%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO060-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n019.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 01:19:44 PM UTC 2026
% Result : Unsatisfiable 152.95s 39.08s
% Output : CNFRefutation 152.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 119 ( 60 unt; 2 def)
% Number of atoms : 410 ( 48 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 258 ( 127 ~; 131 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 201 ( 0 sgn 201 !; 0 ?; 172 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : equidistant(X0,X1,X1,X0),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GEO002-0.ax',transitivity_for_equidistance) ).
fof(f3,axiom,
! [X2,X0,X1] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/GEO002-0.ax',outer_five_segment) ).
fof(f19,axiom,
! [X0,X1] : reflection(X0,X1) = extension(X0,X1,X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-2.ax',reflection) ).
fof(f20,negated_conjecture,
u != reflection(reflection(u,v),v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove__involution) ).
fof(f21,plain,
u != extension(extension(u,v,u,v),v,extension(u,v,u,v),v),
inference(definition_unfolding,[],[f20,f19,f19]) ).
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,negated_conjecture,
extension(extension(u,v,u,v),v,extension(u,v,u,v),v) != u,
inference(cnf_transformation,[],[f21]) ).
tcf(c_88,plain,
equidistant(v,v,v,v),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_92,plain,
( ( v = v )
| ~ equidistant(v,v,v,v) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_315,definition,
iPr_def_10 = extension(u,v,u,v),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_316,definition,
iPr_def_11 = extension(iPr_def_10,v,iPr_def_10,v),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_317,negated_conjecture,
iPr_def_11 != u,
inference(demodulation,[status(thm)],[c_87,c_315,c_316]) ).
tcf(c_322,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_637,plain,
between(u,v,iPr_def_10),
inference(superposition,[status(thm)],[c_315,c_72]) ).
tcf(c_638,plain,
between(iPr_def_10,v,iPr_def_11),
inference(superposition,[status(thm)],[c_316,c_72]) ).
tcf(c_639,plain,
equidistant(v,iPr_def_10,u,v),
inference(superposition,[status(thm)],[c_315,c_73]) ).
tcf(c_656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X1,X0,X2,X3)
| ~ equidistant(X0,X1,X2,X3) ),
inference(superposition,[status(thm)],[c_69,c_70]) ).
tcf(c_657,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,extension(X1,X0,X2,X3),X4,X5) ),
inference(superposition,[status(thm)],[c_73,c_70]) ).
tcf(c_662,plain,
! [X0: $i,X1: $i] :
( equidistant(u,v,X0,X1)
| ~ equidistant(v,iPr_def_10,X0,X1) ),
inference(superposition,[status(thm)],[c_639,c_70]) ).
tcf(c_684,plain,
equidistant(iPr_def_10,v,u,v),
inference(superposition,[status(thm)],[c_639,c_656]) ).
tcf(c_713,plain,
equidistant(u,v,iPr_def_10,v),
inference(superposition,[status(thm)],[c_69,c_662]) ).
tcf(c_720,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : equidistant(X0,X1,extension(X2,X3,X0,X1),X3),
inference(superposition,[status(thm)],[c_69,c_657]) ).
tcf(c_758,plain,
! [X0: $i] :
( ( iPr_def_11 = u )
| ~ equidistant(iPr_def_11,u,X0,X0) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_759,plain,
( ( iPr_def_11 = u )
| ~ equidistant(iPr_def_11,u,v,v) ),
inference(instantiation,[status(thm)],[c_758]) ).
tcf(c_768,plain,
equidistant(v,u,iPr_def_10,v),
inference(superposition,[status(thm)],[c_713,c_656]) ).
tcf(c_769,plain,
! [X0: $i,X1: $i] :
( equidistant(iPr_def_10,v,X0,X1)
| ~ equidistant(u,v,X0,X1) ),
inference(superposition,[status(thm)],[c_713,c_70]) ).
tcf(c_783,plain,
! [X0: $i,X1: $i] :
( equidistant(iPr_def_10,v,X0,X1)
| ~ equidistant(v,u,X0,X1) ),
inference(superposition,[status(thm)],[c_768,c_70]) ).
tcf(c_786,plain,
( equidistant(iPr_def_10,v,v,v)
| ~ equidistant(v,u,v,v) ),
inference(instantiation,[status(thm)],[c_783]) ).
