%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO126+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n018.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 01:19:57 PM UTC 2026
% Result : Theorem 4.18s 2.21s
% Output : CNFRefutation 4.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 72 ( 20 unt; 0 def)
% Number of atoms : 244 ( 20 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 277 ( 105 ~; 106 |; 55 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 149 ( 0 sgn 131 !; 18 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( end_point(X0,X1)
<=> ( ! [X2,X3] :
( ( incident_c(X0,X3)
& incident_c(X0,X2)
& part_of(X3,X1)
& part_of(X2,X1) )
=> ( part_of(X3,X2)
| part_of(X2,X3) ) )
& incident_c(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',end_point_defn) ).
fof(f4,axiom,
! [X0,X1] :
( inner_point(X0,X1)
<=> ( ~ end_point(X0,X1)
& incident_c(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',inner_point_defn) ).
fof(f7,axiom,
! [X0] :
( open(X0)
<=> ? [X1] : end_point(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',open_defn) ).
fof(f10,axiom,
! [X0] :
? [X1] : inner_point(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',c3) ).
fof(f19,axiom,
! [X0,X1] :
( start_point(X0,X1)
<=> ( ! [X2] :
( ( incident_o(X2,X1)
& X0 != X2 )
=> ordered_by(X1,X0,X2) )
& incident_o(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+2.ax',start_point_defn) ).
fof(f22,axiom,
! [X0] :
? [X1] :
( ! [X2] :
( incident_o(X2,X0)
<=> incident_c(X2,X1) )
& open(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+2.ax',o2) ).
fof(f24,axiom,
! [X0] :
? [X1] : start_point(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+2.ax',o4) ).
fof(f28,conjecture,
! [X0] :
? [X1,X2] :
( X1 != X2
& ordered_by(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_4_11) ).
fof(f29,negated_conjecture,
~ ! [X0] :
? [X1,X2] :
( X1 != X2
& ordered_by(X0,X1,X2) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f31,plain,
! [X0,X1] :
( start_point(X0,X1)
=> ( ! [X2] :
( ( incident_o(X2,X1)
& X0 != X2 )
=> ordered_by(X1,X0,X2) )
& incident_o(X0,X1) ) ),
inference(unused_predicate_definition_removal,[],[f19]) ).
fof(f34,plain,
! [X0,X1] :
( end_point(X0,X1)
<=> ( ! [X2,X3] :
( ~ incident_c(X0,X3)
| ~ incident_c(X0,X2)
| ~ part_of(X3,X1)
| ~ part_of(X2,X1)
| part_of(X3,X2)
| part_of(X2,X3) )
& incident_c(X0,X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f35,plain,
! [X0,X1] :
( end_point(X0,X1)
<=> ( ! [X2,X3] :
( ~ incident_c(X0,X3)
| ~ incident_c(X0,X2)
| ~ part_of(X3,X1)
| ~ part_of(X2,X1)
| part_of(X3,X2)
| part_of(X2,X3) )
& incident_c(X0,X1) ) ),
inference(flattening,[],[f34]) ).
fof(f51,plain,
! [X0,X1] :
( ~ start_point(X0,X1)
| ( ! [X2] :
( ~ incident_o(X2,X1)
| X0 = X2
| ordered_by(X1,X0,X2) )
& incident_o(X0,X1) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f52,plain,
! [X0,X1] :
( ~ start_point(X0,X1)
| ( ! [X2] :
( ~ incident_o(X2,X1)
| X0 = X2
| ordered_by(X1,X0,X2) )
& incident_o(X0,X1) ) ),
inference(flattening,[],[f51]) ).
fof(f57,plain,
? [X0] :
! [X1,X2] :
( X1 = X2
| ~ ordered_by(X0,X1,X2) ),
inference(ennf_transformation,[],[f29]) ).
