%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG074+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 : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:09:30 AM UTC 2026
% Result : Theorem 2.17s 1.14s
% Output : Refutation 3.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 108 ( 23 unt; 9 def)
% Number of atoms : 351 ( 78 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 426 ( 183 ~; 177 |; 35 &)
% ( 9 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 13 ( 11 usr; 10 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 66 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( sorti1(X0)
=> ! [X1] :
( sorti1(X1)
=> sorti1(op1(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(f2,axiom,
! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> sorti2(op2(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(f3,axiom,
? [X0] :
( sorti1(X0)
& ? [X1] :
( sorti1(X1)
& op1(X1,X0) != op1(X0,X1)
& op1(op1(X0,X1),X1) = X0
& op1(op1(X0,X1),X0) != X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f4,axiom,
~ ? [X0] :
( sorti2(X0)
& ? [X1] :
( sorti2(X1)
& op2(X1,X0) != op2(X0,X1)
& op2(op2(X0,X1),X1) = X0
& op2(op2(X0,X1),X0) != X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f5,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(f6,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)],[f5]) ).
fof(f7,plain,
! [X0] :
( ! [X1] :
( sorti1(op1(X0,X1))
| ~ sorti1(X1) )
| ~ sorti1(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f8,plain,
! [X0] :
( ! [X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1) )
| ~ sorti2(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
! [X0] :
( ~ sorti2(X0)
| ! [X1] :
( ~ sorti2(X1)
| op2(X0,X1) = op2(X1,X0)
| op2(op2(X0,X1),X1) != X0
| op2(op2(X0,X1),X0) = X1 ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f10,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,[],[f6]) ).
fof(f11,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,[],[f10]) ).
fof(f12,plain,
( sorti1(sK0)
& sorti1(sK1)
& op1(sK0,sK1) != op1(sK1,sK0)
& sK0 = op1(op1(sK0,sK1),sK1)
& sK1 != op1(op1(sK0,sK1),sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f3]) ).
fof(f13,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,[],[f11]) ).
fof(f14,plain,
! [X0,X1] :
( ~ sorti1(X1)
| sorti1(op1(X0,X1))
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
! [X0,X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f16,plain,
sK1 != op1(op1(sK0,sK1),sK0),
inference(cnf_transformation,[],[f12]) ).
fof(f17,plain,
sK0 = op1(op1(sK0,sK1),sK1),
inference(cnf_transformation,[],[f12]) ).
fof(f18,plain,
op1(sK0,sK1) != op1(sK1,sK0),
inference(cnf_transformation,[],[f12]) ).
fof(f19,plain,
sorti1(sK1),
inference(cnf_transformation,[],[f12]) ).
fof(f20,plain,
sorti1(sK0),
inference(cnf_transformation,[],[f12]) ).
fof(f21,plain,
! [X0,X1] :
( op2(op2(X0,X1),X1) != X0
| ~ sorti2(X1)
| op2(X0,X1) = op2(X1,X0)
| ~ sorti2(X0)
| op2(op2(X0,X1),X0) = X1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f23,plain,
! [X6] :
( sorti2(h(X6))
| ~ sorti1(X6) ),
inference(cnf_transformation,[],[f13]) ).
fof(f24,plain,
! [X5] :
( ~ sorti1(X5)
| j(h(X5)) = X5 ),
inference(cnf_transformation,[],[f13]) ).
fof(f26,plain,
! [X2,X3] :
( j(op2(X2,X3)) = op1(j(X2),j(X3))
| ~ sorti2(X3)
| ~ sorti2(X2) ),
inference(cnf_transformation,[],[f13]) ).
fof(f27,plain,
! [X0,X1] :
( h(op1(X0,X1)) = op2(h(X0),h(X1))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f35,plain,
sK1 = j(h(sK1)),
inference(resolution,[],[f19,f24]) ).
fof(f40,definition,
( spl2_1
<=> sorti2(h(sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f41,plain,
( sorti2(h(sK1))
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f42,plain,
( ~ sorti2(h(sK1))
| spl2_1 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f53,plain,
sK0 = j(h(sK0)),
inference(resolution,[],[f20,f24]) ).
