%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG072+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 09:09:30 AM UTC 2026
% Result : Theorem 9.06s 1.90s
% Output : Refutation 9.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 31
% Syntax : Number of formulae : 214 ( 42 unt; 24 def)
% Number of atoms : 687 ( 173 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 850 ( 377 ~; 365 |; 60 &)
% ( 24 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 28 ( 26 usr; 25 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 156 ( 0 sgn 144 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
sorti1(unit1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(f2,axiom,
( ! [X0] :
( sorti1(X0)
=> ( op1(unit1,X0) = X0
& op1(X0,unit1) = X0 ) )
& ? [X1] :
( sorti1(X1)
& unit1 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(f3,axiom,
sorti2(unit2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f4,axiom,
( ! [X0] :
( sorti2(X0)
=> ( op2(unit2,X0) = X0
& op2(X0,unit2) = X0 ) )
& ? [X1] :
( sorti2(X1)
& unit2 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f7,axiom,
? [X0] :
( sorti1(X0)
& ! [X1] :
( sorti1(X1)
=> ! [X2] :
( sorti1(X2)
=> ( op1(X1,X2) != X0
| ( op1(X1,X0) = X2
& X0 != unit1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
fof(f8,axiom,
~ ? [X0] :
( sorti2(X0)
& ! [X1] :
( sorti2(X1)
=> ! [X2] :
( sorti2(X2)
=> ( op2(X1,X2) != X0
| ( op2(X1,X0) = X2
& X0 != unit2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8) ).
fof(f9,conjecture,
( ( ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) )
& ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) ) )
=> ~ ( ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) )
& ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
& ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 )
& ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f10,negated_conjecture,
~ ( ( ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) )
& ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) ) )
=> ~ ( ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) )
& ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
& ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 )
& ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 ) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
( ! [X0] :
( ( op1(unit1,X0) = X0
& op1(X0,unit1) = X0 )
| ~ sorti1(X0) )
& ? [X1] :
( sorti1(X1)
& unit1 = X1 ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f12,plain,
( ! [X0] :
( ( op2(unit2,X0) = X0
& op2(X0,unit2) = X0 )
| ~ sorti2(X0) )
& ? [X1] :
( sorti2(X1)
& unit2 = X1 ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f15,plain,
? [X0] :
( sorti1(X0)
& ! [X1] :
( ! [X2] :
( op1(X1,X2) != X0
| ( op1(X1,X0) = X2
& X0 != unit1 )
| ~ sorti1(X2) )
| ~ sorti1(X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f16,plain,
? [X0] :
( sorti1(X0)
& ! [X1] :
( ! [X2] :
( op1(X1,X2) != X0
| ( op1(X1,X0) = X2
& X0 != unit1 )
| ~ sorti1(X2) )
| ~ sorti1(X1) ) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0] :
( ~ sorti2(X0)
| ? [X1] :
( ? [X2] :
( op2(X1,X2) = X0
& ( op2(X1,X0) != X2
| unit2 = X0 )
& sorti2(X2) )
& sorti2(X1) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f18,plain,
! [X0] :
( ~ sorti2(X0)
| ? [X1] :
( ? [X2] :
( op2(X1,X2) = X0
& ( op2(X1,X0) != X2
| unit2 = X0 )
& sorti2(X2) )
& sorti2(X1) ) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
( ! [X2] :
( ! [X3] :
( h(op1(X2,X3)) = op2(h(X2),h(X3))
| ~ sorti1(X3) )
| ~ sorti1(X2) )
& ! [X4] :
( ! [X5] :
( j(op2(X4,X5)) = op1(j(X4),j(X5))
| ~ sorti2(X5) )
| ~ sorti2(X4) )
& ! [X6] :
( h(j(X6)) = X6
| ~ sorti2(X6) )
& ! [X7] :
( j(h(X7)) = X7
| ~ sorti1(X7) )
& ! [X0] :
( sorti2(h(X0))
| ~ sorti1(X0) )
& ! [X1] :
( sorti1(j(X1))
| ~ sorti2(X1) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f20,plain,
( ! [X2] :
( ! [X3] :
( h(op1(X2,X3)) = op2(h(X2),h(X3))
| ~ sorti1(X3) )
| ~ sorti1(X2) )
& ! [X4] :
( ! [X5] :
( j(op2(X4,X5)) = op1(j(X4),j(X5))
| ~ sorti2(X5) )
| ~ sorti2(X4) )
& ! [X6] :
( h(j(X6)) = X6
| ~ sorti2(X6) )
& ! [X7] :
( j(h(X7)) = X7
| ~ sorti1(X7) )
& ! [X0] :
( sorti2(h(X0))
| ~ sorti1(X0) )
& ! [X1] :
( sorti1(j(X1))
| ~ sorti2(X1) ) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
( ! [X0] :
( ( op1(unit1,X0) = X0
& op1(X0,unit1) = X0 )
| ~ sorti1(X0) )
& sorti1(sK0)
& unit1 = sK0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0)],[f11]) ).
fof(f22,plain,
( ! [X0] :
( ( op2(unit2,X0) = X0
& op2(X0,unit2) = X0 )
| ~ sorti2(X0) )
& sorti2(sK1)
& unit2 = sK1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1)],[f12]) ).
fof(f23,plain,
( sorti1(sK2)
& ! [X1] :
( ! [X2] :
( op1(X1,X2) != sK2
| ( op1(X1,sK2) = X2
& unit1 != sK2 )
| ~ sorti1(X2) )
| ~ sorti1(X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f16]) ).
fof(f24,plain,
! [X0] :
( ~ sorti2(X0)
| ( op2(sK3(X0),sK4(X0)) = X0
& ( sK4(X0) != op2(sK3(X0),X0)
| unit2 = X0 )
& sorti2(sK4(X0))
& sorti2(sK3(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X1,sK3(X0)),skolemize(X2,sK4(X0))],[f18]) ).
fof(f25,plain,
( ! [X0] :
( ! [X1] :
( h(op1(X0,X1)) = op2(h(X0),h(X1))
| ~ sorti1(X1) )
| ~ sorti1(X0) )
& ! [X2] :
( ! [X3] :
( j(op2(X2,X3)) = op1(j(X2),j(X3))
| ~ sorti2(X3) )
| ~ sorti2(X2) )
& ! [X4] :
( h(j(X4)) = X4
| ~ sorti2(X4) )
& ! [X5] :
( j(h(X5)) = X5
| ~ sorti1(X5) )
& ! [X6] :
( sorti2(h(X6))
| ~ sorti1(X6) )
& ! [X7] :
( sorti1(j(X7))
| ~ sorti2(X7) ) ),
inference(rectify,[],[f20]) ).
