%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO233+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n002.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 01:20:29 PM UTC 2026
% Result : Theorem 1.61s 1.17s
% Output : CNFRefutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 19 unt; 2 def)
% Number of atoms : 144 ( 2 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 143 ( 70 ~; 60 |; 9 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn 76 !; 1 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] : ~ unequally_directed_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oag5) ).
fof(f11,axiom,
! [X0,X1,X2] :
( unequally_directed_lines(X0,X1)
=> ( unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oag6) ).
fof(f14,axiom,
! [X0,X1] :
( ( unequally_directed_lines(X0,reverse_line(X1))
& unequally_directed_lines(X0,X1) )
=> ( left_convergent_lines(X0,reverse_line(X1))
| left_convergent_lines(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oag9) ).
fof(f16,axiom,
! [X0,X1] :
~ ( left_convergent_lines(X0,reverse_line(X1))
| left_convergent_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oag11) ).
fof(f18,axiom,
! [X0,X1] :
( ( unequally_directed_lines(X0,reverse_line(X1))
& unequally_directed_lines(X0,X1)
& line(X1)
& line(X0) )
=> point(intersection_point(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oagco2) ).
fof(f22,axiom,
! [X0,X1] :
( ( unequally_directed_lines(X0,reverse_line(X1))
& unequally_directed_lines(X0,X1) )
=> ( ~ apart_point_and_line(intersection_point(X0,X1),X1)
& ~ apart_point_and_line(intersection_point(X0,X1),X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oagco6) ).
fof(f32,conjecture,
! [X0] : ~ unequally_directed_lines(reverse_line(reverse_line(X0)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f33,negated_conjecture,
~ ! [X0] : ~ unequally_directed_lines(reverse_line(reverse_line(X0)),X0),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ unequally_directed_lines(X0,X1)
| unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2) ),
inference(ennf_transformation,[],[f11]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ~ unequally_directed_lines(X0,X1)
| unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2) ),
inference(flattening,[],[f40]) ).
fof(f46,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1))
| left_convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f47,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1))
| left_convergent_lines(X0,X1) ),
inference(flattening,[],[f46]) ).
fof(f49,plain,
! [X0,X1] :
( ~ left_convergent_lines(X0,reverse_line(X1))
& ~ left_convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f52,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ line(X1)
| ~ line(X0)
| point(intersection_point(X0,X1)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f53,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ line(X1)
| ~ line(X0)
| point(intersection_point(X0,X1)) ),
inference(flattening,[],[f52]) ).
fof(f58,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ( ~ apart_point_and_line(intersection_point(X0,X1),X1)
& ~ apart_point_and_line(intersection_point(X0,X1),X0) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f59,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ( ~ apart_point_and_line(intersection_point(X0,X1),X1)
& ~ apart_point_and_line(intersection_point(X0,X1),X0) ) ),
inference(flattening,[],[f58]) ).
fof(f70,plain,
? [X0] : unequally_directed_lines(reverse_line(reverse_line(X0)),X0),
inference(ennf_transformation,[],[f33]) ).
fof(f71,plain,
unequally_directed_lines(reverse_line(reverse_line(sK0)),sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f70]) ).
fof(f78,plain,
! [X0] : ~ unequally_directed_lines(X0,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f79,plain,
! [X2,X0,X1] :
( ~ unequally_directed_lines(X0,X1)
| unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f85,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1))
| left_convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f88,plain,
! [X0,X1] : ~ left_convergent_lines(X0,reverse_line(X1)),
inference(cnf_transformation,[],[f49]) ).
fof(f89,plain,
! [X0,X1] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f49]) ).
fof(f91,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ line(X1)
| ~ line(X0)
| point(intersection_point(X0,X1)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f96,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f107,plain,
unequally_directed_lines(reverse_line(reverse_line(sK0)),sK0),
inference(cnf_transformation,[],[f71]) ).
tcf(c_55,plain,
! [X0: $i] : ~ unequally_directed_lines(X0,X0),
inference(cnf_transformation,[],[f78]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f89]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] : ~ left_convergent_lines(X0,reverse_line(X1)),
inference(cnf_transformation,[],[f88]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( point(intersection_point(X0,X1))
| ~ line(X1)
| ~ line(X0)
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_84,negated_conjecture,
unequally_directed_lines(reverse_line(reverse_line(sK0)),sK0),
inference(cnf_transformation,[],[f107]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_74,c_65,c_66,c_62]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_68,c_109]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(renaming,[status(thm)],[c_125]) ).
