%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP776+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 10:16:10 AM UTC 2026
% Result : Theorem 6.45s 1.92s
% Output : Refutation 9.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 26
% Syntax : Number of formulae : 146 ( 33 unt; 13 def)
% Number of atoms : 322 ( 90 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 335 ( 159 ~; 152 |; 6 &)
% ( 8 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 9 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn 76 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( g(X0)
=> g(inv(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).
fof(f3,axiom,
g(eh),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
fof(f5,axiom,
! [X0] :
( g(X0)
=> product(eh,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).
fof(f7,axiom,
! [X0] :
( g(X0)
=> product(X0,inv(X0)) = eh ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos07) ).
fof(f10,axiom,
! [X0,X1] :
( h(X1)
=> h(opp(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos10) ).
fof(f12,axiom,
! [X0,X1,X2] :
( ( h(X2)
& h(X1)
& h(X0) )
=> sum(sum(X2,X1),X0) = sum(X2,sum(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos12) ).
fof(f13,axiom,
! [X0] :
( h(X0)
=> sum(eg,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos13) ).
fof(f14,axiom,
! [X0] :
( h(X0)
=> sum(X0,eg) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos14) ).
fof(f15,axiom,
! [X0] :
( h(X0)
=> sum(X0,opp(X0)) = eg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos15) ).
fof(f16,axiom,
! [X0] :
( h(X0)
=> sum(opp(X0),X0) = eg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos16) ).
fof(f17,axiom,
! [X0] :
( g(X0)
=> h(f(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos17) ).
fof(f18,axiom,
! [X0,X1] : f(product(X1,X0)) = sum(f(X1),f(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos18) ).
fof(f19,conjecture,
! [X0] :
( f(eh) = eg
& ( ~ g(X0)
| f(inv(X0)) = opp(f(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0] :
( f(eh) = eg
& ( ~ g(X0)
| f(inv(X0)) = opp(f(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f23,plain,
! [X0] :
( g(inv(X0))
| ~ g(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f26,plain,
! [X0] :
( product(eh,X0) = X0
| ~ g(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f28,plain,
! [X0] :
( product(X0,inv(X0)) = eh
| ~ g(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f32,plain,
! [X0,X1] :
( h(opp(X0))
| ~ h(X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f33,plain,
! [X0,X1,X2] :
( sum(sum(X2,X1),X0) = sum(X2,sum(X1,X0))
| ~ h(X2)
| ~ h(X1)
| ~ h(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f34,plain,
! [X0,X1,X2] :
( sum(sum(X2,X1),X0) = sum(X2,sum(X1,X0))
| ~ h(X2)
| ~ h(X1)
| ~ h(X0) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0] :
( sum(eg,X0) = X0
| ~ h(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f36,plain,
! [X0] :
( sum(X0,eg) = X0
| ~ h(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f37,plain,
! [X0] :
( sum(X0,opp(X0)) = eg
| ~ h(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f38,plain,
! [X0] :
( sum(opp(X0),X0) = eg
| ~ h(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f39,plain,
! [X0] :
( h(f(X0))
| ~ g(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f40,plain,
? [X0] :
( eg != f(eh)
| ( g(X0)
& f(inv(X0)) != opp(f(X0)) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f41,plain,
( eg != f(eh)
| ( g(sK0)
& f(inv(sK0)) != opp(f(sK0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f40]) ).
fof(f43,plain,
! [X0] :
( g(inv(X0))
| ~ g(X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f44,plain,
g(eh),
inference(cnf_transformation,[],[f3]) ).
fof(f46,plain,
! [X0] :
( ~ g(X0)
| product(eh,X0) = X0 ),
inference(cnf_transformation,[],[f26]) ).
fof(f48,plain,
! [X0] :
( ~ g(X0)
| eh = product(X0,inv(X0)) ),
inference(cnf_transformation,[],[f28]) ).
fof(f51,plain,
! [X0,X1] :
( h(opp(X0))
| ~ h(X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f53,plain,
! [X2,X0,X1] :
( ~ h(X2)
| sum(sum(X2,X1),X0) = sum(X2,sum(X1,X0))
| ~ h(X1)
| ~ h(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f54,plain,
! [X0] :
( ~ h(X0)
| sum(eg,X0) = X0 ),
inference(cnf_transformation,[],[f35]) ).
