 != sF20,
inference(definition_folding,[],[f147,f184,f182,f180]) ).
fof(f274,plain,
! [X0] : subset(relation_image(sK17,X0),relation_rng(sK17)),
inference(resolution,[],[f145,f146]) ).
fof(f275,plain,
! [X0] : subset(relation_image(sK17,X0),sF18),
inference(forward_demodulation,[],[f274,f180]) ).
fof(f283,plain,
subset(sF20,sF18),
inference(superposition,[],[f275,f184]) ).
fof(f309,plain,
! [X0] :
( ~ in(X0,sF20)
| in(X0,sF18) ),
inference(resolution,[],[f108,f283]) ).
fof(f338,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X1)),X2)
| in(X1,relation_dom(X2))
| ~ relation(X2) ),
inference(superposition,[],[f175,f98]) ).
fof(f341,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),X2)
| in(X1,relation_dom(X2))
| ~ relation(X2) ),
inference(forward_demodulation,[],[f338,f98]) ).
fof(f345,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X1)),X2)
| in(X0,relation_rng(X2))
| ~ relation(X2) ),
inference(superposition,[],[f177,f98]) ).
fof(f348,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),X2)
| in(X0,relation_rng(X2))
| ~ relation(X2) ),
inference(forward_demodulation,[],[f345,f98]) ).
fof(f361,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X1)),X2)
| in(X0,relation_image(X2,X3))
| ~ in(X1,X3)
| ~ relation(X2) ),
inference(superposition,[],[f172,f98]) ).
fof(f364,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),X2)
| in(X0,relation_image(X2,X3))
| ~ in(X1,X3)
| ~ relation(X2) ),
inference(forward_demodulation,[],[f361,f98]) ).
fof(f366,plain,
! [X0] :
( ~ in(X0,sF18)
| in(unordered_pair(unordered_pair(sK9(sK17,X0),X0),singleton(sK9(sK17,X0))),sK17)
| ~ relation(sK17) ),
inference(superposition,[],[f178,f180]) ).
fof(f369,plain,
! [X0] :
( ~ in(X0,sF18)
| in(unordered_pair(unordered_pair(sK9(sK17,X0),X0),singleton(sK9(sK17,X0))),sK17) ),
inference(forward_subsumption_resolution,[],[f366,f146]) ).
fof(f371,plain,
! [X0] :
( in(unordered_pair(singleton(sK9(sK17,X0)),unordered_pair(sK9(sK17,X0),X0)),sK17)
| ~ in(X0,sF18) ),
inference(forward_demodulation,[],[f369,f98]) ).
fof(f373,plain,
! [X0] :
( in(unordered_pair(singleton(sK9(sK17,X0)),unordered_pair(X0,sK9(sK17,X0))),sK17)
| ~ in(X0,sF18) ),
inference(forward_demodulation,[],[f371,f98]) ).
fof(f398,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK7(X0,X1),X2),singleton(X2)),X0)
| relation_rng(X0) = X1
| ~ in(sK7(X0,X1),X1)
| ~ relation(X0) ),
inference(superposition,[],[f165,f98]) ).
fof(f401,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X2),unordered_pair(sK7(X0,X1),X2)),X0)
| relation_rng(X0) = X1
| ~ in(sK7(X0,X1),X1)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f398,f98]) ).
fof(f455,plain,
! [X0] :
( in(unordered_pair(unordered_pair(sK8(sK17,X0),sK7(sK17,X0)),singleton(sK8(sK17,X0))),sK17)
| in(sK7(sK17,X0),X0)
| relation_rng(sK17) = X0 ),
inference(resolution,[],[f166,f146]) ).
fof(f456,plain,
! [X0] :
( in(unordered_pair(singleton(sK8(sK17,X0)),unordered_pair(sK8(sK17,X0),sK7(sK17,X0))),sK17)
| in(sK7(sK17,X0),X0)
| relation_rng(sK17) = X0 ),
inference(forward_demodulation,[],[f455,f98]) ).
