%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO206+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n008.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 01:20:20 PM UTC 2026
% Result : Theorem 0.45s 1.29s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 20 unt; 1 def)
% Number of atoms : 98 ( 1 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 80 ( 36 ~; 32 |; 8 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 51 !; 6 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart6) ).
fof(f13,axiom,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp1) ).
fof(f14,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp2) ).
fof(f15,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/sandbox/benchmark/Axioms/GEO006+2.ax',cup1) ).
fof(f16,conjecture,
! [X0,X1,X2] :
( ( ~ convergent_lines(X1,X2)
& ~ apart_point_and_line(X0,X1) )
=> ~ distinct_lines(X1,parallel_through_point(X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f17,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ convergent_lines(X1,X2)
& ~ apart_point_and_line(X0,X1) )
=> ~ distinct_lines(X1,parallel_through_point(X2,X0)) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(flattening,[],[f22]) ).
fof(f35,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,[],[f15]) ).
fof(f36,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,[],[f35]) ).
fof(f37,plain,
? [X0,X1,X2] :
( ~ convergent_lines(X1,X2)
& ~ apart_point_and_line(X0,X1)
& distinct_lines(X1,parallel_through_point(X2,X0)) ),
inference(ennf_transformation,[],[f17]) ).
fof(f38,plain,
? [X0,X1,X2] :
( ~ convergent_lines(X1,X2)
& ~ apart_point_and_line(X0,X1)
& distinct_lines(X1,parallel_through_point(X2,X0)) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
( ~ convergent_lines(sK1,sK2)
& ~ apart_point_and_line(sK0,sK1)
& distinct_lines(sK1,parallel_through_point(sK2,sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f38]) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f54,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f13]) ).
fof(f55,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f56,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,[],[f36]) ).
fof(f57,plain,
~ convergent_lines(sK1,sK2),
inference(cnf_transformation,[],[f39]) ).
fof(f58,plain,
~ apart_point_and_line(sK0,sK1),
inference(cnf_transformation,[],[f39]) ).
fof(f59,plain,
distinct_lines(sK1,parallel_through_point(sK2,sK0)),
inference(cnf_transformation,[],[f39]) ).
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,[],[f45]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] : ~ convergent_lines(parallel_through_point(X0,X1),X0),
inference(cnf_transformation,[],[f54]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f55]) ).
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,[],[f56]) ).
tcf(c_66,negated_conjecture,
distinct_lines(sK1,parallel_through_point(sK2,sK0)),
inference(cnf_transformation,[],[f59]) ).
tcf(c_67,negated_conjecture,
~ apart_point_and_line(sK0,sK1),
inference(cnf_transformation,[],[f58]) ).
tcf(c_68,negated_conjecture,
~ convergent_lines(sK1,sK2),
inference(cnf_transformation,[],[f57]) ).
tcf(c_168,definition,
iPr_def_10 = parallel_through_point(sK2,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_169,negated_conjecture,
~ convergent_lines(sK1,sK2),
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_171,negated_conjecture,
distinct_lines(sK1,iPr_def_10),
inference(demodulation,[status(thm)],[c_66,c_168]) ).
tcf(c_465,plain,
~ convergent_lines(iPr_def_10,sK2),
inference(superposition,[status(thm)],[c_168,c_63]) ).
tcf(c_466,plain,
~ apart_point_and_line(sK0,iPr_def_10),
inference(superposition,[status(thm)],[c_168,c_64]) ).
tcf(c_722,plain,
! [X0: $i] :
( convergent_lines(sK1,iPr_def_10)
| apart_point_and_line(X0,iPr_def_10)
| apart_point_and_line(X0,sK1)
| ~ distinct_lines(sK1,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_1017,plain,
( apart_point_and_line(sK0,iPr_def_10)
| apart_point_and_line(sK0,sK1)
| convergent_lines(sK1,iPr_def_10)
| ~ distinct_lines(sK1,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_722]) ).
tcf(c_1432,plain,
! [X0: $i] :
( convergent_lines(sK1,iPr_def_10)
| apart_point_and_line(X0,iPr_def_10)
| apart_point_and_line(X0,sK1) ),
inference(superposition,[status(thm)],[c_171,c_65]) ).
tcf(c_2198,plain,
convergent_lines(sK1,iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_1432,c_67,c_171,c_466,c_1017]) ).
tcf(c_2200,plain,
! [X0: $i] :
( convergent_lines(iPr_def_10,X0)
| convergent_lines(sK1,X0) ),
inference(superposition,[status(thm)],[c_2198,c_54]) ).
tcf(c_2227,plain,
convergent_lines(iPr_def_10,sK2),
inference(superposition,[status(thm)],[c_2200,c_169]) ).
tcf(c_2228,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2227,c_465]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO206+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.36 % Computer : n008.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Wed Sep 23 11:29:39 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.42
% 0.12/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.42
% 0.12/0.42 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 0.45/1.29 % SZS status Started for theBenchmark.p
% 0.45/1.29 % SZS status Theorem for theBenchmark.p
% 0.45/1.29
% 0.45/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.45/1.29
% 0.45/1.29 % ------ iProver source info
% 0.45/1.29
% 0.45/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.45/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.45/1.29 % git: non_committed_changes: false
% 0.45/1.29
% 0.45/1.29 % ------ Parsing...
% 0.45/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.45/1.29
% 0.45/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.45/1.29
% 0.45/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.45/1.29
% 0.45/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.45/1.29 % ------ Proving...
% 0.45/1.29 % ------ Problem Properties
% 0.45/1.29
% 0.45/1.29 %
% 0.45/1.29 % clauses 21
% 0.45/1.29 % conjectures 3
% 0.45/1.29 % EPR 14
% 0.45/1.29 % Horn 14
% 0.45/1.29 % unary 9
% 0.45/1.29 % binary 1
% 0.45/1.29 % lits 48
% 0.45/1.29 % lits eq 1
% 0.45/1.29 % fd_pure 0
% 0.45/1.29 % fd_pseudo 0
% 0.45/1.29 % fd_cond 0
% 0.45/1.29 % fd_pseudo_cond 0
% 0.45/1.29 % AC symbols 0
% 0.45/1.29
% 0.45/1.29 % ------ Schedule dynamic 5 is on
% 0.45/1.29
% 0.45/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.45/1.29
% 0.45/1.29
% 0.45/1.29 % ------
% 0.45/1.29 % Current options:
% 0.45/1.29 % ------
% 0.45/1.29
% 0.45/1.29
% 0.45/1.29 %
% 0.45/1.29
% 0.45/1.29 % ------ Proving...
% 0.45/1.29 %
% 0.45/1.29
% 0.45/1.29 % SZS status Theorem for theBenchmark.p
% 0.45/1.29
% 0.45/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.45/1.29
% 0.45/1.29
%------------------------------------------------------------------------------