%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU228+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 : n009.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 12:47:52 PM UTC 2026
% Result : Theorem 6.13s 1.86s
% Output : Refutation 7.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 124 ( 20 unt; 4 def)
% Number of atoms : 514 ( 105 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 634 ( 244 ~; 260 |; 94 &)
% ( 25 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 2 con; 0-3 aty)
% Number of variables : 236 ( 0 sgn 209 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f10,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f12,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).
fof(f14,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f28,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f35,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f145,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f150,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_funct_1) ).
fof(f154,conjecture,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( subset(X0,relation_rng(X1))
=> relation_image(X1,relation_inverse_image(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_funct_1) ).
fof(f155,negated_conjecture,
~ ! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( subset(X0,relation_rng(X1))
=> relation_image(X1,relation_inverse_image(X1,X0)) = X0 ) ),
inference(negated_conjecture,[status(cth)],[f154]) ).
fof(f189,axiom,
! [X0,X1] : set_union2(X0,set_difference(X1,X0)) = set_union2(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(f199,axiom,
! [X0,X1] :
( subset(X0,X1)
=> X1 = set_union2(X0,set_difference(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_xboole_1) ).
fof(f264,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f265,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f264]) ).
fof(f267,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f268,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f267]) ).
fof(f276,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f280,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f281,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f280]) ).
fof(f360,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f145]) ).
fof(f366,plain,
! [X0,X1] :
( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f150]) ).
fof(f367,plain,
! [X0,X1] :
( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f366]) ).
fof(f372,plain,
? [X0,X1] :
( relation_image(X1,relation_inverse_image(X1,X0)) != X0
& subset(X0,relation_rng(X1))
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f155]) ).
fof(f373,plain,
? [X0,X1] :
( relation_image(X1,relation_inverse_image(X1,X0)) != X0
& subset(X0,relation_rng(X1))
& relation(X1)
& function(X1) ),
inference(flattening,[],[f372]) ).
fof(f415,plain,
! [X0,X1] :
( X1 = set_union2(X0,set_difference(X1,X0))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f199]) ).
fof(f480,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f481,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f480]) ).
fof(f486,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != X3 )
| ~ in(X3,X2) )
& ( ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != X3 ) )
& ( ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) )
| ~ in(X3,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f265]) ).
fof(f487,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != X3 )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,relation_dom(X0))
& in(X5,X1)
& apply(X0,X5) = X3 )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| apply(X0,X7) != X6 ) )
& ( ? [X8] :
( in(X8,relation_dom(X0))
& in(X8,X1)
& apply(X0,X8) = X6 )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f486]) ).
fof(f488,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ( ( ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != sK4(X0,X1,X2) )
| ~ in(sK4(X0,X1,X2),X2) )
& ( ( in(sK5(X0,X1,X2),relation_dom(X0))
& in(sK5(X0,X1,X2),X1)
& sK4(X0,X1,X2) = apply(X0,sK5(X0,X1,X2)) )
| in(sK4(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| apply(X0,X7) != X6 ) )
& ( ( in(sK6(X0,X1,X6),relation_dom(X0))
& in(sK6(X0,X1,X6),X1)
& apply(X0,sK6(X0,X1,X6)) = X6 )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X3,sK4(X0,X1,X2)),skolemize(X5,sK5(X0,X1,X2)),skolemize(X8,sK6(X0,X1,X6))],[f487]) ).
fof(f493,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f268]) ).
fof(f494,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f493]) ).
fof(f495,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1) )
& ( ( in(X4,relation_dom(X0))
& in(apply(X0,X4),X1) )
| ~ in(X4,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f494]) ).
fof(f496,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ( ( ~ in(sK9(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK9(X0,X1,X2)),X1)
| ~ in(sK9(X0,X1,X2),X2) )
& ( ( in(sK9(X0,X1,X2),relation_dom(X0))
& in(apply(X0,sK9(X0,X1,X2)),X1) )
| in(sK9(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1) )
& ( ( in(X4,relation_dom(X0))
& in(apply(X0,X4),X1) )
| ~ in(X4,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X3,sK9(X0,X1,X2))],[f495]) ).
fof(f536,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,[],[f276]) ).
fof(f537,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,[],[f536]) ).
fof(f538,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK36(X0,X1),X1)
& in(sK36(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(X2,sK36(X0,X1))],[f537]) ).
