%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO029-3 : 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 : n014.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 0.43s 1.62s
% Output : CNFRefutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 20 unt; 2 def)
% Number of atoms : 82 ( 17 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 54 ( 28 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 6 ( 4 usr; 3 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-4 aty)
% Number of variables : 66 ( 0 sgn 66 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
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(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(f21,axiom,
! [X2,X3,X0,X1] :
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
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(f31,axiom,
! [X2,X3,X0,X1,X4] :
( between(X1,X2,X0)
| X0 != extension(X1,X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b0) ).
fof(f32,plain,
! [X2,X3,X0,X1,X4] :
( between(X1,X2,X0)
| extension(X1,X2,X3,X4) != X0 ),
inference(reorient_equations,[],[f31]) ).
fof(f43,axiom,
! [X2,X3,X0,X1] :
( X2 = X3
| X0 = X1
| ~ equidistant(X1,X2,X1,X3)
| ~ between(X0,X1,X3)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9) ).
fof(f44,axiom,
u != v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_not_v) ).
fof(f45,negated_conjecture,
extension(u,v,u,v) != extension(u,v,v,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equal_extensions) ).
fof(f51,plain,
! [X2,X3,X1,X4] : between(X1,X2,extension(X1,X2,X3,X4)),
inference(equality_resolution,[],[f32]) ).
tcf(c_90,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_93,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[],[f5]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_109,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_117,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[],[f51]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( X0 = X3 )
| ~ between(X3,X0,X2)
| ~ between(X3,X0,X1)
| ~ equidistant(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_126,plain,
u != v,
inference(cnf_transformation,[],[f44]) ).
tcf(c_127,negated_conjecture,
extension(u,v,u,v) != extension(u,v,v,u),
inference(cnf_transformation,[],[f45]) ).
tcf(c_823,definition,
iPr_def_10 = extension(u,v,u,v),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_824,definition,
iPr_def_11 = extension(u,v,v,u),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_825,negated_conjecture,
iPr_def_10 != iPr_def_11,
inference(demodulation,[status(thm)],[c_127,c_824,c_823]) ).
tcf(c_1278,plain,
between(u,v,iPr_def_10),
inference(superposition,[status(thm)],[c_823,c_117]) ).
tcf(c_1280,plain,
between(u,v,iPr_def_11),
inference(superposition,[status(thm)],[c_824,c_117]) ).
tcf(c_1282,plain,
equidistant(v,iPr_def_10,u,v),
inference(superposition,[status(thm)],[c_823,c_93]) ).
tcf(c_1283,plain,
equidistant(v,iPr_def_11,v,u),
inference(superposition,[status(thm)],[c_824,c_93]) ).
tcf(c_1303,plain,
equidistant(u,v,v,iPr_def_10),
inference(superposition,[status(thm)],[c_1282,c_108]) ).
tcf(c_1304,plain,
equidistant(v,u,v,iPr_def_11),
inference(superposition,[status(thm)],[c_1283,c_108]) ).
tcf(c_1324,plain,
equidistant(u,v,v,iPr_def_11),
inference(superposition,[status(thm)],[c_1304,c_109]) ).
tcf(c_1500,plain,
! [X0: $i,X1: $i] :
( equidistant(v,iPr_def_10,X0,X1)
| ~ equidistant(u,v,X0,X1) ),
inference(superposition,[status(thm)],[c_1303,c_90]) ).
tcf(c_4466,plain,
equidistant(v,iPr_def_10,v,iPr_def_11),
inference(superposition,[status(thm)],[c_1324,c_1500]) ).
tcf(c_4538,plain,
! [X0: $i] :
( ( iPr_def_10 = iPr_def_11 )
| ( X0 = v )
| ~ between(X0,v,iPr_def_11)
| ~ between(X0,v,iPr_def_10) ),
inference(superposition,[status(thm)],[c_4466,c_125]) ).
tcf(c_4544,plain,
! [X0: $i] :
( ( X0 = v )
| ~ between(X0,v,iPr_def_11)
| ~ between(X0,v,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4538,c_825]) ).
tcf(c_4571,plain,
( ( u = v )
| ~ between(u,v,iPr_def_11)
| ~ between(u,v,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_4544]) ).
tcf(c_4572,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4571,c_1280,c_1278,c_126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO029-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.79 % Computer : n014.cluster.edu
% 0.12/0.79 % Model : x86_64 x86_64
% 0.12/0.79 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.79 % Memory : 8046.5625MB
% 0.12/0.79 % OS : Linux 6.8.0-71-generic
% 0.12/0.79 % CPULimit : 300
% 0.12/0.79 % WCLimit : 300
% 0.12/0.79 % DateTime : Wed Sep 23 10:28:21 UTC 2026
% 0.12/0.79 % CPUTime :
% 0.12/0.80 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.83 Running first-order theorem proving
% 0.15/0.83 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
% 0.15/0.85
% 0.15/0.85 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.85
% 0.15/0.85 % Detected problem language: tptp
% 0.15/0.86 % Proving...
% 0.43/1.62 % SZS status Started for theBenchmark.p
% 0.43/1.62 % SZS status Unsatisfiable for theBenchmark.p
% 0.43/1.62
% 0.43/1.62 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.43/1.62
% 0.43/1.62 % ------ iProver source info
% 0.43/1.62
% 0.43/1.62 % git: date: 2026-07-19 20:42:38 +0200
% 0.43/1.62 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.43/1.62 % git: non_committed_changes: false
% 0.43/1.62
% 0.43/1.62 % ------ Parsing...% successful
% 0.43/1.62
% 0.43/1.62
% 0.43/1.62 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.43/1.62
% 0.43/1.62 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.43/1.62
% 0.43/1.62 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.43/1.62
% 0.43/1.62 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.43/1.62 % ------ Proving...
% 0.43/1.62 % ------ Problem Properties
% 0.43/1.62
% 0.43/1.62 %
% 0.43/1.62 % clauses 36
% 0.43/1.62 % conjectures 1
% 0.43/1.62 % EPR 23
% 0.43/1.62 % Horn 30
% 0.43/1.62 % unary 13
% 0.43/1.62 % binary 10
% 0.43/1.62 % lits 92
% 0.43/1.62 % lits eq 16
% 0.43/1.62 % fd_pure 0
% 0.43/1.62 % fd_pseudo 0
% 0.43/1.62 % fd_cond 0
% 0.43/1.62 % fd_pseudo_cond 9
% 0.43/1.62 % AC symbols 0
% 0.43/1.62
% 0.43/1.62 % ------ Schedule dynamic 5 is on
% 0.43/1.62
% 0.43/1.62 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.43/1.62
% 0.43/1.62
% 0.43/1.62 % ------
% 0.43/1.62 % Current options:
% 0.43/1.62 % ------
% 0.43/1.62
% 0.43/1.62
% 0.43/1.62 %
% 0.43/1.62
% 0.43/1.62 % ------ Proving...
% 0.43/1.62 %
% 0.43/1.62
% 0.43/1.62 % SZS status Unsatisfiable for theBenchmark.p
% 0.43/1.62
% 0.43/1.62 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.43/1.62
% 0.43/1.62
%------------------------------------------------------------------------------