%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU207+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 12:47:44 PM UTC 2026
% Result : Theorem 11.32s 2.57s
% Output : Refutation 12.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 16
% Syntax : Number of formulae : 137 ( 24 unt; 4 def)
% Number of atoms : 574 ( 62 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 760 ( 323 ~; 331 |; 75 &)
% ( 17 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 6 con; 0-4 aty)
% Number of variables : 392 ( 358 !; 34 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f8,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f11,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(f23,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f29,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(f31,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(f35,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f55,axiom,
! [X0,X1] :
( ( relation(X0)
& relation(X1) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f124,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,relation_dom(X2))
& in(ordered_pair(X3,X0),X2)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_relat_1) ).
fof(f128,conjecture,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_relat_1) ).
fof(f129,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f128]) ).
fof(f136,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X0,relation_dom(X2))
& in(X1,relation_rng(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f184,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f221,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,[],[f11]) ).
fof(f227,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f229,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f233,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) ) ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f239,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f55]) ).
fof(f240,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(flattening,[],[f239]) ).
fof(f296,plain,
! [X0,X1,X2] :
( ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,relation_dom(X2))
& in(ordered_pair(X3,X0),X2)
& in(X3,X1) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f124]) ).
fof(f300,plain,
? [X0] :
( ? [X1] :
( relation_rng(relation_composition(X0,X1)) != relation_image(X1,relation_rng(X0))
& relation(X1) )
& relation(X0) ),
inference(ennf_transformation,[],[f129]) ).
fof(f306,plain,
! [X0,X1,X2] :
( ( in(X0,relation_dom(X2))
& in(X1,relation_rng(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f136]) ).
fof(f307,plain,
! [X0,X1,X2] :
( ( in(X0,relation_dom(X2))
& in(X1,relation_rng(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(flattening,[],[f306]) ).
fof(f375,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f376,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f375]) ).
fof(f385,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,[],[f221]) ).
fof(f386,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,[],[f385]) ).
fof(f387,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ( ( ! [X4] :
( ~ in(ordered_pair(X4,sK6(X0,X1,X2)),X0)
| ~ in(X4,X1) )
| ~ in(sK6(X0,X1,X2),X2) )
& ( ( in(ordered_pair(sK7(X0,X1,X2),sK6(X0,X1,X2)),X0)
& in(sK7(X0,X1,X2),X1) )
| in(sK6(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(ordered_pair(X7,X6),X0)
| ~ in(X7,X1) ) )
& ( ( in(ordered_pair(sK8(X0,X1,X6),X6),X0)
& in(sK8(X0,X1,X6),X1) )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X3,sK6(X0,X1,X2)),skolemize(X5,sK7(X0,X1,X2)),skolemize(X8,sK8(X0,X1,X6))],[f386]) ).
fof(f421,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,[],[f227]) ).
fof(f422,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,[],[f421]) ).
fof(f423,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK29(X0,X1),X1)
& in(sK29(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(X2,sK29(X0,X1))],[f422]) ).
fof(f438,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,[],[f229]) ).
fof(f439,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,[],[f438]) ).
fof(f440,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK38(X0,X1)),X0)
| ~ in(sK38(X0,X1),X1) )
& ( in(ordered_pair(sK39(X0,X1),sK38(X0,X1)),X0)
| in(sK38(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK40(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38,sK39,sK40]),skolemize(X2,sK38(X0,X1)),skolemize(X4,sK39(X0,X1)),skolemize(X7,sK40(X0,X5))],[f439]) ).
fof(f445,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) ) )
& ( ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f233]) ).
fof(f446,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X6] :
( in(ordered_pair(X3,X6),X0)
& in(ordered_pair(X6,X4),X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1) ) )
& ( ? [X10] :
( in(ordered_pair(X7,X10),X0)
& in(ordered_pair(X10,X8),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f445]) ).
fof(f447,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ( ( ! [X5] :
( ~ in(ordered_pair(sK43(X0,X1,X2),X5),X0)
| ~ in(ordered_pair(X5,sK44(X0,X1,X2)),X1) )
| ~ in(ordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK43(X0,X1,X2),sK45(X0,X1,X2)),X0)
& in(ordered_pair(sK45(X0,X1,X2),sK44(X0,X1,X2)),X1) )
| in(ordered_pair(sK43(X0,X1,X2),sK44(X0,X1,X2)),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1) ) )
& ( ( in(ordered_pair(X7,sK46(X0,X1,X7,X8)),X0)
& in(ordered_pair(sK46(X0,X1,X7,X8),X8),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43,sK44,sK45,sK46]),skolemize(X3,sK43(X0,X1,X2)),skolemize(X4,sK44(X0,X1,X2)),skolemize(X6,sK45(X0,X1,X2)),skolemize(X10,sK46(X0,X1,X7,X8))],[f446]) ).
