%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO026-2 : 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 01:19:35 PM UTC 2026
% Result : Unsatisfiable 4.13s 1.48s
% Output : CNFRefutation 4.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of formulae : 41 ( 17 unt; 0 def)
% Number of atoms : 112 ( 25 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 140 ( 69 ~; 71 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 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 : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 73 ( 0 sgn 73 !; 0 ?; 54 :)
% 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(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,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
fof(f20,axiom,
between(u,v,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_x) ).
fof(f21,axiom,
equidistant(v,w,v,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_to_w_equals_v_to_x) ).
fof(f22,axiom,
u != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_not_v) ).
fof(f23,negated_conjecture,
w != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_w_is_x) ).
tcf(c_72,plain,
between(u,v,w),
inference(cnf_transformation,[],[f19]) ).
tcf(c_73,plain,
between(u,v,x),
inference(cnf_transformation,[],[f20]) ).
tcf(c_74,plain,
equidistant(v,w,v,x),
inference(cnf_transformation,[],[f21]) ).
tcf(c_75,plain,
u != v,
inference(cnf_transformation,[],[f22]) ).
tcf(c_76,negated_conjecture,
w != x,
inference(cnf_transformation,[],[f23]) ).
tcf(c_78,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_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_80,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_81,plain,
! [X0: $i,X1: $i] : equidistant(X0,X1,X1,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_134,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_136,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_147,plain,
! [X0: $i] :
( ( u = v )
| ( v != X0 )
| ( u != X0 ) ),
inference(instantiation,[status(thm)],[c_136]) ).
tcf(c_170,plain,
( ( u = v )
| ( v != u )
| ( u != u ) ),
inference(instantiation,[status(thm)],[c_147]) ).
tcf(c_171,plain,
u = u,
inference(instantiation,[status(thm)],[c_134]) ).
tcf(c_200,plain,
equidistant(v,u,u,v),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_369,plain,
equidistant(x,u,u,x),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_612,plain,
! [X0: $i] :
( ( w = x )
| ~ equidistant(w,x,X0,X0) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( equidistant(w,x,X4,X4)
| ( X1 = X0 )
| ~ between(X0,X1,w)
| ~ between(X2,X3,X4)
| ~ equidistant(X1,x,X3,X4)
| ~ equidistant(X1,w,X3,X4)
| ~ equidistant(X0,x,X2,X4)
| ~ equidistant(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_650,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X2,X3,u,v)
| ~ equidistant(X0,X1,u,v)
| ~ equidistant(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_756,plain,
! [X0: $i,X1: $i] :
( equidistant(X0,X1,u,v)
| ~ equidistant(v,u,u,v)
| ~ equidistant(v,u,X0,X1) ),
inference(instantiation,[status(thm)],[c_650]) ).
tcf(c_906,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(v,x,v,X2)
| ~ equidistant(X0,X1,v,x)
| ~ equidistant(X0,X1,v,X2) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_982,plain,
! [X0: $i] :
( equidistant(v,x,v,X0)
| ~ equidistant(v,w,v,x)
| ~ equidistant(v,w,v,X0) ),
inference(instantiation,[status(thm)],[c_906]) ).
tcf(c_1045,plain,
( equidistant(u,v,u,v)
| ~ equidistant(v,u,u,v) ),
inference(instantiation,[status(thm)],[c_756]) ).
tcf(c_1375,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( equidistant(X4,x,X2,X3)
| ~ equidistant(X0,X1,X4,x)
| ~ equidistant(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_1493,plain,
( equidistant(v,x,v,x)
| ~ equidistant(v,w,v,x) ),
inference(instantiation,[status(thm)],[c_982]) ).
tcf(c_1640,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(X0,x,X1,X2)
| ~ equidistant(x,X0,X0,x)
| ~ equidistant(x,X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_1375]) ).
tcf(c_3223,plain,
( equidistant(u,x,u,x)
| ~ equidistant(x,u,u,x) ),
inference(instantiation,[status(thm)],[c_1640]) ).
tcf(c_3546,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(w,x,X2,X2)
| ( X0 = u )
| ~ between(u,X0,w)
| ~ between(X3,X1,X2)
| ~ equidistant(u,x,X3,X2)
| ~ equidistant(u,X0,X3,X1)
| ~ equidistant(X0,x,X1,X2)
| ~ equidistant(X0,w,X1,X2) ),
inference(instantiation,[status(thm)],[c_621]) ).