tcf(c_795,plain,
equidistant(iPr_def_10,v,iPr_def_11,v),
inference(superposition,[status(thm)],[c_316,c_720]) ).
tcf(c_812,plain,
! [X0: $i,X1: $i] :
( equidistant(iPr_def_11,v,X0,X1)
| ~ equidistant(iPr_def_10,v,X0,X1) ),
inference(superposition,[status(thm)],[c_795,c_70]) ).
tcf(c_838,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(iPr_def_11,u,X2,X2)
| ~ equidistant(X0,X1,iPr_def_11,u)
| ~ equidistant(X0,X1,X2,X2) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_856,plain,
! [X0: $i,X1: $i] :
( ( u = X0 )
| ~ equidistant(u,X0,X1,X1) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_1016,plain,
between(u,v,iPr_def_10),
inference(superposition,[status(thm)],[c_315,c_72]) ).
tcf(c_1112,plain,
between(iPr_def_10,v,iPr_def_11),
inference(superposition,[status(thm)],[c_316,c_72]) ).
tcf(c_1113,plain,
equidistant(v,iPr_def_10,u,v),
inference(superposition,[status(thm)],[c_315,c_73]) ).
tcf(c_1141,plain,
! [X0: $i,X1: $i,X2: $i] : extension(X0,X1,X2,X2) = X1,
inference(superposition,[status(thm)],[c_73,c_71]) ).
tcf(c_1199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X1,X0,X2,X3)
| ~ equidistant(X0,X1,X2,X3) ),
inference(superposition,[status(thm)],[c_69,c_70]) ).
tcf(c_1200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,extension(X1,X0,X2,X3),X4,X5) ),
inference(superposition,[status(thm)],[c_73,c_70]) ).
tcf(c_1237,plain,
! [X0: $i,X1: $i] :
( equidistant(u,v,X0,X1)
| ~ equidistant(v,iPr_def_10,X0,X1) ),
inference(superposition,[status(thm)],[c_1113,c_70]) ).
tcf(c_1293,plain,
! [X0: $i,X1: $i] : equidistant(X0,X0,X1,X1),
inference(superposition,[status(thm)],[c_1141,c_73]) ).
tcf(c_1352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X3,X3,X1,X2)
| ~ equidistant(X0,X0,X1,X2) ),
inference(superposition,[status(thm)],[c_1293,c_70]) ).
tcf(c_1356,plain,
( ( u = u )
| ~ equidistant(u,u,u,u) ),
inference(instantiation,[status(thm)],[c_856]) ).
tcf(c_1357,plain,
equidistant(u,u,u,u),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_1682,plain,
equidistant(u,iPr_def_11,iPr_def_11,u),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_1697,plain,
! [X0: $i,X1: $i] : equidistant(X0,X1,X0,X1),
inference(superposition,[status(thm)],[c_69,c_1199]) ).
tcf(c_1699,plain,
equidistant(iPr_def_10,v,u,v),
inference(superposition,[status(thm)],[c_1113,c_1199]) ).
tcf(c_1815,plain,
equidistant(iPr_def_10,v,v,u),
inference(superposition,[status(thm)],[c_69,c_769]) ).
tcf(c_1844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : equidistant(X0,X1,extension(X2,X3,X0,X1),X3),
inference(superposition,[status(thm)],[c_69,c_1200]) ).
tcf(c_1846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : equidistant(X0,X1,X2,extension(X3,X2,X0,X1)),
inference(superposition,[status(thm)],[c_1697,c_1200]) ).
tcf(c_1851,plain,
equidistant(v,iPr_def_10,v,u),
inference(superposition,[status(thm)],[c_1815,c_656]) ).
tcf(c_2179,plain,
equidistant(iPr_def_10,v,iPr_def_11,v),
inference(superposition,[status(thm)],[c_316,c_1844]) ).
tcf(c_2369,plain,
equidistant(iPr_def_11,v,u,v),
inference(superposition,[status(thm)],[c_684,c_812]) ).
tcf(c_2391,plain,
equidistant(v,iPr_def_10,iPr_def_11,v),
inference(superposition,[status(thm)],[c_2179,c_1199]) ).
