%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO234+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 : 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 2.16s 6.17s
% Output : CNFRefutation 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 21 unt; 2 def)
% Number of atoms : 145 ( 2 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 153 ( 76 ~; 56 |; 15 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 73 !; 6 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
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,X1,X2] :
( unequally_directed_lines(X0,reverse_line(X1))
=> ( unequally_directed_lines(X1,reverse_line(X2))
| unequally_directed_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f33,negated_conjecture,
~ ! [X0,X1,X2] :
( unequally_directed_lines(X0,reverse_line(X1))
=> ( unequally_directed_lines(X1,reverse_line(X2))
| unequally_directed_lines(X0,X2) ) ),
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,X1,X2] :
( unequally_directed_lines(X0,reverse_line(X1))
& ~ unequally_directed_lines(X1,reverse_line(X2))
& ~ unequally_directed_lines(X0,X2) ),
inference(ennf_transformation,[],[f33]) ).
fof(f71,plain,
? [X0,X1,X2] :
( unequally_directed_lines(X0,reverse_line(X1))
& ~ unequally_directed_lines(X1,reverse_line(X2))
& ~ unequally_directed_lines(X0,X2) ),
inference(flattening,[],[f70]) ).
fof(f72,plain,
( unequally_directed_lines(sK0,reverse_line(sK1))
& ~ unequally_directed_lines(sK1,reverse_line(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)],[f71]) ).
fof(f80,plain,
! [X2,X0,X1] :
( ~ unequally_directed_lines(X0,X1)
| unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f86,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(f89,plain,
! [X0,X1] : ~ left_convergent_lines(X0,reverse_line(X1)),
inference(cnf_transformation,[],[f49]) ).
fof(f90,plain,
! [X0,X1] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f49]) ).
fof(f92,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(f97,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(f108,plain,
unequally_directed_lines(sK0,reverse_line(sK1)),
inference(cnf_transformation,[],[f72]) ).
fof(f109,plain,
~ unequally_directed_lines(sK1,reverse_line(sK2)),
inference(cnf_transformation,[],[f72]) ).
fof(f110,plain,
~ unequally_directed_lines(sK0,sK2),
inference(cnf_transformation,[],[f72]) ).
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,[],[f80]) ).
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,[],[f86]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f90]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] : ~ left_convergent_lines(X0,reverse_line(X1)),
inference(cnf_transformation,[],[f89]) ).
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,[],[f92]) ).
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,[],[f97]) ).
tcf(c_84,negated_conjecture,
~ unequally_directed_lines(sK0,sK2),
inference(cnf_transformation,[],[f110]) ).
tcf(c_85,negated_conjecture,
~ unequally_directed_lines(sK1,reverse_line(sK2)),
inference(cnf_transformation,[],[f109]) ).
tcf(c_86,negated_conjecture,
unequally_directed_lines(sK0,reverse_line(sK1)),
inference(cnf_transformation,[],[f108]) ).
tcf(c_111,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_127,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_111]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(renaming,[status(thm)],[c_127]) ).
tcf(c_248,definition,
iPr_def_10 = reverse_line(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_249,definition,
iPr_def_11 = reverse_line(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_250,negated_conjecture,
unequally_directed_lines(sK0,iPr_def_10),
inference(demodulation,[status(thm)],[c_86,c_248]) ).
tcf(c_251,negated_conjecture,
~ unequally_directed_lines(sK1,iPr_def_11),
inference(demodulation,[status(thm)],[c_85,c_249]) ).
tcf(c_252,negated_conjecture,
~ unequally_directed_lines(sK0,sK2),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_357,plain,
! [X0: $i] :
( ~ unequally_directed_lines(X0,iPr_def_11)
| ~ unequally_directed_lines(X0,sK2) ),
inference(superposition,[status(thm)],[c_249,c_128]) ).