fof(f55,plain,
! [X0] :
( ~ h(X0)
| sum(X0,eg) = X0 ),
inference(cnf_transformation,[],[f36]) ).
fof(f56,plain,
! [X0] :
( ~ h(X0)
| eg = sum(X0,opp(X0)) ),
inference(cnf_transformation,[],[f37]) ).
fof(f57,plain,
! [X0] :
( ~ h(X0)
| eg = sum(opp(X0),X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f58,plain,
! [X0] :
( h(f(X0))
| ~ g(X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f59,plain,
! [X0,X1] : f(product(X1,X0)) = sum(f(X1),f(X0)),
inference(cnf_transformation,[],[f18]) ).
fof(f60,plain,
( eg != f(eh)
| f(inv(sK0)) != opp(f(sK0)) ),
inference(cnf_transformation,[],[f41]) ).
fof(f61,plain,
( eg != f(eh)
| g(sK0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f62,definition,
sF1 = f(eh),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f63,plain,
f(eh) = sF1,
inference(reorient_equations,[],[f62]) ).
fof(f64,plain,
( eg != sF1
| g(sK0) ),
inference(definition_folding,[],[f61,f63]) ).
fof(f65,definition,
sF2 = inv(sK0),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f66,plain,
inv(sK0) = sF2,
inference(reorient_equations,[],[f65]) ).
fof(f67,definition,
sF3 = f(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f68,plain,
f(sF2) = sF3,
inference(reorient_equations,[],[f67]) ).
fof(f69,definition,
sF4 = f(sK0),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f70,plain,
f(sK0) = sF4,
inference(reorient_equations,[],[f69]) ).
fof(f71,definition,
sF5 = opp(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f72,plain,
opp(sF4) = sF5,
inference(reorient_equations,[],[f71]) ).
fof(f73,plain,
( eg != sF1
| sF3 != sF5 ),
inference(definition_folding,[],[f60,f72,f70,f68,f66,f63]) ).
fof(f75,definition,
( spl6_1
<=> sF3 = sF5 ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f77,plain,
( sF3 != sF5
| spl6_1 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f79,definition,
( spl6_2
<=> eg = sF1 ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f80,plain,
( eg = sF1
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f81,plain,
( eg != sF1
| spl6_2 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f73,f79,f75]) ).
fof(f84,definition,
( spl6_3
<=> g(sK0) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
fof(f86,plain,
( g(sK0)
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f87,plain,
( spl6_3
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f64,f79,f84]) ).
fof(f89,definition,
( spl6_4
<=> ! [X1] : ~ h(X1) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
fof(f90,plain,
( ! [X1] : ~ h(X1)
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f92,definition,
( spl6_5
<=> ! [X0] : h(opp(X0)) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
fof(f93,plain,
( ! [X0] : h(opp(X0))
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f94,plain,
( spl6_4
| spl6_5 ),
inference(avatar_split_clause,[],[f51,f92,f89]) ).
fof(f95,plain,
( h(sF4)
| ~ g(sK0) ),
inference(superposition,[],[f58,f70]) ).
fof(f96,plain,
( h(sF3)
| ~ g(sF2) ),
inference(superposition,[],[f58,f68]) ).
fof(f97,plain,
( h(sF1)
| ~ g(eh) ),
inference(superposition,[],[f58,f63]) ).
fof(f98,plain,
( ~ g(eh)
| ~ spl6_4 ),
inference(forward_subsumption_resolution,[],[f97,f90]) ).
fof(f101,plain,
( $false
| ~ spl6_4 ),
inference(forward_subsumption_resolution,[],[f98,f44]) ).
fof(f102,plain,
~ spl6_4,
inference(avatar_contradiction_clause,[],[f101]) ).
fof(f104,plain,
h(sF1),
inference(forward_subsumption_resolution,[],[f97,f44]) ).
fof(f106,definition,
( spl6_6
<=> g(sF2) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
fof(f107,plain,
( g(sF2)
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f108,plain,
( ~ g(sF2)
| spl6_6 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f110,definition,
( spl6_7
<=> h(sF3) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
fof(f112,plain,
( h(sF3)
| ~ spl6_7 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f113,plain,
( ~ spl6_6
| spl6_7 ),
inference(avatar_split_clause,[],[f96,f110,f106]) ).