fof(f462,plain,
! [X0] :
( in(unordered_pair(singleton(sK8(sK17,X0)),unordered_pair(sK7(sK17,X0),sK8(sK17,X0))),sK17)
| in(sK7(sK17,X0),X0)
| relation_rng(sK17) = X0 ),
inference(forward_demodulation,[],[f456,f98]) ).
fof(f468,plain,
! [X0] :
( in(unordered_pair(singleton(sK8(sK17,X0)),unordered_pair(sK7(sK17,X0),sK8(sK17,X0))),sK17)
| sF18 = X0
| in(sK7(sK17,X0),X0) ),
inference(forward_demodulation,[],[f462,f180]) ).
fof(f755,plain,
! [X0] :
( in(sK9(sK17,X0),relation_dom(sK17))
| ~ relation(sK17)
| ~ in(X0,sF18) ),
inference(resolution,[],[f341,f373]) ).
fof(f764,plain,
! [X0] :
( in(sK9(sK17,X0),relation_dom(sK17))
| ~ in(X0,sF18) ),
inference(forward_subsumption_resolution,[],[f755,f146]) ).
fof(f768,plain,
! [X0] :
( in(sK9(sK17,X0),sF19)
| ~ in(X0,sF18) ),
inference(forward_demodulation,[],[f764,f182]) ).
fof(f781,plain,
! [X0] :
( in(sK7(sK17,X0),relation_rng(sK17))
| ~ relation(sK17)
| sF18 = X0
| in(sK7(sK17,X0),X0) ),
inference(resolution,[],[f348,f468]) ).
fof(f784,plain,
! [X0] :
( in(sK7(sK17,X0),relation_rng(sK17))
| sF18 = X0
| in(sK7(sK17,X0),X0) ),
inference(forward_subsumption_resolution,[],[f781,f146]) ).
fof(f788,plain,
! [X0] :
( in(sK7(sK17,X0),sF18)
| in(sK7(sK17,X0),X0)
| sF18 = X0 ),
inference(forward_demodulation,[],[f784,f180]) ).
fof(f860,plain,
! [X0,X1] :
( in(X0,relation_image(sK17,X1))
| ~ in(sK9(sK17,X0),X1)
| ~ relation(sK17)
| ~ in(X0,sF18) ),
inference(resolution,[],[f364,f373]) ).
fof(f869,plain,
! [X0,X1] :
( ~ in(sK9(sK17,X0),X1)
| in(X0,relation_image(sK17,X1))
| ~ in(X0,sF18) ),
inference(forward_subsumption_resolution,[],[f860,f146]) ).
fof(f881,plain,
! [X0] :
( relation_rng(sK17) = X0
| ~ in(sK7(sK17,X0),X0)
| ~ relation(sK17)
| ~ in(sK7(sK17,X0),sF18) ),
inference(resolution,[],[f401,f373]) ).
fof(f886,plain,
! [X0] :
( relation_rng(sK17) = X0
| ~ in(sK7(sK17,X0),X0)
| ~ in(sK7(sK17,X0),sF18) ),
inference(forward_subsumption_resolution,[],[f881,f146]) ).
fof(f888,plain,
! [X0] :
( ~ in(sK7(sK17,X0),sF18)
| ~ in(sK7(sK17,X0),X0)
| sF18 = X0 ),
inference(forward_demodulation,[],[f886,f180]) ).
fof(f1135,plain,
( in(sK7(sK17,sF20),sF18)
| sF18 = sF20
| in(sK7(sK17,sF20),sF18) ),
inference(resolution,[],[f788,f309]) ).
fof(f1137,plain,
( in(sK7(sK17,sF20),sF18)
| sF18 = sF20 ),
inference(duplicate_literal_removal,[],[f1135]) ).
fof(f1140,plain,
in(sK7(sK17,sF20),sF18),
inference(forward_subsumption_resolution,[],[f1137,f185]) ).
fof(f1187,plain,
! [X0] :
( in(X0,relation_image(sK17,sF19))
| ~ in(X0,sF18)
| ~ in(X0,sF18) ),
inference(resolution,[],[f869,f768]) ).
fof(f1188,plain,
! [X0] :
( in(X0,relation_image(sK17,sF19))
| ~ in(X0,sF18) ),
inference(duplicate_literal_removal,[],[f1187]) ).
