%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO037-2 : 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 : n009.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 3.55s 6.28s
% Output : CNFRefutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 25 unt; 2 def)
% Number of atoms : 71 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 19 ~; 16 |; 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 : 8 ( 8 usr; 7 con; 0-4 aty)
% Number of variables : 63 ( 0 sgn 63 !; 0 ?; 44 :)
% 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(f4,axiom,
! [X2,X3,X0,X1] : between(X0,X1,extension(X0,X1,X2,X3)),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
fof(f12,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',lower_dimension3) ).
fof(f19,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/sandbox/benchmark/theBenchmark.p',prove_lengthen) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] : equidistant(X0,X1,X1,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_69,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_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[],[f5]) ).
tcf(c_79,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(cnf_transformation,[],[f12]) ).
tcf(c_86,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,[],[f19]) ).
tcf(c_106,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_86,c_71]) ).
tcf(c_321,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_322,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_323,plain,
( ( iPr_def_10 = v )
| ~ equidistant(v,iPr_def_10,x,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_106,c_322,c_321]) ).
tcf(c_659,plain,
equidistant(v,iPr_def_10,lower_dimension_point_1,lower_dimension_point_2),
inference(superposition,[status(thm)],[c_321,c_72]) ).
tcf(c_670,plain,
! [X0: $i,X1: $i,X2: $i] : extension(X0,X1,X2,X2) = X1,
inference(superposition,[status(thm)],[c_72,c_70]) ).
tcf(c_678,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X1,X0,X2,X3)
| ~ equidistant(X0,X1,X2,X3) ),
inference(superposition,[status(thm)],[c_68,c_69]) ).
tcf(c_679,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_72,c_69]) ).
tcf(c_684,plain,
! [X0: $i,X1: $i] :
( equidistant(lower_dimension_point_1,lower_dimension_point_2,X0,X1)
| ~ equidistant(v,iPr_def_10,X0,X1) ),
inference(superposition,[status(thm)],[c_659,c_69]) ).
tcf(c_692,plain,
! [X0: $i,X1: $i] : between(X0,X1,X1),
inference(superposition,[status(thm)],[c_670,c_71]) ).
tcf(c_704,plain,
! [X0: $i,X1: $i] : equidistant(X0,X1,X0,X1),
inference(superposition,[status(thm)],[c_68,c_678]) ).
tcf(c_735,plain,
equidistant(lower_dimension_point_1,lower_dimension_point_2,iPr_def_10,v),
inference(superposition,[status(thm)],[c_68,c_684]) ).
tcf(c_744,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : equidistant(X0,X1,X2,extension(X3,X2,X0,X1)),
inference(superposition,[status(thm)],[c_704,c_679]) ).
tcf(c_795,plain,
equidistant(lower_dimension_point_2,lower_dimension_point_1,iPr_def_10,v),
inference(superposition,[status(thm)],[c_735,c_678]) ).
tcf(c_796,plain,
! [X0: $i,X1: $i] :
( equidistant(iPr_def_10,v,X0,X1)
| ~ equidistant(lower_dimension_point_1,lower_dimension_point_2,X0,X1) ),
inference(superposition,[status(thm)],[c_735,c_69]) ).
tcf(c_848,plain,
equidistant(lower_dimension_point_1,lower_dimension_point_2,x,iPr_def_11),
inference(superposition,[status(thm)],[c_322,c_744]) ).
tcf(c_1780,plain,
equidistant(iPr_def_10,v,x,iPr_def_11),
inference(superposition,[status(thm)],[c_848,c_796]) ).
tcf(c_1887,plain,
equidistant(v,iPr_def_10,x,iPr_def_11),
inference(superposition,[status(thm)],[c_1780,c_678]) ).
tcf(c_1899,plain,
v = iPr_def_10,
inference(backward_subsumption_resolution,[status(thm)],[c_323,c_1887]) ).
tcf(c_1913,plain,
equidistant(lower_dimension_point_2,lower_dimension_point_1,iPr_def_10,iPr_def_10),
inference(demodulation,[status(thm)],[c_795,c_1899]) ).
tcf(c_1951,plain,
lower_dimension_point_1 = lower_dimension_point_2,
inference(superposition,[status(thm)],[c_1913,c_70]) ).
tcf(c_1976,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_1),
inference(demodulation,[status(thm)],[c_79,c_1951]) ).
tcf(c_1979,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1976,c_692]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO037-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/5.37 % Computer : n009.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Wed Sep 23 10:30:33 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/5.41 Running first-order theorem proving
% 0.13/5.41 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
% 0.13/5.42
% 0.13/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.42
% 0.13/5.42 % Detected problem language: tptp
% 0.13/5.43 % Proving...
% 3.55/6.28 % SZS status Started for theBenchmark.p
% 3.55/6.28 % SZS status Unsatisfiable for theBenchmark.p
% 3.55/6.28
% 3.55/6.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.55/6.28
% 3.55/6.28 % ------ iProver source info
% 3.55/6.28
% 3.55/6.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.55/6.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.55/6.28 % git: non_committed_changes: false
% 3.55/6.28
% 3.55/6.28 % ------ Parsing...% successful
% 3.55/6.28
% 3.55/6.28
% 3.55/6.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.55/6.28
% 3.55/6.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.55/6.28
% 3.55/6.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.55/6.28
% 3.55/6.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.55/6.28 % ------ Proving...
% 3.55/6.28 % ------ Problem Properties
% 3.55/6.28
% 3.55/6.28 %
% 3.55/6.28 % clauses 21
% 3.55/6.28 % conjectures 0
% 3.55/6.28 % EPR 10
% 3.55/6.28 % Horn 16
% 3.55/6.28 % unary 8
% 3.55/6.28 % binary 3
% 3.55/6.28 % lits 60
% 3.55/6.28 % lits eq 10
% 3.55/6.28 % fd_pure 0
% 3.55/6.28 % fd_pseudo 0
% 3.55/6.28 % fd_cond 0
% 3.55/6.28 % fd_pseudo_cond 7
% 3.55/6.28 % AC symbols 0
% 3.55/6.28
% 3.55/6.28 % ------ Schedule dynamic 5 is on
% 3.55/6.28
% 3.55/6.28 % ------ no conjectures: strip conj schedule
% 3.55/6.28
% 3.55/6.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.55/6.28
% 3.55/6.28
% 3.55/6.28 % ------
% 3.55/6.28 % Current options:
% 3.55/6.28 % ------
% 3.55/6.28
% 3.55/6.28
% 3.55/6.28 %
% 3.55/6.28
% 3.55/6.28 % ------ Proving...
% 3.55/6.28 %
% 3.55/6.28
% 3.55/6.28 % SZS status Unsatisfiable for theBenchmark.p
% 3.55/6.28
% 3.55/6.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.55/6.28
% 3.55/6.28
%------------------------------------------------------------------------------