fof(f54,plain,
( ~ sorti1(sK1)
| spl2_1 ),
inference(resolution,[],[f42,f23]) ).
fof(f55,plain,
( $false
| spl2_1 ),
inference(forward_subsumption_resolution,[],[f54,f19]) ).
fof(f56,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f55]) ).
fof(f60,plain,
! [X0] :
( j(op2(X0,h(sK0))) = op1(j(X0),sK0)
| ~ sorti2(h(sK0))
| ~ sorti2(X0) ),
inference(superposition,[],[f26,f53]) ).
fof(f64,definition,
( spl2_4
<=> sorti2(h(sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f65,plain,
( sorti2(h(sK0))
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f66,plain,
( ~ sorti2(h(sK0))
| spl2_4 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f72,definition,
( spl2_6
<=> ! [X0] :
( j(op2(X0,h(sK0))) = op1(j(X0),sK0)
| ~ sorti2(X0) ) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f73,plain,
( ! [X0] :
( j(op2(X0,h(sK0))) = op1(j(X0),sK0)
| ~ sorti2(X0) )
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f74,plain,
( ~ spl2_4
| spl2_6 ),
inference(avatar_split_clause,[],[f60,f72,f64]) ).
fof(f75,plain,
( ~ sorti1(sK0)
| spl2_4 ),
inference(resolution,[],[f66,f23]) ).
fof(f76,plain,
( $false
| spl2_4 ),
inference(forward_subsumption_resolution,[],[f75,f20]) ).
fof(f77,plain,
spl2_4,
inference(avatar_contradiction_clause,[],[f76]) ).
fof(f79,plain,
! [X0] :
( ~ sorti1(X0)
| sorti1(op1(X0,sK1)) ),
inference(resolution,[],[f14,f19]) ).
fof(f154,definition,
( spl2_7
<=> sorti1(op1(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition]) ).
fof(f155,plain,
( sorti1(op1(sK0,sK1))
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f166,definition,
( spl2_10
<=> h(op1(sK0,sK1)) = op2(h(sK0),h(sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition]) ).
fof(f167,plain,
( h(op1(sK0,sK1)) = op2(h(sK0),h(sK1))
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f168,plain,
( h(op1(sK0,sK1)) != op2(h(sK0),h(sK1))
| spl2_10 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f175,plain,
sorti1(op1(sK0,sK1)),
inference(resolution,[],[f79,f20]) ).
fof(f179,plain,
spl2_7,
inference(avatar_split_clause,[],[f175,f154]) ).
fof(f181,plain,
( op1(sK0,sK1) = j(h(op1(sK0,sK1)))
| ~ spl2_7 ),
inference(resolution,[],[f155,f24]) ).
fof(f331,plain,
( h(op1(sK0,sK1)) != h(op1(sK0,sK1))
| ~ sorti1(sK1)
| ~ sorti1(sK0)
| spl2_10 ),
inference(superposition,[],[f168,f27]) ).
fof(f332,plain,
( ~ sorti1(sK1)
| ~ sorti1(sK0)
| spl2_10 ),
inference(trivial_inequality_removal,[],[f331]) ).
fof(f333,plain,
( ~ sorti1(sK0)
| spl2_10 ),
inference(forward_subsumption_resolution,[],[f332,f19]) ).
fof(f334,plain,
( $false
| spl2_10 ),
inference(forward_subsumption_resolution,[],[f333,f20]) ).
fof(f335,plain,
spl2_10,
inference(avatar_contradiction_clause,[],[f334]) ).
fof(f353,definition,
( spl2_11
<=> h(sK0) = op2(h(op1(sK0,sK1)),h(sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_11])],[avatar_definition]) ).
fof(f354,plain,
( h(sK0) != op2(h(op1(sK0,sK1)),h(sK1))
| spl2_11 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f357,definition,
( spl2_12
<=> sorti2(h(op1(sK0,sK1))) ),
introduced(definition,[new_symbols(definition,[spl2_12])],[avatar_definition]) ).
