%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO125+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 : n011.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 3.37s 16.14s
% Output : CNFRefutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 61 ( 13 unt; 0 def)
% Number of atoms : 243 ( 39 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 288 ( 106 ~; 105 |; 64 &)
% ( 7 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 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 : 11 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-4 aty)
% Number of variables : 170 ( 0 sgn 154 !; 16 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0,X1,X2,X3] :
( between_c(X0,X1,X2,X3)
<=> ( ? [X4] :
( inner_point(X2,X4)
& end_point(X3,X4)
& end_point(X1,X4)
& part_of(X4,X0) )
& X1 != X3 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+1.ax',between_c_defn) ).
fof(f18,axiom,
! [X0,X1,X2,X3] :
( between_o(X0,X1,X2,X3)
<=> ( ( ordered_by(X0,X2,X1)
& ordered_by(X0,X3,X2) )
| ( ordered_by(X0,X2,X3)
& ordered_by(X0,X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+2.ax',between_o_defn) ).
fof(f20,axiom,
! [X0,X1] :
( finish_point(X0,X1)
<=> ( ! [X2] :
( ( incident_o(X2,X1)
& X0 != X2 )
=> ordered_by(X1,X2,X0) )
& incident_o(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+2.ax',finish_point_defn) ).
fof(f21,axiom,
! [X0,X1,X2] :
( ordered_by(X0,X1,X2)
=> ( incident_o(X2,X0)
& incident_o(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+2.ax',o1) ).
fof(f23,axiom,
! [X0,X1,X2,X3] :
( between_o(X3,X0,X1,X2)
<=> ? [X4] :
( between_c(X4,X0,X1,X2)
& ! [X0] :
( incident_o(X0,X3)
<=> incident_c(X0,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+2.ax',o3) ).
fof(f28,conjecture,
! [X0,X1,X2] :
( ( finish_point(X2,X0)
& finish_point(X1,X0) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_4_10_2) ).
fof(f29,negated_conjecture,
~ ! [X0,X1,X2] :
( ( finish_point(X2,X0)
& finish_point(X1,X0) )
=> X1 = X2 ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( between_o(X3,X0,X1,X2)
<=> ? [X4] :
( between_c(X4,X0,X1,X2)
& ! [X5] :
( incident_o(X5,X3)
<=> incident_c(X5,X4) ) ) ),
inference(rectify,[],[f23]) ).
fof(f31,plain,
! [X0,X1] :
( finish_point(X0,X1)
=> ( ! [X2] :
( ( incident_o(X2,X1)
& X0 != X2 )
=> ordered_by(X1,X2,X0) )
& incident_o(X0,X1) ) ),
inference(unused_predicate_definition_removal,[],[f20]) ).
fof(f54,plain,
! [X0,X1] :
( ~ finish_point(X0,X1)
| ( ! [X2] :
( ~ incident_o(X2,X1)
| X0 = X2
| ordered_by(X1,X2,X0) )
& incident_o(X0,X1) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f55,plain,
! [X0,X1] :
( ~ finish_point(X0,X1)
| ( ! [X2] :
( ~ incident_o(X2,X1)
| X0 = X2
| ordered_by(X1,X2,X0) )
& incident_o(X0,X1) ) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ~ ordered_by(X0,X1,X2)
| ( incident_o(X2,X0)
& incident_o(X1,X0) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f60,plain,
? [X0,X1,X2] :
( finish_point(X2,X0)
& finish_point(X1,X0)
& X1 != X2 ),
inference(ennf_transformation,[],[f29]) ).
fof(f61,plain,
? [X0,X1,X2] :
( finish_point(X2,X0)
& finish_point(X1,X0)
& X1 != X2 ),
inference(flattening,[],[f60]) ).
fof(f90,plain,
! [X0,X1,X2,X3] :
( ( ~ between_c(X0,X1,X2,X3)
| ( ? [X4] :
( inner_point(X2,X4)
& end_point(X3,X4)
& end_point(X1,X4)
& part_of(X4,X0) )
& X1 != X3 ) )
& ( ! [X4] :
( ~ inner_point(X2,X4)
| ~ end_point(X3,X4)
| ~ end_point(X1,X4)
| ~ part_of(X4,X0) )
| X1 = X3
| between_c(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f91,plain,
! [X0,X1,X2,X3] :
( ( ~ between_c(X0,X1,X2,X3)
| ( ? [X4] :
( inner_point(X2,X4)
& end_point(X3,X4)
& end_point(X1,X4)
& part_of(X4,X0) )
& X1 != X3 ) )
& ( ! [X4] :
( ~ inner_point(X2,X4)
| ~ end_point(X3,X4)
| ~ end_point(X1,X4)
| ~ part_of(X4,X0) )
| X1 = X3
| between_c(X0,X1,X2,X3) ) ),
inference(flattening,[],[f90]) ).