fof(f471,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(X3,relation_dom(X2))
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,X1) ) )
& ( ? [X3] :
( in(X3,relation_dom(X2))
& in(ordered_pair(X3,X0),X2)
& in(X3,X1) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f296]) ).
fof(f472,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(X3,relation_dom(X2))
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,X1) ) )
& ( ? [X4] :
( in(X4,relation_dom(X2))
& in(ordered_pair(X4,X0),X2)
& in(X4,X1) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(rectify,[],[f471]) ).
fof(f473,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(X3,relation_dom(X2))
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,X1) ) )
& ( ( in(sK57(X0,X1,X2),relation_dom(X2))
& in(ordered_pair(sK57(X0,X1,X2),X0),X2)
& in(sK57(X0,X1,X2),X1) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(X4,sK57(X0,X1,X2))],[f472]) ).
fof(f474,plain,
( relation_rng(relation_composition(sK58,sK59)) != relation_image(sK59,relation_rng(sK58))
& relation(sK59)
& relation(sK58) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58,sK59]),skolemize(X0,sK58),skolemize(X1,sK59)],[f300]) ).
fof(f499,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f510,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f376]) ).
fof(f525,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,[],[f387]) ).
fof(f582,plain,
! [X0,X1] :
( in(sK29(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f423]) ).
fof(f583,plain,
! [X0,X1] :
( ~ in(sK29(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f423]) ).
fof(f607,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK40(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f440]) ).
fof(f612,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f31]) ).
fof(f620,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(sK46(X0,X1,X7,X8),X8),X1)
| ~ in(ordered_pair(X7,X8),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f447]) ).
fof(f621,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(X7,sK46(X0,X1,X7,X8)),X0)
| ~ in(ordered_pair(X7,X8),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f447]) ).
fof(f622,plain,
! [X2,X0,X1,X8,X9,X7] :
( in(ordered_pair(X7,X8),X2)
| ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f447]) ).
fof(f635,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f240]) ).
fof(f725,plain,
! [X2,X0,X1] :
( in(sK57(X0,X1,X2),X1)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f473]) ).
fof(f726,plain,
! [X2,X0,X1] :
( in(ordered_pair(sK57(X0,X1,X2),X0),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f473]) ).
fof(f732,plain,
relation(sK58),
inference(cnf_transformation,[],[f474]) ).
fof(f733,plain,
relation(sK59),
inference(cnf_transformation,[],[f474]) ).
fof(f734,plain,
relation_rng(relation_composition(sK58,sK59)) != relation_image(sK59,relation_rng(sK58)),
inference(cnf_transformation,[],[f474]) ).
fof(f741,plain,
! [X2,X0,X1] :
( in(X1,relation_rng(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f307]) ).
fof(f810,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f184]) ).
fof(f839,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f612,f810]) ).
fof(f861,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),X0)
| ~ in(X7,X1)
| relation_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f525,f839]) ).
fof(f893,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(sK40(X0,X5),X5),unordered_pair(sK40(X0,X5),sK40(X0,X5))),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f607,f839]) ).
fof(f903,plain,
! [X2,X0,X1,X8,X9,X7] :
( in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ in(unordered_pair(unordered_pair(X7,X9),unordered_pair(X7,X7)),X0)
| ~ in(unordered_pair(unordered_pair(X9,X8),unordered_pair(X9,X9)),X1)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f622,f839,f839,f839]) ).
fof(f904,plain,
! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,sK46(X0,X1,X7,X8)),unordered_pair(X7,X7)),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f621,f839,f839]) ).
fof(f905,plain,
! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(sK46(X0,X1,X7,X8),X8),unordered_pair(sK46(X0,X1,X7,X8),sK46(X0,X1,X7,X8))),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f620,f839,f839]) ).
fof(f928,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK57(X0,X1,X2),X0),unordered_pair(sK57(X0,X1,X2),sK57(X0,X1,X2))),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(definition_unfolding,[],[f726,f839]) ).
fof(f934,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| in(X1,relation_rng(X2))
| ~ relation(X2) ),
inference(definition_unfolding,[],[f741,f839]) ).
fof(f972,plain,
! [X0,X1,X6,X7] :
( ~ in(unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),X0)
| in(X6,relation_image(X0,X1))
| ~ in(X7,X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f861]) ).
fof(f1015,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(sK40(X0,X5),X5),unordered_pair(sK40(X0,X5),sK40(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f893]) ).
fof(f1018,plain,
! [X0,X1,X8,X9,X7] :
( in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),relation_composition(X0,X1))
| ~ in(unordered_pair(unordered_pair(X7,X9),unordered_pair(X7,X7)),X0)
| ~ in(unordered_pair(unordered_pair(X9,X8),unordered_pair(X9,X9)),X1)
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f903]) ).