fof(f358,plain,
( sorti2(h(op1(sK0,sK1)))
| ~ spl2_12 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f372,plain,
( h(sK0) != op2(h(op1(sK0,sK1)),h(sK1))
| ~ sorti2(h(sK1))
| h(op1(sK0,sK1)) = op2(h(sK1),h(sK0))
| ~ sorti2(h(sK0))
| h(sK1) = op2(h(op1(sK0,sK1)),h(sK0))
| ~ spl2_10 ),
inference(superposition,[],[f21,f167]) ).
fof(f373,plain,
( sorti2(h(op1(sK0,sK1)))
| ~ sorti2(h(sK1))
| ~ sorti2(h(sK0))
| ~ spl2_10 ),
inference(superposition,[],[f15,f167]) ).
fof(f374,plain,
( sorti2(h(op1(sK0,sK1)))
| ~ sorti2(h(sK0))
| ~ spl2_1
| ~ spl2_10 ),
inference(forward_subsumption_resolution,[],[f373,f41]) ).
fof(f375,plain,
( h(sK0) != op2(h(op1(sK0,sK1)),h(sK1))
| h(op1(sK0,sK1)) = op2(h(sK1),h(sK0))
| ~ sorti2(h(sK0))
| h(sK1) = op2(h(op1(sK0,sK1)),h(sK0))
| ~ spl2_1
| ~ spl2_10 ),
inference(forward_subsumption_resolution,[],[f372,f41]) ).
fof(f376,plain,
( sorti2(h(op1(sK0,sK1)))
| ~ spl2_1
| ~ spl2_4
| ~ spl2_10 ),
inference(forward_subsumption_resolution,[],[f374,f65]) ).
fof(f377,plain,
( h(sK0) != op2(h(op1(sK0,sK1)),h(sK1))
| h(op1(sK0,sK1)) = op2(h(sK1),h(sK0))
| h(sK1) = op2(h(op1(sK0,sK1)),h(sK0))
| ~ spl2_1
| ~ spl2_4
| ~ spl2_10 ),
inference(forward_subsumption_resolution,[],[f375,f65]) ).
fof(f378,plain,
( spl2_12
| ~ spl2_1
| ~ spl2_4
| ~ spl2_10 ),
inference(avatar_split_clause,[],[f376,f166,f64,f40,f357]) ).
fof(f380,definition,
( spl2_13
<=> h(sK1) = op2(h(op1(sK0,sK1)),h(sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_13])],[avatar_definition]) ).
fof(f382,plain,
( h(sK1) = op2(h(op1(sK0,sK1)),h(sK0))
| ~ spl2_13 ),
inference(avatar_component_clause,[],[f380]) ).
fof(f384,definition,
( spl2_14
<=> h(op1(sK0,sK1)) = op2(h(sK1),h(sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_14])],[avatar_definition]) ).
fof(f386,plain,
( h(op1(sK0,sK1)) = op2(h(sK1),h(sK0))
| ~ spl2_14 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f387,plain,
( spl2_13
| spl2_14
| ~ spl2_11
| ~ spl2_1
| ~ spl2_4
| ~ spl2_10 ),
inference(avatar_split_clause,[],[f377,f166,f64,f40,f353,f384,f380]) ).
fof(f1522,plain,
( h(sK0) != h(op1(op1(sK0,sK1),sK1))
| ~ sorti1(sK1)
| ~ sorti1(op1(sK0,sK1))
| spl2_11 ),
inference(superposition,[],[f354,f27]) ).
fof(f1523,plain,
( h(sK0) != h(op1(op1(sK0,sK1),sK1))
| ~ sorti1(op1(sK0,sK1))
| spl2_11 ),
inference(forward_subsumption_resolution,[],[f1522,f19]) ).
fof(f1524,plain,
( h(sK0) != h(op1(op1(sK0,sK1),sK1))
| ~ spl2_7
| spl2_11 ),
inference(forward_subsumption_resolution,[],[f1523,f155]) ).
fof(f1525,plain,
( h(sK0) != h(sK0)
| ~ spl2_7
| spl2_11 ),
inference(forward_demodulation,[],[f1524,f17]) ).
