%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO025-3 : 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 : n016.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 01:19:35 PM UTC 2026
% Result : Unsatisfiable 41.41s 14.87s
% Output : CNFRefutation 41.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 17
% Syntax : Number of formulae : 73 ( 24 unt; 0 def)
% Number of atoms : 211 ( 62 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 273 ( 135 ~; 138 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 1 ( 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 : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 153 ( 0 sgn 153 !; 0 ?; 112 :)
% 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(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(f20,axiom,
! [X0,X1] : equidistant(X0,X1,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
fof(f22,axiom,
! [X2,X3,X0,X1] :
( equidistant(X1,X0,X2,X3)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3) ).
fof(f23,axiom,
! [X2,X3,X0,X1] :
( equidistant(X0,X1,X3,X2)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_1) ).
fof(f24,axiom,
! [X2,X3,X0,X1] :
( equidistant(X1,X0,X3,X2)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_2) ).
fof(f28,axiom,
! [X2,X3,X0,X1,X4,X5] :
( equidistant(X0,X1,X4,X5)
| ~ equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5) ).
fof(f41,axiom,
! [X0,X1] : equidistant(X0,X0,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7) ).
fof(f42,axiom,
equidistant(u,v,u1,v1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_to_v_equals_u1_to_v1) ).
fof(f43,axiom,
equidistant(v,w,v1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_to_w_equals_v1_to_w1) ).
fof(f44,axiom,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
fof(f45,axiom,
between(u1,v1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v1_between_u1_and_w1) ).
fof(f46,negated_conjecture,
~ equidistant(u,w,u1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equal_sums) ).
tcf(c_90,plain,
equidistant(u,v,u1,v1),
inference(cnf_transformation,[],[f42]) ).
tcf(c_91,plain,
equidistant(v,w,v1,w1),
inference(cnf_transformation,[],[f43]) ).
tcf(c_92,plain,
between(u,v,w),
inference(cnf_transformation,[],[f44]) ).
tcf(c_93,plain,
between(u1,v1,w1),
inference(cnf_transformation,[],[f45]) ).
tcf(c_94,negated_conjecture,
~ equidistant(u,w,u1,w1),
inference(cnf_transformation,[],[f46]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] : equidistant(X0,X0,X1,X1),
inference(cnf_transformation,[],[f41]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( equidistant(X0,X1,X4,X5)
| ~ equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X1,X0,X3,X2)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X0,X1,X3,X2)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X1,X0,X2,X3)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] : equidistant(X0,X1,X0,X1),
inference(cnf_transformation,[],[f20]) ).
tcf(c_105,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_106,plain,
! [X0: $i,X1: $i] : equidistant(X0,X1,X1,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_109,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_110,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_111,plain,
equidistant(u,u,u,u),
inference(instantiation,[status(thm)],[c_106]) ).
tcf(c_113,plain,
( ( u = u )
| ~ equidistant(u,u,u,u) ),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_196,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( equidistant(X0,X2,X4,X6)
| ~ equidistant(X1,X3,X5,X7)
| ( X6 != X7 )
| ( X4 != X5 )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_206,plain,
( equidistant(u,w,u1,w1)
| ~ equidistant(w,u,w1,u1) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_362,plain,
w = w,
inference(instantiation,[status(thm)],[c_196]) ).
tcf(c_373,plain,
w1 = w1,
inference(instantiation,[status(thm)],[c_196]) ).
tcf(c_892,plain,
equidistant(u,w,u,w),
inference(instantiation,[status(thm)],[c_104]) ).
tcf(c_1111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(w,u,w1,u1)
| ( X1 = X0 )
| ~ between(X2,X3,w1)
| ~ between(X0,X1,w)
| ~ equidistant(X1,w,X3,w1)
| ~ equidistant(X1,u,X3,u1)
| ~ equidistant(X0,u,X2,u1)
| ~ equidistant(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_2348,plain,
! [X0: $i,X1: $i] :
( equidistant(w,u,w1,u1)
| ( X1 = X0 )
| ~ between(u1,v1,w1)
| ~ between(X0,X1,w)
| ~ equidistant(X1,w,v1,w1)
| ~ equidistant(X1,u,v1,u1)
| ~ equidistant(X0,u,u1,u1)
| ~ equidistant(X0,X1,u1,v1) ),
inference(instantiation,[status(thm)],[c_1111]) ).
tcf(c_3804,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( equidistant(X0,v,X2,X2)
| ~ equidistant(X1,X5,X3,X4)
| ( v != X5 )
| ( X2 != X4 )
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_199]) ).
tcf(c_3805,plain,
( equidistant(u,v,u,u)
| ~ equidistant(u,u,u,u)
| ( v != u )
| ( u != u ) ),
inference(instantiation,[status(thm)],[c_3804]) ).
tcf(c_3955,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(X1,X0,X2,w1)
| ~ equidistant(X0,X1,X2,w1) ),
inference(instantiation,[status(thm)],[c_102]) ).
