%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO177+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n026.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 01:20:07 PM UTC 2026
% Result : Theorem 3.46s 1.29s
% Output : CNFRefutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 17 unt; 1 def)
% Number of atoms : 146 ( 1 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 109 ( 34 ~; 53 |; 14 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 99 ( 0 sgn 91 !; 8 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart2) ).
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(f5,axiom,
! [X0,X1,X2] :
( distinct_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| distinct_lines(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart5) ).
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(f13,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq2) ).
fof(f15,axiom,
! [X0,X1] :
( distinct_lines(X0,X1)
=> convergent_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+1.ax',p1) ).
fof(f16,axiom,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp1) ).
fof(f17,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp2) ).
fof(f36,conjecture,
! [X0,X1,X2,X3] :
( ( distinct_points(X2,X3)
& distinct_points(X0,X1) )
=> ( ( apart_point_and_line(X1,line_connecting(X2,X3))
| apart_point_and_line(X0,line_connecting(X2,X3)) )
=> ( apart_point_and_line(X3,line_connecting(X0,X1))
| apart_point_and_line(X2,line_connecting(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( distinct_points(X2,X3)
& distinct_points(X0,X1) )
=> ( ( apart_point_and_line(X1,line_connecting(X2,X3))
| apart_point_and_line(X0,line_connecting(X2,X3)) )
=> ( apart_point_and_line(X3,line_connecting(X0,X1))
| apart_point_and_line(X2,line_connecting(X0,X1)) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(flattening,[],[f40]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(flattening,[],[f42]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f13]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(flattening,[],[f52]) ).
fof(f56,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f76,plain,
? [X0,X1,X2,X3] :
( distinct_points(X2,X3)
& distinct_points(X0,X1)
& ( apart_point_and_line(X1,line_connecting(X2,X3))
| apart_point_and_line(X0,line_connecting(X2,X3)) )
& ~ apart_point_and_line(X3,line_connecting(X0,X1))
& ~ apart_point_and_line(X2,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f37]) ).
fof(f77,plain,
? [X0,X1,X2,X3] :
( distinct_points(X2,X3)
& distinct_points(X0,X1)
& ( apart_point_and_line(X1,line_connecting(X2,X3))
| apart_point_and_line(X0,line_connecting(X2,X3)) )
& ~ apart_point_and_line(X3,line_connecting(X0,X1))
& ~ apart_point_and_line(X2,line_connecting(X0,X1)) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
( distinct_points(sK2,sK3)
& distinct_points(sK0,sK1)
& ( apart_point_and_line(sK1,line_connecting(sK2,sK3))
| apart_point_and_line(sK0,line_connecting(sK2,sK3)) )
& ~ apart_point_and_line(sK3,line_connecting(sK0,sK1))
& ~ apart_point_and_line(sK2,line_connecting(sK0,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f77]) ).
fof(f80,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f81,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f83,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f84,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f43]) ).
fof(f91,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f93,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f94,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f16]) ).
fof(f95,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f117,plain,
( apart_point_and_line(sK1,line_connecting(sK2,sK3))
| apart_point_and_line(sK0,line_connecting(sK2,sK3)) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_50,plain,
! [X0: $i] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f80]) ).
tcf(c_51,plain,
! [X0: $i] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f81]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
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,[],[f84]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : ~ convergent_lines(parallel_through_point(X0,X1),X0),
inference(cnf_transformation,[],[f94]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f95]) ).
tcf(c_87,negated_conjecture,
( apart_point_and_line(sK1,line_connecting(sK2,sK3))
| apart_point_and_line(sK0,line_connecting(sK2,sK3)) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_458,definition,
iPr_def_10 = line_connecting(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_462,negated_conjecture,
( apart_point_and_line(sK1,iPr_def_10)
| apart_point_and_line(sK0,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_87,c_458]) ).
tcf(c_1474,plain,
! [X0: $i] :
( apart_point_and_line(sK0,iPr_def_10)
| apart_point_and_line(sK1,X0)
| distinct_lines(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_462,c_61]) ).
