%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO223+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 : n010.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 01:20:26 PM UTC 2026
% Result : Theorem 3.56s 1.30s
% Output : CNFRefutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 63 ( 29 unt; 3 def)
% Number of atoms : 160 ( 3 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 113 ( 51 ~; 49 |; 7 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 98 ( 0 sgn 96 !; 2 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(f15,axiom,
! [X0,X1] :
( distinct_lines(X0,X1)
=> convergent_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+1.ax',p1) ).
fof(f16,axiom,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp1) ).
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(f25,axiom,
! [X0,X1,X2] :
( ( ( ~ unorthogonal_lines(X0,X2)
| ~ convergent_lines(X0,X2) )
& ( ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1) ) )
=> ( ~ unorthogonal_lines(X1,X2)
| ~ convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax',cotno1) ).
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(f36,conjecture,
! [X0,X1] : equal_lines(parallel_through_point(X1,X0),orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1] : equal_lines(parallel_through_point(X1,X0),orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
=> equal_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f32]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(flattening,[],[f43]) ).
fof(f57,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f64,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ( unorthogonal_lines(X0,X2)
& convergent_lines(X0,X2) )
| ( unorthogonal_lines(X0,X1)
& convergent_lines(X0,X1) )
| ~ unorthogonal_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(ennf_transformation,[],[f25]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ( unorthogonal_lines(X0,X2)
& convergent_lines(X0,X2) )
| ( unorthogonal_lines(X0,X1)
& convergent_lines(X0,X1) )
| ~ unorthogonal_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1,X2] :
( unorthogonal_lines(X0,X2)
| unorthogonal_lines(X0,X1)
| ~ convergent_lines(X1,X2) ),
inference(ennf_transformation,[],[f26]) ).
fof(f68,plain,
! [X0,X1,X2] :
( unorthogonal_lines(X0,X2)
| unorthogonal_lines(X0,X1)
| ~ convergent_lines(X1,X2) ),
inference(flattening,[],[f67]) ).
fof(f77,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| equal_lines(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f78,plain,
? [X0,X1] : ~ equal_lines(parallel_through_point(X1,X0),orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(ennf_transformation,[],[f37]) ).
fof(f79,plain,
~ equal_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f78]) ).
fof(f82,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f85,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f94,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f95,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f16]) ).
fof(f103,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f21]) ).
fof(f106,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f108,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| unorthogonal_lines(X0,X1)
| ~ unorthogonal_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f111,plain,
! [X2,X0,X1] :
( unorthogonal_lines(X0,X2)
| unorthogonal_lines(X0,X1)
| ~ convergent_lines(X1,X2) ),
inference(cnf_transformation,[],[f68]) ).
fof(f116,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| equal_lines(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f117,plain,
~ equal_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(cnf_transformation,[],[f79]) ).
tcf(c_51,plain,
! [X0: $i] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f82]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : ~ convergent_lines(parallel_through_point(X0,X1),X0),
inference(cnf_transformation,[],[f95]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] : ~ unorthogonal_lines(orthogonal_through_point(X0,X1),X0),
inference(cnf_transformation,[],[f103]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( unorthogonal_lines(X2,X0)
| convergent_lines(X2,X1)
| ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f108]) ).
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,[],[f111]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( equal_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_86,negated_conjecture,
~ equal_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(cnf_transformation,[],[f117]) ).
tcf(c_288,plain,
distinct_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(resolution,[status(thm)],[c_85,c_86]) ).
tcf(c_445,definition,
iPr_def_10 = parallel_through_point(sK1,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_446,definition,
iPr_def_11 = orthogonal_through_point(sK1,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_447,definition,
iPr_def_12 = orthogonal_through_point(iPr_def_11,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_448,plain,
distinct_lines(iPr_def_10,iPr_def_12),
inference(demodulation,[status(thm)],[c_288,c_446,c_447,c_445]) ).
tcf(c_876,plain,
~ convergent_lines(iPr_def_10,sK1),
inference(superposition,[status(thm)],[c_445,c_64]) ).
tcf(c_882,plain,
~ unorthogonal_lines(iPr_def_11,sK1),
inference(superposition,[status(thm)],[c_446,c_72]) ).
tcf(c_884,plain,
~ unorthogonal_lines(iPr_def_12,iPr_def_11),
inference(superposition,[status(thm)],[c_447,c_72]) ).