tcf(c_4425,plain,
( equidistant(w,u,w1,u1)
| ( v = u )
| ~ between(u1,v1,w1)
| ~ between(u,v,w)
| ~ equidistant(v,w,v1,w1)
| ~ equidistant(v,u,v1,u1)
| ~ equidistant(u,v,u1,v1)
| ~ equidistant(u,u,u1,u1) ),
inference(instantiation,[status(thm)],[c_2348]) ).
tcf(c_8391,plain,
( equidistant(w,v,v1,w1)
| ~ equidistant(v,w,v1,w1) ),
inference(instantiation,[status(thm)],[c_3955]) ).
tcf(c_8542,plain,
! [X0: $i] : equidistant(X0,X0,u1,u1),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_8544,plain,
equidistant(u,u,u1,u1),
inference(instantiation,[status(thm)],[c_8542]) ).
tcf(c_16338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(u,w,u1,w1)
| ~ equidistant(X0,X2,X1,X3)
| ( w1 != X3 )
| ( w != X2 )
| ( u1 != X1 )
| ( u != X0 ) ),
inference(instantiation,[status(thm)],[c_199]) ).
tcf(c_16534,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(u,w,u1,w1)
| ~ equidistant(X0,X2,X1,w1)
| ( w1 != w1 )
| ( w != X2 )
| ( u1 != X1 )
| ( u != X0 ) ),
inference(instantiation,[status(thm)],[c_16338]) ).
tcf(c_19182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( equidistant(X0,X1,X4,w1)
| ~ equidistant(X2,X3,X4,w1)
| ~ equidistant(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_19350,plain,
! [X0: $i,X1: $i] :
( ( u1 = X0 )
| ~ equidistant(u1,X0,X1,X1) ),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_19371,plain,
! [X0: $i,X1: $i] :
( equidistant(u,w,u1,w1)
| ~ equidistant(X0,w,X1,w1)
| ( w1 != w1 )
| ( w != w )
| ( u1 != X1 )
| ( u != X0 ) ),
inference(instantiation,[status(thm)],[c_16534]) ).
tcf(c_23704,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(u1,X3,X2,X2)
| ~ equidistant(X0,X1,u1,X3)
| ~ equidistant(X0,X1,X2,X2) ),
inference(instantiation,[status(thm)],[c_105]) ).
tcf(c_23924,plain,
! [X0: $i,X1: $i] :
( equidistant(X0,X1,X1,v)
| ~ equidistant(X0,X1,v,X1) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_26192,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(X1,X0,X2,u1)
| ~ equidistant(X0,X1,u1,X2) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_31205,plain,
! [X0: $i,X1: $i] :
( equidistant(X0,X1,v1,w1)
| ~ equidistant(w,v,v1,w1)
| ~ equidistant(X0,X1,w,v) ),
inference(instantiation,[status(thm)],[c_19182]) ).
tcf(c_35486,plain,
( equidistant(v,u,v1,u1)
| ~ equidistant(u,v,u1,v1) ),
inference(instantiation,[status(thm)],[c_26192]) ).
tcf(c_37417,plain,
! [X0: $i] :
( equidistant(u1,v1,X0,X0)
| ~ equidistant(u,v,u1,v1)
| ~ equidistant(u,v,X0,X0) ),
inference(instantiation,[status(thm)],[c_23704]) ).
tcf(c_37418,plain,
( equidistant(u1,v1,u,u)
| ~ equidistant(u,v,u1,v1)
| ~ equidistant(u,v,u,u) ),
inference(instantiation,[status(thm)],[c_37417]) ).
tcf(c_46610,plain,
! [X0: $i] :
( equidistant(X0,w,w,v)
| ~ equidistant(X0,w,v,w) ),
inference(instantiation,[status(thm)],[c_23924]) ).
tcf(c_46613,plain,
( equidistant(u,w,w,v)
| ~ equidistant(u,w,v,w) ),
inference(instantiation,[status(thm)],[c_46610]) ).
tcf(c_208826,plain,
! [X0: $i] :
( ( u1 = v1 )
| ~ equidistant(u1,v1,X0,X0) ),
inference(instantiation,[status(thm)],[c_19350]) ).
tcf(c_208829,plain,
( ( u1 = v1 )
| ~ equidistant(u1,v1,u,u) ),
inference(instantiation,[status(thm)],[c_208826]) ).
tcf(c_213722,plain,
! [X0: $i] :
( equidistant(X0,w,v1,w1)
| ~ equidistant(w,v,v1,w1)
| ~ equidistant(X0,w,w,v) ),
inference(instantiation,[status(thm)],[c_31205]) ).
tcf(c_213732,plain,
( equidistant(u,w,v1,w1)
| ~ equidistant(w,v,v1,w1)
| ~ equidistant(u,w,w,v) ),
inference(instantiation,[status(thm)],[c_213722]) ).