fof(f26,plain,
sorti1(unit1),
inference(cnf_transformation,[],[f1]) ).
fof(f27,plain,
unit1 = sK0,
inference(cnf_transformation,[],[f21]) ).
fof(f28,plain,
sorti1(sK0),
inference(cnf_transformation,[],[f21]) ).
fof(f29,plain,
! [X0] :
( op1(X0,unit1) = X0
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f31,plain,
sorti2(unit2),
inference(cnf_transformation,[],[f3]) ).
fof(f32,plain,
unit2 = sK1,
inference(cnf_transformation,[],[f22]) ).
fof(f35,plain,
! [X0] :
( op2(unit2,X0) = X0
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f38,plain,
! [X2,X1] :
( op1(X1,X2) != sK2
| unit1 != sK2
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f39,plain,
! [X2,X1] :
( op1(X1,X2) != sK2
| op1(X1,sK2) = X2
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f40,plain,
sorti1(sK2),
inference(cnf_transformation,[],[f23]) ).
fof(f41,plain,
! [X0] :
( ~ sorti2(X0)
| sorti2(sK3(X0)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f42,plain,
! [X0] :
( ~ sorti2(X0)
| sorti2(sK4(X0)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f43,plain,
! [X0] :
( ~ sorti2(X0)
| sK4(X0) != op2(sK3(X0),X0)
| unit2 = X0 ),
inference(cnf_transformation,[],[f24]) ).
fof(f44,plain,
! [X0] :
( ~ sorti2(X0)
| op2(sK3(X0),sK4(X0)) = X0 ),
inference(cnf_transformation,[],[f24]) ).
fof(f45,plain,
! [X7] :
( sorti1(j(X7))
| ~ sorti2(X7) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
! [X6] :
( sorti2(h(X6))
| ~ sorti1(X6) ),
inference(cnf_transformation,[],[f25]) ).
fof(f47,plain,
! [X5] :
( j(h(X5)) = X5
| ~ sorti1(X5) ),
inference(cnf_transformation,[],[f25]) ).
fof(f48,plain,
! [X4] :
( h(j(X4)) = X4
| ~ sorti2(X4) ),
inference(cnf_transformation,[],[f25]) ).
fof(f49,plain,
! [X2,X3] :
( j(op2(X2,X3)) = op1(j(X2),j(X3))
| ~ sorti2(X3)
| ~ sorti2(X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f50,plain,
! [X0,X1] :
( h(op1(X0,X1)) = op2(h(X0),h(X1))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f51,plain,
sorti1(sK0),
inference(definition_unfolding,[],[f26,f27]) ).
fof(f53,plain,
! [X0] :
( op1(X0,sK0) = X0
| ~ sorti1(X0) ),
inference(definition_unfolding,[],[f29,f27]) ).
fof(f54,plain,
sorti2(sK1),
inference(definition_unfolding,[],[f31,f32]) ).
fof(f55,plain,
! [X0] :
( op2(sK1,X0) = X0
| ~ sorti2(X0) ),
inference(definition_unfolding,[],[f35,f32]) ).
fof(f57,plain,
! [X2,X1] :
( op1(X1,X2) != sK2
| sK0 != sK2
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(definition_unfolding,[],[f38,f27]) ).
fof(f58,plain,
! [X0] :
( ~ sorti2(X0)
| sK4(X0) != op2(sK3(X0),X0)
| sK1 = X0 ),
inference(definition_unfolding,[],[f43,f32]) ).
fof(f60,definition,
( spl5_1
<=> ! [X5] :
( j(h(X5)) = X5
| ~ sorti1(X5) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f61,plain,
( ! [X5] :
( j(h(X5)) = X5
| ~ sorti1(X5) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f62,plain,
spl5_1,
inference(avatar_split_clause,[],[f47,f60]) ).
fof(f64,definition,
( spl5_2
<=> ! [X4] :
( h(j(X4)) = X4
| ~ sorti2(X4) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f65,plain,
( ! [X4] :
( h(j(X4)) = X4
| ~ sorti2(X4) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f66,plain,
spl5_2,
inference(avatar_split_clause,[],[f48,f64]) ).
fof(f68,definition,
( spl5_3
<=> ! [X6] :
( sorti2(h(X6))
| ~ sorti1(X6) ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f69,plain,
( ! [X6] :
( sorti2(h(X6))
| ~ sorti1(X6) )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f70,plain,
spl5_3,
inference(avatar_split_clause,[],[f46,f68]) ).
fof(f73,plain,
( ! [X0] :
( ~ sorti1(X0)
| sorti2(sK3(h(X0))) )
| ~ spl5_3 ),
inference(resolution,[],[f69,f41]) ).
fof(f87,definition,
( spl5_5
<=> ! [X7] :
( sorti1(j(X7))
| ~ sorti2(X7) ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
fof(f88,plain,
( ! [X7] :
( sorti1(j(X7))
| ~ sorti2(X7) )
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f89,plain,
spl5_5,
inference(avatar_split_clause,[],[f45,f87]) ).
fof(f95,plain,
( ! [X0] :
( ~ sorti2(X0)
| j(X0) = op1(j(X0),sK0) )
| ~ spl5_5 ),
inference(resolution,[],[f88,f53]) ).
fof(f100,definition,
( spl5_6
<=> ! [X2,X3] :
( j(op2(X2,X3)) = op1(j(X2),j(X3))
| ~ sorti2(X3)
| ~ sorti2(X2) ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
fof(f101,plain,
( ! [X2,X3] :
( j(op2(X2,X3)) = op1(j(X2),j(X3))
| ~ sorti2(X3)
| ~ sorti2(X2) )
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f102,plain,
spl5_6,
inference(avatar_split_clause,[],[f49,f100]) ).
fof(f104,plain,
( ! [X0,X1] :
( j(op2(X1,h(X0))) = op1(j(X1),X0)
| ~ sorti2(h(X0))
| ~ sorti2(X1)
| ~ sorti1(X0) )
| ~ spl5_1
| ~ spl5_6 ),
inference(superposition,[],[f101,f61]) ).
