%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO037-3 : 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 : 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 01:19:38 PM UTC 2026
% Result : Unsatisfiable 2.59s 6.20s
% Output : CNFRefutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 38 ( 19 unt; 2 def)
% Number of atoms : 78 ( 12 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 48 ( 25 ~; 23 |; 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 : 7 ( 7 usr; 6 con; 0-4 aty)
% Number of variables : 71 ( 0 sgn 71 !; 0 ?; 40 :)
% 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(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(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(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(f41,axiom,
! [X0,X1] : equidistant(X0,X0,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7) ).
fof(f65,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_1) ).
fof(f68,negated_conjecture,
( ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2))
| ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lengthen) ).
tcf(c_111,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_112,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[],[f5]) ).
tcf(c_129,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_130,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_131,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_144,plain,
! [X0: $i,X1: $i] : equidistant(X0,X0,X1,X1),
inference(cnf_transformation,[],[f41]) ).
tcf(c_165,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(cnf_transformation,[],[f65]) ).
tcf(c_168,negated_conjecture,
( ( extension(u,v,lower_dimension_point_1,lower_dimension_point_2) = v )
| ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2))
| ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2)) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_211,plain,
( ( extension(u,v,lower_dimension_point_1,lower_dimension_point_2) = v )
| ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_168,c_113]) ).
tcf(c_1187,definition,
iPr_def_10 = extension(u,v,lower_dimension_point_1,lower_dimension_point_2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1188,definition,
iPr_def_11 = extension(w,x,lower_dimension_point_1,lower_dimension_point_2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1189,plain,
( ( iPr_def_10 = v )
| ~ equidistant(v,iPr_def_10,x,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_211,c_1188,c_1187]) ).
tcf(c_1819,plain,
equidistant(v,iPr_def_10,lower_dimension_point_1,lower_dimension_point_2),
inference(superposition,[status(thm)],[c_1187,c_114]) ).
tcf(c_1820,plain,
equidistant(x,iPr_def_11,lower_dimension_point_1,lower_dimension_point_2),
inference(superposition,[status(thm)],[c_1188,c_114]) ).
tcf(c_1864,plain,
equidistant(lower_dimension_point_1,lower_dimension_point_2,v,iPr_def_10),
inference(superposition,[status(thm)],[c_1819,c_129]) ).
tcf(c_1865,plain,
equidistant(lower_dimension_point_1,lower_dimension_point_2,x,iPr_def_11),
inference(superposition,[status(thm)],[c_1820,c_129]) ).
tcf(c_1886,plain,
equidistant(v,iPr_def_10,lower_dimension_point_2,lower_dimension_point_1),
inference(superposition,[status(thm)],[c_1819,c_131]) ).
tcf(c_2234,plain,
! [X0: $i] :
( ( lower_dimension_point_1 = lower_dimension_point_2 )
| ~ equidistant(lower_dimension_point_1,lower_dimension_point_2,X0,X0) ),
inference(instantiation,[status(thm)],[c_112]) ).
tcf(c_2498,plain,
! [X0: $i,X1: $i] :
( equidistant(v,iPr_def_10,X0,X1)
| ~ equidistant(lower_dimension_point_1,lower_dimension_point_2,X0,X1) ),
inference(superposition,[status(thm)],[c_1864,c_111]) ).
tcf(c_2504,plain,
! [X0: $i,X1: $i] :
( equidistant(lower_dimension_point_2,lower_dimension_point_1,X0,X1)
| ~ equidistant(v,iPr_def_10,X0,X1) ),
inference(superposition,[status(thm)],[c_1886,c_111]) ).
tcf(c_5205,plain,
! [X0: $i] :
( equidistant(lower_dimension_point_1,lower_dimension_point_2,X0,X0)
| ~ equidistant(lower_dimension_point_2,lower_dimension_point_1,X0,X0) ),
inference(instantiation,[status(thm)],[c_130]) ).
tcf(c_7185,plain,
equidistant(v,iPr_def_10,x,iPr_def_11),
inference(superposition,[status(thm)],[c_1865,c_2498]) ).
tcf(c_7204,plain,
v = iPr_def_10,
inference(backward_subsumption_resolution,[status(thm)],[c_1189,c_7185]) ).
tcf(c_7369,plain,
! [X0: $i,X1: $i] :
( equidistant(lower_dimension_point_2,lower_dimension_point_1,X0,X1)
| ~ equidistant(iPr_def_10,iPr_def_10,X0,X1) ),
inference(light_normalisation,[status(thm)],[c_2504,c_7204]) ).
tcf(c_7377,plain,
! [X0: $i] : equidistant(lower_dimension_point_2,lower_dimension_point_1,X0,X0),
inference(superposition,[status(thm)],[c_144,c_7369]) ).
tcf(c_7389,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_7377,c_5205,c_2234,c_165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO037-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.39 % Computer : n019.cluster.edu
% 0.10/5.39 % Model : x86_64 x86_64
% 0.10/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.39 % Memory : 8046.5625MB
% 0.10/5.39 % OS : Linux 6.8.0-71-generic
% 0.10/5.39 % CPULimit : 300
% 0.10/5.39 % WCLimit : 300
% 0.10/5.39 % DateTime : Wed Sep 23 10:31:28 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.44 % Detected problem language: tptp
% 0.14/5.45 % Proving...
% 2.59/6.20 % SZS status Started for theBenchmark.p
% 2.59/6.20 % SZS status Unsatisfiable for theBenchmark.p
% 2.59/6.20
% 2.59/6.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.59/6.20
% 2.59/6.20 % ------ iProver source info
% 2.59/6.20
% 2.59/6.20 % git: date: 2026-07-19 20:42:38 +0200
% 2.59/6.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.59/6.20 % git: non_committed_changes: false
% 2.59/6.20
% 2.59/6.20 % ------ Parsing...% successful
% 2.59/6.20
% 2.59/6.20
% 2.59/6.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.59/6.20
% 2.59/6.20 % ------ Preprocessing... sup_sim: 1 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 %
% 2.59/6.20
% 2.59/6.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.59/6.20
% 2.59/6.20 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.59/6.20 % ------ Proving...
% 2.59/6.20 % ------ Problem Properties
% 2.59/6.20
% 2.59/6.20 %
% 2.59/6.20 % clauses 53
% 2.59/6.20 % conjectures 0
% 2.59/6.20 % EPR 36
% 2.59/6.20 % Horn 42
% 2.59/6.20 % unary 17
% 2.59/6.20 % binary 14
% 2.59/6.20 % lits 133
% 2.59/6.20 % lits eq 29
% 2.59/6.20 % fd_pure 0
% 2.59/6.20 % fd_pseudo 0
% 2.59/6.20 % fd_cond 0
% 2.59/6.20 % fd_pseudo_cond 15
% 2.59/6.20 % AC symbols 0
% 2.59/6.20
% 2.59/6.20 % ------ Schedule dynamic 5 is on
% 2.59/6.20
% 2.59/6.20 % ------ no conjectures: strip conj schedule
% 2.59/6.20
% 2.59/6.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.59/6.20
% 2.59/6.20
% 2.59/6.20 % ------
% 2.59/6.20 % Current options:
% 2.59/6.20 % ------
% 2.59/6.20
% 2.59/6.20
% 2.59/6.20 %
% 2.59/6.20
% 2.59/6.20 % ------ Proving...
% 2.59/6.20 %
% 2.59/6.20
% 2.59/6.20 % SZS status Unsatisfiable for theBenchmark.p
% 2.59/6.20
% 2.59/6.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.59/6.20
% 2.59/6.20
%------------------------------------------------------------------------------