%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO029-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n026.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 : Fri Sep 25 01:19:36 PM UTC 2026
% Result : Unsatisfiable 14.84s 2.80s
% Output : CNFRefutation 14.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 89 ( 28 unt; 0 def)
% Number of atoms : 229 ( 38 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 278 ( 138 ~; 140 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-4 aty)
% Number of variables : 171 ( 0 sgn 171 !; 0 ?; 144 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : equidistant(X0,X1,X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',reflexivity_for_equidistance) ).
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',transitivity_for_equidistance) ).
fof(f3,axiom,
! [X2,X0,X1] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',identity_for_equidistance) ).
fof(f4,axiom,
! [X2,X3,X0,X1] : between(X0,X1,extension(X0,X1,X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
fof(f5,axiom,
! [X2,X3,X0,X1] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
fof(f6,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( equidistant(X4,X6,X5,X7)
| X0 = X1
| ~ between(X2,X3,X5)
| ~ between(X0,X1,X4)
| ~ equidistant(X1,X6,X3,X7)
| ~ equidistant(X0,X6,X2,X7)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',outer_five_segment) ).
fof(f19,axiom,
u != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_not_v) ).
fof(f20,negated_conjecture,
extension(u,v,u,v) != extension(u,v,v,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equal_extensions) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] : equidistant(X0,X1,X1,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[],[f5]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( equidistant(X1,X4,X3,X5)
| ( X0 = X6 )
| ~ between(X7,X2,X3)
| ~ between(X6,X0,X1)
| ~ equidistant(X6,X4,X7,X5)
| ~ equidistant(X6,X0,X7,X2)
| ~ equidistant(X0,X4,X2,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_87,plain,
u != v,
inference(cnf_transformation,[],[f19]) ).
tcf(c_88,negated_conjecture,
extension(u,v,u,v) != extension(u,v,v,u),
inference(cnf_transformation,[],[f20]) ).
tcf(c_89,plain,
equidistant(u,u,u,u),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_93,plain,
( ( u = u )
| ~ equidistant(u,u,u,u) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_222,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_224,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( equidistant(X4,X0,X5,X2)
| ~ equidistant(X4,X1,X5,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_546,plain,
! [X0: $i] :
( ( extension(u,v,u,v) = extension(u,v,v,u) )
| ( extension(u,v,v,u) != X0 )
| ( extension(u,v,u,v) != X0 ) ),
inference(instantiation,[status(thm)],[c_222]) ).
tcf(c_552,plain,
! [X0: $i,X1: $i] :
( ( extension(u,v,v,u) = X0 )
| ~ equidistant(extension(u,v,v,u),X0,X1,X1) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( extension(u,v,u,v) = extension(u,v,v,u) )
| ( extension(u,v,v,u) != extension(X0,X1,X2,X3) )
| ( extension(u,v,u,v) != extension(X0,X1,X2,X3) ) ),
inference(instantiation,[status(thm)],[c_546]) ).
tcf(c_580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( equidistant(extension(u,v,u,v),extension(u,v,v,u),X2,X2)
| ( X0 = X3 )
| ~ between(X4,X1,X2)
| ~ equidistant(X3,X0,X4,X1)
| ~ between(X3,X0,extension(u,v,u,v))
| ~ equidistant(X3,extension(u,v,v,u),X4,X2)
| ~ equidistant(X0,extension(u,v,v,u),X1,X2)
| ~ equidistant(X0,extension(u,v,u,v),X1,X2) ),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_595,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(X2,extension(u,v,u,v),X2,extension(u,v,v,u))
| ~ equidistant(X0,X1,X2,extension(u,v,v,u))
| ~ equidistant(X0,X1,X2,extension(u,v,u,v)) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_671,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( equidistant(extension(u,v,u,v),X2,X3,X4)
| ~ equidistant(X0,X1,X3,X4)
| ~ equidistant(X0,X1,extension(u,v,u,v),X2) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_681,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( equidistant(X3,X4,X2,extension(u,v,v,u))
| ~ equidistant(X0,X1,X3,X4)
| ~ equidistant(X0,X1,X2,extension(u,v,v,u)) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X2,extension(u,v,v,u),X2,X3)
| ~ equidistant(X0,X1,X2,X3)
| ~ equidistant(X0,X1,X2,extension(u,v,v,u)) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( equidistant(extension(u,v,u,v),extension(u,v,v,u),extension(X2,X1,X3,X4),extension(X2,X1,X3,X4))
| ( X0 = X5 )
| ~ equidistant(X5,X0,X2,X1)
| ~ between(X5,X0,extension(u,v,u,v))
| ~ between(X2,X1,extension(X2,X1,X3,X4))
| ~ equidistant(X5,extension(u,v,v,u),X2,extension(X2,X1,X3,X4))
| ~ equidistant(X0,extension(u,v,v,u),X1,extension(X2,X1,X3,X4))
| ~ equidistant(X0,extension(u,v,u,v),X1,extension(X2,X1,X3,X4)) ),
inference(instantiation,[status(thm)],[c_580]) ).