fof(f115,definition,
( spl6_8
<=> h(sF4) ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
fof(f117,plain,
( h(sF4)
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,plain,
( ~ spl6_3
| spl6_8 ),
inference(avatar_split_clause,[],[f95,f115,f84]) ).
fof(f120,plain,
! [X0] :
( ~ g(X0)
| eg = sum(opp(f(X0)),f(X0)) ),
inference(resolution,[],[f57,f58]) ).
fof(f124,plain,
( g(sF2)
| ~ g(sK0) ),
inference(superposition,[],[f43,f66]) ).
fof(f127,plain,
eg = sum(sF1,opp(sF1)),
inference(resolution,[],[f104,f56]) ).
fof(f135,plain,
! [X0] :
( ~ g(X0)
| f(X0) = sum(eg,f(X0)) ),
inference(resolution,[],[f54,f58]) ).
fof(f137,plain,
( ! [X0] : opp(X0) = sum(opp(X0),eg)
| ~ spl6_5 ),
inference(resolution,[],[f55,f93]) ).
fof(f140,plain,
sF1 = sum(sF1,eg),
inference(resolution,[],[f55,f104]) ).
fof(f145,plain,
eh = product(eh,eh),
inference(resolution,[],[f44,f46]) ).
fof(f151,plain,
! [X0] : f(product(X0,sF2)) = sum(f(X0),sF3),
inference(superposition,[],[f59,f68]) ).
fof(f152,plain,
! [X0] : f(product(X0,eh)) = sum(f(X0),sF1),
inference(superposition,[],[f59,f63]) ).
fof(f158,plain,
( ! [X2,X0,X1] :
( ~ h(X2)
| ~ h(X1)
| sum(sum(opp(X0),X1),X2) = sum(opp(X0),sum(X1,X2)) )
| ~ spl6_5 ),
inference(resolution,[],[f53,f93]) ).
fof(f160,plain,
! [X2,X0,X1] :
( ~ h(X2)
| ~ h(X1)
| sum(sum(f(X0),X1),X2) = sum(f(X0),sum(X1,X2))
| ~ g(X0) ),
inference(resolution,[],[f53,f58]) ).
fof(f261,plain,
( ! [X2,X0,X1] :
( ~ h(X0)
| sum(sum(f(X1),X0),opp(X2)) = sum(f(X1),sum(X0,opp(X2)))
| ~ g(X1) )
| ~ spl6_5 ),
inference(resolution,[],[f160,f93]) ).
fof(f302,plain,
f(eh) = sum(f(eh),sF1),
inference(superposition,[],[f152,f145]) ).
fof(f305,plain,
sF1 = sum(sF1,sF1),
inference(forward_demodulation,[],[f302,f63]) ).
fof(f426,plain,
( ! [X0,X1] :
( ~ g(X0)
| sum(sum(f(X0),sF1),opp(X1)) = sum(f(X0),sum(sF1,opp(X1))) )
| ~ spl6_5 ),
inference(resolution,[],[f261,f104]) ).
fof(f512,plain,
( ! [X0] : sum(sum(f(eh),sF1),opp(X0)) = sum(f(eh),sum(sF1,opp(X0)))
| ~ spl6_5 ),
inference(resolution,[],[f426,f44]) ).
fof(f514,plain,
( ! [X0] : sum(sum(sF1,sF1),opp(X0)) = sum(sF1,sum(sF1,opp(X0)))
| ~ spl6_5 ),
inference(forward_demodulation,[],[f512,f63]) ).
fof(f515,plain,
( ! [X0] : sum(sF1,opp(X0)) = sum(sF1,sum(sF1,opp(X0)))
| ~ spl6_5 ),
inference(forward_demodulation,[],[f514,f305]) ).
fof(f518,plain,
( eg = sum(sF1,eg)
| ~ spl6_5 ),
inference(superposition,[],[f515,f127]) ).
fof(f520,plain,
( eg = sF1
| ~ spl6_5 ),
inference(forward_demodulation,[],[f518,f140]) ).
fof(f522,plain,
( $false
| spl6_2
| ~ spl6_5 ),
inference(forward_subsumption_resolution,[],[f520,f81]) ).
fof(f523,plain,
( spl6_2
| ~ spl6_5 ),
inference(avatar_contradiction_clause,[],[f522]) ).
fof(f524,plain,
( ~ g(sK0)
| spl6_6 ),
inference(forward_subsumption_resolution,[],[f124,f108]) ).
