%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO223+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n019.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 0.72s 1.06s
% Output : CNFRefutation 0.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of formulae : 78 ( 37 unt; 3 def)
% Number of atoms : 244 ( 3 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 154 ( 50 ~; 92 |; 7 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 133 ( 0 sgn 131 !; 2 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(f15,axiom,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp1) ).
fof(f16,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp2) ).
fof(f17,axiom,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
=> ( convergent_lines(X1,X2)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cup1) ).
fof(f18,axiom,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',occu1) ).
fof(f19,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/sandbox2/benchmark/Axioms/GEO006+3.ax',oac1) ).
fof(f20,axiom,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ooc1) ).
fof(f21,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ooc2) ).
fof(f22,axiom,
! [X0,X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( unorthogonal_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ouo1) ).
fof(f23,conjecture,
! [X0,X1] : ~ distinct_lines(parallel_through_point(X1,X0),orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f24,negated_conjecture,
~ ! [X0,X1] : ~ distinct_lines(parallel_through_point(X1,X0),orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(flattening,[],[f29]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ distinct_lines(X1,X2)
| convergent_lines(X1,X2)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ distinct_lines(X1,X2)
| convergent_lines(X1,X2)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(flattening,[],[f43]) ).
fof(f45,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,[],[f19]) ).
fof(f46,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,[],[f45]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( ~ distinct_lines(X1,X2)
| unorthogonal_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( ~ distinct_lines(X1,X2)
| unorthogonal_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
? [X0,X1] : distinct_lines(parallel_through_point(X1,X0),orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(ennf_transformation,[],[f24]) ).
fof(f50,plain,
distinct_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)],[f49]) ).
fof(f53,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f64,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f65,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f15]) ).
fof(f66,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f16]) ).
fof(f67,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X1,X2)
| convergent_lines(X1,X2)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f68,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1)
| unorthogonal_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f73,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f20]) ).
fof(f74,plain,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f75,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X1,X2)
| unorthogonal_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f76,plain,
distinct_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(cnf_transformation,[],[f50]) ).
tcf(c_51,plain,
! [X0: $i] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f53]) ).
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,[],[f56]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] : ~ convergent_lines(parallel_through_point(X0,X1),X0),
inference(cnf_transformation,[],[f65]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f66]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( unorthogonal_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] : ~ unorthogonal_lines(orthogonal_through_point(X0,X1),X0),
inference(cnf_transformation,[],[f73]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[],[f74]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( unorthogonal_lines(X1,X3)
| unorthogonal_lines(X0,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_74,negated_conjecture,
distinct_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(cnf_transformation,[],[f76]) ).
tcf(c_337,definition,
iPr_def_10 = parallel_through_point(sK1,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_338,definition,
iPr_def_11 = orthogonal_through_point(sK1,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_339,definition,
iPr_def_12 = orthogonal_through_point(iPr_def_11,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_340,negated_conjecture,
distinct_lines(iPr_def_10,iPr_def_12),
inference(demodulation,[status(thm)],[c_74,c_338,c_339,c_337]) ).
tcf(c_720,plain,
~ convergent_lines(iPr_def_10,sK1),
inference(superposition,[status(thm)],[c_337,c_63]) ).
tcf(c_721,plain,
~ apart_point_and_line(sK0,iPr_def_10),
inference(superposition,[status(thm)],[c_337,c_64]) ).
tcf(c_722,plain,
~ unorthogonal_lines(iPr_def_11,sK1),
inference(superposition,[status(thm)],[c_338,c_71]) ).
tcf(c_724,plain,
~ unorthogonal_lines(iPr_def_12,iPr_def_11),
inference(superposition,[status(thm)],[c_339,c_71]) ).
tcf(c_725,plain,
~ apart_point_and_line(sK0,iPr_def_12),
inference(superposition,[status(thm)],[c_339,c_72]) ).
tcf(c_732,plain,
convergent_lines(iPr_def_11,sK1),
inference(superposition,[status(thm)],[c_66,c_722]) ).
tcf(c_805,plain,
! [X0: $i] :
( convergent_lines(iPr_def_11,X0)
| convergent_lines(sK1,X0) ),
inference(superposition,[status(thm)],[c_732,c_54]) ).
tcf(c_833,plain,
! [X0: $i,X1: $i] :
( convergent_lines(iPr_def_11,X0)
| convergent_lines(sK1,X1)
| convergent_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_805,c_54]) ).
tcf(c_993,plain,
! [X0: $i] :
( convergent_lines(iPr_def_10,iPr_def_12)
| apart_point_and_line(X0,iPr_def_12)
| apart_point_and_line(X0,iPr_def_10)
| ~ distinct_lines(iPr_def_10,iPr_def_12) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_994,plain,
( apart_point_and_line(sK0,iPr_def_12)
| apart_point_and_line(sK0,iPr_def_10)
| convergent_lines(iPr_def_10,iPr_def_12)
| ~ distinct_lines(iPr_def_10,iPr_def_12) ),
inference(instantiation,[status(thm)],[c_993]) ).