tcf(c_275095,plain,
! [X0: $i] :
( equidistant(u,w,u1,w1)
| ~ equidistant(X0,w,v1,w1)
| ( w1 != w1 )
| ( w != w )
| ( u1 != v1 )
| ( u != X0 ) ),
inference(instantiation,[status(thm)],[c_19371]) ).
tcf(c_275100,plain,
( equidistant(u,w,u1,w1)
| ~ equidistant(u,w,v1,w1)
| ( w1 != w1 )
| ( w != w )
| ( u1 != v1 )
| ( u != u ) ),
inference(instantiation,[status(thm)],[c_275095]) ).
tcf(c_478286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( equidistant(u,w,X0,X2)
| ~ equidistant(X4,X5,X1,X3)
| ( w != X5 )
| ( u != X4 )
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_199]) ).
tcf(c_479389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( equidistant(u,w,X0,X2)
| ~ equidistant(X4,w,X1,X3)
| ( w != w )
| ( u != X4 )
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_478286]) ).
tcf(c_481353,plain,
! [X0: $i,X1: $i] :
( equidistant(u,w,X0,X1)
| ~ equidistant(u,w,u,w)
| ( w != w )
| ( u != u )
| ( X1 != w )
| ( X0 != u ) ),
inference(instantiation,[status(thm)],[c_479389]) ).
tcf(c_488592,plain,
! [X0: $i] :
( equidistant(u,w,X0,w)
| ~ equidistant(u,w,u,w)
| ( w != w )
| ( u != u )
| ( X0 != u ) ),
inference(instantiation,[status(thm)],[c_481353]) ).
tcf(c_501992,plain,
( equidistant(u,w,v,w)
| ~ equidistant(u,w,u,w)
| ( w != w )
| ( v != u )
| ( u != u ) ),
inference(instantiation,[status(thm)],[c_488592]) ).
tcf(c_501994,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_501992,c_275100,c_213732,c_208829,c_46613,c_37418,c_35486,c_8544,c_8391,c_4425,c_3805,c_892,c_373,c_362,c_206,c_113,c_94,c_90,c_91,c_111,c_92,c_93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO025-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.36 % Computer : n016.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Wed Sep 23 10:30:33 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.40 Running first-order theorem proving
% 0.09/5.40 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
% 0.13/5.41
% 0.13/5.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.41
% 0.13/5.41 % Detected problem language: tptp
% 0.13/5.42 % Proving...
% 41.41/14.87 % SZS status Started for theBenchmark.p
% 41.41/14.87 % SZS status Unsatisfiable for theBenchmark.p
% 41.41/14.87
% 41.41/14.87 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 41.41/14.87
% 41.41/14.87 % ------ iProver source info
% 41.41/14.87
% 41.41/14.87 % git: date: 2026-07-19 20:42:38 +0200
% 41.41/14.87 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 41.41/14.87 % git: non_committed_changes: false
% 41.41/14.87
% 41.41/14.87 % ------ Parsing...% successful
% 41.41/14.87
% 41.41/14.87
% 41.41/14.87 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_eq
% 41.41/14.87 %
% 41.41/14.87
% 41.41/14.87 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 41.41/14.87
% 41.41/14.87 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_eq
% 41.41/14.87 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e % ------ preprocesses with Option_epr_non_horn_eq
% 41.41/14.87 %
% 41.41/14.87
% 41.41/14.87 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 41.41/14.87 % ------ Proving...
% 41.41/14.87 % ------ Problem Properties
% 41.41/14.87
% 41.41/14.87 %
% 41.41/14.87 % clauses 21
% 41.41/14.87 % conjectures 1
% 41.41/14.87 % EPR 21
% 41.41/14.87 % Horn 19
% 41.41/14.87 % unary 8
% 41.41/14.87 % binary 9
% 41.41/14.87 % lits 47
% 41.41/14.87 % lits eq 4
% 41.41/14.87 % fd_pure 0
% 41.41/14.87 % fd_pseudo 0
% 41.41/14.87 % fd_cond 0
% 41.41/14.87 % fd_pseudo_cond 4
% 41.41/14.87 % AC symbols 0
% 41.41/14.87
% 41.41/14.87 % ------ Schedule EPR non Horn eq is on
% 41.41/14.87
% 41.41/14.87 % ------ Option_epr_non_horn_eq Time Limit: Unbounded
% 41.41/14.87
% 41.41/14.87
% 41.41/14.87 % ------
% 41.41/14.87 % Current options:
% 41.41/14.87 % ------
% 41.41/14.87
% 41.41/14.87
% 41.41/14.87 %
% 41.41/14.87
% 41.41/14.87 % ------ Proving...
% 41.41/14.87 %
% 41.41/14.87
% 41.41/14.87 % SZS status Unsatisfiable for theBenchmark.p
% 41.41/14.87
% 41.41/14.87 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 41.41/14.87
% 41.41/14.87
%------------------------------------------------------------------------------