fof(f65,plain,
! [X0,X1] :
( ( ~ end_point(X0,X1)
| ( ! [X2,X3] :
( ~ incident_c(X0,X3)
| ~ incident_c(X0,X2)
| ~ part_of(X3,X1)
| ~ part_of(X2,X1)
| part_of(X3,X2)
| part_of(X2,X3) )
& incident_c(X0,X1) ) )
& ( ? [X2,X3] :
( incident_c(X0,X3)
& incident_c(X0,X2)
& part_of(X3,X1)
& part_of(X2,X1)
& ~ part_of(X3,X2)
& ~ part_of(X2,X3) )
| ~ incident_c(X0,X1)
| end_point(X0,X1) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f66,plain,
! [X0,X1] :
( ( ~ end_point(X0,X1)
| ( ! [X2,X3] :
( ~ incident_c(X0,X3)
| ~ incident_c(X0,X2)
| ~ part_of(X3,X1)
| ~ part_of(X2,X1)
| part_of(X3,X2)
| part_of(X2,X3) )
& incident_c(X0,X1) ) )
& ( ? [X2,X3] :
( incident_c(X0,X3)
& incident_c(X0,X2)
& part_of(X3,X1)
& part_of(X2,X1)
& ~ part_of(X3,X2)
& ~ part_of(X2,X3) )
| ~ incident_c(X0,X1)
| end_point(X0,X1) ) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( ( ~ end_point(X0,X1)
| ( ! [X4,X5] :
( ~ incident_c(X0,X5)
| ~ incident_c(X0,X4)
| ~ part_of(X5,X1)
| ~ part_of(X4,X1)
| part_of(X5,X4)
| part_of(X4,X5) )
& incident_c(X0,X1) ) )
& ( ? [X2,X3] :
( incident_c(X0,X3)
& incident_c(X0,X2)
& part_of(X3,X1)
& part_of(X2,X1)
& ~ part_of(X3,X2)
& ~ part_of(X2,X3) )
| ~ incident_c(X0,X1)
| end_point(X0,X1) ) ),
inference(rectify,[],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( ( ~ end_point(X0,X1)
| ( ! [X4,X5] :
( ~ incident_c(X0,X5)
| ~ incident_c(X0,X4)
| ~ part_of(X5,X1)
| ~ part_of(X4,X1)
| part_of(X5,X4)
| part_of(X4,X5) )
& incident_c(X0,X1) ) )
& ( ( incident_c(X0,sK3(X0,X1))
& incident_c(X0,sK2(X0,X1))
& part_of(sK3(X0,X1),X1)
& part_of(sK2(X0,X1),X1)
& ~ part_of(sK3(X0,X1),sK2(X0,X1))
& ~ part_of(sK2(X0,X1),sK3(X0,X1)) )
| ~ incident_c(X0,X1)
| end_point(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X2,sK2(X0,X1)),skolemize(X3,sK3(X0,X1))],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ( ~ inner_point(X0,X1)
| ( ~ end_point(X0,X1)
& incident_c(X0,X1) ) )
& ( end_point(X0,X1)
| ~ incident_c(X0,X1)
| inner_point(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f70,plain,
! [X0,X1] :
( ( ~ inner_point(X0,X1)
| ( ~ end_point(X0,X1)
& incident_c(X0,X1) ) )
& ( end_point(X0,X1)
| ~ incident_c(X0,X1)
| inner_point(X0,X1) ) ),
inference(flattening,[],[f69]) ).
fof(f76,plain,
! [X0] :
( ( ~ open(X0)
| ? [X1] : end_point(X1,X0) )
& ( ! [X1] : ~ end_point(X1,X0)
| open(X0) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f77,plain,
! [X0] :
( ( ~ open(X0)
| ? [X2] : end_point(X2,X0) )
& ( ! [X1] : ~ end_point(X1,X0)
| open(X0) ) ),
inference(rectify,[],[f76]) ).
fof(f78,plain,
! [X0] :
( ( ~ open(X0)
| end_point(sK6(X0),X0) )
& ( ! [X1] : ~ end_point(X1,X0)
| open(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0))],[f77]) ).
fof(f79,plain,
! [X0] : inner_point(sK7(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X1,sK7(X0))],[f10]) ).
fof(f92,plain,
! [X0] :
? [X1] :
( ! [X2] :
( ( ~ incident_o(X2,X0)
| incident_c(X2,X1) )
& ( ~ incident_c(X2,X1)
| incident_o(X2,X0) ) )
& open(X1) ),
inference(nnf_transformation,[],[f22]) ).
fof(f93,plain,
! [X0] :
( ! [X2] :
( ( ~ incident_o(X2,X0)
| incident_c(X2,sK14(X0)) )
& ( ~ incident_c(X2,sK14(X0))
| incident_o(X2,X0) ) )
& open(sK14(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X1,sK14(X0))],[f92]) ).