fof(f1526,plain,
( $false
| ~ spl2_7
| spl2_11 ),
inference(trivial_inequality_removal,[],[f1525]) ).
fof(f1527,plain,
( ~ spl2_7
| spl2_11 ),
inference(avatar_contradiction_clause,[],[f1526]) ).
fof(f1563,plain,
( j(h(sK1)) = op1(j(h(op1(sK0,sK1))),sK0)
| ~ sorti2(h(op1(sK0,sK1)))
| ~ spl2_6
| ~ spl2_13 ),
inference(superposition,[],[f73,f382]) ).
fof(f1566,plain,
( j(h(sK1)) = op1(j(h(op1(sK0,sK1))),sK0)
| ~ spl2_6
| ~ spl2_12
| ~ spl2_13 ),
inference(forward_subsumption_resolution,[],[f1563,f358]) ).
fof(f1569,plain,
( op1(op1(sK0,sK1),sK0) = j(h(sK1))
| ~ spl2_6
| ~ spl2_7
| ~ spl2_12
| ~ spl2_13 ),
inference(forward_demodulation,[],[f1566,f181]) ).
fof(f1572,plain,
( sK1 = op1(op1(sK0,sK1),sK0)
| ~ spl2_6
| ~ spl2_7
| ~ spl2_12
| ~ spl2_13 ),
inference(forward_demodulation,[],[f1569,f35]) ).
fof(f1573,plain,
( $false
| ~ spl2_6
| ~ spl2_7
| ~ spl2_12
| ~ spl2_13 ),
inference(forward_subsumption_resolution,[],[f1572,f16]) ).
fof(f1574,plain,
( ~ spl2_6
| ~ spl2_7
| ~ spl2_12
| ~ spl2_13 ),
inference(avatar_contradiction_clause,[],[f1573]) ).
fof(f1590,plain,
( j(h(op1(sK0,sK1))) = op1(j(h(sK1)),sK0)
| ~ sorti2(h(sK1))
| ~ spl2_6
| ~ spl2_14 ),
inference(superposition,[],[f73,f386]) ).
fof(f1593,plain,
( j(h(op1(sK0,sK1))) = op1(j(h(sK1)),sK0)
| ~ spl2_1
| ~ spl2_6
| ~ spl2_14 ),
inference(forward_subsumption_resolution,[],[f1590,f41]) ).
fof(f1597,plain,
( op1(sK1,sK0) = j(h(op1(sK0,sK1)))
| ~ spl2_1
| ~ spl2_6
| ~ spl2_14 ),
inference(forward_demodulation,[],[f1593,f35]) ).
fof(f1601,plain,
( op1(sK0,sK1) = op1(sK1,sK0)
| ~ spl2_1
| ~ spl2_6
| ~ spl2_7
| ~ spl2_14 ),
inference(forward_demodulation,[],[f1597,f181]) ).
fof(f1603,plain,
( $false
| ~ spl2_1
| ~ spl2_6
| ~ spl2_7
| ~ spl2_14 ),
inference(forward_subsumption_resolution,[],[f1601,f18]) ).
fof(f1604,plain,
( ~ spl2_1
| ~ spl2_6
| ~ spl2_7
| ~ spl2_14 ),
inference(avatar_contradiction_clause,[],[f1603]) ).
cnf(s3,plain,
spl2_1,
inference(sat_conversion,[],[f56]) ).
cnf(s5,plain,
( ~ spl2_4
| spl2_6 ),
inference(sat_conversion,[],[f74]) ).
cnf(s6,plain,
spl2_4,
inference(sat_conversion,[],[f77]) ).
cnf(s9,plain,
spl2_7,
inference(sat_conversion,[],[f179]) ).
cnf(s10,plain,
spl2_10,
inference(sat_conversion,[],[f335]) ).
cnf(s12,plain,
( ~ spl2_1
| ~ spl2_4
| ~ spl2_10
| spl2_12 ),
inference(sat_conversion,[],[f378]) ).
cnf(s13,plain,
( ~ spl2_1
| ~ spl2_4
| ~ spl2_10
| ~ spl2_11
| spl2_13
| spl2_14 ),
inference(sat_conversion,[],[f387]) ).