fof(f554,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) )
& ( ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f281]) ).
fof(f555,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,relation_dom(X0))
& apply(X0,X4) = X2 )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ? [X7] :
( in(X7,relation_dom(X0))
& apply(X0,X7) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f554]) ).
fof(f556,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != sK45(X0,X1) )
| ~ in(sK45(X0,X1),X1) )
& ( ( in(sK46(X0,X1),relation_dom(X0))
& sK45(X0,X1) = apply(X0,sK46(X0,X1)) )
| in(sK45(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ( in(sK47(X0,X5),relation_dom(X0))
& apply(X0,sK47(X0,X5)) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45,sK46,sK47]),skolemize(X2,sK45(X0,X1)),skolemize(X4,sK46(X0,X1)),skolemize(X7,sK47(X0,X5))],[f555]) ).
fof(f604,plain,
( sK74 != relation_image(sK75,relation_inverse_image(sK75,sK74))
& subset(sK74,relation_rng(sK75))
& relation(sK75)
& function(sK75) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74,sK75]),skolemize(X0,sK74),skolemize(X1,sK75)],[f373]) ).
fof(f653,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f7]) ).
fof(f663,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f481]) ).
fof(f673,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| apply(X0,X7) != X6
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f488]) ).
fof(f685,plain,
! [X2,X0,X1,X4] :
( in(X4,relation_dom(X0))
| ~ in(X4,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f496]) ).
fof(f686,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f496]) ).
fof(f754,plain,
! [X3,X0,X1] :
( ~ in(X3,X0)
| in(X3,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f538]) ).
fof(f755,plain,
! [X0,X1] :
( in(sK36(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f538]) ).
fof(f756,plain,
! [X0,X1] :
( ~ in(sK36(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f538]) ).
fof(f784,plain,
! [X0,X1,X5] :
( apply(X0,sK47(X0,X5)) = X5
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f556]) ).
fof(f785,plain,
! [X0,X1,X5] :
( in(sK47(X0,X5),relation_dom(X0))
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f556]) ).
fof(f941,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(cnf_transformation,[],[f360]) ).
fof(f952,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
| ~ function(X1) ),
inference(cnf_transformation,[],[f367]) ).
fof(f956,plain,
function(sK75),
inference(cnf_transformation,[],[f604]) ).
fof(f957,plain,
relation(sK75),
inference(cnf_transformation,[],[f604]) ).
fof(f958,plain,
subset(sK74,relation_rng(sK75)),
inference(cnf_transformation,[],[f604]) ).
fof(f959,plain,
sK74 != relation_image(sK75,relation_inverse_image(sK75,sK74)),
inference(cnf_transformation,[],[f604]) ).
fof(f1011,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)),
inference(cnf_transformation,[],[f189]) ).
fof(f1027,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,set_difference(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f415]) ).
fof(f1255,plain,
! [X2,X0,X1,X7] :
( in(apply(X0,X7),X2)
| ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f673]) ).
fof(f1256,plain,
! [X0,X1,X7] :
( ~ relation(X0)
| ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| in(apply(X0,X7),relation_image(X0,X1))
| ~ function(X0) ),
inference(equality_resolution,[],[f1255]) ).
fof(f1263,plain,
! [X0,X1,X4] :
( ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,relation_inverse_image(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f686]) ).
fof(f1264,plain,
! [X0,X1,X4] :
( ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| in(X4,relation_dom(X0))
| ~ function(X0) ),
inference(equality_resolution,[],[f685]) ).
fof(f1316,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| in(sK47(X0,X5),relation_dom(X0))
| ~ function(X0) ),
inference(equality_resolution,[],[f785]) ).
fof(f1317,plain,
! [X0,X5] :
( ~ in(X5,relation_rng(X0))
| apply(X0,sK47(X0,X5)) = X5
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f784]) ).
fof(f1370,plain,
! [X0] :
( subset(relation_image(sK75,relation_inverse_image(sK75,X0)),X0)
| ~ function(sK75) ),
inference(resolution,[],[f957,f952]) ).
fof(f1371,plain,
! [X0] : subset(relation_image(sK75,relation_inverse_image(sK75,X0)),X0),
inference(forward_subsumption_resolution,[],[f1370,f956]) ).