fof(f106,plain,
( ! [X0,X1] :
( sK2 != j(op2(X0,X1))
| j(X1) = op1(j(X0),sK2)
| ~ sorti1(j(X1))
| ~ sorti1(j(X0))
| ~ sorti2(X1)
| ~ sorti2(X0) )
| ~ spl5_6 ),
inference(superposition,[],[f39,f101]) ).
fof(f109,plain,
( ! [X0,X1] :
( sK2 != j(op2(X0,X1))
| j(X1) = op1(j(X0),sK2)
| ~ sorti1(j(X0))
| ~ sorti2(X1)
| ~ sorti2(X0) )
| ~ spl5_5
| ~ spl5_6 ),
inference(forward_subsumption_resolution,[],[f106,f88]) ).
fof(f111,plain,
( ! [X0,X1] :
( j(op2(X1,h(X0))) = op1(j(X1),X0)
| ~ sorti2(X1)
| ~ sorti1(X0) )
| ~ spl5_1
| ~ spl5_3
| ~ spl5_6 ),
inference(forward_subsumption_resolution,[],[f104,f69]) ).
fof(f114,plain,
( ! [X0,X1] :
( sK2 != j(op2(X0,X1))
| j(X1) = op1(j(X0),sK2)
| ~ sorti2(X1)
| ~ sorti2(X0) )
| ~ spl5_5
| ~ spl5_6 ),
inference(forward_subsumption_resolution,[],[f109,f88]) ).
fof(f122,definition,
( spl5_8
<=> ! [X0,X1] :
( h(op1(X0,X1)) = op2(h(X0),h(X1))
| ~ sorti1(X1)
| ~ sorti1(X0) ) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
fof(f123,plain,
( ! [X0,X1] :
( h(op1(X0,X1)) = op2(h(X0),h(X1))
| ~ sorti1(X1)
| ~ sorti1(X0) )
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f124,plain,
spl5_8,
inference(avatar_split_clause,[],[f50,f122]) ).
fof(f125,plain,
( ! [X0,X1] :
( op2(X0,h(X1)) = h(op1(j(X0),X1))
| ~ sorti1(X1)
| ~ sorti1(j(X0))
| ~ sorti2(X0) )
| ~ spl5_2
| ~ spl5_8 ),
inference(superposition,[],[f123,f65]) ).
fof(f130,plain,
( ! [X0,X1] :
( op2(X0,h(X1)) = h(op1(j(X0),X1))
| ~ sorti1(X1)
| ~ sorti2(X0) )
| ~ spl5_2
| ~ spl5_5
| ~ spl5_8 ),
inference(forward_subsumption_resolution,[],[f125,f88]) ).
fof(f146,definition,
( spl5_10
<=> ! [X0] :
( ~ sorti1(X0)
| sorti2(sK3(h(X0))) ) ),
introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition]) ).
fof(f147,plain,
( ! [X0] :
( sorti2(sK3(h(X0)))
| ~ sorti1(X0) )
| ~ spl5_10 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f148,plain,
( spl5_10
| ~ spl5_3 ),
inference(avatar_split_clause,[],[f73,f68,f146]) ).
fof(f159,definition,
( spl5_11
<=> sK0 = sK2 ),
introduced(definition,[new_symbols(definition,[spl5_11])],[avatar_definition]) ).
fof(f160,plain,
( sK0 = sK2
| ~ spl5_11 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f161,plain,
( sK0 != sK2
| spl5_11 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f191,definition,
( spl5_15
<=> ! [X0,X1] :
( sK2 != j(op2(X0,X1))
| j(X1) = op1(j(X0),sK2)
| ~ sorti2(X1)
| ~ sorti2(X0) ) ),
introduced(definition,[new_symbols(definition,[spl5_15])],[avatar_definition]) ).
fof(f192,plain,
( ! [X0,X1] :
( sK2 != j(op2(X0,X1))
| j(X1) = op1(j(X0),sK2)
| ~ sorti2(X1)
| ~ sorti2(X0) )
| ~ spl5_15 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f193,plain,
( spl5_15
| ~ spl5_5
| ~ spl5_6 ),
inference(avatar_split_clause,[],[f114,f100,f87,f191]) ).
fof(f197,plain,
( ! [X0] :
( sK2 != j(X0)
| j(sK4(X0)) = op1(j(sK3(X0)),sK2)
| ~ sorti2(sK4(X0))
| ~ sorti2(sK3(X0))
| ~ sorti2(X0) )
| ~ spl5_15 ),
inference(superposition,[],[f192,f44]) ).
fof(f207,plain,
( ! [X0] :
( sK2 != j(X0)
| j(sK4(X0)) = op1(j(sK3(X0)),sK2)
| ~ sorti2(sK3(X0))
| ~ sorti2(X0) )
| ~ spl5_15 ),
inference(forward_subsumption_resolution,[],[f197,f42]) ).
fof(f213,plain,
( ! [X0] :
( sK2 != j(X0)
| j(sK4(X0)) = op1(j(sK3(X0)),sK2)
| ~ sorti2(X0) )
| ~ spl5_15 ),
inference(forward_subsumption_resolution,[],[f207,f41]) ).
fof(f216,definition,
( spl5_16
<=> ! [X0] :
( sK2 != j(X0)
| j(sK4(X0)) = op1(j(sK3(X0)),sK2)
| ~ sorti2(X0) ) ),
introduced(definition,[new_symbols(definition,[spl5_16])],[avatar_definition]) ).
fof(f217,plain,
( ! [X0] :
( sK2 != j(X0)
| j(sK4(X0)) = op1(j(sK3(X0)),sK2)
| ~ sorti2(X0) )
| ~ spl5_16 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f218,plain,
( spl5_16
| ~ spl5_15 ),
inference(avatar_split_clause,[],[f213,f191,f216]) ).
fof(f219,plain,
( ! [X0] :
( sK2 != X0
| j(sK4(h(X0))) = op1(j(sK3(h(X0))),sK2)
| ~ sorti2(h(X0))
| ~ sorti1(X0) )
| ~ spl5_1
| ~ spl5_16 ),
inference(superposition,[],[f217,f61]) ).
fof(f222,plain,
( ! [X0] :
( sK2 != X0
| j(sK4(h(X0))) = op1(j(sK3(h(X0))),sK2)
| ~ sorti1(X0) )
| ~ spl5_1
| ~ spl5_3
| ~ spl5_16 ),
inference(forward_subsumption_resolution,[],[f219,f69]) ).
