%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO196+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 : n014.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 01:20:16 PM UTC 2026
% Result : Theorem 4.27s 6.33s
% Output : CNFRefutation 4.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 17 unt; 0 def)
% Number of atoms : 129 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 121 ( 47 ~; 47 |; 21 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 113 ( 0 sgn 105 !; 8 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GEO006+0.ax',apart5) ).
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/sandbox/benchmark/Axioms/GEO006+0.ax',ceq2) ).
fof(f15,axiom,
! [X0,X1] :
( distinct_lines(X0,X1)
=> convergent_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+1.ax',p1) ).
fof(f16,axiom,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp1) ).
fof(f17,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp2) ).
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] :
( ( incident_point_and_line(intersection_point(X0,X1),X3)
& incident_point_and_line(intersection_point(X0,X1),X2)
& convergent_lines(X2,X3)
& convergent_lines(X0,X1) )
=> ( incident_point_and_line(intersection_point(X2,X3),X1)
& incident_point_and_line(intersection_point(X2,X3),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( incident_point_and_line(intersection_point(X0,X1),X3)
& incident_point_and_line(intersection_point(X0,X1),X2)
& convergent_lines(X2,X3)
& convergent_lines(X0,X1) )
=> ( incident_point_and_line(intersection_point(X2,X3),X1)
& incident_point_and_line(intersection_point(X2,X3),X0) ) ),
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(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] :
( incident_point_and_line(intersection_point(X0,X1),X3)
& incident_point_and_line(intersection_point(X0,X1),X2)
& convergent_lines(X2,X3)
& convergent_lines(X0,X1)
& ( ~ incident_point_and_line(intersection_point(X2,X3),X1)
| ~ incident_point_and_line(intersection_point(X2,X3),X0) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f77,plain,
? [X0,X1,X2,X3] :
( incident_point_and_line(intersection_point(X0,X1),X3)
& incident_point_and_line(intersection_point(X0,X1),X2)
& convergent_lines(X2,X3)
& convergent_lines(X0,X1)
& ( ~ incident_point_and_line(intersection_point(X2,X3),X1)
| ~ incident_point_and_line(intersection_point(X2,X3),X0) ) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( ( ~ incident_point_and_line(X0,X1)
| ~ apart_point_and_line(X0,X1) )
& ( apart_point_and_line(X0,X1)
| incident_point_and_line(X0,X1) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f79,plain,
( incident_point_and_line(intersection_point(sK0,sK1),sK3)
& incident_point_and_line(intersection_point(sK0,sK1),sK2)
& convergent_lines(sK2,sK3)
& convergent_lines(sK0,sK1)
& ( ~ incident_point_and_line(intersection_point(sK2,sK3),sK1)
| ~ incident_point_and_line(intersection_point(sK2,sK3),sK0) ) ),
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(f82,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f84,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f92,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(f94,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f95,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f16]) ).
fof(f96,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f117,plain,
! [X0,X1] :
( apart_point_and_line(X0,X1)
| incident_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f122,plain,
( ~ incident_point_and_line(intersection_point(sK2,sK3),sK1)
| ~ incident_point_and_line(intersection_point(sK2,sK3),sK0) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_51,plain,
! [X0: $i] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f82]) ).
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,[],[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,[],[f92]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : ~ convergent_lines(parallel_through_point(X0,X1),X0),
inference(cnf_transformation,[],[f95]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f96]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( incident_point_and_line(X0,X1)
| apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_87,negated_conjecture,
( ~ incident_point_and_line(intersection_point(sK2,sK3),sK1)
| ~ incident_point_and_line(intersection_point(sK2,sK3),sK0) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_92,plain,
~ convergent_lines(sK0,sK0),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(X0,X1)
| incident_point_and_line(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_85]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i] :
( incident_point_and_line(X0,X1)
| apart_point_and_line(X0,X1) ),
inference(renaming,[status(thm)],[c_112]) ).
tcf(c_202,plain,
! [X0: $i,X1: $i,X2: $i] :
( incident_point_and_line(X2,X0)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_61,c_113]) ).
tcf(c_658,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1,X1_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2] :
( incident_point_and_line(X0_iProver_incident_point_and_line_1,X0_iProver_incident_point_and_line_2)
| apart_point_and_line(X0_iProver_incident_point_and_line_1,X1_iProver_incident_point_and_line_2)
| distinct_lines(X0_iProver_incident_point_and_line_2,X1_iProver_incident_point_and_line_2) ),
inference(subtyping,[status(esa)],[c_202]) ).
tcf(c_664,negated_conjecture,
( ~ incident_point_and_line(intersection_point(sK2,sK3),sK1)
| ~ incident_point_and_line(intersection_point(sK2,sK3),sK0) ),
inference(subtyping,[status(esa)],[c_87]) ).
tcf(c_678,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1] : ~ apart_point_and_line(X0_iProver_incident_point_and_line_1,parallel_through_point(X0_iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1)),
inference(subtyping,[status(esa)],[c_65]) ).
tcf(c_679,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1] : ~ convergent_lines(parallel_through_point(X0_iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1),X0_iProver_incident_point_and_line_2),
inference(subtyping,[status(esa)],[c_64]) ).
tcf(c_680,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X1_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2] :
( convergent_lines(X0_iProver_incident_point_and_line_2,X1_iProver_incident_point_and_line_2)
| ~ distinct_lines(X0_iProver_incident_point_and_line_2,X1_iProver_incident_point_and_line_2) ),
inference(subtyping,[status(esa)],[c_63]) ).