fof(f1373,plain,
! [X0] :
( ~ subset(X0,relation_image(sK75,relation_inverse_image(sK75,X0)))
| relation_image(sK75,relation_inverse_image(sK75,X0)) = X0 ),
inference(resolution,[],[f663,f1371]) ).
fof(f1390,plain,
! [X2,X0,X1] :
( ~ subset(X0,X2)
| in(sK36(X0,X1),X2)
| subset(X0,X1) ),
inference(resolution,[],[f755,f754]) ).
fof(f1398,plain,
! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK75,X1))
| in(X0,relation_dom(sK75))
| ~ function(sK75) ),
inference(resolution,[],[f1264,f957]) ).
fof(f1399,plain,
! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK75,X1))
| in(X0,relation_dom(sK75)) ),
inference(forward_subsumption_resolution,[],[f1398,f956]) ).
fof(f1444,plain,
! [X0,X1] :
( ~ in(X0,relation_dom(sK75))
| ~ in(X0,X1)
| in(apply(sK75,X0),relation_image(sK75,X1))
| ~ function(sK75) ),
inference(resolution,[],[f1256,f957]) ).
fof(f1445,plain,
! [X0,X1] :
( ~ in(X0,relation_dom(sK75))
| ~ in(X0,X1)
| in(apply(sK75,X0),relation_image(sK75,X1)) ),
inference(forward_subsumption_resolution,[],[f1444,f956]) ).
fof(f1509,plain,
! [X0] : set_union2(relation_image(sK75,relation_inverse_image(sK75,X0)),X0) = X0,
inference(resolution,[],[f941,f1371]) ).
fof(f1518,plain,
! [X0] : set_union2(X0,relation_image(sK75,relation_inverse_image(sK75,X0))) = X0,
inference(forward_demodulation,[],[f1509,f653]) ).
fof(f1639,plain,
! [X0] :
( in(sK36(sK74,X0),relation_rng(sK75))
| subset(sK74,X0) ),
inference(resolution,[],[f1390,f958]) ).
fof(f1644,plain,
! [X0] :
( subset(sK74,X0)
| sK36(sK74,X0) = apply(sK75,sK47(sK75,sK36(sK74,X0)))
| ~ relation(sK75)
| ~ function(sK75) ),
inference(resolution,[],[f1639,f1317]) ).
fof(f1649,plain,
! [X0] :
( subset(sK74,X0)
| sK36(sK74,X0) = apply(sK75,sK47(sK75,sK36(sK74,X0)))
| ~ function(sK75) ),
inference(forward_subsumption_resolution,[],[f1644,f957]) ).
fof(f1651,plain,
! [X0] :
( subset(sK74,X0)
| sK36(sK74,X0) = apply(sK75,sK47(sK75,sK36(sK74,X0))) ),
inference(forward_subsumption_resolution,[],[f1649,f956]) ).
fof(f1841,plain,
! [X0] :
( ~ in(X0,relation_rng(sK75))
| in(sK47(sK75,X0),relation_dom(sK75))
| ~ function(sK75) ),
inference(resolution,[],[f1316,f957]) ).
fof(f1842,plain,
! [X0] :
( in(sK47(sK75,X0),relation_dom(sK75))
| ~ in(X0,relation_rng(sK75)) ),
inference(forward_subsumption_resolution,[],[f1841,f956]) ).
fof(f1870,plain,
( sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74))) = apply(sK75,sK47(sK75,sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74)))))
| sK74 = relation_image(sK75,relation_inverse_image(sK75,sK74)) ),
inference(resolution,[],[f1651,f1373]) ).
fof(f1873,plain,
sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74))) = apply(sK75,sK47(sK75,sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74))))),
inference(forward_subsumption_resolution,[],[f1870,f959]) ).
fof(f1876,plain,
! [X0] :
( ~ in(sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74))),X0)
| ~ in(sK47(sK75,sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74)))),relation_dom(sK75))
| in(sK47(sK75,sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74)))),relation_inverse_image(sK75,X0))
| ~ relation(sK75)
| ~ function(sK75) ),
inference(superposition,[],[f1263,f1873]) ).
fof(f1877,plain,
! [X0] :
( ~ in(sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74))),X0)
| ~ in(sK47(sK75,sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74)))),relation_dom(sK75))
| in(sK47(sK75,sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74)))),relation_inverse_image(sK75,X0))
| ~ function(sK75) ),
inference(forward_subsumption_resolution,[],[f1876,f957]) ).