tcf(c_2392,plain,
! [X0: $i,X1: $i] :
( equidistant(iPr_def_11,v,X0,X1)
| ~ equidistant(iPr_def_10,v,X0,X1) ),
inference(superposition,[status(thm)],[c_2179,c_70]) ).
tcf(c_2423,plain,
! [X0: $i,X1: $i] :
( equidistant(iPr_def_11,v,X0,X1)
| ~ equidistant(v,iPr_def_10,X0,X1) ),
inference(superposition,[status(thm)],[c_2391,c_70]) ).
tcf(c_2424,plain,
equidistant(u,v,iPr_def_11,v),
inference(superposition,[status(thm)],[c_2391,c_1237]) ).
tcf(c_2429,plain,
! [X0: $i,X1: $i] :
( equidistant(u,v,X0,X1)
| ~ equidistant(iPr_def_11,v,X0,X1) ),
inference(superposition,[status(thm)],[c_2369,c_70]) ).
tcf(c_2440,plain,
( equidistant(u,v,v,v)
| ~ equidistant(iPr_def_11,v,v,v) ),
inference(instantiation,[status(thm)],[c_2429]) ).
tcf(c_2520,plain,
! [X0: $i,X1: $i] :
( equidistant(iPr_def_11,v,X0,X1)
| ~ equidistant(u,v,X0,X1) ),
inference(superposition,[status(thm)],[c_2424,c_70]) ).
tcf(c_2660,plain,
equidistant(iPr_def_10,v,v,iPr_def_11),
inference(superposition,[status(thm)],[c_316,c_1846]) ).
tcf(c_2662,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : equidistant(X0,X1,X2,extension(X3,X2,X1,X0)),
inference(superposition,[status(thm)],[c_1846,c_1199]) ).
tcf(c_2876,plain,
equidistant(v,iPr_def_10,v,iPr_def_11),
inference(superposition,[status(thm)],[c_2660,c_1199]) ).
tcf(c_2877,plain,
! [X0: $i,X1: $i] :
( equidistant(v,iPr_def_11,X0,X1)
| ~ equidistant(iPr_def_10,v,X0,X1) ),
inference(superposition,[status(thm)],[c_2660,c_70]) ).
tcf(c_3475,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X2,X3,u,u)
| ~ equidistant(X0,X1,u,u)
| ~ equidistant(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_4099,plain,
! [X0: $i] : equidistant(iPr_def_11,X0,X0,iPr_def_11),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_4101,plain,
equidistant(iPr_def_11,v,v,iPr_def_11),
inference(instantiation,[status(thm)],[c_4099]) ).
tcf(c_4112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( equidistant(iPr_def_11,X0,X4,X2)
| ~ equidistant(iPr_def_11,X1,X4,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_322]) ).
tcf(c_4576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( equidistant(X4,X0,iPr_def_11,X2)
| ~ equidistant(X4,X1,iPr_def_11,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_322]) ).
tcf(c_5254,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(iPr_def_10,X1,iPr_def_11,X3)
| ( X0 = v )
| ~ between(X2,v,iPr_def_11)
| ~ between(X0,v,iPr_def_10)
| ~ equidistant(v,X1,v,X3)
| ~ equidistant(X0,v,X2,v)
| ~ equidistant(X0,X1,X2,X3) ),
inference(superposition,[status(thm)],[c_2876,c_74]) ).
tcf(c_6911,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : equidistant(X0,X0,X1,extension(X2,X1,X3,X3)),
inference(superposition,[status(thm)],[c_2662,c_1352]) ).
tcf(c_9895,plain,
equidistant(iPr_def_11,v,v,iPr_def_10),
inference(superposition,[status(thm)],[c_69,c_2392]) ).
tcf(c_9898,plain,
equidistant(iPr_def_11,v,u,v),
inference(superposition,[status(thm)],[c_1699,c_2392]) ).
tcf(c_10239,plain,
! [X0: $i,X1: $i] :
( equidistant(v,iPr_def_10,X0,X1)
| ~ equidistant(iPr_def_11,v,X0,X1) ),
inference(superposition,[status(thm)],[c_9895,c_70]) ).