tcf(c_890,plain,
convergent_lines(iPr_def_10,iPr_def_12),
inference(superposition,[status(thm)],[c_448,c_63]) ).
tcf(c_892,plain,
convergent_lines(iPr_def_12,iPr_def_11),
inference(superposition,[status(thm)],[c_75,c_884]) ).
tcf(c_922,plain,
! [X0: $i] :
( convergent_lines(iPr_def_12,X0)
| convergent_lines(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_890,c_54]) ).
tcf(c_924,plain,
! [X0: $i] :
( convergent_lines(iPr_def_12,X0)
| convergent_lines(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_892,c_54]) ).
tcf(c_983,plain,
convergent_lines(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_924,c_51]) ).
tcf(c_1351,plain,
! [X0: $i,X1: $i] :
( unorthogonal_lines(X0,iPr_def_12)
| convergent_lines(iPr_def_10,X1)
| unorthogonal_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_922,c_80]) ).
tcf(c_1482,plain,
( unorthogonal_lines(iPr_def_11,iPr_def_12)
| convergent_lines(iPr_def_10,sK1) ),
inference(superposition,[status(thm)],[c_1351,c_882]) ).
tcf(c_1488,plain,
unorthogonal_lines(iPr_def_11,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_1482,c_876]) ).
tcf(c_3283,plain,
! [X0: $i] :
( unorthogonal_lines(X0,iPr_def_11)
| convergent_lines(X0,iPr_def_12)
| ~ unorthogonal_lines(iPr_def_11,iPr_def_12) ),
inference(superposition,[status(thm)],[c_983,c_78]) ).
tcf(c_3302,plain,
! [X0: $i] :
( unorthogonal_lines(X0,iPr_def_11)
| convergent_lines(X0,iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3283,c_1488]) ).
tcf(c_6383,plain,
convergent_lines(iPr_def_12,iPr_def_12),
inference(superposition,[status(thm)],[c_3302,c_884]) ).
tcf(c_6388,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_6383,c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO223+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n010.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Wed Sep 23 11:34:12 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 3.56/1.30 % SZS status Started for theBenchmark.p
% 3.56/1.30 % SZS status Theorem for theBenchmark.p
% 3.56/1.30
% 3.56/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.56/1.30
% 3.56/1.30 % ------ iProver source info
% 3.56/1.30
% 3.56/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 3.56/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.56/1.30 % git: non_committed_changes: false
% 3.56/1.30
% 3.56/1.30 % ------ Parsing...
% 3.56/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.56/1.30
% 3.56/1.30 % ------ Preprocessing... sf_s rm: 4 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.56/1.30
% 3.56/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.56/1.30
% 3.56/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.56/1.30 % ------ Proving...
% 3.56/1.30 % ------ Problem Properties
% 3.56/1.30
% 3.56/1.30 %
% 3.56/1.30 % clauses 32
% 3.56/1.30 % conjectures 0
% 3.56/1.30 % EPR 21
% 3.56/1.30 % Horn 16
% 3.56/1.30 % unary 11
% 3.56/1.30 % binary 6
% 3.56/1.30 % lits 79
% 3.56/1.30 % lits eq 3
% 3.56/1.30 % fd_pure 0
% 3.56/1.30 % fd_pseudo 0
% 3.56/1.30 % fd_cond 0
% 3.56/1.30 % fd_pseudo_cond 0
% 3.56/1.30 % AC symbols 0
% 3.56/1.30
% 3.56/1.30 % ------ Schedule dynamic 5 is on
% 3.56/1.30
% 3.56/1.30 % ------ no conjectures: strip conj schedule
% 3.56/1.30
% 3.56/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.56/1.30
% 3.56/1.30
% 3.56/1.30 % ------
% 3.56/1.30 % Current options:
% 3.56/1.30 % ------
% 3.56/1.30
% 3.56/1.30
% 3.56/1.30 %
% 3.56/1.30
% 3.56/1.30 % ------ Proving...
% 3.56/1.30 %
% 3.56/1.30
% 3.56/1.30 % SZS status Theorem for theBenchmark.p
% 3.56/1.30
% 3.56/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.56/1.30
% 3.56/1.30
%------------------------------------------------------------------------------