fof(f97,plain,
! [X0] : start_point(sK17(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X1,sK17(X0))],[f24]) ).
fof(f105,plain,
! [X1,X2] :
( X1 = X2
| ~ ordered_by(sK22,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(X0,sK22)],[f57]) ).
fof(f116,plain,
! [X0,X1] :
( ~ end_point(X0,X1)
| incident_c(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f123,plain,
! [X0,X1] :
( ~ inner_point(X0,X1)
| ~ end_point(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f124,plain,
! [X0,X1] :
( ~ inner_point(X0,X1)
| incident_c(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f125,plain,
! [X0,X1] :
( end_point(X0,X1)
| ~ incident_c(X0,X1)
| inner_point(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f134,plain,
! [X0] :
( ~ open(X0)
| end_point(sK6(X0),X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f138,plain,
! [X0] : inner_point(sK7(X0),X0),
inference(cnf_transformation,[],[f79]) ).
fof(f160,plain,
! [X2,X0,X1] :
( ~ start_point(X0,X1)
| ~ incident_o(X2,X1)
| X0 = X2
| ordered_by(X1,X0,X2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f164,plain,
! [X2,X0] :
( ~ incident_o(X2,X0)
| incident_c(X2,sK14(X0)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f165,plain,
! [X2,X0] :
( ~ incident_c(X2,sK14(X0))
| incident_o(X2,X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f166,plain,
! [X0] : open(sK14(X0)),
inference(cnf_transformation,[],[f93]) ).
fof(f172,plain,
! [X0] : start_point(sK17(X0),X0),
inference(cnf_transformation,[],[f97]) ).
fof(f182,plain,
! [X2,X1] :
( X1 = X2
| ~ ordered_by(sK22,X1,X2) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( incident_c(X0,X1)
| ~ end_point(X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( inner_point(X0,X1)
| end_point(X0,X1)
| ~ incident_c(X0,X1) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( incident_c(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( ~ inner_point(X0,X1)
| ~ end_point(X0,X1) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_78,plain,
! [X0: $i] :
( end_point(sK6(X0),X0)
| ~ open(X0) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_81,plain,
! [X0: $i] : inner_point(sK7(X0),X0),
inference(cnf_transformation,[],[f138]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordered_by(X1,X2,X0)
| ( X0 = X2 )
| ~ start_point(X2,X1)
| ~ incident_o(X0,X1) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_107,plain,
! [X0: $i] : open(sK14(X0)),
inference(cnf_transformation,[],[f166]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] :
( incident_o(X0,X1)
| ~ incident_c(X0,sK14(X1)) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( incident_c(X0,sK14(X1))
| ~ incident_o(X0,X1) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_115,plain,
! [X0: $i] : start_point(sK17(X0),X0),
inference(cnf_transformation,[],[f172]) ).
tcf(c_125,negated_conjecture,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ordered_by(sK22,X0,X1) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_1393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ordered_by(X0,X2,X3)
| ( X2 = X3 )
| ~ incident_o(X3,X0)
| ( X0 != X1 )
| ( sK17(X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_104,c_115]) ).
tcf(c_1394,plain,
! [X0: $i,X1: $i] :
( ordered_by(X1,sK17(X1),X0)
| ( sK17(X1) = X0 )
| ~ incident_o(X0,X1) ),
inference(unflattening,[status(thm)],[c_1393]) ).
tcf(c_7122,negated_conjecture,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ordered_by(sK22,X0,X1) ),
inference(demodulation,[status(thm)],[c_125]) ).
tcf(c_8821,plain,
! [X0: $i] : incident_c(sK7(X0),X0),
inference(superposition,[status(thm)],[c_81,c_67]) ).
tcf(c_8826,plain,
! [X0: $i] :
( incident_c(sK6(X0),X0)
| ~ open(X0) ),
inference(superposition,[status(thm)],[c_78,c_64]) ).
tcf(c_8848,plain,
! [X0: $i] :
( ~ open(X0)
| ~ inner_point(sK6(X0),X0) ),
inference(superposition,[status(thm)],[c_78,c_68]) ).
tcf(c_8880,plain,
! [X0: $i] : incident_o(sK7(sK14(X0)),X0),
inference(superposition,[status(thm)],[c_8821,c_108]) ).
