%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO210+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n016.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 01:20:21 PM UTC 2026
% Result : Theorem 1.84s 6.29s
% Output : CNFRefutation 1.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 15 unt; 1 def)
% Number of atoms : 129 ( 1 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 113 ( 46 ~; 41 |; 17 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 9 ( 7 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn 80 !; 6 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0,X1] :
( distinct_lines(X0,X1)
=> convergent_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+1.ax',p1) ).
fof(f20,axiom,
! [X0,X1,X2] :
( ( unorthogonal_lines(X0,X1)
& convergent_lines(X0,X1) )
=> ( ( unorthogonal_lines(X1,X2)
& convergent_lines(X1,X2) )
| ( unorthogonal_lines(X0,X2)
& convergent_lines(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',oac1) ).
fof(f21,axiom,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ooc1) ).
fof(f24,axiom,
! [X0,X1] :
~ ( ~ unorthogonal_lines(X0,X1)
& ~ convergent_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax',coipo1) ).
fof(f26,axiom,
! [X0,X1,X2] :
( ( ~ unorthogonal_lines(X0,X2)
& ~ unorthogonal_lines(X0,X1) )
=> ~ convergent_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax',couo1) ).
fof(f32,axiom,
! [X0,X1] :
( equal_lines(X0,X1)
<=> ~ distinct_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',ax2) ).
fof(f35,axiom,
! [X0,X1] :
( orthogonal_lines(X0,X1)
<=> ~ unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',a5) ).
fof(f36,conjecture,
! [X0,X1,X2] :
( ( orthogonal_lines(X1,X2)
& incident_point_and_line(X0,X1) )
=> equal_lines(X1,orthogonal_through_point(X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2] :
( ( orthogonal_lines(X1,X2)
& incident_point_and_line(X0,X1) )
=> equal_lines(X1,orthogonal_through_point(X2,X0)) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( orthogonal_lines(X0,X1)
=> ~ unorthogonal_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f35]) ).
fof(f40,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
=> equal_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f32]) ).
fof(f59,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1)
| ( unorthogonal_lines(X1,X2)
& convergent_lines(X1,X2) )
| ( unorthogonal_lines(X0,X2)
& convergent_lines(X0,X2) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1)
| ( unorthogonal_lines(X1,X2)
& convergent_lines(X1,X2) )
| ( unorthogonal_lines(X0,X2)
& convergent_lines(X0,X2) ) ),
inference(flattening,[],[f62]) ).
fof(f66,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f69,plain,
! [X0,X1,X2] :
( unorthogonal_lines(X0,X2)
| unorthogonal_lines(X0,X1)
| ~ convergent_lines(X1,X2) ),
inference(ennf_transformation,[],[f26]) ).
fof(f70,plain,
! [X0,X1,X2] :
( unorthogonal_lines(X0,X2)
| unorthogonal_lines(X0,X1)
| ~ convergent_lines(X1,X2) ),
inference(flattening,[],[f69]) ).
fof(f79,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| equal_lines(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f81,plain,
! [X0,X1] :
( ~ orthogonal_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f82,plain,
? [X0,X1,X2] :
( orthogonal_lines(X1,X2)
& incident_point_and_line(X0,X1)
& ~ equal_lines(X1,orthogonal_through_point(X2,X0)) ),
inference(ennf_transformation,[],[f37]) ).
fof(f83,plain,
? [X0,X1,X2] :
( orthogonal_lines(X1,X2)
& incident_point_and_line(X0,X1)
& ~ equal_lines(X1,orthogonal_through_point(X2,X0)) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
( orthogonal_lines(sK1,sK2)
& incident_point_and_line(sK0,sK1)
& ~ equal_lines(sK1,orthogonal_through_point(sK2,sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f83]) ).
fof(f99,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f104,plain,
! [X2,X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1)
| unorthogonal_lines(X1,X2)
| unorthogonal_lines(X0,X2) ),
inference(cnf_transformation,[],[f63]) ).
fof(f108,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f21]) ).
fof(f111,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f116,plain,
! [X2,X0,X1] :
( unorthogonal_lines(X0,X2)
| unorthogonal_lines(X0,X1)
| ~ convergent_lines(X1,X2) ),
inference(cnf_transformation,[],[f70]) ).
fof(f121,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| equal_lines(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f123,plain,
! [X0,X1] :
( ~ orthogonal_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f124,plain,
orthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f84]) ).
fof(f126,plain,
~ equal_lines(sK1,orthogonal_through_point(sK2,sK0)),
inference(cnf_transformation,[],[f84]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X0,X2)
| ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] : ~ unorthogonal_lines(orthogonal_through_point(X0,X1),X0),
inference(cnf_transformation,[],[f108]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( unorthogonal_lines(X2,X1)
| unorthogonal_lines(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( equal_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( ~ orthogonal_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_88,negated_conjecture,
~ equal_lines(sK1,orthogonal_through_point(sK2,sK0)),
inference(cnf_transformation,[],[f126]) ).