tcf(c_358,plain,
! [X0: $i] :
( ~ unequally_directed_lines(X0,iPr_def_10)
| ~ unequally_directed_lines(X0,sK1) ),
inference(superposition,[status(thm)],[c_248,c_128]) ).
tcf(c_370,plain,
! [X0: $i] :
( unequally_directed_lines(iPr_def_10,X0)
| unequally_directed_lines(sK0,X0) ),
inference(superposition,[status(thm)],[c_250,c_56]) ).
tcf(c_381,plain,
unequally_directed_lines(iPr_def_10,sK2),
inference(superposition,[status(thm)],[c_370,c_252]) ).
tcf(c_414,plain,
~ unequally_directed_lines(sK0,sK1),
inference(superposition,[status(thm)],[c_250,c_358]) ).
tcf(c_418,plain,
unequally_directed_lines(iPr_def_10,sK1),
inference(superposition,[status(thm)],[c_370,c_414]) ).
tcf(c_419,plain,
! [X0: $i] :
( unequally_directed_lines(iPr_def_10,X0)
| unequally_directed_lines(sK1,X0) ),
inference(superposition,[status(thm)],[c_418,c_56]) ).
tcf(c_715,plain,
unequally_directed_lines(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_419,c_251]) ).
tcf(c_726,plain,
~ unequally_directed_lines(iPr_def_10,sK2),
inference(superposition,[status(thm)],[c_715,c_357]) ).
tcf(c_727,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_726,c_381]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO234+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.36 % Computer : n007.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Wed Sep 23 11:34:57 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/5.40 Running first-order theorem proving
% 0.13/5.40 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
% 0.13/5.41
% 0.13/5.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.41
% 0.13/5.42 % Detected problem language: tptp
% 0.13/5.43 % Proving...
% 2.16/6.17 % SZS status Started for theBenchmark.p
% 2.16/6.17 % SZS status Theorem for theBenchmark.p
% 2.16/6.17
% 2.16/6.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.16/6.17
% 2.16/6.17 % ------ iProver source info
% 2.16/6.17
% 2.16/6.17 % git: date: 2026-07-19 20:42:38 +0200
% 2.16/6.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.16/6.17 % git: non_committed_changes: false
% 2.16/6.17
% 2.16/6.17 % ------ Parsing...
% 2.16/6.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.16/6.17
% 2.16/6.17 % ------ Preprocessing... sf_s rm: 15 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.16/6.17
% 2.16/6.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.16/6.17
% 2.16/6.17 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.16/6.17 % ------ Proving...
% 2.16/6.17 % ------ Problem Properties
% 2.16/6.17
% 2.16/6.17 %
% 2.16/6.17 % clauses 10
% 2.16/6.17 % conjectures 3
% 2.16/6.17 % EPR 5
% 2.16/6.17 % Horn 9
% 2.16/6.17 % unary 8
% 2.16/6.17 % binary 1
% 2.16/6.17 % lits 13
% 2.16/6.17 % lits eq 2
% 2.16/6.17 % fd_pure 0
% 2.16/6.17 % fd_pseudo 0
% 2.16/6.17 % fd_cond 0
% 2.16/6.17 % fd_pseudo_cond 0
% 2.16/6.17 % AC symbols 0
% 2.16/6.17
% 2.16/6.17 % ------ Schedule dynamic 5 is on
% 2.16/6.17
% 2.16/6.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.16/6.17
% 2.16/6.17
% 2.16/6.17 % ------
% 2.16/6.17 % Current options:
% 2.16/6.17 % ------
% 2.16/6.17
% 2.16/6.17
% 2.16/6.17 %
% 2.16/6.17
% 2.16/6.17 % ------ Proving...
% 2.16/6.17 %
% 2.16/6.17
% 2.16/6.17 % SZS status Theorem for theBenchmark.p
% 2.16/6.17
% 2.16/6.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.16/6.17
% 2.16/6.17
%------------------------------------------------------------------------------