tcf(c_1780,plain,
! [X0: $i] :
( convergent_lines(iPr_def_10,iPr_def_12)
| apart_point_and_line(X0,iPr_def_12)
| apart_point_and_line(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_340,c_65]) ).
tcf(c_2739,plain,
convergent_lines(iPr_def_10,iPr_def_12),
inference(global_subsumption_just,[status(thm)],[c_1780,c_340,c_721,c_725,c_994]) ).
tcf(c_2744,plain,
! [X0: $i] :
( convergent_lines(iPr_def_10,X0)
| distinct_lines(iPr_def_12,X0) ),
inference(superposition,[status(thm)],[c_2739,c_62]) ).
tcf(c_3258,plain,
! [X0: $i,X1: $i,X2: $i] :
( unorthogonal_lines(iPr_def_12,X2)
| apart_point_and_line(X0,iPr_def_12)
| convergent_lines(iPr_def_10,X1)
| unorthogonal_lines(X1,X2)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_2744,c_73]) ).
tcf(c_6032,plain,
! [X0: $i] :
( apart_point_and_line(sK0,iPr_def_12)
| convergent_lines(iPr_def_10,iPr_def_10)
| unorthogonal_lines(iPr_def_12,X0)
| unorthogonal_lines(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_3258,c_721]) ).
tcf(c_6043,plain,
! [X0: $i] :
( unorthogonal_lines(iPr_def_12,X0)
| unorthogonal_lines(iPr_def_10,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6032,c_725,c_51]) ).
tcf(c_6961,plain,
( convergent_lines(iPr_def_11,iPr_def_10)
| convergent_lines(sK1,sK1) ),
inference(superposition,[status(thm)],[c_833,c_720]) ).
tcf(c_6966,plain,
convergent_lines(iPr_def_11,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_6961,c_51]) ).
tcf(c_7230,plain,
! [X0: $i] :
( convergent_lines(iPr_def_11,X0)
| convergent_lines(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_6966,c_54]) ).
tcf(c_7253,plain,
unorthogonal_lines(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_6043,c_724]) ).
tcf(c_9323,plain,
convergent_lines(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_7230,c_51]) ).
tcf(c_9375,plain,
! [X0: $i] :
( unorthogonal_lines(iPr_def_11,X0)
| convergent_lines(iPr_def_10,X0)
| ~ unorthogonal_lines(iPr_def_10,iPr_def_11) ),
inference(superposition,[status(thm)],[c_9323,c_68]) ).
tcf(c_9380,plain,
! [X0: $i] :
( unorthogonal_lines(iPr_def_11,X0)
| convergent_lines(iPr_def_10,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9375,c_7253]) ).
tcf(c_9473,plain,
convergent_lines(iPr_def_10,sK1),
inference(superposition,[status(thm)],[c_9380,c_722]) ).
tcf(c_9474,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_9473,c_720]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO223+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n019.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 11:33:49 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/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
% 0.10/0.42 % Proving...
% 0.72/1.06 % SZS status Started for theBenchmark.p
% 0.72/1.06 % SZS status Theorem for theBenchmark.p
% 0.72/1.06
% 0.72/1.06 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.72/1.06
% 0.72/1.06 % ------ iProver source info
% 0.72/1.06
% 0.72/1.06 % git: date: 2026-07-19 20:42:38 +0200
% 0.72/1.06 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.72/1.06 % git: non_committed_changes: false
% 0.72/1.06
% 0.72/1.06 % ------ Parsing...
% 0.72/1.06 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.72/1.06
% 0.72/1.06 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.72/1.06
% 0.72/1.06 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.72/1.06
% 0.72/1.06 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.72/1.06 % ------ Proving...
% 0.72/1.06 % ------ Problem Properties
% 0.72/1.06
% 0.72/1.06 %
% 0.72/1.06 % clauses 28
% 0.72/1.06 % conjectures 1
% 0.72/1.06 % EPR 17
% 0.72/1.06 % Horn 15
% 0.72/1.06 % unary 11
% 0.72/1.06 % binary 5
% 0.72/1.06 % lits 66
% 0.72/1.06 % lits eq 3
% 0.72/1.06 % fd_pure 0
% 0.72/1.06 % fd_pseudo 0
% 0.72/1.06 % fd_cond 0
% 0.72/1.06 % fd_pseudo_cond 0
% 0.72/1.06 % AC symbols 0
% 0.72/1.06
% 0.72/1.06 % ------ Schedule dynamic 5 is on
% 0.72/1.06
% 0.72/1.06 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.72/1.06
% 0.72/1.06
% 0.72/1.06 % ------
% 0.72/1.06 % Current options:
% 0.72/1.06 % ------
% 0.72/1.06
% 0.72/1.06
% 0.72/1.06 %
% 0.72/1.06
% 0.72/1.06 % ------ Proving...
% 0.72/1.06 %
% 0.72/1.06
% 0.72/1.06 % SZS status Theorem for theBenchmark.p
% 0.72/1.06
% 0.72/1.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.72/1.07
% 0.72/1.07
%------------------------------------------------------------------------------