tcf(c_238,definition,
iPr_def_10 = reverse_line(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_239,definition,
iPr_def_11 = reverse_line(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_240,negated_conjecture,
unequally_directed_lines(iPr_def_11,sK0),
inference(demodulation,[status(thm)],[c_84,c_238,c_239]) ).
tcf(c_337,plain,
! [X0: $i] :
( ~ unequally_directed_lines(X0,iPr_def_10)
| ~ unequally_directed_lines(X0,sK0) ),
inference(superposition,[status(thm)],[c_238,c_126]) ).
tcf(c_338,plain,
! [X0: $i] :
( ~ unequally_directed_lines(X0,iPr_def_11)
| ~ unequally_directed_lines(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_239,c_126]) ).
tcf(c_343,plain,
( ~ unequally_directed_lines(sK0,iPr_def_11)
| ~ unequally_directed_lines(sK0,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_338]) ).
tcf(c_358,plain,
! [X0: $i] :
( unequally_directed_lines(iPr_def_11,X0)
| unequally_directed_lines(sK0,X0) ),
inference(superposition,[status(thm)],[c_240,c_56]) ).
tcf(c_366,plain,
! [X0: $i,X1: $i] :
( unequally_directed_lines(iPr_def_11,X0)
| unequally_directed_lines(sK0,X1)
| unequally_directed_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_358,c_56]) ).
tcf(c_388,plain,
! [X0: $i] :
( unequally_directed_lines(iPr_def_11,X0)
| unequally_directed_lines(X0,sK0) ),
inference(superposition,[status(thm)],[c_366,c_55]) ).
tcf(c_399,plain,
! [X0: $i] :
( unequally_directed_lines(sK0,iPr_def_10)
| unequally_directed_lines(iPr_def_11,X0)
| ~ unequally_directed_lines(X0,sK0) ),
inference(superposition,[status(thm)],[c_366,c_337]) ).
tcf(c_402,plain,
( unequally_directed_lines(iPr_def_11,iPr_def_11)
| unequally_directed_lines(sK0,iPr_def_11) ),
inference(equality_factoring,[status(thm)],[c_366]) ).
tcf(c_404,plain,
unequally_directed_lines(sK0,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_402,c_55]) ).
tcf(c_458,plain,
! [X0: $i] : unequally_directed_lines(iPr_def_11,X0),
inference(global_subsumption_just,[status(thm)],[c_388,c_343,c_404,c_388,c_399]) ).
tcf(c_460,plain,
$false,
inference(superposition,[status(thm)],[c_458,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO233+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n002.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 11:38:35 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 1.61/1.17 % SZS status Started for theBenchmark.p
% 1.61/1.17 % SZS status Theorem for theBenchmark.p
% 1.61/1.17
% 1.61/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.61/1.17
% 1.61/1.17 % ------ iProver source info
% 1.61/1.17
% 1.61/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 1.61/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.61/1.17 % git: non_committed_changes: false
% 1.61/1.17
% 1.61/1.17 % ------ Parsing...
% 1.61/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.61/1.17
% 1.61/1.17 % ------ Preprocessing... sf_s rm: 15 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.61/1.17
% 1.61/1.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.61/1.17
% 1.61/1.17 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.61/1.17 % ------ Proving...
% 1.61/1.17 % ------ Problem Properties
% 1.61/1.17
% 1.61/1.17 %
% 1.61/1.17 % clauses 8
% 1.61/1.17 % conjectures 1
% 1.61/1.17 % EPR 3
% 1.61/1.17 % Horn 7
% 1.61/1.17 % unary 6
% 1.61/1.17 % binary 1
% 1.61/1.17 % lits 11
% 1.61/1.17 % lits eq 2
% 1.61/1.17 % fd_pure 0
% 1.61/1.17 % fd_pseudo 0
% 1.61/1.17 % fd_cond 0
% 1.61/1.17 % fd_pseudo_cond 0
% 1.61/1.17 % AC symbols 0
% 1.61/1.17
% 1.61/1.17 % ------ Schedule dynamic 5 is on
% 1.61/1.17
% 1.61/1.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.61/1.17
% 1.61/1.17
% 1.61/1.17 % ------
% 1.61/1.17 % Current options:
% 1.61/1.17 % ------
% 1.61/1.17
% 1.61/1.17
% 1.61/1.17 %
% 1.61/1.17
% 1.61/1.17 % ------ Proving...
% 1.61/1.17 %
% 1.61/1.17
% 1.61/1.17 % SZS status Theorem for theBenchmark.p
% 1.61/1.17
% 1.61/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.61/1.17
% 1.61/1.17
%------------------------------------------------------------------------------