fof(f1879,definition,
( spl88_11
<=> in(sK47(sK75,sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74)))),relation_dom(sK75)) ),
introduced(definition,[new_symbols(definition,[spl88_11])],[avatar_definition]) ).
fof(f1880,plain,
( ~ in(sK47(sK75,sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74)))),relation_dom(sK75))
| spl88_11 ),
inference(avatar_component_clause,[],[f1879]) ).
fof(f1885,plain,
! [X0] :
( ~ in(sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74))),X0)
| ~ in(sK47(sK75,sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74)))),relation_dom(sK75))
| in(sK47(sK75,sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74)))),relation_inverse_image(sK75,X0)) ),
inference(forward_subsumption_resolution,[],[f1877,f956]) ).
fof(f1887,definition,
( spl88_13
<=> ! [X0] :
( ~ in(sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74))),X0)
| in(sK47(sK75,sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74)))),relation_inverse_image(sK75,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl88_13])],[avatar_definition]) ).
fof(f1888,plain,
( ! [X0] :
( ~ in(sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74))),X0)
| in(sK47(sK75,sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74)))),relation_inverse_image(sK75,X0)) )
| ~ spl88_13 ),
inference(avatar_component_clause,[],[f1887]) ).
fof(f1889,plain,
( ~ spl88_11
| spl88_13 ),
inference(avatar_split_clause,[],[f1885,f1887,f1879]) ).
fof(f1890,plain,
( ~ in(sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74))),relation_rng(sK75))
| spl88_11 ),
inference(resolution,[],[f1880,f1842]) ).
fof(f1891,plain,
( subset(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74)))
| spl88_11 ),
inference(resolution,[],[f1890,f1639]) ).
fof(f1901,plain,
( relation_image(sK75,relation_inverse_image(sK75,sK74)) = set_union2(sK74,set_difference(relation_image(sK75,relation_inverse_image(sK75,sK74)),sK74))
| spl88_11 ),
inference(resolution,[],[f1891,f1027]) ).
fof(f1910,plain,
( relation_image(sK75,relation_inverse_image(sK75,sK74)) = set_union2(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74)))
| spl88_11 ),
inference(forward_demodulation,[],[f1901,f1011]) ).
fof(f1917,plain,
( sK74 = relation_image(sK75,relation_inverse_image(sK75,sK74))
| spl88_11 ),
inference(forward_demodulation,[],[f1910,f1518]) ).
fof(f1922,plain,
( $false
| spl88_11 ),
inference(forward_subsumption_resolution,[],[f1917,f959]) ).
fof(f1923,plain,
spl88_11,
inference(avatar_contradiction_clause,[],[f1922]) ).
fof(f1934,plain,
( in(sK47(sK75,sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74)))),relation_inverse_image(sK75,sK74))
| subset(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74)))
| ~ spl88_13 ),
inference(resolution,[],[f1888,f755]) ).
fof(f1938,definition,
( spl88_14
<=> subset(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74))) ),
introduced(definition,[new_symbols(definition,[spl88_14])],[avatar_definition]) ).
fof(f1939,plain,
( subset(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74)))
| ~ spl88_14 ),
inference(avatar_component_clause,[],[f1938]) ).
fof(f1946,definition,
( spl88_16
<=> in(sK47(sK75,sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74)))),relation_inverse_image(sK75,sK74)) ),
introduced(definition,[new_symbols(definition,[spl88_16])],[avatar_definition]) ).
fof(f1947,plain,
( in(sK47(sK75,sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74)))),relation_inverse_image(sK75,sK74))
| ~ spl88_16 ),
inference(avatar_component_clause,[],[f1946]) ).
fof(f1948,plain,
( spl88_14
| spl88_16
| ~ spl88_13 ),
inference(avatar_split_clause,[],[f1934,f1887,f1946,f1938]) ).
fof(f1958,plain,
( relation_image(sK75,relation_inverse_image(sK75,sK74)) = set_union2(sK74,set_difference(relation_image(sK75,relation_inverse_image(sK75,sK74)),sK74))
| ~ spl88_14 ),
inference(resolution,[],[f1939,f1027]) ).