fof(f525,plain,
( $false
| ~ spl6_3
| spl6_6 ),
inference(forward_subsumption_resolution,[],[f524,f86]) ).
fof(f526,plain,
( ~ spl6_3
| spl6_6 ),
inference(avatar_contradiction_clause,[],[f525]) ).
fof(f530,plain,
( eh = product(sK0,inv(sK0))
| ~ spl6_3 ),
inference(resolution,[],[f86,f48]) ).
fof(f532,plain,
( eg = sum(opp(f(sK0)),f(sK0))
| ~ spl6_3 ),
inference(resolution,[],[f86,f120]) ).
fof(f558,plain,
( eg = sum(opp(sF4),sF4)
| ~ spl6_3 ),
inference(forward_demodulation,[],[f532,f70]) ).
fof(f560,plain,
( eh = product(sK0,sF2)
| ~ spl6_3 ),
inference(forward_demodulation,[],[f530,f66]) ).
fof(f563,plain,
( eg = sum(sF5,sF4)
| ~ spl6_3 ),
inference(forward_demodulation,[],[f558,f72]) ).
fof(f593,plain,
( f(eh) = sum(f(sK0),sF3)
| ~ spl6_3 ),
inference(superposition,[],[f151,f560]) ).
fof(f597,plain,
( f(eh) = sum(sF4,sF3)
| ~ spl6_3 ),
inference(forward_demodulation,[],[f593,f70]) ).
fof(f599,plain,
( sF1 = sum(sF4,sF3)
| ~ spl6_3 ),
inference(forward_demodulation,[],[f597,f63]) ).
fof(f601,plain,
( eg = sum(sF4,sF3)
| ~ spl6_2
| ~ spl6_3 ),
inference(forward_demodulation,[],[f599,f80]) ).
fof(f631,plain,
( f(sF2) = sum(eg,f(sF2))
| ~ spl6_6 ),
inference(resolution,[],[f107,f135]) ).
fof(f646,plain,
( sF3 = sum(eg,sF3)
| ~ spl6_6 ),
inference(forward_demodulation,[],[f631,f68]) ).
fof(f699,plain,
( ! [X0,X1] :
( ~ h(X0)
| sum(sum(opp(X1),X0),sF3) = sum(opp(X1),sum(X0,sF3)) )
| ~ spl6_5
| ~ spl6_7 ),
inference(resolution,[],[f112,f158]) ).
fof(f1292,plain,
( ! [X0] : sum(sum(opp(X0),sF4),sF3) = sum(opp(X0),sum(sF4,sF3))
| ~ spl6_5
| ~ spl6_7
| ~ spl6_8 ),
inference(resolution,[],[f699,f117]) ).
fof(f1294,plain,
( ! [X0] : sum(opp(X0),eg) = sum(sum(opp(X0),sF4),sF3)
| ~ spl6_2
| ~ spl6_3
| ~ spl6_5
| ~ spl6_7
| ~ spl6_8 ),
inference(forward_demodulation,[],[f1292,f601]) ).
fof(f1301,plain,
( ! [X0] : opp(X0) = sum(sum(opp(X0),sF4),sF3)
| ~ spl6_2
| ~ spl6_3
| ~ spl6_5
| ~ spl6_7
| ~ spl6_8 ),
inference(forward_demodulation,[],[f1294,f137]) ).
fof(f1306,plain,
( sF5 = sum(sum(sF5,sF4),sF3)
| ~ spl6_2
| ~ spl6_3
| ~ spl6_5
| ~ spl6_7
| ~ spl6_8 ),
inference(superposition,[],[f1301,f72]) ).
fof(f1309,plain,
( sF5 = sum(eg,sF3)
| ~ spl6_2
| ~ spl6_3
| ~ spl6_5
| ~ spl6_7
| ~ spl6_8 ),
inference(forward_demodulation,[],[f1306,f563]) ).
fof(f1311,plain,
( sF3 = sF5
| ~ spl6_2
| ~ spl6_3
| ~ spl6_5
| ~ spl6_6
| ~ spl6_7
| ~ spl6_8 ),
inference(forward_demodulation,[],[f1309,f646]) ).
fof(f1312,plain,
( $false
| spl6_1
| ~ spl6_2
| ~ spl6_3
| ~ spl6_5
| ~ spl6_6
| ~ spl6_7
| ~ spl6_8 ),
inference(forward_subsumption_resolution,[],[f1311,f77]) ).