tcf(c_10349,plain,
! [X0: $i,X1: $i] :
( equidistant(u,v,X0,X1)
| ~ equidistant(iPr_def_11,v,X0,X1) ),
inference(superposition,[status(thm)],[c_9898,c_70]) ).
tcf(c_14017,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(iPr_def_11,X0,X1,X2)
| ~ equidistant(iPr_def_11,X1,X1,iPr_def_11)
| ( X2 != iPr_def_11 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_4112]) ).
tcf(c_14018,plain,
( equidistant(iPr_def_11,v,v,v)
| ~ equidistant(iPr_def_11,v,v,iPr_def_11)
| ( v != iPr_def_11 )
| ( v != v ) ),
inference(instantiation,[status(thm)],[c_14017]) ).
tcf(c_18804,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X3,u,X3,X0)
| ~ equidistant(X3,X2,X3,X1)
| ( u != X2 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_322]) ).
tcf(c_18805,plain,
( equidistant(v,u,v,v)
| ~ equidistant(v,v,v,v)
| ( v != v )
| ( u != v ) ),
inference(instantiation,[status(thm)],[c_18804]) ).
tcf(c_20200,plain,
! [X0: $i,X1: $i] :
( equidistant(X0,X1,u,u)
| ~ equidistant(u,u,u,u)
| ~ equidistant(u,u,X0,X1) ),
inference(instantiation,[status(thm)],[c_3475]) ).
tcf(c_21413,plain,
! [X0: $i,X1: $i] :
( equidistant(u,X0,iPr_def_11,X1)
| ~ equidistant(u,iPr_def_11,iPr_def_11,u)
| ( X1 != u )
| ( X0 != iPr_def_11 ) ),
inference(instantiation,[status(thm)],[c_4576]) ).
tcf(c_34716,plain,
( ( iPr_def_11 = u )
| ~ equidistant(iPr_def_11,u,u,u) ),
inference(instantiation,[status(thm)],[c_758]) ).
tcf(c_45465,plain,
( equidistant(iPr_def_11,u,u,u)
| ~ equidistant(u,u,iPr_def_11,u)
| ~ equidistant(u,u,u,u) ),
inference(instantiation,[status(thm)],[c_20200]) ).
tcf(c_45946,plain,
! [X0: $i] :
( equidistant(u,X0,iPr_def_11,u)
| ~ equidistant(u,iPr_def_11,iPr_def_11,u)
| ( u != u )
| ( X0 != iPr_def_11 ) ),
inference(instantiation,[status(thm)],[c_21413]) ).
tcf(c_45948,plain,
! [X0: $i,X1: $i] :
( equidistant(iPr_def_11,u,X1,X1)
| ~ equidistant(u,X0,iPr_def_11,u)
| ~ equidistant(u,X0,X1,X1) ),
inference(instantiation,[status(thm)],[c_838]) ).
tcf(c_45949,plain,
( equidistant(u,v,iPr_def_11,u)
| ~ equidistant(u,iPr_def_11,iPr_def_11,u)
| ( v != iPr_def_11 )
| ( u != u ) ),
inference(instantiation,[status(thm)],[c_45946]) ).
tcf(c_45950,plain,
( equidistant(iPr_def_11,u,v,v)
| ~ equidistant(u,v,iPr_def_11,u)
| ~ equidistant(u,v,v,v) ),
inference(instantiation,[status(thm)],[c_45948]) ).
tcf(c_329118,plain,
! [X0: $i,X1: $i,X2: $i] : extension(X0,X1,X2,X2) = X1,
inference(superposition,[status(thm)],[c_73,c_71]) ).
tcf(c_329123,plain,
! [X0: $i,X1: $i] : equidistant(X0,X0,X1,X1),
inference(demodulation,[status(thm)],[c_6911,c_329118]) ).
tcf(c_329838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X3,X3,X1,X2)
| ~ equidistant(X0,X0,X1,X2) ),
inference(superposition,[status(thm)],[c_329123,c_70]) ).
tcf(c_331450,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(iPr_def_10,X0,iPr_def_11,X2)
| ( u = v )
| ~ between(u,v,iPr_def_10)
| ~ between(X1,v,iPr_def_11)
| ~ equidistant(u,v,X1,v)
| ~ equidistant(v,X0,v,X2)
| ~ equidistant(u,X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_5254]) ).
