%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO194+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 : 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 01:20:14 PM UTC 2026
% Result : Theorem 2.33s 1.27s
% Output : CNFRefutation 2.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 58 ( 18 unt; 1 def)
% Number of atoms : 185 ( 1 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 167 ( 62 ~; 79 |; 17 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 89 ( 0 sgn 83 !; 6 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci3) ).
fof(f10,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci4) ).
fof(f11,axiom,
! [X0,X1,X2,X3] :
( ( distinct_lines(X2,X3)
& distinct_points(X0,X1) )
=> ( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',cu1) ).
fof(f12,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq1) ).
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,conjecture,
! [X0,X1,X2] :
( ( convergent_lines(X0,X2)
& convergent_lines(X2,X1)
& convergent_lines(X0,X1) )
=> ( apart_point_and_line(intersection_point(X0,X1),X2)
=> apart_point_and_line(intersection_point(X0,X2),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] :
( ( convergent_lines(X0,X2)
& convergent_lines(X2,X1)
& convergent_lines(X0,X1) )
=> ( apart_point_and_line(intersection_point(X0,X1),X2)
=> apart_point_and_line(intersection_point(X0,X2),X1) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f25,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f26,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ),
inference(ennf_transformation,[],[f11]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(ennf_transformation,[],[f12]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(flattening,[],[f29]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
? [X0,X1,X2] :
( convergent_lines(X0,X2)
& convergent_lines(X2,X1)
& convergent_lines(X0,X1)
& apart_point_and_line(intersection_point(X0,X1),X2)
& ~ apart_point_and_line(intersection_point(X0,X2),X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
? [X0,X1,X2] :
( convergent_lines(X0,X2)
& convergent_lines(X2,X1)
& convergent_lines(X0,X1)
& apart_point_and_line(intersection_point(X0,X1),X2)
& ~ apart_point_and_line(intersection_point(X0,X2),X1) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
( convergent_lines(sK0,sK2)
& convergent_lines(sK2,sK1)
& convergent_lines(sK0,sK1)
& apart_point_and_line(intersection_point(sK0,sK1),sK2)
& ~ apart_point_and_line(intersection_point(sK0,sK2),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f36]) ).
fof(f40,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f46,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f47,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f52,plain,
convergent_lines(sK0,sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f56,plain,
~ apart_point_and_line(intersection_point(sK0,sK2),sK1),
inference(cnf_transformation,[],[f37]) ).
tcf(c_51,plain,
! [X0: $i] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f40]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(X2,X1)
| distinct_points(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
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,[],[f51]) ).
tcf(c_63,negated_conjecture,
~ apart_point_and_line(intersection_point(sK0,sK2),sK1),
inference(cnf_transformation,[],[f56]) ).
tcf(c_64,negated_conjecture,
apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(cnf_transformation,[],[f55]) ).
tcf(c_65,negated_conjecture,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f54]) ).
tcf(c_67,negated_conjecture,
convergent_lines(sK0,sK2),
inference(cnf_transformation,[],[f52]) ).
tcf(c_68,plain,
~ convergent_lines(sK0,sK0),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_151,definition,
iPr_def_10 = intersection_point(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_155,negated_conjecture,
convergent_lines(sK0,sK1),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_156,negated_conjecture,
apart_point_and_line(iPr_def_10,sK2),
inference(demodulation,[status(thm)],[c_64,c_151]) ).
tcf(c_628,plain,
( ~ convergent_lines(sK0,sK2)
| ~ apart_point_and_line(intersection_point(sK0,sK2),sK0) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_631,plain,
( ~ convergent_lines(sK0,sK2)
| ~ apart_point_and_line(intersection_point(sK0,sK2),sK2) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_727,plain,
! [X0: $i] :
( apart_point_and_line(X0,sK2)
| distinct_points(iPr_def_10,X0)
| ~ apart_point_and_line(iPr_def_10,sK2) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_732,plain,
! [X0: $i] :
( convergent_lines(sK0,X0)
| distinct_lines(sK1,X0)
| ~ convergent_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_733,plain,
( convergent_lines(sK0,sK0)
| distinct_lines(sK1,sK0)
| ~ convergent_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_732]) ).
tcf(c_750,plain,
( ~ apart_point_and_line(iPr_def_10,sK0)
| ~ convergent_lines(sK0,sK1) ),
inference(superposition,[status(thm)],[c_151,c_57]) ).