fof(f1313,plain,
( spl6_1
| ~ spl6_2
| ~ spl6_3
| ~ spl6_5
| ~ spl6_6
| ~ spl6_7
| ~ spl6_8 ),
inference(avatar_contradiction_clause,[],[f1312]) ).
cnf(s1,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f82]) ).
cnf(s2,plain,
( ~ spl6_2
| spl6_3 ),
inference(sat_conversion,[],[f87]) ).
cnf(s3,plain,
( spl6_4
| spl6_5 ),
inference(sat_conversion,[],[f94]) ).
cnf(s4,plain,
~ spl6_4,
inference(sat_conversion,[],[f102]) ).
cnf(s6,plain,
( ~ spl6_6
| spl6_7 ),
inference(sat_conversion,[],[f113]) ).
cnf(s7,plain,
( ~ spl6_3
| spl6_8 ),
inference(sat_conversion,[],[f118]) ).
cnf(s10,plain,
( spl6_2
| ~ spl6_5 ),
inference(sat_conversion,[],[f523]) ).
cnf(s11,plain,
( ~ spl6_3
| spl6_6 ),
inference(sat_conversion,[],[f526]) ).
cnf(s12,plain,
( spl6_1
| ~ spl6_2
| ~ spl6_3
| ~ spl6_5
| ~ spl6_6
| ~ spl6_7
| ~ spl6_8 ),
inference(sat_conversion,[],[f1313]) ).
cnf(s13,plain,
spl6_5,
inference(rat,[],[s3,s4]) ).
cnf(s14,plain,
spl6_2,
inference(rat,[],[s10,s13]) ).
cnf(s17,plain,
spl6_3,
inference(rat,[],[s2,s14]) ).
cnf(s18,plain,
spl6_6,
inference(rat,[],[s11,s17]) ).
cnf(s19,plain,
spl6_8,
inference(rat,[],[s7,s17]) ).
cnf(s20,plain,
spl6_7,
inference(rat,[],[s6,s18]) ).
cnf(s21,plain,
spl6_1,
inference(rat,[],[s12,s19,s17,s18,s13,s14,s20]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s1,s14,s21]) ).
fof(f1314,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP776+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 % Computer : n010.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sun Sep 27 10:44:16 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.45 Running first-order theorem proving
% 0.16/0.45 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
% 6.45/1.92 % (775901)Detected formulas, will run a generic FOF schedule.
% 6.45/1.92 % (775969)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1953562161:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.45/1.92 % (775968)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2530202274:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.45/1.92 % (775964)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=3277198546:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.45/1.92 % (775965)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=2956026799:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.45/1.92 % (775970)dis-21_1_sil=8000:lcm=predicate:random_seed=2223303926: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)
% 6.45/1.92 % (775966)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=2961256388:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.45/1.92 % (775967)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=489070107:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.45/1.92 % (775970)Refutation not found, incomplete strategy
% 6.45/1.92 % (775970)------------------------------
% 6.45/1.92 % (775970)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.45/1.92 % (775970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.92 % (775970)CaDiCaL version: 2.1.3
% 6.45/1.92 % (775970)Termination reason: Refutation not found, incomplete strategy
% 6.45/1.92 % (775970)Time elapsed: 0.002 s
% 6.45/1.92 % (775970)Peak memory usage: 88 MB
% 6.45/1.92 % (775970)Instructions burned: 1 (million)
% 6.45/1.92 % (775967)Refutation not found, incomplete strategy
% 6.45/1.92 % (775967)------------------------------
% 6.45/1.92 % (775967)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.45/1.92 % (775967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.92 % (775967)CaDiCaL version: 2.1.3
% 6.45/1.92 % (775967)Termination reason: Refutation not found, incomplete strategy
% 6.45/1.92 % (775967)Time elapsed: 0.002 s
% 6.45/1.92 % (775967)Peak memory usage: 88 MB
% 6.45/1.92 % (775967)Instructions burned: 1 (million)
% 6.45/1.92 % (775968)Instruction limit reached!