cnf(s15,plain,
( ~ spl2_7
| spl2_11 ),
inference(sat_conversion,[],[f1527]) ).
cnf(s17,plain,
( ~ spl2_6
| ~ spl2_7
| ~ spl2_12
| ~ spl2_13 ),
inference(sat_conversion,[],[f1574]) ).
cnf(s18,plain,
( ~ spl2_1
| ~ spl2_6
| ~ spl2_7
| ~ spl2_14 ),
inference(sat_conversion,[],[f1604]) ).
cnf(s20,plain,
spl2_11,
inference(rat,[],[s15,s9]) ).
cnf(s22,plain,
spl2_6,
inference(rat,[],[s5,s6]) ).
cnf(s24,plain,
~ spl2_14,
inference(rat,[],[s18,s22,s9,s3]) ).
cnf(s25,plain,
spl2_13,
inference(rat,[],[s13,s24,s6,s20,s10,s3]) ).
cnf(s26,plain,
spl2_12,
inference(rat,[],[s12,s6,s10,s3]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s17,s22,s9,s25,s26]) ).
fof(f1607,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG074+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n004.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % 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 19:24:52 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
% 2.17/1.14 % (672238)Detected formulas, will run a generic FOF schedule.
% 2.17/1.14 % (672245)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=4279006968:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.17/1.14 % (672249)dis-21_1_sil=8000:lcm=predicate:random_seed=173378012:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.17/1.14 % (672246)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4045974333:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.17/1.14 % (672244)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=1255500695:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.17/1.14 % (672243)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=4216516095:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.17/1.14 % (672247)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2210159045:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.17/1.14 % (672248)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2293390222:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.17/1.14 % (672249)Refutation not found, incomplete strategy
% 2.17/1.14 % (672249)------------------------------
% 2.17/1.14 % (672249)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.17/1.14 % (672249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.17/1.14 % (672249)CaDiCaL version: 2.1.3
% 2.17/1.14 % (672249)Termination reason: Refutation not found, incomplete strategy
% 2.17/1.14 % (672249)Time elapsed: 0.002 s
% 2.17/1.14 % (672249)Peak memory usage: 88 MB
% 2.17/1.14 % (672249)Instructions burned: 1 (million)
% 2.17/1.14 % (672248)First to succeed.
% 2.17/1.14 % (672248)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-672238"
% 2.17/1.14 % (672246)Also succeeded, but the first one will report.
% 2.17/1.14 % (672247)Instruction limit reached!
% 2.17/1.14 % (672247)------------------------------
% 2.17/1.14 % (672247)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.17/1.14 % (672247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.17/1.14 % (672247)CaDiCaL version: 2.1.3
% 2.17/1.14 % (672247)Termination reason: Instruction limit
% 2.17/1.14 % (672247)Termination phase: Saturation
% 2.17/1.14 % (672247)Time elapsed: 0.069 s
% 2.17/1.14 % (672247)Peak memory usage: 88 MB
% 2.17/1.14 % (672247)Instructions burned: 119 (million)
% 2.17/1.14 % (672257)lrs+10_1_sil=8000:sp=occurrence:random_seed=2631201326:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.17/1.14 % (672249)------------------------------
% 2.17/1.14 % (672249)------------------------------
% 2.17/1.14 % (672248)Refutation found. Thanks to Tanya!
% 2.17/1.14 % SZS status Theorem for theBenchmark
% 2.17/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 3.98/1.33 % (672248)------------------------------
% 3.98/1.33 % (672248)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.33 % (672248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.33 % (672248)CaDiCaL version: 2.1.3
% 3.98/1.33 % (672248)Termination reason: Refutation
% 3.98/1.33 % (672248)Time elapsed: 0.043 s
% 3.98/1.33 % (672248)Peak memory usage: 90 MB
% 3.98/1.33 % (672248)Instructions burned: 65 (million)
% 3.98/1.33 % (672248)------------------------------
% 3.98/1.33 % (672248)------------------------------
% 3.98/1.33 % (672238)Success in time 0.471 s
% 3.98/1.33 % Vampire exiting
%------------------------------------------------------------------------------