fof(f254,definition,
( spl5_20
<=> ! [X0,X1] :
( j(op2(X1,h(X0))) = op1(j(X1),X0)
| ~ sorti2(X1)
| ~ sorti1(X0) ) ),
introduced(definition,[new_symbols(definition,[spl5_20])],[avatar_definition]) ).
fof(f255,plain,
( ! [X0,X1] :
( j(op2(X1,h(X0))) = op1(j(X1),X0)
| ~ sorti2(X1)
| ~ sorti1(X0) )
| ~ spl5_20 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f256,plain,
( spl5_20
| ~ spl5_1
| ~ spl5_3
| ~ spl5_6 ),
inference(avatar_split_clause,[],[f111,f100,f68,f60,f254]) ).
fof(f259,plain,
( ! [X0] :
( j(h(X0)) = op1(j(sK1),X0)
| ~ sorti2(sK1)
| ~ sorti1(X0)
| ~ sorti2(h(X0)) )
| ~ spl5_20 ),
inference(superposition,[],[f255,f55]) ).
fof(f280,plain,
( ! [X0] :
( j(h(X0)) = op1(j(sK1),X0)
| ~ sorti1(X0)
| ~ sorti2(h(X0)) )
| ~ spl5_20 ),
inference(forward_subsumption_resolution,[],[f259,f54]) ).
fof(f284,plain,
( ! [X0] :
( j(h(X0)) = op1(j(sK1),X0)
| ~ sorti1(X0) )
| ~ spl5_3
| ~ spl5_20 ),
inference(forward_subsumption_resolution,[],[f280,f69]) ).
fof(f286,definition,
( spl5_21
<=> ! [X0] :
( j(h(X0)) = op1(j(sK1),X0)
| ~ sorti1(X0) ) ),
introduced(definition,[new_symbols(definition,[spl5_21])],[avatar_definition]) ).
fof(f287,plain,
( ! [X0] :
( j(h(X0)) = op1(j(sK1),X0)
| ~ sorti1(X0) )
| ~ spl5_21 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f288,plain,
( spl5_21
| ~ spl5_3
| ~ spl5_20 ),
inference(avatar_split_clause,[],[f284,f254,f68,f286]) ).
fof(f365,definition,
( spl5_25
<=> ! [X0] :
( ~ sorti2(X0)
| j(X0) = op1(j(X0),sK0) ) ),
introduced(definition,[new_symbols(definition,[spl5_25])],[avatar_definition]) ).
fof(f366,plain,
( ! [X0] :
( j(X0) = op1(j(X0),sK0)
| ~ sorti2(X0) )
| ~ spl5_25 ),
inference(avatar_component_clause,[],[f365]) ).
fof(f367,plain,
( spl5_25
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f95,f87,f365]) ).
fof(f372,plain,
( j(sK1) = j(h(sK0))
| ~ sorti1(sK0)
| ~ sorti2(sK1)
| ~ spl5_21
| ~ spl5_25 ),
inference(superposition,[],[f287,f366]) ).
fof(f378,plain,
( j(sK1) = j(h(sK0))
| ~ sorti2(sK1)
| ~ spl5_21
| ~ spl5_25 ),
inference(forward_subsumption_resolution,[],[f372,f51]) ).
fof(f382,plain,
( j(sK1) = j(h(sK0))
| ~ spl5_21
| ~ spl5_25 ),
inference(forward_subsumption_resolution,[],[f378,f54]) ).
fof(f402,definition,
( spl5_27
<=> ! [X0,X1] :
( op2(X0,h(X1)) = h(op1(j(X0),X1))
| ~ sorti1(X1)
| ~ sorti2(X0) ) ),
introduced(definition,[new_symbols(definition,[spl5_27])],[avatar_definition]) ).
fof(f403,plain,
( ! [X0,X1] :
( op2(X0,h(X1)) = h(op1(j(X0),X1))
| ~ sorti1(X1)
| ~ sorti2(X0) )
| ~ spl5_27 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f404,plain,
( spl5_27
| ~ spl5_2
| ~ spl5_5
| ~ spl5_8 ),
inference(avatar_split_clause,[],[f130,f122,f87,f64,f402]) ).
fof(f469,definition,
( spl5_30
<=> j(sK1) = j(h(sK0)) ),
introduced(definition,[new_symbols(definition,[spl5_30])],[avatar_definition]) ).
fof(f471,plain,
( j(sK1) = j(h(sK0))
| ~ spl5_30 ),
inference(avatar_component_clause,[],[f469]) ).
fof(f472,plain,
( spl5_30
| ~ spl5_21
| ~ spl5_25 ),
inference(avatar_split_clause,[],[f382,f365,f286,f469]) ).
fof(f475,plain,
( sK0 = j(sK1)
| ~ sorti1(sK0)
| ~ spl5_1
| ~ spl5_30 ),
inference(superposition,[],[f61,f471]) ).
fof(f486,plain,
( sK0 = j(sK1)
| ~ spl5_1
| ~ spl5_30 ),
inference(forward_subsumption_resolution,[],[f475,f51]) ).
fof(f491,definition,
( spl5_31
<=> sK0 = j(sK1) ),
introduced(definition,[new_symbols(definition,[spl5_31])],[avatar_definition]) ).
fof(f493,plain,
( sK0 = j(sK1)
| ~ spl5_31 ),
inference(avatar_component_clause,[],[f491]) ).
fof(f494,plain,
( spl5_31
| ~ spl5_1
| ~ spl5_30 ),
inference(avatar_split_clause,[],[f486,f469,f60,f491]) ).
fof(f506,plain,
( sK0 = op1(sK0,sK0)
| ~ sorti2(sK1)
| ~ spl5_25
| ~ spl5_31 ),
inference(superposition,[],[f366,f493]) ).
fof(f509,plain,
( sK0 = op1(sK0,sK0)
| ~ spl5_25
| ~ spl5_31 ),
inference(forward_subsumption_resolution,[],[f506,f54]) ).
fof(f784,definition,
( spl5_46
<=> sK0 = op1(sK0,sK0) ),
introduced(definition,[new_symbols(definition,[spl5_46])],[avatar_definition]) ).
fof(f786,plain,
( sK0 = op1(sK0,sK0)
| ~ spl5_46 ),
inference(avatar_component_clause,[],[f784]) ).