% 6.45/1.92 % (775968)------------------------------
% 6.45/1.92 % (775968)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.45/1.92 % (775968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.92 % (775968)CaDiCaL version: 2.1.3
% 6.45/1.92 % (775968)Termination reason: Instruction limit
% 6.45/1.92 % (775968)Termination phase: Saturation
% 6.45/1.92 % (775968)Time elapsed: 0.068 s
% 6.45/1.92 % (775968)Peak memory usage: 88 MB
% 6.45/1.92 % (775968)Instructions burned: 121 (million)
% 6.45/1.92 % (775969)Instruction limit reached!
% 6.45/1.92 % (775969)------------------------------
% 6.45/1.92 % (775969)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.45/1.92 % (775969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.92 % (775969)CaDiCaL version: 2.1.3
% 6.45/1.92 % (775969)Termination reason: Instruction limit
% 6.45/1.92 % (775969)Termination phase: Saturation
% 6.45/1.92 % (775969)Time elapsed: 0.085 s
% 6.45/1.92 % (775969)Peak memory usage: 89 MB
% 6.45/1.92 % (775969)Instructions burned: 140 (million)
% 6.45/1.92 % (775978)lrs+10_1_sil=8000:sp=occurrence:random_seed=2975743271:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.45/1.92 % (775979)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3340055830:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.45/1.92 % (775979)Refutation not found, incomplete strategy
% 6.45/1.92 % (775979)------------------------------
% 6.45/1.92 % (775979)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.45/1.92 % (775979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.92 % (775979)CaDiCaL version: 2.1.3
% 6.45/1.92 % (775979)Termination reason: Refutation not found, incomplete strategy
% 6.45/1.92 % (775979)Time elapsed: 0.003 s
% 6.45/1.92 % (775979)Peak memory usage: 89 MB
% 6.45/1.92 % (775979)Instructions burned: 8 (million)
% 6.45/1.92 % (775970)------------------------------
% 6.45/1.92 % (775970)------------------------------
% 6.45/1.92 % (775967)------------------------------
% 6.45/1.92 % (775967)------------------------------
% 6.45/1.92 % (775979)------------------------------
% 6.45/1.92 % (775979)------------------------------
% 6.45/1.92 % (775978)Instruction limit reached!
% 6.45/1.92 % (775978)------------------------------
% 6.45/1.92 % (775978)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.45/1.92 % (775978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.92 % (775978)CaDiCaL version: 2.1.3
% 6.45/1.92 % (775978)Termination reason: Instruction limit
% 6.45/1.92 % (775978)Termination phase: Saturation
% 6.45/1.92 % (775978)Time elapsed: 0.169 s
% 6.45/1.92 % (775978)Peak memory usage: 92 MB
% 6.45/1.92 % (775978)Instructions burned: 286 (million)
% 6.45/1.92 % (775982)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1625215184:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 6.45/1.92 % (775983)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=3133078049:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 6.45/1.92 % (775985)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=31364077:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.45/1.92 % (775984)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2669279820:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 6.45/1.92 % (775983)Instruction limit reached!
% 6.45/1.92 % (775983)------------------------------
% 6.45/1.92 % (775983)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.45/1.92 % (775983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.92 % (775983)CaDiCaL version: 2.1.3
% 6.45/1.92 % (775983)Termination reason: Instruction limit
% 6.45/1.92 % (775983)Termination phase: Saturation
% 6.45/1.92 % (775983)Time elapsed: 0.124 s
% 6.45/1.92 % (775983)Peak memory usage: 93 MB
% 6.45/1.92 % (775983)Instructions burned: 249 (million)
% 6.45/1.92 % (775984)Refutation not found, incomplete strategy
% 6.45/1.92 % (775984)------------------------------
% 6.45/1.92 % (775984)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.45/1.92 % (775984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.92 % (775984)CaDiCaL version: 2.1.3
% 6.45/1.92 % (775984)Termination reason: Refutation not found, incomplete strategy
% 6.45/1.92 % (775984)Time elapsed: 0.002 s
% 6.45/1.92 % (775984)Peak memory usage: 88 MB
% 6.45/1.92 % (775984)Instructions burned: 1 (million)
% 6.45/1.92 % (775966)Refutation not found, incomplete strategy
% 6.45/1.92 % (775966)------------------------------
% 6.45/1.92 % (775966)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.45/1.92 % (775966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.92 % (775966)CaDiCaL version: 2.1.3
% 6.45/1.92 % (775966)Termination reason: Refutation not found, incomplete strategy
% 6.45/1.92 % (775966)Time elapsed: 0.600 s
% 6.45/1.92 % (775966)Peak memory usage: 126 MB
% 6.45/1.92 % (775966)Instructions burned: 890 (million)
% 6.45/1.92 % (775982)Instruction limit reached!
