%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO231+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 : n007.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 2.58s 1.31s
% Output : CNFRefutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 70 ( 14 unt; 0 def)
% Number of atoms : 178 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 192 ( 84 ~; 75 |; 23 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 131 ( 0 sgn 125 !; 6 ?; 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(f5,axiom,
! [X0,X1] :
( equally_directed_opposite_lines(X0,X1)
<=> ~ unequally_directed_opposite_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',a5_defns) ).
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(f17,axiom,
! [X0,X1,X2] :
( ( unequally_directed_lines(X0,reverse_line(X1))
& unequally_directed_lines(X0,X1) )
=> ( ( unequally_directed_lines(X1,reverse_line(X2))
& unequally_directed_lines(X1,X2) )
| ( unequally_directed_lines(X0,reverse_line(X2))
& unequally_directed_lines(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',ax7_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,X2] :
( ( equally_directed_lines(X0,X2)
& equally_directed_opposite_lines(X0,X1) )
=> equally_directed_opposite_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f38,negated_conjecture,
~ ! [X0,X1,X2] :
( ( equally_directed_lines(X0,X2)
& equally_directed_opposite_lines(X0,X1) )
=> equally_directed_opposite_lines(X1,X2) ),
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(f51,plain,
! [X0,X1,X2] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ( unequally_directed_lines(X1,reverse_line(X2))
& unequally_directed_lines(X1,X2) )
| ( unequally_directed_lines(X0,reverse_line(X2))
& unequally_directed_lines(X0,X2) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ( unequally_directed_lines(X1,reverse_line(X2))
& unequally_directed_lines(X1,X2) )
| ( unequally_directed_lines(X0,reverse_line(X2))
& unequally_directed_lines(X0,X2) ) ),
inference(flattening,[],[f51]) ).
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,X2] :
( equally_directed_lines(X0,X2)
& equally_directed_opposite_lines(X0,X1)
& ~ equally_directed_opposite_lines(X1,X2) ),
inference(ennf_transformation,[],[f38]) ).
fof(f79,plain,
? [X0,X1,X2] :
( equally_directed_lines(X0,X2)
& equally_directed_opposite_lines(X0,X1)
& ~ equally_directed_opposite_lines(X1,X2) ),
inference(flattening,[],[f78]) ).
fof(f80,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(f81,plain,
! [X0,X1] :
( ( ~ equally_directed_opposite_lines(X0,X1)
| ~ unequally_directed_opposite_lines(X0,X1) )
& ( unequally_directed_opposite_lines(X0,X1)
| equally_directed_opposite_lines(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f82,plain,
( equally_directed_lines(sK0,sK2)
& equally_directed_opposite_lines(sK0,sK1)
& ~ equally_directed_opposite_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f79]) ).
fof(f83,plain,
! [X0,X1] :
( ~ unequally_directed_opposite_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f80]) ).
fof(f84,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f86,plain,
! [X0,X1] :
( ~ equally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f87,plain,
! [X0,X1] :
( ~ equally_directed_opposite_lines(X0,X1)
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f88,plain,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
| equally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f96,plain,
! [X2,X0,X1] :
( ~ unequally_directed_lines(X0,X1)
| unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f100,plain,
! [X2,X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f101,plain,
! [X0,X1] :
( unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f102,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(f105,plain,
! [X0,X1] : ~ left_convergent_lines(X0,reverse_line(X1)),
inference(cnf_transformation,[],[f56]) ).
fof(f106,plain,
! [X0,X1] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f56]) ).
fof(f113,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(f124,plain,
equally_directed_lines(sK0,sK2),
inference(cnf_transformation,[],[f82]) ).
fof(f125,plain,
equally_directed_opposite_lines(sK0,sK1),
inference(cnf_transformation,[],[f82]) ).
fof(f126,plain,
~ equally_directed_opposite_lines(sK1,sK2),
inference(cnf_transformation,[],[f82]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( unequally_directed_opposite_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( ~ equally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( equally_directed_opposite_lines(X0,X1)
| unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ~ equally_directed_opposite_lines(X0,X1)
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_62,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,[],[f96]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2)
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_68,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,[],[f102]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f106]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] : ~ left_convergent_lines(X0,reverse_line(X1)),
inference(cnf_transformation,[],[f105]) ).
tcf(c_80,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,[],[f113]) ).