fof(f787,plain,
( spl5_46
| ~ spl5_25
| ~ spl5_31 ),
inference(avatar_split_clause,[],[f509,f491,f365,f784]) ).
fof(f788,plain,
( sK0 != sK2
| sK0 != sK2
| ~ sorti1(sK0)
| ~ sorti1(sK0)
| ~ spl5_46 ),
inference(superposition,[],[f57,f786]) ).
fof(f793,plain,
( sK0 != sK2
| ~ sorti1(sK0)
| ~ spl5_46 ),
inference(duplicate_literal_removal,[],[f788]) ).
fof(f1024,definition,
( spl5_63
<=> ! [X0] :
( sK2 != X0
| j(sK4(h(X0))) = op1(j(sK3(h(X0))),sK2)
| ~ sorti1(X0) ) ),
introduced(definition,[new_symbols(definition,[spl5_63])],[avatar_definition]) ).
fof(f1025,plain,
( ! [X0] :
( sK2 != X0
| j(sK4(h(X0))) = op1(j(sK3(h(X0))),sK2)
| ~ sorti1(X0) )
| ~ spl5_63 ),
inference(avatar_component_clause,[],[f1024]) ).
fof(f1026,plain,
( spl5_63
| ~ spl5_1
| ~ spl5_3
| ~ spl5_16 ),
inference(avatar_split_clause,[],[f222,f216,f68,f60,f1024]) ).
fof(f1027,plain,
( j(sK4(h(sK2))) = op1(j(sK3(h(sK2))),sK2)
| ~ sorti1(sK2)
| ~ spl5_63 ),
inference(equality_resolution,[],[f1025]) ).
fof(f1028,plain,
( j(sK4(h(sK2))) = op1(j(sK3(h(sK2))),sK2)
| ~ spl5_63 ),
inference(forward_subsumption_resolution,[],[f1027,f40]) ).
fof(f1030,definition,
( spl5_64
<=> j(sK4(h(sK2))) = op1(j(sK3(h(sK2))),sK2) ),
introduced(definition,[new_symbols(definition,[spl5_64])],[avatar_definition]) ).
fof(f1032,plain,
( j(sK4(h(sK2))) = op1(j(sK3(h(sK2))),sK2)
| ~ spl5_64 ),
inference(avatar_component_clause,[],[f1030]) ).
fof(f1033,plain,
( spl5_64
| ~ spl5_63 ),
inference(avatar_split_clause,[],[f1028,f1024,f1030]) ).
fof(f1036,plain,
( op2(sK3(h(sK2)),h(sK2)) = h(j(sK4(h(sK2))))
| ~ sorti1(sK2)
| ~ sorti2(sK3(h(sK2)))
| ~ spl5_27
| ~ spl5_64 ),
inference(superposition,[],[f403,f1032]) ).
fof(f1043,plain,
( op2(sK3(h(sK2)),h(sK2)) = h(j(sK4(h(sK2))))
| ~ sorti2(sK3(h(sK2)))
| ~ spl5_27
| ~ spl5_64 ),
inference(forward_subsumption_resolution,[],[f1036,f40]) ).
fof(f1056,definition,
( spl5_67
<=> sorti2(sK3(h(sK2))) ),
introduced(definition,[new_symbols(definition,[spl5_67])],[avatar_definition]) ).
fof(f1057,plain,
( sorti2(sK3(h(sK2)))
| ~ spl5_67 ),
inference(avatar_component_clause,[],[f1056]) ).
fof(f1058,plain,
( ~ sorti2(sK3(h(sK2)))
| spl5_67 ),
inference(avatar_component_clause,[],[f1056]) ).
fof(f1060,plain,
( ~ sorti1(sK2)
| ~ spl5_10
| spl5_67 ),
inference(resolution,[],[f1058,f147]) ).
fof(f1062,plain,
( $false
| ~ spl5_10
| spl5_67 ),
inference(forward_subsumption_resolution,[],[f1060,f40]) ).
fof(f1063,plain,
( ~ spl5_10
| spl5_67 ),
inference(avatar_contradiction_clause,[],[f1062]) ).
fof(f1065,plain,
( op2(sK3(h(sK2)),h(sK2)) = h(j(sK4(h(sK2))))
| ~ spl5_27
| ~ spl5_64
| ~ spl5_67 ),
inference(backward_subsumption_resolution,[],[f1043,f1057]) ).
fof(f1147,definition,
( spl5_71
<=> op2(sK3(h(sK2)),h(sK2)) = h(j(sK4(h(sK2)))) ),
introduced(definition,[new_symbols(definition,[spl5_71])],[avatar_definition]) ).
fof(f1149,plain,
( op2(sK3(h(sK2)),h(sK2)) = h(j(sK4(h(sK2))))
| ~ spl5_71 ),
inference(avatar_component_clause,[],[f1147]) ).
fof(f1150,plain,
( spl5_71
| ~ spl5_27
| ~ spl5_64
| ~ spl5_67 ),
inference(avatar_split_clause,[],[f1065,f1056,f1030,f402,f1147]) ).
fof(f1152,plain,
( sK4(h(sK2)) != h(j(sK4(h(sK2))))
| ~ sorti2(h(sK2))
| sK1 = h(sK2)
| ~ spl5_71 ),
inference(superposition,[],[f58,f1149]) ).
fof(f1429,definition,
( spl5_91
<=> sK1 = h(sK2) ),
introduced(definition,[new_symbols(definition,[spl5_91])],[avatar_definition]) ).
fof(f1431,plain,
( sK1 = h(sK2)
| ~ spl5_91 ),
inference(avatar_component_clause,[],[f1429]) ).
fof(f1433,definition,
( spl5_92
<=> sorti2(h(sK2)) ),
introduced(definition,[new_symbols(definition,[spl5_92])],[avatar_definition]) ).
fof(f1434,plain,
( sorti2(h(sK2))
| ~ spl5_92 ),
inference(avatar_component_clause,[],[f1433]) ).
fof(f1435,plain,
( ~ sorti2(h(sK2))
| spl5_92 ),
inference(avatar_component_clause,[],[f1433]) ).
fof(f1437,definition,
( spl5_93
<=> sK4(h(sK2)) = h(j(sK4(h(sK2)))) ),
introduced(definition,[new_symbols(definition,[spl5_93])],[avatar_definition]) ).
fof(f1439,plain,
( sK4(h(sK2)) != h(j(sK4(h(sK2))))
| spl5_93 ),
inference(avatar_component_clause,[],[f1437]) ).