fof(f92,plain,
! [X0,X1,X2,X3] :
( ( ~ between_c(X0,X1,X2,X3)
| ( ? [X5] :
( inner_point(X2,X5)
& end_point(X3,X5)
& end_point(X1,X5)
& part_of(X5,X0) )
& X1 != X3 ) )
& ( ! [X4] :
( ~ inner_point(X2,X4)
| ~ end_point(X3,X4)
| ~ end_point(X1,X4)
| ~ part_of(X4,X0) )
| X1 = X3
| between_c(X0,X1,X2,X3) ) ),
inference(rectify,[],[f91]) ).
fof(f93,plain,
! [X0,X1,X2,X3] :
( ( ~ between_c(X0,X1,X2,X3)
| ( inner_point(X2,sK13(X0,X1,X2,X3))
& end_point(X3,sK13(X0,X1,X2,X3))
& end_point(X1,sK13(X0,X1,X2,X3))
& part_of(sK13(X0,X1,X2,X3),X0)
& X1 != X3 ) )
& ( ! [X4] :
( ~ inner_point(X2,X4)
| ~ end_point(X3,X4)
| ~ end_point(X1,X4)
| ~ part_of(X4,X0) )
| X1 = X3
| between_c(X0,X1,X2,X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X5,sK13(X0,X1,X2,X3))],[f92]) ).
fof(f94,plain,
! [X0,X1,X2,X3] :
( ( ~ between_o(X0,X1,X2,X3)
| ( ordered_by(X0,X2,X1)
& ordered_by(X0,X3,X2) )
| ( ordered_by(X0,X2,X3)
& ordered_by(X0,X1,X2) ) )
& ( ( ( ~ ordered_by(X0,X2,X1)
| ~ ordered_by(X0,X3,X2) )
& ( ~ ordered_by(X0,X2,X3)
| ~ ordered_by(X0,X1,X2) ) )
| between_o(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f95,plain,
! [X0,X1,X2,X3] :
( ( ~ between_o(X0,X1,X2,X3)
| ( ordered_by(X0,X2,X1)
& ordered_by(X0,X3,X2) )
| ( ordered_by(X0,X2,X3)
& ordered_by(X0,X1,X2) ) )
& ( ( ( ~ ordered_by(X0,X2,X1)
| ~ ordered_by(X0,X3,X2) )
& ( ~ ordered_by(X0,X2,X3)
| ~ ordered_by(X0,X1,X2) ) )
| between_o(X0,X1,X2,X3) ) ),
inference(flattening,[],[f94]) ).
fof(f98,plain,
! [X0,X1,X2,X3] :
( ( ~ between_o(X3,X0,X1,X2)
| ? [X4] :
( between_c(X4,X0,X1,X2)
& ! [X5] :
( ( ~ incident_o(X5,X3)
| incident_c(X5,X4) )
& ( ~ incident_c(X5,X4)
| incident_o(X5,X3) ) ) ) )
& ( ! [X4] :
( ~ between_c(X4,X0,X1,X2)
| ? [X5] :
( ( incident_o(X5,X3)
| incident_c(X5,X4) )
& ( ~ incident_o(X5,X3)
| ~ incident_c(X5,X4) ) ) )
| between_o(X3,X0,X1,X2) ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f99,plain,
! [X0,X1,X2,X3] :
( ( ~ between_o(X3,X0,X1,X2)
| ? [X6] :
( between_c(X6,X0,X1,X2)
& ! [X7] :
( ( ~ incident_o(X7,X3)
| incident_c(X7,X6) )
& ( ~ incident_c(X7,X6)
| incident_o(X7,X3) ) ) ) )
& ( ! [X4] :
( ~ between_c(X4,X0,X1,X2)
| ? [X5] :
( ( incident_o(X5,X3)
| incident_c(X5,X4) )
& ( ~ incident_o(X5,X3)
| ~ incident_c(X5,X4) ) ) )
| between_o(X3,X0,X1,X2) ) ),
inference(rectify,[],[f98]) ).
fof(f100,plain,
! [X0,X1,X2,X3] :
( ( ~ between_o(X3,X0,X1,X2)
| ( between_c(sK16(X0,X1,X2,X3),X0,X1,X2)
& ! [X7] :
( ( ~ incident_o(X7,X3)
| incident_c(X7,sK16(X0,X1,X2,X3)) )
& ( ~ incident_c(X7,sK16(X0,X1,X2,X3))
| incident_o(X7,X3) ) ) ) )
& ( ! [X4] :
( ~ between_c(X4,X0,X1,X2)
| ( ( incident_o(sK15(X3,X4),X3)
| incident_c(sK15(X3,X4),X4) )
& ( ~ incident_o(sK15(X3,X4),X3)
| ~ incident_c(sK15(X3,X4),X4) ) ) )
| between_o(X3,X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16]),skolemize(X5,sK15(X3,X4)),skolemize(X6,sK16(X0,X1,X2,X3))],[f99]) ).