fof(f1019,plain,
! [X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,sK46(X0,X1,X7,X8)),unordered_pair(X7,X7)),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f904]) ).
fof(f1020,plain,
! [X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(sK46(X0,X1,X7,X8),X8),unordered_pair(sK46(X0,X1,X7,X8),sK46(X0,X1,X7,X8))),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f905]) ).
fof(f1027,definition,
sF67 = relation_composition(sK58,sK59),
introduced(definition,[new_symbols(definition,[sF67])],[function_definition]) ).
fof(f1028,plain,
relation_composition(sK58,sK59) = sF67,
inference(reorient_equations,[],[f1027]) ).
fof(f1029,definition,
sF68 = relation_rng(sF67),
introduced(definition,[new_symbols(definition,[sF68])],[function_definition]) ).
fof(f1030,plain,
relation_rng(sF67) = sF68,
inference(reorient_equations,[],[f1029]) ).
fof(f1031,definition,
sF69 = relation_rng(sK58),
introduced(definition,[new_symbols(definition,[sF69])],[function_definition]) ).
fof(f1032,plain,
relation_rng(sK58) = sF69,
inference(reorient_equations,[],[f1031]) ).
fof(f1033,definition,
sF70 = relation_image(sK59,sF69),
introduced(definition,[new_symbols(definition,[sF70])],[function_definition]) ).
fof(f1034,plain,
relation_image(sK59,sF69) = sF70,
inference(reorient_equations,[],[f1033]) ).
fof(f1035,plain,
sF68 != sF70,
inference(definition_folding,[],[f734,f1034,f1032,f1030,f1028]) ).
fof(f1042,plain,
! [X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(sK46(X0,X1,X7,X8),X8),unordered_pair(sK46(X0,X1,X7,X8),sK46(X0,X1,X7,X8))),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f1020,f635]) ).
fof(f1043,plain,
! [X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,sK46(X0,X1,X7,X8)),unordered_pair(X7,X7)),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f1019,f635]) ).
fof(f1044,plain,
! [X0,X1,X8,X9,X7] :
( ~ in(unordered_pair(unordered_pair(X9,X8),unordered_pair(X9,X9)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X9),unordered_pair(X7,X7)),X0)
| in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f1018,f635]) ).
fof(f1057,plain,
! [X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X8,sK46(X0,X1,X7,X8)),unordered_pair(sK46(X0,X1,X7,X8),sK46(X0,X1,X7,X8))),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f1042,f499]) ).
fof(f1058,plain,
! [X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,X7),unordered_pair(X7,sK46(X0,X1,X7,X8))),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f1043,f499]) ).
fof(f1082,plain,
( relation(sF67)
| ~ relation(sK58)
| ~ relation(sK59) ),
inference(superposition,[],[f635,f1028]) ).
fof(f1083,plain,
( relation(sF67)
| ~ relation(sK59) ),
inference(forward_subsumption_resolution,[],[f1082,f732]) ).
fof(f1084,plain,
relation(sF67),
inference(forward_subsumption_resolution,[],[f1083,f733]) ).
fof(f1111,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(unordered_pair(X0,sK57(X1,X2,X3)),unordered_pair(X0,X0)),X4)
| in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(X4,X3))
| ~ relation(X3)
| ~ relation(X4)
| ~ in(X1,relation_image(X3,X2))
| ~ relation(X3) ),
inference(resolution,[],[f1044,f928]) ).
fof(f1113,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(unordered_pair(X0,sK57(X1,X2,X3)),unordered_pair(X0,X0)),X4)
| in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(X4,X3))
| ~ relation(X3)
| ~ relation(X4)
| ~ in(X1,relation_image(X3,X2)) ),
inference(duplicate_literal_removal,[],[f1111]) ).
fof(f1117,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(sK40(X0,sK57(X1,X2,X3)),X1),unordered_pair(sK40(X0,sK57(X1,X2,X3)),sK40(X0,sK57(X1,X2,X3)))),relation_composition(X0,X3))
| ~ relation(X3)
| ~ relation(X0)
| ~ in(X1,relation_image(X3,X2))
| ~ in(sK57(X1,X2,X3),relation_rng(X0))
| ~ relation(X0) ),
inference(resolution,[],[f1113,f1015]) ).
fof(f1121,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(sK40(X0,sK57(X1,X2,X3)),X1),unordered_pair(sK40(X0,sK57(X1,X2,X3)),sK40(X0,sK57(X1,X2,X3)))),relation_composition(X0,X3))
| ~ relation(X3)
| ~ relation(X0)
| ~ in(X1,relation_image(X3,X2))
| ~ in(sK57(X1,X2,X3),relation_rng(X0)) ),
inference(duplicate_literal_removal,[],[f1117]) ).