tcf(c_341346,plain,
! [X0: $i] :
( ( v = iPr_def_11 )
| ~ equidistant(iPr_def_10,v,X0,X0) ),
inference(resolution,[status(thm)],[c_2877,c_71]) ).
tcf(c_341483,plain,
! [X0: $i] : ~ equidistant(iPr_def_10,v,X0,X0),
inference(global_subsumption_just,[status(thm)],[c_341346,c_88,c_92,c_317,c_759,c_1356,c_1357,c_1682,c_2440,c_4101,c_14018,c_45949,c_45950,c_341346]) ).
tcf(c_341485,plain,
~ equidistant(iPr_def_10,v,v,v),
inference(instantiation,[status(thm)],[c_341483]) ).
tcf(c_341768,plain,
! [X0: $i] : equidistant(u,X0,X0,u),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_355164,plain,
! [X0: $i,X1: $i] :
( equidistant(iPr_def_10,X0,iPr_def_11,X1)
| ( u = v )
| ~ between(iPr_def_10,v,iPr_def_11)
| ~ between(u,v,iPr_def_10)
| ~ equidistant(u,v,iPr_def_10,v)
| ~ equidistant(v,X0,v,X1)
| ~ equidistant(u,X0,iPr_def_10,X1) ),
inference(instantiation,[status(thm)],[c_331450]) ).
tcf(c_376886,plain,
! [X0: $i] :
( equidistant(iPr_def_10,X0,iPr_def_11,u)
| ( u = v )
| ~ between(iPr_def_10,v,iPr_def_11)
| ~ between(u,v,iPr_def_10)
| ~ equidistant(u,v,iPr_def_10,v)
| ~ equidistant(v,X0,v,u)
| ~ equidistant(u,X0,iPr_def_10,u) ),
inference(instantiation,[status(thm)],[c_355164]) ).
tcf(c_411637,plain,
( equidistant(iPr_def_10,iPr_def_10,iPr_def_11,u)
| ( u = v )
| ~ between(iPr_def_10,v,iPr_def_11)
| ~ between(u,v,iPr_def_10)
| ~ equidistant(v,iPr_def_10,v,u)
| ~ equidistant(u,iPr_def_10,iPr_def_10,u)
| ~ equidistant(u,v,iPr_def_10,v) ),
inference(instantiation,[status(thm)],[c_376886]) ).
tcf(c_411638,plain,
equidistant(u,iPr_def_10,iPr_def_10,u),
inference(instantiation,[status(thm)],[c_341768]) ).
tcf(c_773402,plain,
equidistant(iPr_def_11,v,iPr_def_10,v),
inference(superposition,[status(thm)],[c_69,c_2423]) ).
tcf(c_773414,plain,
equidistant(iPr_def_11,v,v,u),
inference(superposition,[status(thm)],[c_69,c_2520]) ).
tcf(c_785326,plain,
! [X0: $i,X1: $i] :
( equidistant(iPr_def_10,X1,iPr_def_11,X0)
| ( X0 = v )
| ~ between(X1,v,iPr_def_11)
| ~ between(X0,v,iPr_def_10)
| ~ equidistant(v,X1,v,X0)
| ~ equidistant(X0,v,X1,v) ),
inference(superposition,[status(thm)],[c_69,c_5254]) ).
tcf(c_790659,plain,
equidistant(v,iPr_def_10,v,u),
inference(superposition,[status(thm)],[c_773414,c_10239]) ).
tcf(c_801533,plain,
equidistant(u,v,iPr_def_10,v),
inference(superposition,[status(thm)],[c_773402,c_10349]) ).
tcf(c_823424,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(u,u,X1,X2)
| ~ equidistant(X0,X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_329838]) ).
tcf(c_851417,plain,
! [X0: $i] :
( equidistant(u,u,iPr_def_11,u)
| ~ equidistant(X0,X0,iPr_def_11,u) ),
inference(instantiation,[status(thm)],[c_823424]) ).
tcf(c_993388,plain,
( equidistant(iPr_def_10,iPr_def_10,iPr_def_11,u)
| ( u = v )
| ~ between(iPr_def_10,v,iPr_def_11)
| ~ between(u,v,iPr_def_10)
| ~ equidistant(v,iPr_def_10,v,u) ),
inference(superposition,[status(thm)],[c_801533,c_785326]) ).