tcf(c_7655,plain,
( ( w = x )
| ~ equidistant(w,x,x,x) ),
inference(instantiation,[status(thm)],[c_612]) ).
tcf(c_11575,plain,
! [X0: $i,X1: $i] :
( equidistant(w,x,x,x)
| ( X0 = u )
| ~ between(u,X1,x)
| ~ between(u,X0,w)
| ~ equidistant(u,x,u,x)
| ~ equidistant(u,X0,u,X1)
| ~ equidistant(X0,x,X1,x)
| ~ equidistant(X0,w,X1,x) ),
inference(instantiation,[status(thm)],[c_3546]) ).
tcf(c_11576,plain,
( equidistant(w,x,x,x)
| ( v = u )
| ~ between(u,v,x)
| ~ between(u,v,w)
| ~ equidistant(v,x,v,x)
| ~ equidistant(v,w,v,x)
| ~ equidistant(u,x,u,x)
| ~ equidistant(u,v,u,v) ),
inference(instantiation,[status(thm)],[c_11575]) ).
tcf(c_11577,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11576,c_7655,c_3223,c_1493,c_1045,c_369,c_200,c_171,c_170,c_74,c_75,c_76,c_72,c_73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO026-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.57 % Computer : n026.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Wed Sep 23 10:27:54 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.57 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.61 Running first-order theorem proving
% 0.09/0.61 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
% 0.09/0.62
% 0.09/0.62 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.62
% 0.09/0.62 % Detected problem language: tptp
% 0.14/0.63 % Proving...
% 4.13/1.48 % SZS status Started for theBenchmark.p
% 4.13/1.48 % SZS status Unsatisfiable for theBenchmark.p
% 4.13/1.48
% 4.13/1.48 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.13/1.48
% 4.13/1.48 % ------ iProver source info
% 4.13/1.48
% 4.13/1.48 % git: date: 2026-07-19 20:42:38 +0200
% 4.13/1.48 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.13/1.48 % git: non_committed_changes: false
% 4.13/1.48
% 4.13/1.48 % ------ Parsing...% successful
% 4.13/1.48
% 4.13/1.48
% 4.13/1.48 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_eq
% 4.13/1.48 %
% 4.13/1.48
% 4.13/1.48 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.13/1.48
% 4.13/1.48 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_eq
% 4.13/1.48 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e % ------ preprocesses with Option_epr_non_horn_eq
% 4.13/1.48 %
% 4.13/1.48
% 4.13/1.48 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.13/1.48 % ------ Proving...
% 4.13/1.48 % ------ Problem Properties
% 4.13/1.48
% 4.13/1.48 %
% 4.13/1.48 % clauses 11
% 4.13/1.48 % conjectures 1
% 4.13/1.48 % EPR 11
% 4.13/1.48 % Horn 9
% 4.13/1.48 % unary 6
% 4.13/1.48 % binary 2
% 4.13/1.48 % lits 28
% 4.13/1.48 % lits eq 6
% 4.13/1.48 % fd_pure 0
% 4.13/1.48 % fd_pseudo 0
% 4.13/1.48 % fd_cond 0
% 4.13/1.48 % fd_pseudo_cond 4
% 4.13/1.48 % AC symbols 0
% 4.13/1.48
% 4.13/1.48 % ------ Schedule EPR non Horn eq is on
% 4.13/1.48
% 4.13/1.48 % ------ Option_epr_non_horn_eq Time Limit: Unbounded
% 4.13/1.48
% 4.13/1.48
% 4.13/1.48 % ------
% 4.13/1.48 % Current options:
% 4.13/1.48 % ------
% 4.13/1.48
% 4.13/1.48
% 4.13/1.48 %
% 4.13/1.48
% 4.13/1.48 % ------ Proving...
% 4.13/1.48 %
% 4.13/1.48
% 4.13/1.48 % SZS status Unsatisfiable for theBenchmark.p
% 4.13/1.48
% 4.13/1.48 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.13/1.48
% 4.13/1.48
%------------------------------------------------------------------------------