%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO175+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 : n015.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 01:20:06 PM UTC 2026
% Result : Theorem 0.94s 1.29s
% Output : CNFRefutation 0.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 18 unt; 1 def)
% Number of atoms : 147 ( 1 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 139 ( 55 ~; 61 |; 17 &)
% ( 0 <=>; 6 =>; 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 66 !; 8 ?; 16 :)
% 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(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,X3] :
( ( distinct_points(X0,intersection_point(X2,X3))
& convergent_lines(X2,X3)
& distinct_points(X0,X1) )
=> ( apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( distinct_points(X0,intersection_point(X2,X3))
& convergent_lines(X2,X3)
& distinct_points(X0,X1) )
=> ( apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ) ),
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(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,X3] :
( distinct_points(X0,intersection_point(X2,X3))
& convergent_lines(X2,X3)
& distinct_points(X0,X1)
& ~ apart_point_and_line(X0,X3)
& ~ apart_point_and_line(X0,X2) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
? [X0,X1,X2,X3] :
( distinct_points(X0,intersection_point(X2,X3))
& convergent_lines(X2,X3)
& distinct_points(X0,X1)
& ~ apart_point_and_line(X0,X3)
& ~ apart_point_and_line(X0,X2) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
( distinct_points(sK0,intersection_point(sK2,sK3))
& convergent_lines(sK2,sK3)
& distinct_points(sK0,sK1)
& ~ apart_point_and_line(sK0,sK3)
& ~ apart_point_and_line(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[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(f51,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f52,plain,
distinct_points(sK0,intersection_point(sK2,sK3)),
inference(cnf_transformation,[],[f37]) ).
fof(f53,plain,
convergent_lines(sK2,sK3),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
~ apart_point_and_line(sK0,sK3),
inference(cnf_transformation,[],[f37]) ).
fof(f56,plain,
~ apart_point_and_line(sK0,sK2),
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_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(sK0,sK2),
inference(cnf_transformation,[],[f56]) ).
tcf(c_64,negated_conjecture,
~ apart_point_and_line(sK0,sK3),
inference(cnf_transformation,[],[f55]) ).
tcf(c_66,negated_conjecture,
convergent_lines(sK2,sK3),
inference(cnf_transformation,[],[f53]) ).
tcf(c_67,negated_conjecture,
distinct_points(sK0,intersection_point(sK2,sK3)),
inference(cnf_transformation,[],[f52]) ).
tcf(c_151,definition,
iPr_def_10 = intersection_point(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_152,negated_conjecture,
distinct_points(sK0,iPr_def_10),
inference(demodulation,[status(thm)],[c_67,c_151]) ).
tcf(c_153,negated_conjecture,
convergent_lines(sK2,sK3),
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_744,plain,
! [X0: $i] :
( convergent_lines(sK2,X0)
| distinct_lines(sK3,X0)
| ~ convergent_lines(sK2,sK3) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_754,plain,
( ~ apart_point_and_line(iPr_def_10,sK2)
| ~ convergent_lines(sK2,sK3) ),
inference(superposition,[status(thm)],[c_151,c_57]) ).
tcf(c_755,plain,
~ apart_point_and_line(iPr_def_10,sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_754,c_153]) ).
tcf(c_764,plain,
( ~ apart_point_and_line(iPr_def_10,sK3)
| ~ convergent_lines(sK2,sK3) ),
inference(superposition,[status(thm)],[c_151,c_58]) ).
tcf(c_765,plain,
~ apart_point_and_line(iPr_def_10,sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_764,c_153]) ).
tcf(c_838,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(iPr_def_10,X1)
| apart_point_and_line(iPr_def_10,X0)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| ~ distinct_points(sK0,iPr_def_10)
| ~ distinct_lines(X0,X1) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_993,plain,
~ convergent_lines(sK2,sK2),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_1415,plain,
( convergent_lines(sK2,sK2)
| distinct_lines(sK3,sK2)
| ~ convergent_lines(sK2,sK3) ),
inference(instantiation,[status(thm)],[c_744]) ).
tcf(c_1924,plain,
! [X0: $i] :
( apart_point_and_line(iPr_def_10,sK3)
| apart_point_and_line(sK0,sK3)
| apart_point_and_line(iPr_def_10,X0)
| apart_point_and_line(sK0,X0)
| ~ distinct_points(sK0,iPr_def_10)
| ~ distinct_lines(sK3,X0) ),
inference(instantiation,[status(thm)],[c_838]) ).
tcf(c_2070,plain,
( apart_point_and_line(iPr_def_10,sK3)
| apart_point_and_line(iPr_def_10,sK2)
| apart_point_and_line(sK0,sK3)
| apart_point_and_line(sK0,sK2)
| ~ distinct_lines(sK3,sK2)
| ~ distinct_points(sK0,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_1924]) ).
tcf(c_2071,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2070,c_1415,c_993,c_765,c_755,c_152,c_63,c_64,c_66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO175+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n015.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Wed Sep 23 11:19:57 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 0.94/1.29 % SZS status Started for theBenchmark.p
% 0.94/1.29 % SZS status Theorem for theBenchmark.p
% 0.94/1.29
% 0.94/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.94/1.29
% 0.94/1.29 % ------ iProver source info
% 0.94/1.29
% 0.94/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.94/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.94/1.29 % git: non_committed_changes: false
% 0.94/1.29
% 0.94/1.29 % ------ Parsing...
% 0.94/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.94/1.29
% 0.94/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.94/1.29
% 0.94/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.94/1.29
% 0.94/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.94/1.29 % ------ Proving...
% 0.94/1.29 % ------ Problem Properties
% 0.94/1.29
% 0.94/1.29 %
% 0.94/1.29 % clauses 20
% 0.94/1.29 % conjectures 5
% 0.94/1.29 % EPR 15
% 0.94/1.29 % Horn 13
% 0.94/1.29 % unary 9
% 0.94/1.29 % binary 4
% 0.94/1.29 % lits 41
% 0.94/1.29 % lits eq 1
% 0.94/1.29 % fd_pure 0
% 0.94/1.29 % fd_pseudo 0
% 0.94/1.29 % fd_cond 0
% 0.94/1.29 % fd_pseudo_cond 0
% 0.94/1.29 % AC symbols 0
% 0.94/1.29
% 0.94/1.29 % ------ Schedule dynamic 5 is on
% 0.94/1.29
% 0.94/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.94/1.29
% 0.94/1.29
% 0.94/1.29 % ------
% 0.94/1.29 % Current options:
% 0.94/1.29 % ------
% 0.94/1.29
% 0.94/1.29
% 0.94/1.29 %
% 0.94/1.29
% 0.94/1.29 % ------ Proving...
% 0.94/1.29 %
% 0.94/1.29
% 0.94/1.29 % SZS status Theorem for theBenchmark.p
% 0.94/1.29
% 0.94/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.94/1.29
% 0.94/1.29
%------------------------------------------------------------------------------