tcf(c_688,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X1_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X2_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2] :
( distinct_lines(X1_iProver_incident_point_and_line_2,X2_iProver_incident_point_and_line_2)
| distinct_lines(X0_iProver_incident_point_and_line_2,X2_iProver_incident_point_and_line_2)
| ~ distinct_lines(X0_iProver_incident_point_and_line_2,X1_iProver_incident_point_and_line_2) ),
inference(subtyping,[status(esa)],[c_53]) ).
tcf(c_690,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2] : ~ convergent_lines(X0_iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_2),
inference(subtyping,[status(esa)],[c_51]) ).
tcf(c_738,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1] : ~ distinct_lines(parallel_through_point(X0_iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1),X0_iProver_incident_point_and_line_2),
inference(resolution,[status(thm)],[c_680,c_679]) ).
tcf(c_742,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1,X1_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2] :
( distinct_lines(X0_iProver_incident_point_and_line_2,X1_iProver_incident_point_and_line_2)
| ~ distinct_lines(X0_iProver_incident_point_and_line_2,parallel_through_point(X1_iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1)) ),
inference(resolution,[status(thm)],[c_738,c_688]) ).
tcf(c_901,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1,X1_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2] :
( incident_point_and_line(X0_iProver_incident_point_and_line_1,X0_iProver_incident_point_and_line_2)
| distinct_lines(X0_iProver_incident_point_and_line_2,parallel_through_point(X1_iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1)) ),
inference(superposition,[status(thm)],[c_658,c_678]) ).
tcf(c_904,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1,X1_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2] :
( incident_point_and_line(X0_iProver_incident_point_and_line_1,X0_iProver_incident_point_and_line_2)
| apart_point_and_line(X0_iProver_incident_point_and_line_1,X1_iProver_incident_point_and_line_2)
| convergent_lines(X0_iProver_incident_point_and_line_2,X1_iProver_incident_point_and_line_2) ),
inference(superposition,[status(thm)],[c_658,c_680]) ).
tcf(c_1559,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1,X1_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2] :
( incident_point_and_line(X0_iProver_incident_point_and_line_1,X0_iProver_incident_point_and_line_2)
| convergent_lines(X0_iProver_incident_point_and_line_2,X1_iProver_incident_point_and_line_2) ),
inference(global_subsumption_just,[status(thm)],[c_904,c_680,c_742,c_901]) ).
tcf(c_1562,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2] :
( convergent_lines(sK0,X0_iProver_incident_point_and_line_2)
| ~ incident_point_and_line(intersection_point(sK2,sK3),sK1) ),
inference(superposition,[status(thm)],[c_1559,c_664]) ).
tcf(c_1568,plain,
( convergent_lines(sK0,sK0)
| ~ incident_point_and_line(intersection_point(sK2,sK3),sK1) ),
inference(instantiation,[status(thm)],[c_1562]) ).
tcf(c_1731,plain,
~ incident_point_and_line(intersection_point(sK2,sK3),sK1),
inference(global_subsumption_just,[status(thm)],[c_1562,c_92,c_1568]) ).
tcf(c_1733,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2] : convergent_lines(sK1,X0_iProver_incident_point_and_line_2),
inference(superposition,[status(thm)],[c_1559,c_1731]) ).
tcf(c_1736,plain,
$false,
inference(superposition,[status(thm)],[c_1733,c_690]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO196+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.39 % Computer : n014.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Wed Sep 23 11:25:09 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/5.43 Running first-order theorem proving
% 0.16/5.44 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
% 0.16/5.45
% 0.16/5.45 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.45
% 0.16/5.45 % Detected problem language: tptp
% 0.16/5.46 % Proving...
% 4.27/6.33 % SZS status Started for theBenchmark.p
% 4.27/6.33 % SZS status Theorem for theBenchmark.p
% 4.27/6.33
% 4.27/6.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.27/6.33
% 4.27/6.33 % ------ iProver source info
% 4.27/6.33
% 4.27/6.33 % git: date: 2026-07-19 20:42:38 +0200
% 4.27/6.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.27/6.33 % git: non_committed_changes: false
% 4.27/6.33
% 4.27/6.33 % ------ Parsing...
% 4.27/6.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.27/6.33
% 4.27/6.33 % ------ Preprocessing... sf_s rm: 4 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.27/6.33
% 4.27/6.33 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.27/6.33 % ------ Proving...
% 4.27/6.33 % ------ Problem Properties
% 4.27/6.33
% 4.27/6.33 %
% 4.27/6.33 % clauses 35
% 4.27/6.33 % conjectures 5
% 4.27/6.33 % EPR 24
% 4.27/6.33 % Horn 18
% 4.27/6.33 % unary 11
% 4.27/6.33 % binary 9
% 4.27/6.33 % lits 85
% 4.27/6.33 % lits eq 0
% 4.27/6.33 % fd_pure 0
% 4.27/6.33 % fd_pseudo 0
% 4.27/6.33 % fd_cond 0
% 4.27/6.33 % fd_pseudo_cond 0
% 4.27/6.33 % AC symbols 0
% 4.27/6.33
% 4.27/6.33 % ------ Input Options Time Limit: Unbounded
% 4.27/6.33
% 4.27/6.33
% 4.27/6.33 % ------
% 4.27/6.33 % Current options:
% 4.27/6.33 % ------
% 4.27/6.33
% 4.27/6.33
% 4.27/6.33 %
% 4.27/6.33
% 4.27/6.33 % ------ Proving...
% 4.27/6.33 %
% 4.27/6.33
% 4.27/6.33 % SZS status Theorem for theBenchmark.p
% 4.27/6.33
% 4.27/6.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.27/6.33
% 4.27/6.33
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