%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO266+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 : n009.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 01:20:38 PM UTC 2026
% Result : Theorem 2.35s 1.27s
% Output : CNFRefutation 2.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 73 ( 13 unt; 0 def)
% Number of atoms : 164 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 173 ( 82 ~; 73 |; 9 &)
% ( 4 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 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 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 109 ( 0 sgn 105 !; 4 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
<=> unequally_directed_lines(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',a1_defns) ).
fof(f4,axiom,
! [X0,X1] :
( equally_directed_lines(X0,X1)
<=> ~ unequally_directed_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',a4_defns) ).
fof(f15,axiom,
! [X0] : equally_directed_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',ax5_basics) ).
fof(f16,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/GEO009+0.ax',ax6_basics) ).
fof(f18,axiom,
! [X0,X1] :
( unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',ax8_basics) ).
fof(f19,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/GEO009+0.ax',ax9_basics) ).
fof(f21,axiom,
! [X0,X1] :
~ ( left_convergent_lines(X0,reverse_line(X1))
| left_convergent_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',ax11_basics) ).
fof(f27,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/GEO009+0.ax',ax6_cons_objs) ).
fof(f37,conjecture,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
<=> unequally_directed_opposite_lines(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f38,negated_conjecture,
~ ! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
<=> unequally_directed_opposite_lines(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( equally_directed_lines(X0,X1)
=> ~ unequally_directed_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f43,plain,
! [X0,X1] :
( ~ equally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ~ unequally_directed_lines(X0,X1)
| unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2) ),
inference(ennf_transformation,[],[f16]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ~ unequally_directed_lines(X0,X1)
| unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2) ),
inference(flattening,[],[f49]) ).
fof(f53,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,[],[f19]) ).
fof(f54,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,[],[f53]) ).
fof(f56,plain,
! [X0,X1] :
( ~ left_convergent_lines(X0,reverse_line(X1))
& ~ left_convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f65,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,[],[f27]) ).
fof(f66,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,[],[f65]) ).
fof(f78,plain,
? [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
<~> unequally_directed_opposite_lines(X1,X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f79,plain,
! [X0,X1] :
( ( ~ unequally_directed_opposite_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) )
& ( ~ unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_opposite_lines(X0,X1) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f80,plain,
? [X0,X1] :
( ( unequally_directed_opposite_lines(X0,X1)
| unequally_directed_opposite_lines(X1,X0) )
& ( ~ unequally_directed_opposite_lines(X0,X1)
| ~ unequally_directed_opposite_lines(X1,X0) ) ),
inference(nnf_transformation,[],[f78]) ).
fof(f81,plain,
( ( unequally_directed_opposite_lines(sK0,sK1)
| unequally_directed_opposite_lines(sK1,sK0) )
& ( ~ unequally_directed_opposite_lines(sK0,sK1)
| ~ unequally_directed_opposite_lines(sK1,sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f80]) ).
fof(f82,plain,
! [X0,X1] :
( ~ unequally_directed_opposite_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f83,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f85,plain,
! [X0,X1] :
( ~ equally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f92,plain,
! [X0] : equally_directed_lines(X0,X0),
inference(cnf_transformation,[],[f15]) ).
fof(f93,plain,
! [X2,X0,X1] :
( ~ unequally_directed_lines(X0,X1)
| unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f98,plain,
! [X0,X1] :
( unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f99,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,[],[f54]) ).
fof(f102,plain,
! [X0,X1] : ~ left_convergent_lines(X0,reverse_line(X1)),
inference(cnf_transformation,[],[f56]) ).
fof(f103,plain,
! [X0,X1] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f56]) ).
fof(f110,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,[],[f66]) ).
fof(f121,plain,
( unequally_directed_opposite_lines(sK0,sK1)
| unequally_directed_opposite_lines(sK1,sK0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f122,plain,
( ~ unequally_directed_opposite_lines(sK0,sK1)
| ~ unequally_directed_opposite_lines(sK1,sK0) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( unequally_directed_opposite_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( ~ equally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_59,plain,
! [X0: $i] : equally_directed_lines(X0,X0),
inference(cnf_transformation,[],[f92]) ).
tcf(c_60,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,[],[f93]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_66,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,[],[f99]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f103]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] : ~ left_convergent_lines(X0,reverse_line(X1)),
inference(cnf_transformation,[],[f102]) ).
tcf(c_78,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,[],[f110]) ).
tcf(c_88,negated_conjecture,
( ~ unequally_directed_opposite_lines(sK0,sK1)
| ~ unequally_directed_opposite_lines(sK1,sK0) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_89,negated_conjecture,
( unequally_directed_opposite_lines(sK0,sK1)
| unequally_directed_opposite_lines(sK1,sK0) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_90,plain,
equally_directed_lines(sK0,sK0),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_103,plain,
( ~ equally_directed_lines(sK0,sK0)
| ~ unequally_directed_lines(sK0,sK0) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_78,c_69,c_70,c_66]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_opposite_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_50,c_118]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(renaming,[status(thm)],[c_137]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i] :
( unequally_directed_opposite_lines(X0,X1)
| unequally_directed_lines(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_65,c_49]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( unequally_directed_lines(X0,X1)
| unequally_directed_opposite_lines(X0,X1) ),
inference(renaming,[status(thm)],[c_139]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i] :
( ~ equally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_52]) ).