tcf(c_1529,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK0,iPr_def_10)
| apart_point_and_line(sK1,X0)
| distinct_lines(iPr_def_10,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_1474,c_53]) ).
tcf(c_1646,plain,
! [X0: $i] :
( apart_point_and_line(sK0,iPr_def_10)
| apart_point_and_line(sK1,X0)
| distinct_lines(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1529,c_50]) ).
tcf(c_2055,plain,
! [X0: $i] :
( apart_point_and_line(sK0,iPr_def_10)
| apart_point_and_line(sK1,X0)
| convergent_lines(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1646,c_63]) ).
tcf(c_6173,plain,
! [X0: $i] :
( apart_point_and_line(sK0,iPr_def_10)
| convergent_lines(parallel_through_point(X0,sK1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_2055,c_65]) ).
tcf(c_6297,plain,
apart_point_and_line(sK0,iPr_def_10),
inference(superposition,[status(thm)],[c_6173,c_64]) ).
tcf(c_6298,plain,
! [X0: $i] :
( apart_point_and_line(sK0,X0)
| distinct_lines(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_6297,c_61]) ).
tcf(c_6312,plain,
! [X0: $i] :
( apart_point_and_line(sK0,X0)
| convergent_lines(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_6298,c_63]) ).
tcf(c_6348,plain,
! [X0: $i] : convergent_lines(iPr_def_10,parallel_through_point(X0,sK0)),
inference(superposition,[status(thm)],[c_6312,c_65]) ).
tcf(c_6371,plain,
! [X0: $i,X1: $i] :
( convergent_lines(iPr_def_10,X1)
| convergent_lines(parallel_through_point(X0,sK0),X1) ),
inference(superposition,[status(thm)],[c_6348,c_54]) ).
tcf(c_6600,plain,
! [X0: $i] : convergent_lines(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_6371,c_64]) ).
tcf(c_6602,plain,
$false,
inference(superposition,[status(thm)],[c_6600,c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO177+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 11:20:27 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 3.46/1.29 % SZS status Started for theBenchmark.p
% 3.46/1.29 % SZS status Theorem for theBenchmark.p
% 3.46/1.29
% 3.46/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.46/1.29
% 3.46/1.29 % ------ iProver source info
% 3.46/1.29
% 3.46/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 3.46/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.46/1.29 % git: non_committed_changes: false
% 3.46/1.29
% 3.46/1.29 % ------ Parsing...
% 3.46/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.46/1.29
% 3.46/1.29 % ------ Preprocessing... sf_s rm: 4 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.46/1.29
% 3.46/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.46/1.29
% 3.46/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.46/1.29 % ------ Proving...
% 3.46/1.29 % ------ Problem Properties
% 3.46/1.29
% 3.46/1.29 %
% 3.46/1.29 % clauses 35
% 3.46/1.29 % conjectures 5
% 3.46/1.29 % EPR 25
% 3.46/1.29 % Horn 18
% 3.46/1.29 % unary 13
% 3.46/1.29 % binary 7
% 3.46/1.29 % lits 83
% 3.46/1.29 % lits eq 2
% 3.46/1.29 % fd_pure 0
% 3.46/1.29 % fd_pseudo 0
% 3.46/1.29 % fd_cond 0
% 3.46/1.29 % fd_pseudo_cond 0
% 3.46/1.29 % AC symbols 0
% 3.46/1.29
% 3.46/1.29 % ------ Schedule dynamic 5 is on
% 3.46/1.29
% 3.46/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.46/1.29
% 3.46/1.29
% 3.46/1.29 % ------
% 3.46/1.29 % Current options:
% 3.46/1.29 % ------
% 3.46/1.29
% 3.46/1.29
% 3.46/1.29 %
% 3.46/1.29
% 3.46/1.29 % ------ Proving...
% 3.46/1.29 %
% 3.46/1.29
% 3.46/1.29 % SZS status Theorem for theBenchmark.p
% 3.46/1.29
% 3.46/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.46/1.29
% 3.46/1.29
%------------------------------------------------------------------------------