%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO185+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 01:20:11 PM UTC 2026
% Result : Theorem 2.57s 6.30s
% Output : CNFRefutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 13 unt; 1 def)
% Number of atoms : 118 ( 1 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 109 ( 50 ~; 35 |; 15 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 8 ( 6 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 69 ( 0 sgn 61 !; 8 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GEO006+0.ax',ci4) ).
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/sandbox/benchmark/Axioms/GEO006+0.ax',ceq1) ).
fof(f31,axiom,
! [X0,X1] :
( equal_points(X0,X1)
<=> ~ distinct_points(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',ax1) ).
fof(f34,axiom,
! [X0,X1] :
( incident_point_and_line(X0,X1)
<=> ~ apart_point_and_line(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',a4) ).
fof(f36,conjecture,
! [X0,X1,X2,X3] :
( ( equal_points(X0,intersection_point(X2,X3))
& convergent_lines(X2,X3)
& distinct_points(X0,X1) )
=> ( incident_point_and_line(X0,X3)
& incident_point_and_line(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( equal_points(X0,intersection_point(X2,X3))
& convergent_lines(X2,X3)
& distinct_points(X0,X1) )
=> ( incident_point_and_line(X0,X3)
& incident_point_and_line(X0,X2) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,X1)
=> incident_point_and_line(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f34]) ).
fof(f39,plain,
! [X0,X1] :
( equal_points(X0,X1)
=> ~ distinct_points(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f48,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f49,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f52,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(f53,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(flattening,[],[f52]) ).
fof(f78,plain,
! [X0,X1] :
( ~ equal_points(X0,X1)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f79,plain,
! [X0,X1] :
( apart_point_and_line(X0,X1)
| incident_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f80,plain,
? [X0,X1,X2,X3] :
( equal_points(X0,intersection_point(X2,X3))
& convergent_lines(X2,X3)
& distinct_points(X0,X1)
& ( ~ incident_point_and_line(X0,X3)
| ~ incident_point_and_line(X0,X2) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f81,plain,
? [X0,X1,X2,X3] :
( equal_points(X0,intersection_point(X2,X3))
& convergent_lines(X2,X3)
& distinct_points(X0,X1)
& ( ~ incident_point_and_line(X0,X3)
| ~ incident_point_and_line(X0,X2) ) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
( equal_points(sK0,intersection_point(sK2,sK3))
& convergent_lines(sK2,sK3)
& distinct_points(sK0,sK1)
& ( ~ incident_point_and_line(sK0,sK3)
| ~ incident_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)],[f81]) ).
fof(f91,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f92,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f94,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f119,plain,
! [X0,X1] :
( ~ equal_points(X0,X1)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f120,plain,
! [X0,X1] :
( apart_point_and_line(X0,X1)
| incident_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f121,plain,
equal_points(sK0,intersection_point(sK2,sK3)),
inference(cnf_transformation,[],[f82]) ).
fof(f122,plain,
convergent_lines(sK2,sK3),
inference(cnf_transformation,[],[f82]) ).
fof(f124,plain,
( ~ incident_point_and_line(sK0,sK3)
| ~ incident_point_and_line(sK0,sK2) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f92]) ).
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,[],[f94]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( ~ equal_points(X0,X1)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( incident_point_and_line(X0,X1)
| apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_87,negated_conjecture,
( ~ incident_point_and_line(sK0,sK3)
| ~ incident_point_and_line(sK0,sK2) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_89,negated_conjecture,
convergent_lines(sK2,sK3),
inference(cnf_transformation,[],[f122]) ).
tcf(c_90,negated_conjecture,
equal_points(sK0,intersection_point(sK2,sK3)),
inference(cnf_transformation,[],[f121]) ).
tcf(c_304,plain,
~ distinct_points(sK0,intersection_point(sK2,sK3)),
inference(resolution,[status(thm)],[c_85,c_90]) ).
tcf(c_473,definition,
iPr_def_10 = intersection_point(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_474,plain,
~ distinct_points(sK0,iPr_def_10),
inference(demodulation,[status(thm)],[c_304,c_473]) ).
tcf(c_475,negated_conjecture,
convergent_lines(sK2,sK3),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_477,negated_conjecture,
( ~ incident_point_and_line(sK0,sK3)
| ~ incident_point_and_line(sK0,sK2) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_940,plain,
( apart_point_and_line(sK0,sK2)
| ~ incident_point_and_line(sK0,sK3) ),
inference(superposition,[status(thm)],[c_86,c_477]) ).