fof(f1440,plain,
( spl5_91
| ~ spl5_92
| ~ spl5_93
| ~ spl5_71 ),
inference(avatar_split_clause,[],[f1152,f1147,f1437,f1433,f1429]) ).
fof(f1441,plain,
( ~ sorti1(sK2)
| ~ spl5_3
| spl5_92 ),
inference(resolution,[],[f1435,f69]) ).
fof(f1442,plain,
( $false
| ~ spl5_3
| spl5_92 ),
inference(forward_subsumption_resolution,[],[f1441,f40]) ).
fof(f1443,plain,
( ~ spl5_3
| spl5_92 ),
inference(avatar_contradiction_clause,[],[f1442]) ).
fof(f1450,plain,
( sorti2(sK4(h(sK2)))
| ~ spl5_92 ),
inference(resolution,[],[f1434,f42]) ).
fof(f1476,plain,
( sK4(h(sK2)) != sK4(h(sK2))
| ~ sorti2(sK4(h(sK2)))
| ~ spl5_2
| spl5_93 ),
inference(superposition,[],[f1439,f65]) ).
fof(f1477,plain,
( ~ sorti2(sK4(h(sK2)))
| ~ spl5_2
| spl5_93 ),
inference(trivial_inequality_removal,[],[f1476]) ).
fof(f1478,plain,
( $false
| ~ spl5_2
| ~ spl5_92
| spl5_93 ),
inference(forward_subsumption_resolution,[],[f1477,f1450]) ).
fof(f1479,plain,
( ~ spl5_2
| ~ spl5_92
| spl5_93 ),
inference(avatar_contradiction_clause,[],[f1478]) ).
fof(f1510,plain,
( sK2 = j(sK1)
| ~ sorti1(sK2)
| ~ spl5_1
| ~ spl5_91 ),
inference(superposition,[],[f61,f1431]) ).
fof(f1536,plain,
( sK2 = j(sK1)
| ~ spl5_1
| ~ spl5_91 ),
inference(forward_subsumption_resolution,[],[f1510,f40]) ).
fof(f1538,plain,
( sK0 = sK2
| ~ spl5_1
| ~ spl5_31
| ~ spl5_91 ),
inference(forward_demodulation,[],[f1536,f493]) ).
fof(f1540,plain,
( $false
| ~ spl5_1
| spl5_11
| ~ spl5_31
| ~ spl5_91 ),
inference(forward_subsumption_resolution,[],[f1538,f161]) ).
fof(f1541,plain,
( ~ spl5_1
| spl5_11
| ~ spl5_31
| ~ spl5_91 ),
inference(avatar_contradiction_clause,[],[f1540]) ).
fof(f1555,plain,
( ~ sorti1(sK0)
| ~ spl5_11
| ~ spl5_46 ),
inference(forward_subsumption_resolution,[],[f793,f160]) ).
fof(f1574,plain,
( $false
| ~ spl5_11
| ~ spl5_46 ),
inference(forward_subsumption_resolution,[],[f1555,f28]) ).
fof(f1575,plain,
( ~ spl5_11
| ~ spl5_46 ),
inference(avatar_contradiction_clause,[],[f1574]) ).
cnf(s1,plain,
spl5_1,
inference(sat_conversion,[],[f62]) ).
cnf(s2,plain,
spl5_2,
inference(sat_conversion,[],[f66]) ).
cnf(s3,plain,
spl5_3,
inference(sat_conversion,[],[f70]) ).
cnf(s5,plain,
spl5_5,
inference(sat_conversion,[],[f89]) ).
cnf(s6,plain,
spl5_6,
inference(sat_conversion,[],[f102]) ).
cnf(s8,plain,
spl5_8,
inference(sat_conversion,[],[f124]) ).
cnf(s10,plain,
( ~ spl5_3
| spl5_10 ),
inference(sat_conversion,[],[f148]) ).
cnf(s14,plain,
( ~ spl5_5
| ~ spl5_6
| spl5_15 ),
inference(sat_conversion,[],[f193]) ).
cnf(s15,plain,
( ~ spl5_15
| spl5_16 ),
inference(sat_conversion,[],[f218]) ).
cnf(s19,plain,
( ~ spl5_1
| ~ spl5_3
| ~ spl5_6
| spl5_20 ),
inference(sat_conversion,[],[f256]) ).
cnf(s20,plain,
( ~ spl5_3
| ~ spl5_20
| spl5_21 ),
inference(sat_conversion,[],[f288]) ).
cnf(s24,plain,
( ~ spl5_5
| spl5_25 ),
inference(sat_conversion,[],[f367]) ).
cnf(s26,plain,
( ~ spl5_2
| ~ spl5_5
| ~ spl5_8
| spl5_27 ),
inference(sat_conversion,[],[f404]) ).
cnf(s29,plain,
( ~ spl5_21
| ~ spl5_25
| spl5_30 ),
inference(sat_conversion,[],[f472]) ).
cnf(s30,plain,
( ~ spl5_1
| ~ spl5_30
| spl5_31 ),
inference(sat_conversion,[],[f494]) ).
cnf(s45,plain,
( ~ spl5_25
| ~ spl5_31
| spl5_46 ),
inference(sat_conversion,[],[f787]) ).
cnf(s62,plain,
( ~ spl5_1
| ~ spl5_3
| ~ spl5_16
| spl5_63 ),
inference(sat_conversion,[],[f1026]) ).
cnf(s63,plain,
( ~ spl5_63
| spl5_64 ),
inference(sat_conversion,[],[f1033]) ).
cnf(s66,plain,
( ~ spl5_10
| spl5_67 ),
inference(sat_conversion,[],[f1063]) ).
cnf(s70,plain,
( ~ spl5_27
| ~ spl5_64
| ~ spl5_67
| spl5_71 ),
inference(sat_conversion,[],[f1150]) ).
cnf(s89,plain,
( ~ spl5_71
| spl5_91
| ~ spl5_92
| ~ spl5_93 ),
inference(sat_conversion,[],[f1440]) ).
cnf(s90,plain,
( ~ spl5_3
| spl5_92 ),
inference(sat_conversion,[],[f1443]) ).
cnf(s93,plain,
( ~ spl5_2
| ~ spl5_92
| spl5_93 ),
inference(sat_conversion,[],[f1479]) ).