fof(f1124,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X1,sK40(X0,sK57(X1,X2,X3))),unordered_pair(sK40(X0,sK57(X1,X2,X3)),sK40(X0,sK57(X1,X2,X3)))),relation_composition(X0,X3))
| ~ relation(X3)
| ~ relation(X0)
| ~ in(X1,relation_image(X3,X2))
| ~ in(sK57(X1,X2,X3),relation_rng(X0)) ),
inference(forward_demodulation,[],[f1121,f499]) ).
fof(f1152,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK40(sK58,sK57(X0,X1,sK59))),unordered_pair(sK40(sK58,sK57(X0,X1,sK59)),sK40(sK58,sK57(X0,X1,sK59)))),sF67)
| ~ relation(sK59)
| ~ relation(sK58)
| ~ in(X0,relation_image(sK59,X1))
| ~ in(sK57(X0,X1,sK59),relation_rng(sK58)) ),
inference(superposition,[],[f1124,f1028]) ).
fof(f1153,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK40(sK58,sK57(X0,X1,sK59))),unordered_pair(sK40(sK58,sK57(X0,X1,sK59)),sK40(sK58,sK57(X0,X1,sK59)))),sF67)
| ~ relation(sK58)
| ~ in(X0,relation_image(sK59,X1))
| ~ in(sK57(X0,X1,sK59),relation_rng(sK58)) ),
inference(forward_subsumption_resolution,[],[f1152,f733]) ).
fof(f1154,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK40(sK58,sK57(X0,X1,sK59))),unordered_pair(sK40(sK58,sK57(X0,X1,sK59)),sK40(sK58,sK57(X0,X1,sK59)))),sF67)
| ~ in(X0,relation_image(sK59,X1))
| ~ in(sK57(X0,X1,sK59),relation_rng(sK58)) ),
inference(forward_subsumption_resolution,[],[f1153,f732]) ).
fof(f1155,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK40(sK58,sK57(X0,X1,sK59))),unordered_pair(sK40(sK58,sK57(X0,X1,sK59)),sK40(sK58,sK57(X0,X1,sK59)))),sF67)
| ~ in(sK57(X0,X1,sK59),sF69)
| ~ in(X0,relation_image(sK59,X1)) ),
inference(forward_demodulation,[],[f1154,f1032]) ).
fof(f1227,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),X2)
| in(X0,relation_image(X2,X3))
| ~ in(X1,X3)
| ~ relation(X2) ),
inference(superposition,[],[f972,f499]) ).
fof(f1228,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),X2)
| in(X0,relation_rng(X2))
| ~ relation(X2) ),
inference(superposition,[],[f934,f499]) ).
fof(f1234,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),X2)
| in(X1,relation_rng(X2))
| ~ relation(X2) ),
inference(superposition,[],[f934,f499]) ).
fof(f1253,plain,
! [X0,X1] :
( in(X0,relation_rng(sF67))
| ~ relation(sF67)
| ~ in(sK57(X0,X1,sK59),sF69)
| ~ in(X0,relation_image(sK59,X1)) ),
inference(resolution,[],[f1228,f1155]) ).
fof(f1268,plain,
! [X0,X1] :
( in(X0,relation_rng(sF67))
| ~ in(sK57(X0,X1,sK59),sF69)
| ~ in(X0,relation_image(sK59,X1)) ),
inference(forward_subsumption_resolution,[],[f1253,f1084]) ).
fof(f1284,plain,
! [X0,X1] :
( ~ in(sK57(X0,X1,sK59),sF69)
| in(X0,sF68)
| ~ in(X0,relation_image(sK59,X1)) ),
inference(forward_demodulation,[],[f1268,f1030]) ).
fof(f1300,plain,
! [X0] :
( in(X0,sF68)
| ~ in(X0,relation_image(sK59,sF69))
| ~ in(X0,relation_image(sK59,sF69))
| ~ relation(sK59) ),
inference(resolution,[],[f1284,f725]) ).
fof(f1301,plain,
! [X0] :
( in(X0,sF68)
| ~ in(X0,relation_image(sK59,sF69))
| ~ relation(sK59) ),
inference(duplicate_literal_removal,[],[f1300]) ).
fof(f1302,plain,
! [X0] :
( in(X0,sF68)
| ~ in(X0,relation_image(sK59,sF69)) ),
inference(forward_subsumption_resolution,[],[f1301,f733]) ).
fof(f1303,plain,
! [X0] :
( ~ in(X0,sF70)
| in(X0,sF68) ),
inference(forward_demodulation,[],[f1302,f1034]) ).