fof(f109,plain,
( finish_point(sK24,sK22)
& finish_point(sK23,sK22)
& sK23 != sK24 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22,sK23,sK24]),skolemize(X0,sK22),skolemize(X1,sK23),skolemize(X2,sK24)],[f61]) ).
fof(f156,plain,
! [X2,X3,X0,X1] :
( ~ between_c(X0,X1,X2,X3)
| X1 != X3 ),
inference(cnf_transformation,[],[f93]) ).
fof(f163,plain,
! [X2,X3,X0,X1] :
( ~ ordered_by(X0,X2,X3)
| ~ ordered_by(X0,X1,X2)
| between_o(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f95]) ).
fof(f166,plain,
! [X2,X0,X1] :
( ~ finish_point(X0,X1)
| ~ incident_o(X2,X1)
| X0 = X2
| ordered_by(X1,X2,X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f167,plain,
! [X0,X1] :
( ~ finish_point(X0,X1)
| incident_o(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f168,plain,
! [X2,X0,X1] :
( ~ ordered_by(X0,X1,X2)
| incident_o(X2,X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f173,plain,
! [X2,X3,X0,X1] :
( ~ between_o(X3,X0,X1,X2)
| between_c(sK16(X0,X1,X2,X3),X0,X1,X2) ),
inference(cnf_transformation,[],[f100]) ).
fof(f188,plain,
finish_point(sK24,sK22),
inference(cnf_transformation,[],[f109]) ).
fof(f189,plain,
finish_point(sK23,sK22),
inference(cnf_transformation,[],[f109]) ).
fof(f190,plain,
sK23 != sK24,
inference(cnf_transformation,[],[f109]) ).
fof(f195,plain,
! [X2,X3,X0] : ~ between_c(X0,X3,X2,X3),
inference(equality_resolution,[],[f156]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i] : ~ between_c(X0,X1,X2,X1),
inference(cnf_transformation,[],[f195]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between_o(X0,X1,X2,X3)
| ~ ordered_by(X0,X2,X3)
| ~ ordered_by(X0,X1,X2) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i] :
( incident_o(X0,X1)
| ~ finish_point(X0,X1) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordered_by(X1,X0,X2)
| ( X0 = X2 )
| ~ finish_point(X2,X1)
| ~ incident_o(X0,X1) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i,X2: $i] :
( incident_o(X2,X0)
| ~ ordered_by(X0,X1,X2) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between_c(sK16(X1,X2,X3,X0),X1,X2,X3)
| ~ between_o(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_127,negated_conjecture,
sK23 != sK24,
inference(cnf_transformation,[],[f190]) ).
tcf(c_128,negated_conjecture,
finish_point(sK23,sK22),
inference(cnf_transformation,[],[f189]) ).
tcf(c_129,negated_conjecture,
finish_point(sK24,sK22),
inference(cnf_transformation,[],[f188]) ).
tcf(c_258,plain,
! [X0: $i,X1: $i] :
( ~ finish_point(X0,X1)
| incident_o(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_105]) ).
tcf(c_259,plain,
! [X0: $i,X1: $i] :
( incident_o(X0,X1)
| ~ finish_point(X0,X1) ),
inference(renaming,[status(thm)],[c_258]) ).
tcf(c_1442,plain,
! [X0: $i,X1: $i] :
( incident_o(X0,X1)
| ( X1 != sK22 )
| ( X0 != sK23 ) ),
inference(resolution_lifted,[status(thm)],[c_259,c_128]) ).
tcf(c_1443,plain,
incident_o(sK23,sK22),
inference(unflattening,[status(thm)],[c_1442]) ).
tcf(c_1452,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordered_by(X0,X2,X1)
| ( X1 = X2 )
| ~ incident_o(X2,X0)
| ( X1 != sK23 )
| ( X0 != sK22 ) ),
inference(resolution_lifted,[status(thm)],[c_106,c_128]) ).
tcf(c_1453,plain,
! [X0: $i] :
( ordered_by(sK22,X0,sK23)
| ( sK23 = X0 )
| ~ incident_o(X0,sK22) ),
inference(unflattening,[status(thm)],[c_1452]) ).
tcf(c_1464,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordered_by(X0,X2,X1)
| ( X1 = X2 )
| ~ incident_o(X2,X0)
| ( X1 != sK24 )
| ( X0 != sK22 ) ),
inference(resolution_lifted,[status(thm)],[c_106,c_129]) ).