tcf(c_90,negated_conjecture,
orthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f124]) ).
tcf(c_306,plain,
distinct_lines(sK1,orthogonal_through_point(sK2,sK0)),
inference(resolution,[status(thm)],[c_85,c_88]) ).
tcf(c_316,plain,
~ unorthogonal_lines(sK1,sK2),
inference(resolution,[status(thm)],[c_87,c_90]) ).
tcf(c_477,definition,
iPr_def_10 = orthogonal_through_point(sK2,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_480,plain,
distinct_lines(sK1,iPr_def_10),
inference(demodulation,[status(thm)],[c_306,c_477]) ).
tcf(c_898,plain,
~ unorthogonal_lines(iPr_def_10,sK2),
inference(superposition,[status(thm)],[c_477,c_72]) ).
tcf(c_909,plain,
convergent_lines(sK1,iPr_def_10),
inference(superposition,[status(thm)],[c_480,c_63]) ).
tcf(c_910,plain,
convergent_lines(iPr_def_10,sK2),
inference(superposition,[status(thm)],[c_75,c_898]) ).
tcf(c_1223,plain,
! [X0: $i] :
( unorthogonal_lines(sK1,sK2)
| unorthogonal_lines(X0,sK2)
| ~ unorthogonal_lines(sK1,X0)
| ~ convergent_lines(sK1,X0) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_1550,plain,
! [X0: $i] :
( unorthogonal_lines(X0,iPr_def_10)
| unorthogonal_lines(X0,sK2) ),
inference(superposition,[status(thm)],[c_910,c_80]) ).
tcf(c_1586,plain,
( unorthogonal_lines(sK1,iPr_def_10)
| unorthogonal_lines(sK1,sK2) ),
inference(instantiation,[status(thm)],[c_1550]) ).
tcf(c_1645,plain,
( unorthogonal_lines(iPr_def_10,sK2)
| unorthogonal_lines(sK1,sK2)
| ~ unorthogonal_lines(sK1,iPr_def_10)
| ~ convergent_lines(sK1,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_1223]) ).
tcf(c_1646,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1645,c_1586,c_909,c_898,c_316]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO210+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Wed Sep 23 11:35:17 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/5.42 Running first-order theorem proving
% 0.13/5.42 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
% 0.13/5.43
% 0.13/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.43
% 0.13/5.43 % Detected problem language: tptp
% 0.13/5.44 % Proving...
% 1.84/6.29 % SZS status Started for theBenchmark.p
% 1.84/6.29 % SZS status Theorem for theBenchmark.p
% 1.84/6.29
% 1.84/6.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.84/6.29
% 1.84/6.29 % ------ iProver source info
% 1.84/6.29
% 1.84/6.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.84/6.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.84/6.29 % git: non_committed_changes: false
% 1.84/6.29
% 1.84/6.29 % ------ Parsing...
% 1.84/6.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.84/6.29
% 1.84/6.29 % ------ Preprocessing... sf_s rm: 4 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.84/6.29
% 1.84/6.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.84/6.29
% 1.84/6.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.84/6.29 % ------ Proving...
% 1.84/6.29 % ------ Problem Properties
% 1.84/6.29
% 1.84/6.29 %
% 1.84/6.29 % clauses 32
% 1.84/6.29 % conjectures 0
% 1.84/6.29 % EPR 23
% 1.84/6.29 % Horn 16
% 1.84/6.29 % unary 11
% 1.84/6.29 % binary 6
% 1.84/6.29 % lits 79
% 1.84/6.29 % lits eq 1
% 1.84/6.29 % fd_pure 0
% 1.84/6.29 % fd_pseudo 0
% 1.84/6.29 % fd_cond 0
% 1.84/6.29 % fd_pseudo_cond 0
% 1.84/6.29 % AC symbols 0
% 1.84/6.29
% 1.84/6.29 % ------ Schedule dynamic 5 is on
% 1.84/6.29
% 1.84/6.29 % ------ no conjectures: strip conj schedule
% 1.84/6.29
% 1.84/6.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.84/6.29
% 1.84/6.29
% 1.84/6.29 % ------
% 1.84/6.29 % Current options:
% 1.84/6.29 % ------
% 1.84/6.29
% 1.84/6.29
% 1.84/6.29 %
% 1.84/6.29
% 1.84/6.29 % ------ Proving...
% 1.84/6.29 %
% 1.84/6.29
% 1.84/6.29 % SZS status Theorem for theBenchmark.p
% 1.84/6.29
% 1.84/6.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.84/6.29
% 1.84/6.29
%------------------------------------------------------------------------------