%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO234+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 : n010.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 2.33s 1.28s
% Output : CNFRefutation 2.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 69 ( 21 unt; 0 def)
% Number of atoms : 151 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 157 ( 75 ~; 61 |; 13 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 109 ( 0 sgn 103 !; 6 ?; 39 :)
% 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,X2] :
( unequally_directed_opposite_lines(X0,X1)
=> ( unequally_directed_opposite_lines(X1,X2)
| unequally_directed_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f38,negated_conjecture,
~ ! [X0,X1,X2] :
( unequally_directed_opposite_lines(X0,X1)
=> ( unequally_directed_opposite_lines(X1,X2)
| unequally_directed_lines(X0,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(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] :
( unequally_directed_opposite_lines(X0,X1)
& ~ unequally_directed_opposite_lines(X1,X2)
& ~ unequally_directed_lines(X0,X2) ),
inference(ennf_transformation,[],[f38]) ).
fof(f79,plain,
? [X0,X1,X2] :
( unequally_directed_opposite_lines(X0,X1)
& ~ unequally_directed_opposite_lines(X1,X2)
& ~ unequally_directed_lines(X0,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,
( unequally_directed_opposite_lines(sK0,sK1)
& ~ unequally_directed_opposite_lines(sK1,sK2)
& ~ unequally_directed_lines(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f79]) ).
fof(f82,plain,
! [X0,X1] :
( ~ unequally_directed_opposite_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f80]) ).
fof(f83,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
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),
inference(cnf_transformation,[],[f81]) ).
fof(f122,plain,
~ unequally_directed_opposite_lines(sK1,sK2),
inference(cnf_transformation,[],[f81]) ).
fof(f123,plain,
~ unequally_directed_lines(sK0,sK2),
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_lines(sK0,sK2),
inference(cnf_transformation,[],[f123]) ).
tcf(c_89,negated_conjecture,
~ unequally_directed_opposite_lines(sK1,sK2),
inference(cnf_transformation,[],[f122]) ).
tcf(c_90,negated_conjecture,
unequally_directed_opposite_lines(sK0,sK1),
inference(cnf_transformation,[],[f121]) ).
tcf(c_119,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_138,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_119]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(renaming,[status(thm)],[c_138]) ).
tcf(c_140,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_141,plain,
! [X0: $i,X1: $i] :
( unequally_directed_lines(X0,X1)
| unequally_directed_opposite_lines(X0,X1) ),
inference(renaming,[status(thm)],[c_140]) ).
tcf(c_148,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_339,plain,
! [X0: $i] : ~ unequally_directed_lines(X0,X0),
inference(resolution,[status(thm)],[c_148,c_59]) ).
tcf(c_352,plain,
unequally_directed_lines(sK1,sK2),
inference(resolution,[status(thm)],[c_141,c_89]) ).
tcf(c_356,plain,
~ unequally_directed_lines(sK0,sK1),
inference(resolution,[status(thm)],[c_139,c_90]) ).
tcf(c_403,plain,
~ unequally_directed_lines(sK0,sK1),
inference(demodulation,[status(thm)],[c_356]) ).
tcf(c_404,plain,
unequally_directed_lines(sK1,sK2),
inference(demodulation,[status(thm)],[c_352]) ).
tcf(c_422,plain,
! [X0: $i,X1: $i] :
( unequally_directed_lines(sK2,X1)
| unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(sK2,X0) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_467,plain,
! [X0: $i] :
( unequally_directed_lines(sK2,sK2)
| unequally_directed_lines(X0,sK2)
| ~ unequally_directed_lines(sK2,X0) ),
inference(instantiation,[status(thm)],[c_422]) ).
tcf(c_468,plain,
~ unequally_directed_lines(sK2,sK2),
inference(instantiation,[status(thm)],[c_339]) ).
tcf(c_469,plain,
( unequally_directed_lines(sK2,sK2)
| unequally_directed_lines(sK0,sK2)
| ~ unequally_directed_lines(sK2,sK0) ),
inference(instantiation,[status(thm)],[c_467]) ).
tcf(c_577,plain,
! [X0: $i] :
( unequally_directed_lines(sK1,X0)
| unequally_directed_lines(sK2,X0) ),
inference(superposition,[status(thm)],[c_404,c_60]) ).
tcf(c_691,plain,
! [X0: $i,X1: $i] :
( unequally_directed_lines(sK1,X1)
| unequally_directed_lines(sK2,X0)
| unequally_directed_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_577,c_60]) ).
tcf(c_1199,plain,
( unequally_directed_lines(sK1,sK1)
| unequally_directed_lines(sK2,sK0) ),
inference(superposition,[status(thm)],[c_691,c_403]) ).
tcf(c_1207,plain,
unequally_directed_lines(sK2,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_1199,c_339]) ).
tcf(c_1235,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1207,c_468,c_469,c_88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO234+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n010.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 11:37:27 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 2.33/1.28 % SZS status Started for theBenchmark.p
% 2.33/1.28 % SZS status Theorem for theBenchmark.p
% 2.33/1.28
% 2.33/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.33/1.28
% 2.33/1.28 % ------ iProver source info
% 2.33/1.28
% 2.33/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.33/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.33/1.28 % git: non_committed_changes: false
% 2.33/1.28
% 2.33/1.28 % ------ Parsing...
% 2.33/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.33/1.28
% 2.33/1.28 % ------ 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 %
% 2.33/1.28
% 2.33/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.33/1.28 % ------ Proving...
% 2.33/1.28 % ------ Problem Properties
% 2.33/1.28
% 2.33/1.28 %
% 2.33/1.28 % clauses 8
% 2.33/1.28 % conjectures 1
% 2.33/1.28 % EPR 5
% 2.33/1.28 % Horn 6
% 2.33/1.28 % unary 5
% 2.33/1.28 % binary 2
% 2.33/1.28 % lits 12
% 2.33/1.28 % lits eq 0
% 2.33/1.28 % fd_pure 0
% 2.33/1.28 % fd_pseudo 0
% 2.33/1.28 % fd_cond 0
% 2.33/1.28 % fd_pseudo_cond 0
% 2.33/1.28 % AC symbols 0
% 2.33/1.28
% 2.33/1.28 % ------ Schedule dynamic 5 is on
% 2.33/1.28
% 2.33/1.28 % ------ no equalities: superposition off
% 2.33/1.28
% 2.33/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.33/1.28
% 2.33/1.28
% 2.33/1.28 % ------
% 2.33/1.28 % Current options:
% 2.33/1.28 % ------
% 2.33/1.28
% 2.33/1.28
% 2.33/1.28 %
% 2.33/1.28
% 2.33/1.28 % ------ Proving...
% 2.33/1.28 %
% 2.33/1.28
% 2.33/1.28 % SZS status Theorem for theBenchmark.p
% 2.33/1.28
% 2.33/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.33/1.28
% 2.33/1.28
%------------------------------------------------------------------------------