fof(f1189,plain,
! [X0] :
( ~ in(X0,sF18)
| in(X0,sF20) ),
inference(forward_demodulation,[],[f1188,f184]) ).
fof(f1331,plain,
( ~ in(sK7(sK17,sF20),sF20)
| sF18 = sF20 ),
inference(resolution,[],[f1140,f888]) ).
fof(f1336,plain,
~ in(sK7(sK17,sF20),sF20),
inference(forward_subsumption_resolution,[],[f1331,f185]) ).
fof(f1577,plain,
in(sK7(sK17,sF20),sF20),
inference(resolution,[],[f1189,f1140]) ).
fof(f1578,plain,
$false,
inference(forward_subsumption_resolution,[],[f1577,f1336]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU206+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n004.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Mon Sep 28 04:02:38 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.41 Running first-order model finding
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.65/0.75 % (4137991)Will run a generic schedule for satisfiability detection.
% 1.65/0.75 % (4138000)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=812902089:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.65/0.75 % (4137997)% WARNING: option uhcvi not known.
% 1.65/0.75 % (4137996)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4141125925_2999 on theBenchmark for (2999ds/0Mi)
% 1.65/0.75 % (4137997)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3655317427:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.65/0.75 % (4138001)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2224755272:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.65/0.75 % (4137998)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4138849003:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.65/0.75 % (4137999)dis+10_1_sil=32000:sp=arity:random_seed=1619447453:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.65/0.75 % (4138002)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1221054778:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.65/0.75 % TRYING [1]
% 1.65/0.75 % TRYING [2]
% 1.65/0.75 % TRYING [3]
% 1.65/0.75 % TRYING [4]
% 1.65/0.75 % (4138000)Instruction limit reached!
% 1.65/0.75 % (4138000)------------------------------
% 1.65/0.75 % (4138000)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.65/0.75 % (4138000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/0.75 % (4138000)CaDiCaL version: 2.1.3
% 1.65/0.75 % (4138000)Termination reason: Instruction limit
% 1.65/0.75 % (4138000)Termination phase: Saturation
% 1.65/0.75 % (4138000)Time elapsed: 0.040 s
% 1.65/0.75 % (4138000)Peak memory usage: 13 MB
% 1.65/0.75 % (4138000)Instructions burned: 118 (million)
% 1.65/0.75 % (4138010)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2750665773:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.65/0.75 % TRYING [1]
% 1.65/0.75 % TRYING [2]
% 1.65/0.75 % TRYING [3]
% 1.65/0.75 % TRYING [5]
% 1.65/0.75 % TRYING [4]
% 1.65/0.75 % (4137999)Instruction limit reached!
% 1.65/0.75 % (4137999)------------------------------
% 1.65/0.75 % (4137999)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.65/0.75 % (4137999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/0.75 % (4137999)CaDiCaL version: 2.1.3
% 1.65/0.75 % (4137999)Termination reason: Instruction limit
% 1.65/0.75 % (4137999)Termination phase: Saturation
% 1.65/0.75 % (4137999)Time elapsed: 0.063 s
% 1.65/0.75 % (4137999)Peak memory usage: 12 MB
% 1.65/0.75 % (4137999)Instructions burned: 104 (million)
% 1.65/0.75 % TRYING [5]
% 1.65/0.75 % (4138001)Instruction limit reached!
% 1.65/0.75 % (4138001)------------------------------
% 1.65/0.75 % (4138001)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.65/0.75 % (4138001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/0.75 % (4138001)CaDiCaL version: 2.1.3
% 1.65/0.75 % (4138001)Termination reason: Instruction limit
% 1.65/0.75 % (4138001)Termination phase: Saturation
% 1.65/0.75 % (4138001)Time elapsed: 0.083 s
% 1.65/0.75 % (4138001)Peak memory usage: 13 MB
% 1.65/0.75 % (4138001)Instructions burned: 132 (million)
% 1.65/0.75 % (4138012)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1652544001:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.65/0.75 % TRYING [6]
% 1.65/0.75 % (4138002)Instruction limit reached!