tcf(c_993482,plain,
( equidistant(iPr_def_10,iPr_def_10,iPr_def_11,u)
| ( u = v ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_993388,c_1112,c_1016,c_790659]) ).
tcf(c_994182,plain,
equidistant(iPr_def_10,iPr_def_10,iPr_def_11,u),
inference(global_subsumption_just,[status(thm)],[c_993482,c_88,c_92,c_637,c_638,c_713,c_786,c_1851,c_18805,c_341485,c_411637,c_411638]) ).
tcf(c_994220,plain,
! [X0: $i] : equidistant(X0,X0,iPr_def_11,u),
inference(superposition,[status(thm)],[c_994182,c_329838]) ).
tcf(c_994222,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_994220,c_851417,c_45465,c_34716,c_1357,c_317]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO060-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 10:38:49 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 152.95/39.08 % SZS status Started for theBenchmark.p
% 152.95/39.08 % SZS status Unsatisfiable for theBenchmark.p
% 152.95/39.08
% 152.95/39.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 152.95/39.08
% 152.95/39.08 % ------ iProver source info
% 152.95/39.08
% 152.95/39.08 % git: date: 2026-07-19 20:42:38 +0200
% 152.95/39.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 152.95/39.08 % git: non_committed_changes: false
% 152.95/39.08
% 152.95/39.08 % ------ Parsing...% successful
% 152.95/39.08
% 152.95/39.08
% 152.95/39.08 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 152.95/39.08
% 152.95/39.08 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 152.95/39.08
% 152.95/39.08 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 152.95/39.08
% 152.95/39.08 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 152.95/39.08 % ------ Proving...
% 152.95/39.08 % ------ Problem Properties
% 152.95/39.08
% 152.95/39.08 %
% 152.95/39.08 % clauses 21
% 152.95/39.08 % conjectures 1
% 152.95/39.08 % EPR 10
% 152.95/39.08 % Horn 16
% 152.95/39.08 % unary 9
% 152.95/39.08 % binary 2
% 152.95/39.08 % lits 59
% 152.95/39.08 % lits eq 10
% 152.95/39.08 % fd_pure 0
% 152.95/39.08 % fd_pseudo 0
% 152.95/39.08 % fd_cond 0
% 152.95/39.08 % fd_pseudo_cond 7
% 152.95/39.08 % AC symbols 0
% 152.95/39.08
% 152.95/39.08 % ------ Schedule dynamic 5 is on
% 152.95/39.08
% 152.95/39.08 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 152.95/39.08
% 152.95/39.08
% 152.95/39.08 % ------
% 152.95/39.08 % Current options:
% 152.95/39.08 % ------
% 152.95/39.08
% 152.95/39.08
% 152.95/39.08 %
% 152.95/39.08
% 152.95/39.08 % ------ Proving...
% 152.95/39.08 % Proof_search_loop: time out after: 4873 full_loop iterations
% 152.95/39.08
% 152.95/39.08 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 152.95/39.08
% 152.95/39.08
% 152.95/39.08 % ------
% 152.95/39.08 % Current options:
% 152.95/39.08 % ------
% 152.95/39.08
% 152.95/39.08
% 152.95/39.08 %
% 152.95/39.08
% 152.95/39.08 % ------ Proving...
% 152.95/39.08 % Proof_search_loop: time out after: 5774 full_loop iterations
% 152.95/39.08
% 152.95/39.08 % ------ Option_1: Negative Selections Time Limit: 35.
% 152.95/39.08
% 152.95/39.08
% 152.95/39.08 % ------
% 152.95/39.08 % Current options:
% 152.95/39.08 % ------
% 152.95/39.08
% 152.95/39.08
% 152.95/39.08 %
% 152.95/39.08
% 152.95/39.08 % ------ Proving...
% 152.95/39.08 %
% 152.95/39.08
% 152.95/39.08 % SZS status Unsatisfiable for theBenchmark.p
% 152.95/39.08
% 152.95/39.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 152.95/39.09
% 152.95/39.09
%------------------------------------------------------------------------------