fof(f1310,plain,
! [X0] :
( in(sK29(sF70,X0),sF68)
| subset(sF70,X0) ),
inference(resolution,[],[f1303,f582]) ).
fof(f1339,plain,
( subset(sF70,sF68)
| subset(sF70,sF68) ),
inference(resolution,[],[f1310,f583]) ).
fof(f1340,plain,
subset(sF70,sF68),
inference(duplicate_literal_removal,[],[f1339]) ).
fof(f1341,plain,
( ~ subset(sF68,sF70)
| sF68 = sF70 ),
inference(resolution,[],[f1340,f510]) ).
fof(f1342,plain,
~ subset(sF68,sF70),
inference(forward_subsumption_resolution,[],[f1341,f1035]) ).
fof(f1347,plain,
! [X2,X3,X0,X1] :
( in(sK46(X0,X1,X2,X3),relation_rng(X0))
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[],[f1234,f1058]) ).
fof(f1353,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),relation_composition(X0,X1))
| ~ relation(X0)
| in(sK46(X0,X1,X2,X3),relation_rng(X0))
| ~ relation(X1) ),
inference(duplicate_literal_removal,[],[f1347]) ).
fof(f1373,plain,
! [X2,X3,X0,X1,X4] :
( in(X0,relation_image(X1,X2))
| ~ in(sK46(X3,X1,X4,X0),X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X4,X0),unordered_pair(X4,X4)),relation_composition(X3,X1))
| ~ relation(X1)
| ~ relation(X3) ),
inference(resolution,[],[f1227,f1057]) ).
fof(f1397,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(unordered_pair(X4,X0),unordered_pair(X4,X4)),relation_composition(X3,X1))
| ~ in(sK46(X3,X1,X4,X0),X2)
| ~ relation(X1)
| in(X0,relation_image(X1,X2))
| ~ relation(X3) ),
inference(duplicate_literal_removal,[],[f1373]) ).
fof(f1423,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sF67)
| ~ in(sK46(sK58,sK59,X0,X1),X2)
| ~ relation(sK59)
| in(X1,relation_image(sK59,X2))
| ~ relation(sK58) ),
inference(superposition,[],[f1397,f1028]) ).
fof(f1424,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sF67)
| ~ in(sK46(sK58,sK59,X0,X1),X2)
| in(X1,relation_image(sK59,X2))
| ~ relation(sK58) ),
inference(forward_subsumption_resolution,[],[f1423,f733]) ).
fof(f1428,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sF67)
| ~ in(sK46(sK58,sK59,X0,X1),X2)
| in(X1,relation_image(sK59,X2)) ),
inference(forward_subsumption_resolution,[],[f1424,f732]) ).
fof(f1430,plain,
! [X0,X1] :
( ~ in(sK46(sK58,sK59,sK40(sF67,X0),X0),X1)
| in(X0,relation_image(sK59,X1))
| ~ in(X0,relation_rng(sF67))
| ~ relation(sF67) ),
inference(resolution,[],[f1428,f1015]) ).
fof(f1437,plain,
! [X0,X1] :
( ~ in(sK46(sK58,sK59,sK40(sF67,X0),X0),X1)
| in(X0,relation_image(sK59,X1))
| ~ in(X0,relation_rng(sF67)) ),
inference(forward_subsumption_resolution,[],[f1430,f1084]) ).
fof(f1439,plain,
! [X0,X1] :
( ~ in(sK46(sK58,sK59,sK40(sF67,X0),X0),X1)
| ~ in(X0,sF68)
| in(X0,relation_image(sK59,X1)) ),
inference(forward_demodulation,[],[f1437,f1030]) ).
fof(f1623,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sF67)
| ~ relation(sK58)
| in(sK46(sK58,sK59,X0,X1),relation_rng(sK58))
| ~ relation(sK59) ),
inference(superposition,[],[f1353,f1028]) ).
fof(f1624,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sF67)
| in(sK46(sK58,sK59,X0,X1),relation_rng(sK58))
| ~ relation(sK59) ),
inference(forward_subsumption_resolution,[],[f1623,f732]) ).
fof(f1628,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sF67)
| in(sK46(sK58,sK59,X0,X1),relation_rng(sK58)) ),
inference(forward_subsumption_resolution,[],[f1624,f733]) ).
fof(f1629,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sF67)
| in(sK46(sK58,sK59,X0,X1),sF69) ),
inference(forward_demodulation,[],[f1628,f1032]) ).
fof(f1631,plain,
! [X0] :
( in(sK46(sK58,sK59,sK40(sF67,X0),X0),sF69)
| ~ in(X0,relation_rng(sF67))
| ~ relation(sF67) ),
inference(resolution,[],[f1629,f1015]) ).