tcf(c_839,plain,
! [X0: $i] : equidistant(extension(u,v,u,v),X0,X0,extension(u,v,u,v)),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_844,plain,
! [X0: $i] : equidistant(extension(u,v,v,u),X0,X0,extension(u,v,v,u)),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_845,plain,
equidistant(extension(u,v,v,u),u,u,extension(u,v,v,u)),
inference(instantiation,[status(thm)],[c_844]) ).
tcf(c_893,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( equidistant(extension(u,v,v,u),X2,X3,X4)
| ~ equidistant(X0,X1,X3,X4)
| ~ equidistant(X0,X1,extension(u,v,v,u),X2) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_920,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( equidistant(X3,X4,extension(u,v,u,v),X2)
| ~ equidistant(X0,X1,X3,X4)
| ~ equidistant(X0,X1,extension(u,v,u,v),X2) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_958,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(extension(u,v,u,v),X0,X1,X2)
| ~ equidistant(X0,extension(u,v,u,v),X1,X2)
| ~ equidistant(X0,extension(u,v,u,v),extension(u,v,u,v),X0) ),
inference(instantiation,[status(thm)],[c_671]) ).
tcf(c_994,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(X1,X2,X0,extension(u,v,v,u))
| ~ equidistant(extension(u,v,v,u),X0,X1,X2)
| ~ equidistant(extension(u,v,v,u),X0,X0,extension(u,v,v,u)) ),
inference(instantiation,[status(thm)],[c_681]) ).
tcf(c_1025,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( equidistant(v,X4,X2,X3)
| ~ equidistant(X0,X1,v,X4)
| ~ equidistant(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_1254,plain,
equidistant(v,extension(u,v,v,u),v,u),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_1328,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(X2,v,X2,u)
| ~ equidistant(X2,X1,X2,X0)
| ( v != X1 )
| ( u != X0 ) ),
inference(instantiation,[status(thm)],[c_224]) ).
tcf(c_1329,plain,
( equidistant(u,v,u,u)
| ~ equidistant(u,u,u,u)
| ( v != u )
| ( u != u ) ),
inference(instantiation,[status(thm)],[c_1328]) ).
tcf(c_1436,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(extension(u,v,u,v),extension(u,v,v,u),extension(X0,X1,X2,X3),extension(X0,X1,X2,X3))
| ( v = u )
| ~ equidistant(u,v,X0,X1)
| ~ between(u,v,extension(u,v,u,v))
| ~ between(X0,X1,extension(X0,X1,X2,X3))
| ~ equidistant(v,extension(u,v,v,u),X1,extension(X0,X1,X2,X3))
| ~ equidistant(v,extension(u,v,u,v),X1,extension(X0,X1,X2,X3))
| ~ equidistant(u,extension(u,v,v,u),X0,extension(X0,X1,X2,X3)) ),
inference(instantiation,[status(thm)],[c_747]) ).
tcf(c_1512,plain,
equidistant(extension(u,v,u,v),extension(u,v,v,u),extension(u,v,v,u),extension(u,v,u,v)),
inference(instantiation,[status(thm)],[c_839]) ).
tcf(c_1515,plain,
equidistant(extension(u,v,u,v),extension(u,v,u,v),extension(u,v,u,v),extension(u,v,u,v)),
inference(instantiation,[status(thm)],[c_839]) ).
tcf(c_1554,plain,
! [X0: $i] :
( ( u = v )
| ~ equidistant(u,v,X0,X0) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_1556,plain,
( ( u = v )
| ~ equidistant(u,v,u,u) ),
inference(instantiation,[status(thm)],[c_1554]) ).
tcf(c_1825,plain,
! [X0: $i,X1: $i] :
( ( extension(u,v,u,v) = X0 )
| ~ equidistant(extension(u,v,u,v),X0,X1,X1) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_1864,plain,
! [X0: $i] : equidistant(X0,extension(u,v,u,v),extension(u,v,u,v),X0),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_2020,plain,
( equidistant(extension(u,v,u,v),v,u,v)
| ~ equidistant(v,extension(u,v,u,v),u,v)
| ~ equidistant(v,extension(u,v,u,v),extension(u,v,u,v),v) ),
inference(instantiation,[status(thm)],[c_958]) ).