cnf(s94,plain,
( ~ spl5_1
| spl5_11
| ~ spl5_31
| ~ spl5_91 ),
inference(sat_conversion,[],[f1541]) ).
cnf(s95,plain,
( ~ spl5_11
| ~ spl5_46 ),
inference(sat_conversion,[],[f1575]) ).
cnf(s98,plain,
spl5_25,
inference(rat,[],[s24,s5]) ).
cnf(s101,plain,
spl5_15,
inference(rat,[],[s14,s6,s5]) ).
cnf(s104,plain,
spl5_16,
inference(rat,[],[s15,s101]) ).
cnf(s105,plain,
spl5_92,
inference(rat,[],[s90,s3]) ).
cnf(s109,plain,
spl5_10,
inference(rat,[],[s10,s3]) ).
cnf(s116,plain,
spl5_67,
inference(rat,[],[s66,s109]) ).
cnf(s139,plain,
spl5_93,
inference(rat,[],[s93,s105,s2]) ).
cnf(s146,plain,
spl5_27,
inference(rat,[],[s26,s5,s8,s2]) ).
cnf(s149,plain,
spl5_63,
inference(rat,[],[s62,s3,s104,s1]) ).
cnf(s150,plain,
spl5_20,
inference(rat,[],[s19,s3,s6,s1]) ).
cnf(s152,plain,
spl5_64,
inference(rat,[],[s63,s149]) ).
cnf(s153,plain,
spl5_21,
inference(rat,[],[s20,s3,s150]) ).
cnf(s155,plain,
spl5_71,
inference(rat,[],[s70,s146,s116,s152]) ).
cnf(s158,plain,
spl5_30,
inference(rat,[],[s29,s98,s153]) ).
cnf(s159,plain,
spl5_91,
inference(rat,[],[s89,s139,s105,s155]) ).
cnf(s164,plain,
spl5_31,
inference(rat,[],[s30,s1,s158]) ).
cnf(s165,plain,
spl5_46,
inference(rat,[],[s45,s98,s164]) ).
cnf(s167,plain,
spl5_11,
inference(rat,[],[s94,s159,s1,s164]) ).
cnf(s168,plain,
$false,
inference(rat,[],[s95,s165,s167]) ).
fof(f1610,plain,
$false,
inference(avatar_sat_refutation,[],[s168]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG072+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n006.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 19:24:25 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 9.06/1.90 % (91135)Detected formulas, will run a generic FOF schedule.
% 9.06/1.90 % (91146)dis-21_1_sil=8000:lcm=predicate:random_seed=542987801: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)
% 9.06/1.90 % (91146)Refutation not found, incomplete strategy
% 9.06/1.90 % (91146)------------------------------
% 9.06/1.90 % (91146)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.06/1.90 % (91146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.06/1.90 % (91146)CaDiCaL version: 2.1.3
% 9.06/1.90 % (91146)Termination reason: Refutation not found, incomplete strategy
% 9.06/1.90 % (91146)Time elapsed: 0.001 s
% 9.06/1.90 % (91146)Peak memory usage: 88 MB
% 9.06/1.90 % (91146)Instructions burned: 1 (million)
% 9.06/1.90 % (91143)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=554386446:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.06/1.90 % (91145)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1408066821:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 9.06/1.90 % (91142)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=1468840068:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.06/1.90 % (91140)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=1120664139:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 9.06/1.90 % (91144)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2820688485:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 9.06/1.90 % (91141)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=2802743851:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 9.06/1.90 % (91143)Instruction limit reached!
% 9.06/1.90 % (91143)------------------------------
% 9.06/1.90 % (91143)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.06/1.90 % (91143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.06/1.90 % (91143)CaDiCaL version: 2.1.3
% 9.06/1.90 % (91143)Termination reason: Instruction limit
% 9.06/1.90 % (91143)Termination phase: Saturation
% 9.06/1.90 % (91143)Time elapsed: 0.062 s
% 9.06/1.90 % (91143)Peak memory usage: 88 MB
% 9.06/1.90 % (91143)Instructions burned: 109 (million)
% 9.06/1.90 % (91144)Instruction limit reached!
% 9.06/1.90 % (91144)------------------------------
% 9.06/1.90 % (91144)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.06/1.90 % (91144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.06/1.90 % (91144)CaDiCaL version: 2.1.3
% 9.06/1.90 % (91144)Termination reason: Instruction limit
% 9.06/1.90 % (91144)Termination phase: Saturation
% 9.06/1.90 % (91144)Time elapsed: 0.068 s
% 9.06/1.90 % (91144)Peak memory usage: 88 MB
% 9.06/1.90 % (91144)Instructions burned: 120 (million)
% 9.06/1.90 % (91145)Instruction limit reached!
% 9.06/1.90 % (91145)------------------------------
% 9.06/1.90 % (91145)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.06/1.90 % (91145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.06/1.90 % (91145)CaDiCaL version: 2.1.3
% 9.06/1.90 % (91145)Termination reason: Instruction limit
% 9.06/1.90 % (91145)Termination phase: Saturation
% 9.06/1.90 % (91145)Time elapsed: 0.089 s
% 9.06/1.90 % (91145)Peak memory usage: 89 MB
% 9.06/1.90 % (91145)Instructions burned: 139 (million)
% 9.06/1.90 % (91146)------------------------------
% 9.06/1.90 % (91146)------------------------------
% 9.06/1.90 % (91155)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1692265333:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 9.06/1.90 % (91157)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=2190634002:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 9.06/1.90 % (91154)lrs+10_1_sil=8000:sp=occurrence:random_seed=2681516194:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 9.06/1.90 % (91156)lrs+1011_1_sil=32000:sp=occurrence:random_seed=990288819:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 9.06/1.90 % (91157)Instruction limit reached!
% 9.06/1.90 % (91157)------------------------------
% 9.06/1.90 % (91157)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.06/1.90 % (91157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.06/1.90 % (91157)CaDiCaL version: 2.1.3
% 9.06/1.90 % (91157)Termination reason: Instruction limit
% 9.06/1.90 % (91157)Termination phase: Saturation
% 9.06/1.90 % (91157)Time elapsed: 0.071 s
% 9.06/1.90 % (91157)Peak memory usage: 94 MB
% 9.06/1.90 % (91157)Instructions burned: 248 (million)
% 9.06/1.90 % (91155)Instruction limit reached!