fof(f1967,plain,
( relation_image(sK75,relation_inverse_image(sK75,sK74)) = set_union2(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74)))
| ~ spl88_14 ),
inference(forward_demodulation,[],[f1958,f1011]) ).
fof(f1974,plain,
( sK74 = relation_image(sK75,relation_inverse_image(sK75,sK74))
| ~ spl88_14 ),
inference(forward_demodulation,[],[f1967,f1518]) ).
fof(f1979,plain,
( $false
| ~ spl88_14 ),
inference(forward_subsumption_resolution,[],[f1974,f959]) ).
fof(f1980,plain,
~ spl88_14,
inference(avatar_contradiction_clause,[],[f1979]) ).
fof(f1985,plain,
( in(sK47(sK75,sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74)))),relation_dom(sK75))
| ~ spl88_16 ),
inference(resolution,[],[f1947,f1399]) ).
fof(f2023,plain,
( ! [X0] :
( ~ in(sK47(sK75,sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74)))),X0)
| in(apply(sK75,sK47(sK75,sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74))))),relation_image(sK75,X0)) )
| ~ spl88_16 ),
inference(resolution,[],[f1985,f1445]) ).
fof(f2027,plain,
( ! [X0] :
( ~ in(sK47(sK75,sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74)))),X0)
| in(sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74))),relation_image(sK75,X0)) )
| ~ spl88_16 ),
inference(forward_demodulation,[],[f2023,f1873]) ).
fof(f2030,plain,
( in(sK36(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74))),relation_image(sK75,relation_inverse_image(sK75,sK74)))
| ~ spl88_16 ),
inference(resolution,[],[f2027,f1947]) ).
fof(f2034,plain,
( subset(sK74,relation_image(sK75,relation_inverse_image(sK75,sK74)))
| ~ spl88_16 ),
inference(resolution,[],[f2030,f756]) ).
fof(f2046,plain,
( spl88_14
| ~ spl88_16 ),
inference(avatar_split_clause,[],[f2034,f1946,f1938]) ).
cnf(s8,plain,
( ~ spl88_11
| spl88_13 ),
inference(sat_conversion,[],[f1889]) ).
cnf(s16,plain,
spl88_11,
inference(sat_conversion,[],[f1923]) ).
cnf(s19,plain,
( ~ spl88_13
| spl88_14
| spl88_16 ),
inference(sat_conversion,[],[f1948]) ).
cnf(s27,plain,
~ spl88_14,
inference(sat_conversion,[],[f1980]) ).
cnf(s29,plain,
( spl88_14
| ~ spl88_16 ),
inference(sat_conversion,[],[f2046]) ).
cnf(s30,plain,
~ spl88_16,
inference(rat,[],[s29,s27]) ).
cnf(s31,plain,
~ spl88_13,
inference(rat,[],[s19,s30,s27]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s8,s31,s16]) ).
fof(f2048,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU228+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n009.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 04:10:45 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 6.13/1.86 % (2653515)Detected formulas, will run a generic FOF schedule.
% 6.13/1.86 % (2653521)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=2965731367:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.13/1.86 % (2653525)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3831950672:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.13/1.86 % (2653524)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1066228907:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.13/1.86 % (2653520)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=1946361618:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.13/1.86 % (2653523)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1817683734:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.13/1.86 % (2653526)dis-21_1_sil=8000:lcm=predicate:random_seed=3670994206: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)
% 6.13/1.86 % (2653522)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=2574711537:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.13/1.86 % (2653526)Instruction limit reached!
% 6.13/1.86 % (2653526)------------------------------
% 6.13/1.86 % (2653526)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.13/1.86 % (2653526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.13/1.86 % (2653526)CaDiCaL version: 2.1.3
% 6.13/1.86 % (2653526)Termination reason: Instruction limit
% 6.13/1.86 % (2653526)Termination phase: Saturation
% 6.13/1.86 % (2653526)Time elapsed: 0.063 s
% 6.13/1.86 % (2653526)Peak memory usage: 90 MB
% 6.13/1.86 % (2653526)Instructions burned: 131 (million)
% 6.13/1.86 % (2653523)Instruction limit reached!