tcf(c_2048,plain,
! [X0: $i] :
( equidistant(X0,extension(u,v,v,u),X0,extension(u,v,v,u))
| ~ equidistant(extension(u,v,v,u),X0,X0,extension(u,v,v,u)) ),
inference(instantiation,[status(thm)],[c_994]) ).
tcf(c_2049,plain,
( equidistant(u,extension(u,v,v,u),u,extension(u,v,v,u))
| ~ equidistant(extension(u,v,v,u),u,u,extension(u,v,v,u)) ),
inference(instantiation,[status(thm)],[c_2048]) ).
tcf(c_2138,plain,
! [X0: $i,X1: $i] :
( equidistant(extension(u,v,v,u),extension(u,v,u,v),X0,X1)
| ~ equidistant(extension(u,v,u,v),extension(u,v,v,u),X0,X1)
| ~ equidistant(extension(u,v,u,v),extension(u,v,v,u),extension(u,v,v,u),extension(u,v,u,v)) ),
inference(instantiation,[status(thm)],[c_893]) ).
tcf(c_2174,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(X1,X2,extension(u,v,u,v),X0)
| ~ equidistant(X0,extension(u,v,u,v),X1,X2)
| ~ equidistant(X0,extension(u,v,u,v),extension(u,v,u,v),X0) ),
inference(instantiation,[status(thm)],[c_920]) ).
tcf(c_2409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( equidistant(X2,X3,v,X4)
| ~ equidistant(X0,X1,v,X4)
| ~ equidistant(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_2434,plain,
! [X0: $i,X1: $i] :
( equidistant(v,u,X0,X1)
| ~ equidistant(v,extension(u,v,v,u),v,u)
| ~ equidistant(v,extension(u,v,v,u),X0,X1) ),
inference(instantiation,[status(thm)],[c_1025]) ).
tcf(c_2497,plain,
! [X0: $i,X1: $i,X2: $i] : equidistant(v,extension(X0,v,X1,X2),X1,X2),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_3375,plain,
! [X0: $i] : equidistant(v,X0,X0,v),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_3376,plain,
equidistant(v,u,u,v),
inference(instantiation,[status(thm)],[c_3375]) ).
tcf(c_3796,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X2,v,X2,X3)
| ~ equidistant(X0,X1,X2,v)
| ~ equidistant(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_3801,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X2,v,X3,u)
| ~ equidistant(X0,X1,X3,u)
| ~ equidistant(X0,X1,X2,v) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_3868,plain,
between(u,v,extension(u,v,v,u)),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_3871,plain,
between(u,v,extension(u,v,u,v)),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_5113,plain,
! [X0: $i] :
( ( extension(u,v,v,u) = extension(u,v,u,v) )
| ~ equidistant(extension(u,v,v,u),extension(u,v,u,v),X0,X0) ),
inference(instantiation,[status(thm)],[c_552]) ).
tcf(c_5277,plain,
equidistant(v,extension(u,v,u,v),extension(u,v,u,v),v),
inference(instantiation,[status(thm)],[c_1864]) ).
tcf(c_5496,plain,
equidistant(extension(u,v,u,v),v,v,extension(u,v,u,v)),
inference(instantiation,[status(thm)],[c_839]) ).
tcf(c_5501,plain,
equidistant(extension(u,v,v,u),v,v,extension(u,v,v,u)),
inference(instantiation,[status(thm)],[c_844]) ).
tcf(c_5532,plain,
( equidistant(v,extension(u,v,u,v),v,extension(u,v,v,u))
| ~ equidistant(v,extension(u,v,v,u),v,extension(u,v,v,u))
| ~ equidistant(v,extension(u,v,v,u),v,extension(u,v,u,v)) ),
inference(instantiation,[status(thm)],[c_595]) ).
tcf(c_5902,plain,
( ( extension(u,v,u,v) = extension(u,v,u,v) )
| ~ equidistant(extension(u,v,u,v),extension(u,v,u,v),extension(u,v,u,v),extension(u,v,u,v)) ),
inference(instantiation,[status(thm)],[c_1825]) ).
tcf(c_6201,plain,
( equidistant(v,extension(u,v,v,u),v,extension(u,v,v,u))
| ~ equidistant(extension(u,v,v,u),v,v,extension(u,v,v,u)) ),
inference(instantiation,[status(thm)],[c_2048]) ).