tcf(c_1465,plain,
! [X0: $i] :
( ordered_by(sK22,X0,sK24)
| ( sK24 = X0 )
| ~ incident_o(X0,sK22) ),
inference(unflattening,[status(thm)],[c_1464]) ).
tcf(c_8240,plain,
! [X0: $i] :
( ordered_by(sK22,X0,sK24)
| ( sK24 = X0 )
| ~ incident_o(X0,sK22) ),
inference(demodulation,[status(thm)],[c_1465]) ).
tcf(c_8241,plain,
! [X0: $i] :
( ordered_by(sK22,X0,sK23)
| ( sK23 = X0 )
| ~ incident_o(X0,sK22) ),
inference(demodulation,[status(thm)],[c_1453]) ).
tcf(c_8243,plain,
incident_o(sK23,sK22),
inference(demodulation,[status(thm)],[c_1443]) ).
tcf(c_8244,negated_conjecture,
sK23 != sK24,
inference(demodulation,[status(thm)],[c_127]) ).
tcf(c_11790,plain,
! [X0: $i,X1: $i,X2: $i] : ~ between_o(X0,X1,X2,X1),
inference(superposition,[status(thm)],[c_116,c_92]) ).
tcf(c_11854,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ordered_by(X0,X2,X1)
| ~ ordered_by(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_97,c_11790]) ).
tcf(c_11895,plain,
! [X0: $i] :
( ( X0 = sK23 )
| ~ incident_o(X0,sK22)
| ~ ordered_by(sK22,sK23,X0) ),
inference(superposition,[status(thm)],[c_8241,c_11854]) ).
tcf(c_11926,plain,
! [X0: $i] :
( ( X0 = sK23 )
| ~ ordered_by(sK22,sK23,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11895,c_108]) ).
tcf(c_11934,plain,
( ( sK23 = sK24 )
| ~ incident_o(sK23,sK22) ),
inference(superposition,[status(thm)],[c_8240,c_11926]) ).
tcf(c_11935,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_11934,c_8244,c_8243]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO125+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/15.42 % CPULimit : 300
% 0.08/15.42 % WCLimit : 300
% 0.08/15.42 % DateTime : Wed Sep 23 11:01:55 UTC 2026
% 0.08/15.42 % CPUTime :
% 0.08/15.42 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/15.46 Running first-order theorem proving
% 0.08/15.46 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
% 0.08/15.47
% 0.08/15.47 % ======== iProver multi-core TPTP/SMT =========
% 0.08/15.47
% 0.08/15.47 % Detected problem language: tptp
% 0.08/15.48 % Proving...
% 3.37/16.14 % SZS status Started for theBenchmark.p
% 3.37/16.14 % SZS status Theorem for theBenchmark.p
% 3.37/16.14
% 3.37/16.14 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.37/16.14
% 3.37/16.14 % ------ iProver source info
% 3.37/16.14
% 3.37/16.14 % git: date: 2026-07-19 20:42:38 +0200
% 3.37/16.14 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.37/16.14 % git: non_committed_changes: false
% 3.37/16.14
% 3.37/16.14 % ------ Parsing...
% 3.37/16.14 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.37/16.14
% 3.37/16.14 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 3.37/16.14
% 3.37/16.14 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.37/16.14
% 3.37/16.14 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.37/16.14 % ------ Proving...
% 3.37/16.14 % ------ Problem Properties
% 3.37/16.14
% 3.37/16.14 %
% 3.37/16.14 % clauses 80
% 3.37/16.14 % conjectures 1
% 3.37/16.14 % EPR 29
% 3.37/16.14 % Horn 50
% 3.37/16.14 % unary 7
% 3.37/16.14 % binary 28
% 3.37/16.14 % lits 235
% 3.37/16.14 % lits eq 24
% 3.37/16.14 % fd_pure 0
% 3.37/16.14 % fd_pseudo 0
% 3.37/16.14 % fd_cond 2
% 3.37/16.14 % fd_pseudo_cond 16
% 3.37/16.14 % AC symbols 0
% 3.37/16.14
% 3.37/16.14 % ------ Schedule dynamic 5 is on
% 3.37/16.14
% 3.37/16.14 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.37/16.14
% 3.37/16.14
% 3.37/16.14 % ------
% 3.37/16.14 % Current options:
% 3.37/16.14 % ------
% 3.37/16.14
% 3.37/16.14
% 3.37/16.14 %
% 3.37/16.14
% 3.37/16.14 % ------ Proving...
% 3.37/16.14 %
% 3.37/16.14
% 3.37/16.14 % SZS status Theorem for theBenchmark.p
% 3.37/16.14
% 3.37/16.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.37/16.14
% 3.37/16.14
%------------------------------------------------------------------------------