fof(f1638,plain,
! [X0] :
( in(sK46(sK58,sK59,sK40(sF67,X0),X0),sF69)
| ~ in(X0,relation_rng(sF67)) ),
inference(forward_subsumption_resolution,[],[f1631,f1084]) ).
fof(f1640,plain,
! [X0] :
( in(sK46(sK58,sK59,sK40(sF67,X0),X0),sF69)
| ~ in(X0,sF68) ),
inference(forward_demodulation,[],[f1638,f1030]) ).
fof(f1641,plain,
! [X0] :
( ~ in(X0,sF68)
| ~ in(X0,sF68)
| in(X0,relation_image(sK59,sF69)) ),
inference(resolution,[],[f1640,f1439]) ).
fof(f1642,plain,
! [X0] :
( ~ in(X0,sF68)
| in(X0,relation_image(sK59,sF69)) ),
inference(duplicate_literal_removal,[],[f1641]) ).
fof(f1643,plain,
! [X0] :
( ~ in(X0,sF68)
| in(X0,sF70) ),
inference(forward_demodulation,[],[f1642,f1034]) ).
fof(f1654,plain,
! [X0] :
( in(sK29(sF68,X0),sF70)
| subset(sF68,X0) ),
inference(resolution,[],[f1643,f582]) ).
fof(f1686,plain,
( subset(sF68,sF70)
| subset(sF68,sF70) ),
inference(resolution,[],[f1654,f583]) ).
fof(f1688,plain,
subset(sF68,sF70),
inference(duplicate_literal_removal,[],[f1686]) ).
fof(f1689,plain,
$false,
inference(forward_subsumption_resolution,[],[f1688,f1342]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU207+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n019.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % 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 04:03:18 UTC 2026
% 0.14/0.38 % CPUTime :
% 0.14/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.32/2.57 % (3647269)Detected formulas, will run a generic FOF schedule.
% 11.32/2.57 % (3647280)dis-21_1_sil=8000:lcm=predicate:random_seed=1895853236: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)
% 11.32/2.57 % (3647279)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1732101416:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 11.32/2.57 % (3647276)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=1632908314:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 11.32/2.57 % (3647275)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=1945000933:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 11.32/2.57 % (3647278)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1728575896:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 11.32/2.57 % (3647277)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3828718924:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 11.32/2.57 % (3647274)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=2592953298:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 11.32/2.57 % (3647280)Instruction limit reached!
% 11.32/2.57 % (3647280)------------------------------
% 11.32/2.57 % (3647280)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.32/2.57 % (3647280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.32/2.57 % (3647280)CaDiCaL version: 2.1.3
% 11.32/2.57 % (3647280)Termination reason: Instruction limit
% 11.32/2.57 % (3647280)Termination phase: Saturation
% 11.32/2.57 % (3647280)Time elapsed: 0.041 s
% 11.32/2.57 % (3647280)Peak memory usage: 90 MB
% 11.32/2.57 % (3647280)Instructions burned: 130 (million)
% 11.32/2.57 % (3647277)Instruction limit reached!
% 11.32/2.57 % (3647277)------------------------------
% 11.32/2.57 % (3647277)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.32/2.57 % (3647277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.32/2.57 % (3647277)CaDiCaL version: 2.1.3
% 11.32/2.57 % (3647277)Termination reason: Instruction limit
% 11.32/2.57 % (3647277)Termination phase: Saturation
% 11.32/2.57 % (3647277)Time elapsed: 0.072 s
% 11.32/2.57 % (3647277)Peak memory usage: 90 MB
% 11.32/2.57 % (3647277)Instructions burned: 109 (million)
% 11.32/2.57 % (3647278)Instruction limit reached!
% 11.32/2.57 % (3647278)------------------------------
% 11.32/2.57 % (3647278)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.32/2.57 % (3647278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.32/2.57 % (3647278)CaDiCaL version: 2.1.3
% 11.32/2.57 % (3647278)Termination reason: Instruction limit
% 11.32/2.57 % (3647278)Termination phase: Saturation
% 11.32/2.57 % (3647278)Time elapsed: 0.080 s
% 11.32/2.57 % (3647278)Peak memory usage: 89 MB
% 11.32/2.57 % (3647278)Instructions burned: 121 (million)
% 11.32/2.57 % (3647279)Instruction limit reached!
% 11.32/2.57 % (3647279)------------------------------
% 11.32/2.57 % (3647279)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.32/2.57 % (3647279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.32/2.57 % (3647279)CaDiCaL version: 2.1.3
% 11.32/2.57 % (3647279)Termination reason: Instruction limit
% 11.32/2.57 % (3647279)Termination phase: Saturation
% 11.32/2.57 % (3647279)Time elapsed: 0.096 s
% 11.32/2.57 % (3647279)Peak memory usage: 90 MB
% 11.32/2.57 % (3647279)Instructions burned: 140 (million)
% 11.32/2.57 % (3647288)lrs+10_1_sil=8000:sp=occurrence:random_seed=2921493142:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 11.32/2.57 % (3647289)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3061019697:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 11.32/2.57 % (3647288)Instruction limit reached!