tcf(c_751,plain,
~ apart_point_and_line(iPr_def_10,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_750,c_155]) ).
tcf(c_758,plain,
( ~ apart_point_and_line(iPr_def_10,sK1)
| ~ convergent_lines(sK0,sK1) ),
inference(superposition,[status(thm)],[c_151,c_58]) ).
tcf(c_759,plain,
~ apart_point_and_line(iPr_def_10,sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_758,c_155]) ).
tcf(c_1104,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(iPr_def_10,X1)
| apart_point_and_line(iPr_def_10,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_points(iPr_def_10,X2)
| ~ distinct_lines(X0,X1) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_1708,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(iPr_def_10,sK1)
| apart_point_and_line(iPr_def_10,X1)
| apart_point_and_line(X0,sK1)
| apart_point_and_line(X0,X1)
| ~ distinct_lines(sK1,X1)
| ~ distinct_points(iPr_def_10,X0) ),
inference(instantiation,[status(thm)],[c_1104]) ).
tcf(c_1959,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK2)
| distinct_points(iPr_def_10,intersection_point(sK0,sK2))
| ~ apart_point_and_line(iPr_def_10,sK2) ),
inference(instantiation,[status(thm)],[c_727]) ).
tcf(c_2484,plain,
! [X0: $i] :
( apart_point_and_line(iPr_def_10,sK1)
| apart_point_and_line(iPr_def_10,X0)
| apart_point_and_line(intersection_point(sK0,sK2),sK1)
| apart_point_and_line(intersection_point(sK0,sK2),X0)
| ~ distinct_lines(sK1,X0)
| ~ distinct_points(iPr_def_10,intersection_point(sK0,sK2)) ),
inference(instantiation,[status(thm)],[c_1708]) ).
tcf(c_2487,plain,
( apart_point_and_line(iPr_def_10,sK1)
| apart_point_and_line(iPr_def_10,sK0)
| apart_point_and_line(intersection_point(sK0,sK2),sK1)
| apart_point_and_line(intersection_point(sK0,sK2),sK0)
| ~ distinct_lines(sK1,sK0)
| ~ distinct_points(iPr_def_10,intersection_point(sK0,sK2)) ),
inference(instantiation,[status(thm)],[c_2484]) ).
tcf(c_2488,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2487,c_1959,c_759,c_751,c_733,c_631,c_628,c_156,c_63,c_68,c_65,c_67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO194+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n010.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 11:24:27 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 2.33/1.27 % SZS status Started for theBenchmark.p
% 2.33/1.27 % SZS status Theorem for theBenchmark.p
% 2.33/1.27
% 2.33/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.33/1.27
% 2.33/1.27 % ------ iProver source info
% 2.33/1.27
% 2.33/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.33/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.33/1.27 % git: non_committed_changes: false
% 2.33/1.27
% 2.33/1.27 % ------ Parsing...
% 2.33/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.33/1.27
% 2.33/1.27 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.33/1.27
% 2.33/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.33/1.27
% 2.33/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.33/1.27 % ------ Proving...
% 2.33/1.27 % ------ Problem Properties
% 2.33/1.27
% 2.33/1.27 %
% 2.33/1.27 % clauses 21
% 2.33/1.27 % conjectures 5
% 2.33/1.27 % EPR 15
% 2.33/1.27 % Horn 14
% 2.33/1.27 % unary 10
% 2.33/1.27 % binary 4
% 2.33/1.27 % lits 42
% 2.33/1.27 % lits eq 2
% 2.33/1.27 % fd_pure 0
% 2.33/1.27 % fd_pseudo 0
% 2.33/1.27 % fd_cond 0
% 2.33/1.27 % fd_pseudo_cond 0
% 2.33/1.27 % AC symbols 0
% 2.33/1.27
% 2.33/1.27 % ------ Schedule dynamic 5 is on
% 2.33/1.27
% 2.33/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.33/1.27
% 2.33/1.27
% 2.33/1.27 % ------
% 2.33/1.27 % Current options:
% 2.33/1.27 % ------
% 2.33/1.27
% 2.33/1.27
% 2.33/1.27 %
% 2.33/1.27
% 2.33/1.27 % ------ Proving...
% 2.33/1.27 %
% 2.33/1.27
% 2.33/1.27 % SZS status Theorem for theBenchmark.p
% 2.33/1.27
% 2.33/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.33/1.27
% 2.33/1.27
%------------------------------------------------------------------------------