% 6.13/1.86 % (2653523)------------------------------
% 6.13/1.86 % (2653523)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.13/1.86 % (2653523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.13/1.86 % (2653523)CaDiCaL version: 2.1.3
% 6.13/1.86 % (2653523)Termination reason: Instruction limit
% 6.13/1.86 % (2653523)Termination phase: Saturation
% 6.13/1.86 % (2653523)Time elapsed: 0.071 s
% 6.13/1.86 % (2653523)Peak memory usage: 90 MB
% 6.13/1.86 % (2653523)Instructions burned: 111 (million)
% 6.13/1.86 % (2653524)Instruction limit reached!
% 6.13/1.86 % (2653524)------------------------------
% 6.13/1.86 % (2653524)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.13/1.86 % (2653524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.13/1.86 % (2653524)CaDiCaL version: 2.1.3
% 6.13/1.86 % (2653524)Termination reason: Instruction limit
% 6.13/1.86 % (2653524)Termination phase: Saturation
% 6.13/1.86 % (2653524)Time elapsed: 0.081 s
% 6.13/1.86 % (2653524)Peak memory usage: 89 MB
% 6.13/1.86 % (2653524)Instructions burned: 120 (million)
% 6.13/1.86 % (2653525)Instruction limit reached!
% 6.13/1.86 % (2653525)------------------------------
% 6.13/1.86 % (2653525)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.13/1.86 % (2653525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.13/1.86 % (2653525)CaDiCaL version: 2.1.3
% 6.13/1.86 % (2653525)Termination reason: Instruction limit
% 6.13/1.86 % (2653525)Termination phase: Saturation
% 6.13/1.86 % (2653525)Time elapsed: 0.101 s
% 6.13/1.86 % (2653525)Peak memory usage: 90 MB
% 6.13/1.86 % (2653525)Instructions burned: 139 (million)
% 6.13/1.86 % (2653535)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2601817548:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.13/1.86 % (2653534)lrs+10_1_sil=8000:sp=occurrence:random_seed=2644138015:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.13/1.86 % (2653536)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2133160148:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.13/1.86 % (2653537)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=642737686:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.13/1.86 % (2653535)Instruction limit reached!
% 6.13/1.86 % (2653535)------------------------------
% 6.13/1.86 % (2653535)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.13/1.86 % (2653535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.13/1.86 % (2653535)CaDiCaL version: 2.1.3
% 6.13/1.86 % (2653535)Termination reason: Instruction limit
% 6.13/1.86 % (2653535)Termination phase: Saturation
% 6.13/1.86 % (2653535)Time elapsed: 0.090 s
% 6.13/1.86 % (2653535)Peak memory usage: 91 MB
% 6.13/1.86 % (2653535)Instructions burned: 157 (million)
% 6.13/1.86 % (2653537)Instruction limit reached!
% 6.13/1.86 % (2653537)------------------------------
% 6.13/1.86 % (2653537)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.13/1.86 % (2653537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.13/1.86 % (2653537)CaDiCaL version: 2.1.3
% 6.13/1.86 % (2653537)Termination reason: Instruction limit
% 6.13/1.86 % (2653537)Termination phase: Saturation
% 6.13/1.86 % (2653537)Time elapsed: 0.147 s
% 6.13/1.86 % (2653537)Peak memory usage: 93 MB
% 6.13/1.86 % (2653537)Instructions burned: 249 (million)
% 6.13/1.86 % (2653534)Instruction limit reached!
% 6.13/1.86 % (2653534)------------------------------
% 6.13/1.86 % (2653534)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.13/1.86 % (2653534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.13/1.86 % (2653534)CaDiCaL version: 2.1.3
% 6.13/1.86 % (2653534)Termination reason: Instruction limit
% 6.13/1.86 % (2653534)Termination phase: Saturation
% 6.13/1.86 % (2653534)Time elapsed: 0.186 s
% 6.13/1.86 % (2653534)Peak memory usage: 93 MB
% 6.13/1.86 % (2653534)Instructions burned: 286 (million)
% 6.13/1.86 % (2653542)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=4155551747:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.13/1.86 % (2653536)Instruction limit reached!
% 6.13/1.86 % (2653536)------------------------------
% 6.13/1.86 % (2653536)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.13/1.86 % (2653536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.13/1.86 % (2653536)CaDiCaL version: 2.1.3
% 6.13/1.86 % (2653536)Termination reason: Instruction limit
% 6.13/1.86 % (2653536)Termination phase: Saturation
% 6.13/1.86 % (2653536)Time elapsed: 0.219 s
% 6.13/1.86 % (2653536)Peak memory usage: 92 MB
% 6.13/1.86 % (2653536)Instructions burned: 325 (million)
% 6.13/1.86 % (2653542)Instruction limit reached!