% 11.32/2.57 % (3647288)------------------------------
% 11.32/2.57 % (3647288)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.32/2.57 % (3647288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.32/2.57 % (3647288)CaDiCaL version: 2.1.3
% 11.32/2.57 % (3647288)Termination reason: Instruction limit
% 11.32/2.57 % (3647288)Termination phase: Saturation
% 11.32/2.57 % (3647288)Time elapsed: 0.102 s
% 11.32/2.57 % (3647288)Peak memory usage: 93 MB
% 11.32/2.57 % (3647288)Instructions burned: 286 (million)
% 11.32/2.57 % (3647290)lrs+1011_1_sil=32000:sp=occurrence:random_seed=430785339:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 11.32/2.57 % (3647291)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3017463479:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 11.32/2.57 % (3647289)Instruction limit reached!
% 11.32/2.57 % (3647289)------------------------------
% 11.32/2.57 % (3647289)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.32/2.57 % (3647289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.32/2.57 % (3647289)CaDiCaL version: 2.1.3
% 11.32/2.57 % (3647289)Termination reason: Instruction limit
% 11.32/2.57 % (3647289)Termination phase: Saturation
% 11.32/2.57 % (3647289)Time elapsed: 0.076 s
% 11.32/2.57 % (3647289)Peak memory usage: 91 MB
% 11.32/2.57 % (3647289)Instructions burned: 159 (million)
% 11.32/2.57 % (3647295)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=516995751:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 11.32/2.57 % (3647291)Instruction limit reached!
% 11.32/2.57 % (3647291)------------------------------
% 11.32/2.57 % (3647291)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.32/2.57 % (3647291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.32/2.57 % (3647291)CaDiCaL version: 2.1.3
% 11.32/2.57 % (3647291)Termination reason: Instruction limit
% 11.32/2.57 % (3647291)Termination phase: Saturation
% 11.32/2.57 % (3647291)Time elapsed: 0.139 s
% 11.32/2.57 % (3647291)Peak memory usage: 94 MB
% 11.32/2.57 % (3647291)Instructions burned: 250 (million)
% 11.32/2.57 % (3647295)Instruction limit reached!
% 11.32/2.57 % (3647295)------------------------------
% 11.32/2.57 % (3647295)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.32/2.57 % (3647295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.32/2.57 % (3647295)CaDiCaL version: 2.1.3
% 11.32/2.57 % (3647295)Termination reason: Instruction limit
% 11.32/2.57 % (3647295)Termination phase: Saturation
% 11.32/2.57 % (3647295)Time elapsed: 0.097 s
% 11.32/2.57 % (3647295)Peak memory usage: 90 MB
% 11.32/2.57 % (3647295)Instructions burned: 295 (million)
% 11.32/2.57 % (3647290)Instruction limit reached!
% 11.32/2.57 % (3647290)------------------------------
% 11.32/2.57 % (3647290)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.32/2.57 % (3647290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.32/2.57 % (3647290)CaDiCaL version: 2.1.3
% 11.32/2.57 % (3647290)Termination reason: Instruction limit
% 11.32/2.57 % (3647290)Termination phase: Saturation
% 11.32/2.57 % (3647290)Time elapsed: 0.220 s
% 11.32/2.57 % (3647290)Peak memory usage: 93 MB
% 11.32/2.57 % (3647290)Instructions burned: 326 (million)
% 11.32/2.57 % (3647297)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1274251315:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 11.32/2.57 % (3647299)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1728164659:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 11.32/2.57 % (3647300)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2965061324:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 11.32/2.57 % (3647300)Instruction limit reached!
% 11.32/2.57 % (3647300)------------------------------
% 11.32/2.57 % (3647300)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.32/2.57 % (3647300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.32/2.57 % (3647300)CaDiCaL version: 2.1.3
% 11.32/2.57 % (3647300)Termination reason: Instruction limit
% 11.32/2.57 % (3647300)Termination phase: Saturation
% 11.32/2.57 % (3647300)Time elapsed: 0.036 s
% 11.32/2.57 % (3647300)Peak memory usage: 90 MB
% 11.32/2.57 % (3647300)Instructions burned: 131 (million)
% 11.32/2.57 % (3647302)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=164525474:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 11.32/2.57 % (3647299)Instruction limit reached!