tcf(c_6239,plain,
( equidistant(extension(u,v,v,u),extension(u,v,u,v),extension(u,v,v,u),extension(u,v,v,u))
| ~ equidistant(extension(u,v,u,v),extension(u,v,v,u),extension(u,v,v,u),extension(u,v,v,u))
| ~ equidistant(extension(u,v,u,v),extension(u,v,v,u),extension(u,v,v,u),extension(u,v,u,v)) ),
inference(instantiation,[status(thm)],[c_2138]) ).
tcf(c_6469,plain,
( ( extension(u,v,u,v) = extension(u,v,v,u) )
| ( extension(u,v,v,u) != extension(u,v,u,v) )
| ( extension(u,v,u,v) != extension(u,v,u,v) ) ),
inference(instantiation,[status(thm)],[c_563]) ).
tcf(c_6550,plain,
( equidistant(v,u,v,extension(u,v,v,u))
| ~ equidistant(v,extension(u,v,v,u),v,u)
| ~ equidistant(v,extension(u,v,v,u),v,extension(u,v,v,u)) ),
inference(instantiation,[status(thm)],[c_2434]) ).
tcf(c_6551,plain,
( equidistant(v,u,v,u)
| ~ equidistant(v,extension(u,v,v,u),v,u) ),
inference(instantiation,[status(thm)],[c_2434]) ).
tcf(c_6826,plain,
! [X0: $i,X1: $i] :
( equidistant(X0,X1,v,extension(u,v,u,v))
| ~ equidistant(extension(u,v,u,v),v,X0,X1)
| ~ equidistant(extension(u,v,u,v),v,v,extension(u,v,u,v)) ),
inference(instantiation,[status(thm)],[c_2409]) ).
tcf(c_6841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X1,X2,v,X3)
| ~ equidistant(v,X0,v,X3)
| ~ equidistant(v,X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_2409]) ).
tcf(c_7018,plain,
equidistant(v,extension(u,v,u,v),u,v),
inference(instantiation,[status(thm)],[c_2497]) ).
tcf(c_9677,plain,
( equidistant(u,v,extension(u,v,u,v),v)
| ~ equidistant(v,extension(u,v,u,v),u,v)
| ~ equidistant(v,extension(u,v,u,v),extension(u,v,u,v),v) ),
inference(instantiation,[status(thm)],[c_2174]) ).
tcf(c_10242,plain,
! [X0: $i,X1: $i] :
( equidistant(v,extension(u,v,v,u),v,X1)
| ~ equidistant(v,X0,v,X1)
| ~ equidistant(v,X0,v,extension(u,v,v,u)) ),
inference(instantiation,[status(thm)],[c_736]) ).
tcf(c_12510,plain,
( equidistant(extension(u,v,u,v),extension(u,v,v,u),extension(u,v,v,u),extension(u,v,v,u))
| ( v = u )
| ~ equidistant(u,v,u,v)
| ~ between(u,v,extension(u,v,v,u))
| ~ between(u,v,extension(u,v,u,v))
| ~ equidistant(v,extension(u,v,v,u),v,extension(u,v,v,u))
| ~ equidistant(v,extension(u,v,u,v),v,extension(u,v,v,u))
| ~ equidistant(u,extension(u,v,v,u),u,extension(u,v,v,u)) ),
inference(instantiation,[status(thm)],[c_1436]) ).
tcf(c_12806,plain,
! [X0: $i] :
( equidistant(u,v,u,X0)
| ~ equidistant(extension(u,v,u,v),v,u,v)
| ~ equidistant(extension(u,v,u,v),v,u,X0) ),
inference(instantiation,[status(thm)],[c_3796]) ).
tcf(c_13041,plain,
! [X0: $i] :
( equidistant(extension(u,v,u,v),v,X0,u)
| ~ equidistant(u,v,X0,u)
| ~ equidistant(u,v,extension(u,v,u,v),v) ),
inference(instantiation,[status(thm)],[c_3801]) ).
tcf(c_13601,plain,
( ( extension(u,v,v,u) = extension(u,v,u,v) )
| ~ equidistant(extension(u,v,v,u),extension(u,v,u,v),extension(u,v,v,u),extension(u,v,v,u)) ),
inference(instantiation,[status(thm)],[c_5113]) ).
tcf(c_18305,plain,
! [X0: $i] :
( equidistant(v,extension(u,v,v,u),v,extension(u,v,u,v))
| ~ equidistant(v,X0,v,extension(u,v,v,u))
| ~ equidistant(v,X0,v,extension(u,v,u,v)) ),
inference(instantiation,[status(thm)],[c_10242]) ).