% 1.65/0.75 % (4138002)------------------------------
% 1.65/0.75 % (4138002)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.65/0.75 % (4138002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/0.75 % (4138002)CaDiCaL version: 2.1.3
% 1.65/0.75 % (4138002)Termination reason: Instruction limit
% 1.65/0.75 % (4138002)Termination phase: Saturation
% 1.65/0.75 % (4138002)Time elapsed: 0.101 s
% 1.65/0.75 % (4138002)Peak memory usage: 14 MB
% 1.65/0.75 % (4138002)Instructions burned: 160 (million)
% 1.65/0.75 % (4138014)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=963268896:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.65/0.75 % (4138016)ott-21_1_sil=16000:fs=off:random_seed=2463208326:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.65/0.75 % TRYING [6]
% 1.65/0.75 % (4138012)Instruction limit reached!
% 1.65/0.75 % (4138012)------------------------------
% 1.65/0.75 % (4138012)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.65/0.75 % (4138012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/0.75 % (4138012)CaDiCaL version: 2.1.3
% 1.65/0.75 % (4138012)Termination reason: Instruction limit
% 1.65/0.75 % (4138012)Termination phase: Saturation
% 1.65/0.75 % (4138012)Time elapsed: 0.086 s
% 1.65/0.75 % (4138012)Peak memory usage: 12 MB
% 1.65/0.75 % (4138012)Instructions burned: 131 (million)
% 1.65/0.75 % (4138018)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=781943057:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 1.65/0.75 % TRYING [7]
% 1.65/0.75 % (4138010)Instruction limit reached!
% 1.65/0.75 % (4138010)------------------------------
% 1.65/0.75 % (4138010)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.65/0.75 % (4138010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/0.75 % (4138010)CaDiCaL version: 2.1.3
% 1.65/0.75 % (4138010)Termination reason: Instruction limit
% 1.65/0.75 % (4138010)Termination phase: Finite model building constraint generation
% 1.65/0.75 % (4138010)Time elapsed: 0.155 s
% 1.65/0.75 % (4138010)Peak memory usage: 32 MB
% 1.65/0.75 % (4138010)Instructions burned: 722 (million)
% 1.65/0.75 % (4138020)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1411067178:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 1.65/0.75 % TRYING [1]
% 1.65/0.75 % TRYING [2]
% 1.65/0.75 % TRYING [3]
% 1.65/0.75 % (4138016)Instruction limit reached!
% 1.65/0.75 % (4138016)------------------------------
% 1.65/0.75 % (4138016)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.65/0.75 % (4138016)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/0.75 % (4138016)CaDiCaL version: 2.1.3
% 1.65/0.75 % (4138016)Termination reason: Instruction limit
% 1.65/0.75 % (4138016)Termination phase: Saturation
% 1.65/0.75 % (4138016)Time elapsed: 0.098 s
% 1.65/0.75 % (4138016)Peak memory usage: 13 MB
% 1.65/0.75 % (4138016)Instructions burned: 183 (million)
% 1.65/0.75 % TRYING [4]
% 1.65/0.75 % (4138022)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=575060642:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 1.65/0.75 % (4138022) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4137991-4138022"...
% 1.65/0.75 % (4138022)...printing done.
% 1.65/0.75 % (4138022)Refutation found. Thanks to Tanya!
% 1.65/0.75 % SZS status Theorem for theBenchmark
% 1.65/0.75 % SZS output start Proof for theBenchmark
% See solution above
% 1.65/0.75 % (4138022)------------------------------
% 1.65/0.75 % (4138022)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.65/0.75 % (4138022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/0.75 % (4138022)CaDiCaL version: 2.1.3
% 1.65/0.75 % (4138022)Termination reason: Refutation
% 1.65/0.75 % (4138022)Time elapsed: 0.043 s
% 1.65/0.75 % (4138022)Peak memory usage: 12 MB
% 1.65/0.75 % (4138022)Instructions burned: 67 (million)
% 1.65/0.75 % (4137991)Success in time 0.327 s
% 1.65/0.75 % Vampire exiting
%------------------------------------------------------------------------------