% 6.13/1.86 % (2653542)------------------------------
% 6.13/1.86 % (2653542)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.13/1.86 % (2653542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.13/1.86 % (2653542)CaDiCaL version: 2.1.3
% 6.13/1.86 % (2653542)Termination reason: Instruction limit
% 6.13/1.86 % (2653542)Termination phase: Saturation
% 6.13/1.86 % (2653542)Time elapsed: 0.102 s
% 6.13/1.86 % (2653542)Peak memory usage: 91 MB
% 6.13/1.86 % (2653542)Instructions burned: 294 (million)
% 6.13/1.86 % (2653544)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3529492863:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.13/1.86 % (2653543)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3931470149:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.13/1.86 % (2653546)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=397651541:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 6.13/1.86 % (2653521)First to succeed.
% 6.13/1.86 % (2653544)Instruction limit reached!
% 6.13/1.86 % (2653544)------------------------------
% 6.13/1.86 % (2653544)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.13/1.86 % (2653544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.13/1.86 % (2653544)CaDiCaL version: 2.1.3
% 6.13/1.86 % (2653544)Termination reason: Instruction limit
% 6.13/1.86 % (2653544)Termination phase: Saturation
% 6.13/1.86 % (2653544)Time elapsed: 0.071 s
% 6.13/1.86 % (2653544)Peak memory usage: 90 MB
% 6.13/1.86 % (2653544)Instructions burned: 114 (million)
% 6.13/1.86 % (2653521)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2653515"
% 6.13/1.86 % (2653547)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3633599074:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 6.13/1.86 % (2653546)Instruction limit reached!
% 6.13/1.86 % (2653546)------------------------------
% 6.13/1.86 % (2653546)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.13/1.86 % (2653546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.13/1.86 % (2653546)CaDiCaL version: 2.1.3
% 6.13/1.86 % (2653546)Termination reason: Instruction limit
% 6.13/1.86 % (2653546)Termination phase: Saturation
% 6.13/1.86 % (2653546)Time elapsed: 0.067 s
% 6.13/1.86 % (2653546)Peak memory usage: 89 MB
% 6.13/1.86 % (2653546)Instructions burned: 127 (million)
% 6.13/1.86 % (2653547)Instruction limit reached!
% 6.13/1.86 % (2653547)------------------------------
% 6.13/1.86 % (2653547)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.13/1.86 % (2653547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.13/1.86 % (2653547)CaDiCaL version: 2.1.3
% 6.13/1.86 % (2653547)Termination reason: Instruction limit
% 6.13/1.86 % (2653547)Termination phase: Saturation
% 6.13/1.86 % (2653547)Time elapsed: 0.039 s
% 6.13/1.86 % (2653547)Peak memory usage: 89 MB
% 6.13/1.86 % (2653547)Instructions burned: 116 (million)
% 6.13/1.86 % (2653551)lrs+10_1_sil=8000:sp=occurrence:random_seed=3694353036:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.13/1.86 % (2653554)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3192317449:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 6.13/1.86 % (2653553)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=96092921:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 6.13/1.86 % (2653520)Also succeeded, but the first one will report.
% 6.13/1.86 % (2653521)Refutation found. Thanks to Tanya!
% 6.13/1.86 % SZS status Theorem for theBenchmark
% 6.13/1.86 % SZS output start Proof for theBenchmark
% See solution above
% 7.50/1.95 % (2653521)------------------------------
% 7.50/1.95 % (2653521)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.50/1.95 % (2653521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.50/1.95 % (2653521)CaDiCaL version: 2.1.3
% 7.50/1.95 % (2653521)Termination reason: Refutation
% 7.50/1.95 % (2653521)Time elapsed: 0.629 s
% 7.50/1.95 % (2653521)Peak memory usage: 135 MB
% 7.50/1.95 % (2653521)Instructions burned: 1326 (million)
% 7.50/1.95 % (2653521)------------------------------
% 7.50/1.95 % (2653521)------------------------------
% 7.50/1.95 % (2653515)Success in time 0.998 s
% 7.50/1.95 % Vampire exiting
%------------------------------------------------------------------------------