tcf(c_18306,plain,
( equidistant(v,extension(u,v,v,u),v,extension(u,v,u,v))
| ~ equidistant(v,u,v,extension(u,v,v,u))
| ~ equidistant(v,u,v,extension(u,v,u,v)) ),
inference(instantiation,[status(thm)],[c_18305]) ).
tcf(c_20062,plain,
! [X0: $i,X1: $i] :
( equidistant(X0,v,v,X1)
| ~ equidistant(v,X0,v,X1)
| ~ equidistant(v,X0,X0,v) ),
inference(instantiation,[status(thm)],[c_6841]) ).
tcf(c_20063,plain,
( equidistant(u,v,v,u)
| ~ equidistant(v,u,v,u)
| ~ equidistant(v,u,u,v) ),
inference(instantiation,[status(thm)],[c_20062]) ).
tcf(c_21932,plain,
( equidistant(u,v,u,v)
| ~ equidistant(extension(u,v,u,v),v,u,v) ),
inference(instantiation,[status(thm)],[c_12806]) ).
tcf(c_22004,plain,
( equidistant(extension(u,v,u,v),v,v,u)
| ~ equidistant(u,v,v,u)
| ~ equidistant(u,v,extension(u,v,u,v),v) ),
inference(instantiation,[status(thm)],[c_13041]) ).
tcf(c_29324,plain,
( equidistant(v,u,v,extension(u,v,u,v))
| ~ equidistant(extension(u,v,u,v),v,v,u)
| ~ equidistant(extension(u,v,u,v),v,v,extension(u,v,u,v)) ),
inference(instantiation,[status(thm)],[c_6826]) ).
tcf(c_29326,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_29324,c_22004,c_21932,c_20063,c_18306,c_13601,c_12510,c_9677,c_7018,c_6551,c_6550,c_6469,c_6239,c_6201,c_5902,c_5532,c_5501,c_5496,c_5277,c_3871,c_3868,c_3376,c_2049,c_2020,c_1556,c_1515,c_1512,c_1329,c_1254,c_845,c_88,c_93,c_89,c_87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO029-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.35 % Computer : n026.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Wed Sep 23 10:30:24 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.39 Running first-order theorem proving
% 0.11/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.40
% 0.11/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.40
% 0.11/0.40 % Detected problem language: tptp
% 0.11/0.41 % Proving...
% 14.84/2.80 % SZS status Started for theBenchmark.p
% 14.84/2.80 % SZS status Unsatisfiable for theBenchmark.p
% 14.84/2.80
% 14.84/2.80 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 14.84/2.80
% 14.84/2.80 % ------ iProver source info
% 14.84/2.80
% 14.84/2.80 % git: date: 2026-07-19 20:42:38 +0200
% 14.84/2.80 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 14.84/2.80 % git: non_committed_changes: false
% 14.84/2.80
% 14.84/2.80 % ------ Parsing...% successful
% 14.84/2.80
% 14.84/2.80
% 14.84/2.80 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 14.84/2.80
% 14.84/2.80 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 14.84/2.80
% 14.84/2.80 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 14.84/2.80
% 14.84/2.80 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 14.84/2.80 % ------ Proving...
% 14.84/2.80 % ------ Problem Properties
% 14.84/2.80
% 14.84/2.80 %
% 14.84/2.80 % clauses 20
% 14.84/2.80 % conjectures 1
% 14.84/2.80 % EPR 10
% 14.84/2.80 % Horn 15
% 14.84/2.80 % unary 8
% 14.84/2.80 % binary 2
% 14.84/2.80 % lits 58
% 14.84/2.80 % lits eq 9
% 14.84/2.80 % fd_pure 0
% 14.84/2.80 % fd_pseudo 0
% 14.84/2.80 % fd_cond 0
% 14.84/2.80 % fd_pseudo_cond 7
% 14.84/2.80 % AC symbols 0
% 14.84/2.80
% 14.84/2.80 % ------ Input Options Time Limit: Unbounded
% 14.84/2.80
% 14.84/2.80
% 14.84/2.80 % ------
% 14.84/2.80 % Current options:
% 14.84/2.80 % ------
% 14.84/2.80
% 14.84/2.80
% 14.84/2.80 %
% 14.84/2.80
% 14.84/2.80 % ------ Proving...
% 14.84/2.80 %
% 14.84/2.80
% 14.84/2.80 % SZS status Unsatisfiable for theBenchmark.p
% 14.84/2.80
% 14.84/2.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 14.84/2.81
% 14.84/2.81
%------------------------------------------------------------------------------