tcf(c_8882,plain,
! [X0: $i] :
( incident_o(sK6(sK14(X0)),X0)
| ~ open(sK14(X0)) ),
inference(superposition,[status(thm)],[c_8826,c_108]) ).
tcf(c_8885,plain,
! [X0: $i] : incident_o(sK6(sK14(X0)),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_8882,c_107]) ).
tcf(c_9025,plain,
! [X0: $i,X1: $i] :
( inner_point(X0,sK14(X1))
| end_point(X0,sK14(X1))
| ~ incident_o(X0,X1) ),
inference(superposition,[status(thm)],[c_109,c_66]) ).
tcf(c_9546,plain,
! [X0: $i] :
( end_point(sK6(sK14(X0)),sK14(X0))
| ~ open(sK14(X0))
| ~ incident_o(sK6(sK14(X0)),X0) ),
inference(superposition,[status(thm)],[c_9025,c_8848]) ).
tcf(c_9551,plain,
! [X0: $i] : end_point(sK6(sK14(X0)),sK14(X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_9546,c_107,c_8885]) ).
tcf(c_9591,plain,
! [X0: $i] : ~ inner_point(sK6(sK14(X0)),sK14(X0)),
inference(superposition,[status(thm)],[c_9551,c_68]) ).
tcf(c_20492,plain,
! [X0: $i] :
( ( sK17(sK22) = X0 )
| ~ incident_o(X0,sK22) ),
inference(superposition,[status(thm)],[c_1394,c_7122]) ).
tcf(c_20522,plain,
sK7(sK14(sK22)) = sK17(sK22),
inference(superposition,[status(thm)],[c_8880,c_20492]) ).
tcf(c_20524,plain,
sK6(sK14(sK22)) = sK17(sK22),
inference(superposition,[status(thm)],[c_8885,c_20492]) ).
tcf(c_21053,plain,
inner_point(sK17(sK22),sK14(sK22)),
inference(superposition,[status(thm)],[c_20522,c_81]) ).
tcf(c_21589,plain,
~ inner_point(sK17(sK22),sK14(sK22)),
inference(superposition,[status(thm)],[c_20524,c_9591]) ).
tcf(c_21593,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_21589,c_21053]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO126+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 11:03:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 4.18/2.21 % SZS status Started for theBenchmark.p
% 4.18/2.21 % SZS status Theorem for theBenchmark.p
% 4.18/2.21
% 4.18/2.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.18/2.21
% 4.18/2.21 % ------ iProver source info
% 4.18/2.21
% 4.18/2.21 % git: date: 2026-07-19 20:42:38 +0200
% 4.18/2.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.18/2.21 % git: non_committed_changes: false
% 4.18/2.21
% 4.18/2.21 % ------ Parsing...
% 4.18/2.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.18/2.21
% 4.18/2.21 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 4.18/2.21
% 4.18/2.21 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.18/2.21
% 4.18/2.21 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.18/2.21 % ------ Proving...
% 4.18/2.21 % ------ Problem Properties
% 4.18/2.21
% 4.18/2.21 %
% 4.18/2.21 % clauses 76
% 4.18/2.21 % conjectures 1
% 4.18/2.21 % EPR 25
% 4.18/2.21 % Horn 48
% 4.18/2.21 % unary 4
% 4.18/2.21 % binary 29
% 4.18/2.21 % lits 228
% 4.18/2.21 % lits eq 22
% 4.18/2.21 % fd_pure 0
% 4.18/2.21 % fd_pseudo 0
% 4.18/2.21 % fd_cond 0
% 4.18/2.21 % fd_pseudo_cond 17
% 4.18/2.21 % AC symbols 0
% 4.18/2.21
% 4.18/2.21 % ------ Schedule dynamic 5 is on
% 4.18/2.21
% 4.18/2.21 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
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% 4.18/2.21
% 4.18/2.21 % ------
% 4.18/2.21 % Current options:
% 4.18/2.21 % ------
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% 4.18/2.21
% 4.18/2.21 %
% 4.18/2.21
% 4.18/2.21 % ------ Proving...
% 4.18/2.21 %
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% 4.18/2.21 % SZS status Theorem for theBenchmark.p
% 4.18/2.21
% 4.18/2.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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