tcf(c_951,plain,
( apart_point_and_line(sK0,sK3)
| apart_point_and_line(sK0,sK2) ),
inference(superposition,[status(thm)],[c_86,c_940]) ).
tcf(c_1540,plain,
( ~ apart_point_and_line(iPr_def_10,sK2)
| ~ convergent_lines(sK2,sK3) ),
inference(superposition,[status(thm)],[c_473,c_57]) ).
tcf(c_1541,plain,
~ apart_point_and_line(iPr_def_10,sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_1540,c_475]) ).
tcf(c_1550,plain,
( ~ apart_point_and_line(iPr_def_10,sK3)
| ~ convergent_lines(sK2,sK3) ),
inference(superposition,[status(thm)],[c_473,c_58]) ).
tcf(c_1551,plain,
~ apart_point_and_line(iPr_def_10,sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_1550,c_475]) ).
tcf(c_1558,plain,
! [X0: $i] :
( apart_point_and_line(sK0,sK2)
| apart_point_and_line(X0,sK3)
| distinct_points(sK0,X0) ),
inference(superposition,[status(thm)],[c_951,c_60]) ).
tcf(c_1585,plain,
( apart_point_and_line(iPr_def_10,sK3)
| apart_point_and_line(sK0,sK2) ),
inference(superposition,[status(thm)],[c_1558,c_474]) ).
tcf(c_1586,plain,
apart_point_and_line(sK0,sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_1585,c_1551]) ).
tcf(c_1588,plain,
! [X0: $i] :
( apart_point_and_line(X0,sK2)
| distinct_points(sK0,X0) ),
inference(superposition,[status(thm)],[c_1586,c_60]) ).
tcf(c_1617,plain,
apart_point_and_line(iPr_def_10,sK2),
inference(superposition,[status(thm)],[c_1588,c_474]) ).
tcf(c_1618,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1617,c_1541]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO185+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.38 % Computer : n010.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Wed Sep 23 11:20:50 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 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
% 0.15/5.43
% 0.15/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.43
% 0.15/5.44 % Detected problem language: tptp
% 0.15/5.45 % Proving...
% 2.57/6.30 % SZS status Started for theBenchmark.p
% 2.57/6.30 % SZS status Theorem for theBenchmark.p
% 2.57/6.30
% 2.57/6.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.57/6.30
% 2.57/6.30 % ------ iProver source info
% 2.57/6.30
% 2.57/6.30 % git: date: 2026-07-19 20:42:38 +0200
% 2.57/6.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.57/6.30 % git: non_committed_changes: false
% 2.57/6.30
% 2.57/6.30 % ------ Parsing...
% 2.57/6.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.57/6.30
% 2.57/6.30 % ------ 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 %
% 2.57/6.30
% 2.57/6.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.57/6.30
% 2.57/6.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.57/6.30 % ------ Proving...
% 2.57/6.30 % ------ Problem Properties
% 2.57/6.30
% 2.57/6.30 %
% 2.57/6.30 % clauses 34
% 2.57/6.30 % conjectures 3
% 2.57/6.30 % EPR 25
% 2.57/6.30 % Horn 17
% 2.57/6.30 % unary 11
% 2.57/6.30 % binary 8
% 2.57/6.30 % lits 83
% 2.57/6.30 % lits eq 1
% 2.57/6.30 % fd_pure 0
% 2.57/6.30 % fd_pseudo 0
% 2.57/6.30 % fd_cond 0
% 2.57/6.30 % fd_pseudo_cond 0
% 2.57/6.30 % AC symbols 0
% 2.57/6.30
% 2.57/6.30 % ------ Schedule dynamic 5 is on
% 2.57/6.30
% 2.57/6.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.57/6.30
% 2.57/6.30
% 2.57/6.30 % ------
% 2.57/6.30 % Current options:
% 2.57/6.30 % ------
% 2.57/6.30
% 2.57/6.30
% 2.57/6.30 %
% 2.57/6.30
% 2.57/6.30 % ------ Proving...
% 2.57/6.30 %
% 2.57/6.30
% 2.57/6.30 % SZS status Theorem for theBenchmark.p
% 2.57/6.30
% 2.57/6.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.57/6.30
% 2.57/6.30
%------------------------------------------------------------------------------