% 6.45/1.92 % (775982)------------------------------
% 6.45/1.92 % (775982)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.45/1.92 % (775982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.92 % (775982)CaDiCaL version: 2.1.3
% 6.45/1.92 % (775982)Termination reason: Instruction limit
% 6.45/1.92 % (775982)Termination phase: Saturation
% 6.45/1.92 % (775982)Time elapsed: 0.191 s
% 6.45/1.92 % (775982)Peak memory usage: 93 MB
% 6.45/1.92 % (775982)Instructions burned: 326 (million)
% 6.45/1.92 % (775990)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1195149918:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 6.45/1.92 % (775990)Refutation not found, incomplete strategy
% 6.45/1.92 % (775990)------------------------------
% 6.45/1.92 % (775990)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.45/1.92 % (775990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.92 % (775990)CaDiCaL version: 2.1.3
% 6.45/1.92 % (775990)Termination reason: Refutation not found, incomplete strategy
% 6.45/1.92 % (775990)Time elapsed: 0.002 s
% 6.45/1.92 % (775990)Peak memory usage: 88 MB
% 6.45/1.92 % (775990)Instructions burned: 1 (million)
% 6.45/1.92 % (775991)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2934786333:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 6.45/1.92 % (775984)------------------------------
% 6.45/1.92 % (775984)------------------------------
% 6.45/1.92 % (775991)Refutation not found, incomplete strategy
% 6.45/1.92 % (775991)------------------------------
% 6.45/1.92 % (775991)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.45/1.92 % (775991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.92 % (775991)CaDiCaL version: 2.1.3
% 6.45/1.92 % (775991)Termination reason: Refutation not found, incomplete strategy
% 6.45/1.92 % (775991)Time elapsed: 0.001 s
% 6.45/1.92 % (775991)Peak memory usage: 88 MB
% 6.45/1.92 % (775964)First to succeed.
% 6.45/1.92 % (775964)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-775901"
% 6.45/1.92 % (775966)------------------------------
% 6.45/1.92 % (775966)------------------------------
% 6.45/1.92 % (775994)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=712473390:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2990 on theBenchmark for (2990ds/114Mi)
% 6.45/1.92 % (775994)Refutation not found, incomplete strategy
% 6.45/1.92 % (775994)------------------------------
% 6.45/1.92 % (775994)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.45/1.92 % (775994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.92 % (775994)CaDiCaL version: 2.1.3
% 6.45/1.92 % (775994)Termination reason: Refutation not found, incomplete strategy
% 6.45/1.92 % (775994)Time elapsed: 0.002 s
% 6.45/1.92 % (775994)Peak memory usage: 88 MB
% 6.45/1.92 % (775990)------------------------------
% 6.45/1.92 % (775990)------------------------------
% 6.45/1.92 % (775985)Also succeeded, but the first one will report.
% 6.45/1.92 % (775995)lrs+10_1_sil=8000:sp=occurrence:random_seed=2511988300:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2989 on theBenchmark for (2989ds/907Mi)
% 6.45/1.92 % (775991)------------------------------
% 6.45/1.92 % (775991)------------------------------
% 6.45/1.92 % (775964)Refutation found. Thanks to Tanya!
% 6.45/1.92 % SZS status Theorem for theBenchmark
% 6.45/1.92 % SZS output start Proof for theBenchmark
% See solution above
% 9.13/2.11 % (775964)------------------------------
% 9.13/2.11 % (775964)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.13/2.11 % (775964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.13/2.11 % (775964)CaDiCaL version: 2.1.3
% 9.13/2.11 % (775964)Termination reason: Refutation
% 9.13/2.11 % (775964)Time elapsed: 0.816 s
% 9.13/2.11 % (775964)Peak memory usage: 131 MB
% 9.13/2.11 % (775964)Instructions burned: 1203 (million)
% 9.13/2.11 % (775964)------------------------------
% 9.13/2.11 % (775964)------------------------------
% 9.13/2.11 % (775901)Success in time 1.253 s
% 9.13/2.11 % Vampire exiting
%------------------------------------------------------------------------------