% 9.06/1.90 % (91155)------------------------------
% 9.06/1.90 % (91155)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.06/1.90 % (91155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.06/1.90 % (91155)CaDiCaL version: 2.1.3
% 9.06/1.90 % (91155)Termination reason: Instruction limit
% 9.06/1.90 % (91155)Termination phase: Saturation
% 9.06/1.90 % (91155)Time elapsed: 0.078 s
% 9.06/1.90 % (91155)Peak memory usage: 90 MB
% 9.06/1.90 % (91155)Instructions burned: 159 (million)
% 9.06/1.90 % (91163)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4016289109:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 9.06/1.90 % (91154)Instruction limit reached!
% 9.06/1.90 % (91154)------------------------------
% 9.06/1.90 % (91154)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.06/1.90 % (91154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.06/1.90 % (91154)CaDiCaL version: 2.1.3
% 9.06/1.90 % (91154)Termination reason: Instruction limit
% 9.06/1.90 % (91154)Termination phase: Saturation
% 9.06/1.90 % (91154)Time elapsed: 0.164 s
% 9.06/1.90 % (91154)Peak memory usage: 93 MB
% 9.06/1.90 % (91154)Instructions burned: 286 (million)
% 9.06/1.90 % (91162)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1021380813:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 9.06/1.90 % (91156)Instruction limit reached!
% 9.06/1.90 % (91156)------------------------------
% 9.06/1.90 % (91156)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.06/1.90 % (91156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.06/1.90 % (91156)CaDiCaL version: 2.1.3
% 9.06/1.90 % (91156)Termination reason: Instruction limit
% 9.06/1.90 % (91156)Termination phase: Saturation
% 9.06/1.90 % (91156)Time elapsed: 0.205 s
% 9.06/1.90 % (91156)Peak memory usage: 93 MB
% 9.06/1.90 % (91156)Instructions burned: 326 (million)
% 9.06/1.90 % (91165)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=725042529:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 9.06/1.90 % (91167)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3110973802:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 9.06/1.90 % (91162)Instruction limit reached!
% 9.06/1.90 % (91162)------------------------------
% 9.06/1.90 % (91162)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.06/1.90 % (91162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.06/1.90 % (91162)CaDiCaL version: 2.1.3
% 9.06/1.90 % (91162)Termination reason: Instruction limit
% 9.06/1.90 % (91162)Termination phase: Saturation
% 9.06/1.90 % (91162)Time elapsed: 0.164 s
% 9.06/1.90 % (91162)Peak memory usage: 90 MB
% 9.06/1.90 % (91162)Instructions burned: 294 (million)
% 9.06/1.90 % (91165)Instruction limit reached!
% 9.06/1.90 % (91165)------------------------------
% 9.06/1.90 % (91165)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.06/1.90 % (91165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.06/1.90 % (91165)CaDiCaL version: 2.1.3
% 9.06/1.90 % (91165)Termination reason: Instruction limit
% 9.06/1.90 % (91165)Termination phase: Saturation
% 9.06/1.90 % (91165)Time elapsed: 0.082 s
% 9.06/1.90 % (91165)Peak memory usage: 92 MB
% 9.06/1.90 % (91165)Instructions burned: 114 (million)
% 9.06/1.90 % (91167)Instruction limit reached!
% 9.06/1.90 % (91167)------------------------------
% 9.06/1.90 % (91167)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.06/1.90 % (91167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.06/1.90 % (91167)CaDiCaL version: 2.1.3
% 9.06/1.90 % (91167)Termination reason: Instruction limit
% 9.06/1.90 % (91167)Termination phase: Saturation
% 9.06/1.90 % (91167)Time elapsed: 0.060 s
% 9.06/1.90 % (91167)Peak memory usage: 89 MB
% 9.06/1.90 % (91167)Instructions burned: 127 (million)
% 9.06/1.90 % (91170)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1085289992:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 9.06/1.90 % (91171)lrs+10_1_sil=8000:sp=occurrence:random_seed=2626481426:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 9.06/1.90 % (91172)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=866768223:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 9.06/1.90 % (91170)Instruction limit reached!
% 9.06/1.90 % (91170)------------------------------
% 9.06/1.90 % (91170)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.06/1.90 % (91170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.06/1.90 % (91170)CaDiCaL version: 2.1.3
% 9.06/1.90 % (91170)Termination reason: Instruction limit
% 9.06/1.90 % (91170)Termination phase: Saturation
% 9.06/1.90 % (91170)Time elapsed: 0.058 s
% 9.06/1.90 % (91170)Peak memory usage: 88 MB
% 9.06/1.90 % (91170)Instructions burned: 114 (million)
% 9.06/1.90 % (91142)First to succeed.
% 9.06/1.90 % (91142)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-91135"
% 9.06/1.90 % (91141)Also succeeded, but the first one will report.
% 9.06/1.90 % (91176)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=884722661:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 9.06/1.90 % (91163)Also succeeded, but the first one will report.
% 9.06/1.90 % (91172)Instruction limit reached!
% 9.06/1.90 % (91172)------------------------------
% 9.06/1.90 % (91172)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.06/1.90 % (91172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.06/1.90 % (91172)CaDiCaL version: 2.1.3
% 9.06/1.90 % (91172)Termination reason: Instruction limit
% 9.06/1.90 % (91172)Termination phase: Saturation
% 9.06/1.90 % (91172)Time elapsed: 0.241 s
% 9.06/1.90 % (91172)Peak memory usage: 91 MB
% 9.06/1.90 % (91172)Instructions burned: 438 (million)
% 9.06/1.90 % (91142)Refutation found. Thanks to Tanya!
% 9.06/1.90 % SZS status Theorem for theBenchmark
% 9.06/1.90 % SZS output start Proof for theBenchmark
% See solution above
% 9.06/1.99 % (91142)------------------------------
% 9.06/1.99 % (91142)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.06/1.99 % (91142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.06/1.99 % (91142)CaDiCaL version: 2.1.3
% 9.06/1.99 % (91142)Termination reason: Refutation
% 9.06/1.99 % (91142)Time elapsed: 0.820 s
% 9.06/1.99 % (91142)Peak memory usage: 131 MB
% 9.06/1.99 % (91142)Instructions burned: 1197 (million)
% 9.06/1.99 % (91142)------------------------------
% 9.06/1.99 % (91142)------------------------------
% 9.06/1.99 % (91135)Success in time 1.231 s
% 9.06/1.99 % Vampire exiting
%------------------------------------------------------------------------------