% 11.32/2.57 % (3647299)------------------------------
% 11.32/2.57 % (3647299)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.32/2.57 % (3647299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.32/2.57 % (3647299)CaDiCaL version: 2.1.3
% 11.32/2.57 % (3647299)Termination reason: Instruction limit
% 11.32/2.57 % (3647299)Termination phase: Saturation
% 11.32/2.57 % (3647299)Time elapsed: 0.069 s
% 11.32/2.57 % (3647299)Peak memory usage: 90 MB
% 11.32/2.57 % (3647299)Instructions burned: 113 (million)
% 11.32/2.57 % (3647302)Instruction limit reached!
% 11.32/2.57 % (3647302)------------------------------
% 11.32/2.57 % (3647302)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.32/2.57 % (3647302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.32/2.57 % (3647302)CaDiCaL version: 2.1.3
% 11.32/2.57 % (3647302)Termination reason: Instruction limit
% 11.32/2.57 % (3647302)Termination phase: Saturation
% 11.32/2.57 % (3647302)Time elapsed: 0.068 s
% 11.32/2.57 % (3647302)Peak memory usage: 89 MB
% 11.32/2.57 % (3647302)Instructions burned: 115 (million)
% 11.32/2.57 % (3647306)lrs+10_1_sil=8000:sp=occurrence:random_seed=1898518005:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 11.32/2.57 % (3647307)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3841894320:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 11.32/2.57 % (3647308)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3035977418:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 11.32/2.57 % (3647306)Instruction limit reached!
% 11.32/2.57 % (3647306)------------------------------
% 11.32/2.57 % (3647306)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.32/2.57 % (3647306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.32/2.57 % (3647306)CaDiCaL version: 2.1.3
% 11.32/2.57 % (3647306)Termination reason: Instruction limit
% 11.32/2.57 % (3647306)Termination phase: Saturation
% 11.32/2.57 % (3647306)Time elapsed: 0.302 s
% 11.32/2.57 % (3647306)Peak memory usage: 100 MB
% 11.32/2.57 % (3647306)Instructions burned: 909 (million)
% 11.32/2.57 % (3647307)Instruction limit reached!
% 11.32/2.57 % (3647307)------------------------------
% 11.32/2.57 % (3647307)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.32/2.57 % (3647307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.32/2.57 % (3647307)CaDiCaL version: 2.1.3
% 11.32/2.57 % (3647307)Termination reason: Instruction limit
% 11.32/2.57 % (3647307)Termination phase: Saturation
% 11.32/2.57 % (3647307)Time elapsed: 0.281 s
% 11.32/2.57 % (3647307)Peak memory usage: 93 MB
% 11.32/2.57 % (3647307)Instructions burned: 437 (million)
% 11.32/2.57 % (3647312)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=4057501417:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 11.32/2.57 % (3647312)Instruction limit reached!
% 11.32/2.57 % (3647312)------------------------------
% 11.32/2.57 % (3647312)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.32/2.57 % (3647312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.32/2.57 % (3647312)CaDiCaL version: 2.1.3
% 11.32/2.57 % (3647312)Termination reason: Instruction limit
% 11.32/2.57 % (3647312)Termination phase: Saturation
% 11.32/2.57 % (3647312)Time elapsed: 0.044 s
% 11.32/2.57 % (3647312)Peak memory usage: 92 MB
% 11.32/2.57 % (3647312)Instructions burned: 134 (million)
% 11.32/2.57 % (3647313)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=427741780:st=8:i=592:sd=3:ep=RST:ss=axioms_2987 on theBenchmark for (2987ds/592Mi)
% 11.32/2.57 % (3647297)First to succeed.
% 11.32/2.57 % (3647297)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3647269"
% 11.32/2.57 % (3647274)Also succeeded, but the first one will report.
% 11.32/2.57 % (3647315)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=672401961:st=3:i=13193:sd=3:ss=axioms_2986 on theBenchmark for (2986ds/13193Mi)
% 11.32/2.57 % (3647297)Refutation found. Thanks to Tanya!
% 11.32/2.57 % SZS status Theorem for theBenchmark
% 11.32/2.57 % SZS output start Proof for theBenchmark
% See solution above
% 12.55/2.77 % (3647297)------------------------------
% 12.55/2.77 % (3647297)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.55/2.77 % (3647297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.55/2.77 % (3647297)CaDiCaL version: 2.1.3
% 12.55/2.77 % (3647297)Termination reason: Refutation
% 12.55/2.77 % (3647297)Time elapsed: 0.804 s
% 12.55/2.77 % (3647297)Peak memory usage: 133 MB
% 12.55/2.77 % (3647297)Instructions burned: 1221 (million)
% 12.55/2.77 % (3647297)------------------------------
% 12.55/2.77 % (3647297)------------------------------
% 12.55/2.77 % (3647269)Success in time 1.701 s
% 12.55/2.77 % Vampire exiting
%------------------------------------------------------------------------------