tcf(c_347,plain,
! [X0: $i] : ~ unequally_directed_lines(X0,X0),
inference(resolution,[status(thm)],[c_151,c_59]) ).
tcf(c_359,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_opposite_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_138]) ).
tcf(c_360,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(renaming,[status(thm)],[c_359]) ).
tcf(c_361,plain,
! [X0: $i,X1: $i] :
( unequally_directed_opposite_lines(X0,X1)
| unequally_directed_lines(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_140]) ).
tcf(c_362,plain,
! [X0: $i,X1: $i] :
( unequally_directed_lines(X0,X1)
| unequally_directed_opposite_lines(X0,X1) ),
inference(renaming,[status(thm)],[c_361]) ).
tcf(c_425,negated_conjecture,
( unequally_directed_opposite_lines(sK0,sK1)
| unequally_directed_opposite_lines(sK1,sK0) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_426,negated_conjecture,
( ~ unequally_directed_opposite_lines(sK0,sK1)
| ~ unequally_directed_opposite_lines(sK1,sK0) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_427,plain,
( unequally_directed_lines(sK0,sK1)
| unequally_directed_opposite_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_362]) ).
tcf(c_442,plain,
! [X0: $i] :
( unequally_directed_lines(sK0,X0)
| unequally_directed_lines(sK1,X0)
| ~ unequally_directed_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_445,plain,
( unequally_directed_lines(sK0,sK0)
| unequally_directed_lines(sK1,sK0)
| ~ unequally_directed_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_442]) ).
tcf(c_516,plain,
( unequally_directed_lines(sK1,sK0)
| ~ unequally_directed_opposite_lines(sK0,sK1) ),
inference(superposition,[status(thm)],[c_362,c_426]) ).
tcf(c_542,plain,
unequally_directed_lines(sK1,sK0),
inference(global_subsumption_just,[status(thm)],[c_516,c_90,c_103,c_427,c_445,c_516]) ).
tcf(c_647,plain,
( unequally_directed_opposite_lines(sK1,sK0)
| ~ unequally_directed_lines(sK0,sK1) ),
inference(superposition,[status(thm)],[c_425,c_360]) ).
tcf(c_666,plain,
! [X0: $i] :
( unequally_directed_lines(sK0,X0)
| unequally_directed_lines(sK1,X0) ),
inference(superposition,[status(thm)],[c_542,c_60]) ).
tcf(c_692,plain,
( ~ unequally_directed_lines(sK1,sK0)
| ~ unequally_directed_opposite_lines(sK1,sK0) ),
inference(instantiation,[status(thm)],[c_360]) ).
tcf(c_811,plain,
~ unequally_directed_lines(sK0,sK1),
inference(global_subsumption_just,[status(thm)],[c_647,c_90,c_103,c_427,c_445,c_516,c_647,c_692]) ).
tcf(c_813,plain,
unequally_directed_lines(sK1,sK1),
inference(superposition,[status(thm)],[c_666,c_811]) ).
tcf(c_814,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_813,c_347]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO266+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 11:45:44 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.41 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 2.35/1.27 % SZS status Started for theBenchmark.p
% 2.35/1.27 % SZS status Theorem for theBenchmark.p
% 2.35/1.27
% 2.35/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.35/1.27
% 2.35/1.27 % ------ iProver source info
% 2.35/1.27
% 2.35/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.35/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.35/1.27 % git: non_committed_changes: false
% 2.35/1.27
% 2.35/1.27 % ------ Parsing...
% 2.35/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.35/1.27
% 2.35/1.27 % ------ Preprocessing... sf_s rm: 16 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.35/1.27
% 2.35/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.35/1.27 % ------ Proving...
% 2.35/1.27 % ------ Problem Properties
% 2.35/1.27
% 2.35/1.27 %
% 2.35/1.27 % clauses 9
% 2.35/1.27 % conjectures 2
% 2.35/1.27 % EPR 6
% 2.35/1.27 % Horn 5
% 2.35/1.27 % unary 2
% 2.35/1.27 % binary 6
% 2.35/1.27 % lits 17
% 2.35/1.27 % lits eq 0
% 2.35/1.27 % fd_pure 0
% 2.35/1.27 % fd_pseudo 0
% 2.35/1.27 % fd_cond 0
% 2.35/1.27 % fd_pseudo_cond 0
% 2.35/1.27 % AC symbols 0
% 2.35/1.27
% 2.35/1.27 % ------ Schedule dynamic 5 is on
% 2.35/1.27
% 2.35/1.27 % ------ no equalities: superposition off
% 2.35/1.27
% 2.35/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.35/1.27
% 2.35/1.27
% 2.35/1.27 % ------
% 2.35/1.27 % Current options:
% 2.35/1.27 % ------
% 2.35/1.27
% 2.35/1.27
% 2.35/1.27 %
% 2.35/1.27
% 2.35/1.27 % ------ Proving...
% 2.35/1.27 %
% 2.35/1.27
% 2.35/1.27 % SZS status Theorem for theBenchmark.p
% 2.35/1.27
% 2.35/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.35/1.27
% 2.35/1.27
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