tcf(c_90,negated_conjecture,
~ equally_directed_opposite_lines(sK1,sK2),
inference(cnf_transformation,[],[f126]) ).
tcf(c_91,negated_conjecture,
equally_directed_opposite_lines(sK0,sK1),
inference(cnf_transformation,[],[f125]) ).
tcf(c_92,negated_conjecture,
equally_directed_lines(sK0,sK2),
inference(cnf_transformation,[],[f124]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_80,c_71,c_72,c_68]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i,X2: $i] :
( unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_63,c_62]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,X1)
| equally_directed_opposite_lines(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_53,c_50,c_123]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i] :
( equally_directed_opposite_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1) ),
inference(renaming,[status(thm)],[c_150]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i] :
( unequally_directed_lines(X0,X1)
| ~ equally_directed_opposite_lines(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_67,c_54,c_49]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i] :
( ~ equally_directed_opposite_lines(X0,X1)
| ~ equally_directed_lines(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_67,c_54,c_52,c_49]) ).
tcf(c_238,plain,
! [X0: $i,X1: $i,X2: $i] :
( unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2)
| ~ equally_directed_opposite_lines(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_128,c_152]) ).
tcf(c_375,plain,
~ equally_directed_opposite_lines(sK0,sK2),
inference(resolution,[status(thm)],[c_156,c_92]) ).
tcf(c_418,plain,
~ unequally_directed_lines(sK1,sK2),
inference(resolution,[status(thm)],[c_151,c_90]) ).
tcf(c_462,plain,
~ unequally_directed_lines(sK0,sK2),
inference(resolution,[status(thm)],[c_151,c_375]) ).
tcf(c_661,plain,
! [X0: $i] :
( unequally_directed_lines(sK0,X0)
| unequally_directed_lines(sK1,X0)
| ~ equally_directed_opposite_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_238]) ).
tcf(c_711,plain,
( unequally_directed_lines(sK0,sK2)
| unequally_directed_lines(sK1,sK2)
| ~ equally_directed_opposite_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_661]) ).
tcf(c_712,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_711,c_462,c_418,c_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO231+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n007.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 11:33:21 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.44
% 0.11/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.44
% 0.11/0.44 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 2.58/1.31 % SZS status Started for theBenchmark.p
% 2.58/1.31 % SZS status Theorem for theBenchmark.p
% 2.58/1.31
% 2.58/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.58/1.31
% 2.58/1.31 % ------ iProver source info
% 2.58/1.31
% 2.58/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 2.58/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.58/1.31 % git: non_committed_changes: false
% 2.58/1.31
% 2.58/1.31 % ------ Parsing...
% 2.58/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.58/1.31
% 2.58/1.31 % ------ Preprocessing... sf_s rm: 16 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.58/1.31
% 2.58/1.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.58/1.31 % ------ Proving...
% 2.58/1.31 % ------ Problem Properties
% 2.58/1.31
% 2.58/1.31 %
% 2.58/1.31 % clauses 10
% 2.58/1.31 % conjectures 2
% 2.58/1.31 % EPR 7
% 2.58/1.31 % Horn 8
% 2.58/1.31 % unary 5
% 2.58/1.31 % binary 4
% 2.58/1.31 % lits 16
% 2.58/1.31 % lits eq 0
% 2.58/1.31 % fd_pure 0
% 2.58/1.32 % fd_pseudo 0
% 2.58/1.32 % fd_cond 0
% 2.58/1.32 % fd_pseudo_cond 0
% 2.58/1.32 % AC symbols 0
% 2.58/1.32
% 2.58/1.32 % ------ Schedule dynamic 5 is on
% 2.58/1.32
% 2.58/1.32 % ------ no equalities: superposition off
% 2.58/1.32
% 2.58/1.32 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.58/1.32
% 2.58/1.32
% 2.58/1.32 % ------
% 2.58/1.32 % Current options:
% 2.58/1.32 % ------
% 2.58/1.32
% 2.58/1.32
% 2.58/1.32 %
% 2.58/1.32
% 2.58/1.32 % ------ Proving...
% 2.58/1.32 %
% 2.58/1.32
% 2.58/1.32 % SZS status Theorem for theBenchmark.p
% 2.58/1.32
% 2.58/1.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.58/1.32
% 2.58/1.32
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