%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO248+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 : Wed Oct 7 10:18:39 AM UTC 2026
% Result : Theorem 0.09s 0.21s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 46 ( 40 unt; 0 typ; 0 def)
% Number of atoms : 172 ( 44 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 271 ( 22 ~; 23 |; 6 &; 211 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 5 con; 0-4 aty)
% Number of variables : 82 ( 0 ^; 82 !; 0 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apart_point_and_line,type,
apart_point_and_line: $i > $i > $o ).
thf(tp_before_on_line,type,
before_on_line: $i > $i > $i > $o ).
thf(tp_between_on_line,type,
between_on_line: $i > $i > $i > $i > $o ).
thf(tp_convergent_lines,type,
convergent_lines: $i > $i > $o ).
thf(tp_distinct_lines,type,
distinct_lines: $i > $i > $o ).
thf(tp_distinct_points,type,
distinct_points: $i > $i > $o ).
thf(tp_divides_points,type,
divides_points: $i > $i > $i > $o ).
thf(tp_intersection_point,type,
intersection_point: $i > $i > $i ).
thf(tp_left_apart_point,type,
left_apart_point: $i > $i > $o ).
thf(tp_left_convergent_lines,type,
left_convergent_lines: $i > $i > $o ).
thf(tp_line,type,
line: $i > $o ).
thf(tp_line_connecting,type,
line_connecting: $i > $i > $i ).
thf(tp_parallel_through_point,type,
parallel_through_point: $i > $i > $i ).
thf(tp_point,type,
point: $i > $o ).
thf(tp_reverse_line,type,
reverse_line: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY12,type,
sK2_SY12: $i ).
thf(tp_sK3_SY14,type,
sK3_SY14: $i ).
thf(tp_unequally_directed_lines,type,
unequally_directed_lines: $i > $i > $o ).
thf(3,axiom,
! [A: $i,B: $i,L: $i] :
( ( left_apart_point @ A @ L )
=> ( ( distinct_points @ A @ B )
| ( left_apart_point @ B @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oagsub1) ).
thf(6,axiom,
! [A: $i,L: $i] :
~ ( unequally_directed_lines @ ( parallel_through_point @ L @ A ) @ L ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oagco10) ).
thf(9,axiom,
! [A: $i,L: $i] :
~ ( apart_point_and_line @ A @ ( parallel_through_point @ L @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oagco7) ).
thf(17,axiom,
! [A: $i,L: $i] :
~ ( ( left_apart_point @ A @ L )
| ( left_apart_point @ A @ ( reverse_line @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oag10) ).
thf(32,conjecture,
! [A: $i,B: $i,L: $i] :
( ( ( left_apart_point @ A @ L )
& ( left_apart_point @ B @ ( parallel_through_point @ L @ A ) ) )
=> ( left_apart_point @ B @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(33,negated_conjecture,
( ( ! [A: $i,B: $i,L: $i] :
( ( ( left_apart_point @ A @ L )
& ( left_apart_point @ B @ ( parallel_through_point @ L @ A ) ) )
=> ( left_apart_point @ B @ L ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[32]) ).
thf(34,plain,
( ( ! [A: $i,B: $i,L: $i] :
( ( ( left_apart_point @ A @ L )
& ( left_apart_point @ B @ ( parallel_through_point @ L @ A ) ) )
=> ( left_apart_point @ B @ L ) ) )
= $false ),
inference(unfold_def,[status(thm)],[33]) ).
thf(35,plain,
( ( ! [A: $i,B: $i,L: $i] :
( ( left_apart_point @ A @ L )
=> ( ( distinct_points @ A @ B )
| ( left_apart_point @ B @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(36,plain,
( ( ! [A: $i,L: $i] :
~ ( unequally_directed_lines @ ( parallel_through_point @ L @ A ) @ L ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(37,plain,
( ( ! [A: $i,L: $i] :
~ ( apart_point_and_line @ A @ ( parallel_through_point @ L @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(38,plain,
( ( ! [A: $i,L: $i] :
~ ( ( left_apart_point @ A @ L )
| ( left_apart_point @ A @ ( reverse_line @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(39,plain,
( ( ! [SY12: $i,SY13: $i] :
( ( ( left_apart_point @ sK1_A @ SY13 )
& ( left_apart_point @ SY12 @ ( parallel_through_point @ SY13 @ sK1_A ) ) )
=> ( left_apart_point @ SY12 @ SY13 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[34]) ).
thf(40,plain,
( ( ! [SY14: $i] :
( ( ( left_apart_point @ sK1_A @ SY14 )
& ( left_apart_point @ sK2_SY12 @ ( parallel_through_point @ SY14 @ sK1_A ) ) )
=> ( left_apart_point @ sK2_SY12 @ SY14 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(41,plain,
( ( ( ( left_apart_point @ sK1_A @ sK3_SY14 )
& ( left_apart_point @ sK2_SY12 @ ( parallel_through_point @ sK3_SY14 @ sK1_A ) ) )
=> ( left_apart_point @ sK2_SY12 @ sK3_SY14 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[40]) ).
thf(42,plain,
( ( left_apart_point @ sK1_A @ sK3_SY14 )
= $true ),
inference(standard_cnf,[status(thm)],[41]) ).
thf(43,plain,
( ( left_apart_point @ sK2_SY12 @ ( parallel_through_point @ sK3_SY14 @ sK1_A ) )
= $true ),
inference(standard_cnf,[status(thm)],[41]) ).
thf(44,plain,
( ( left_apart_point @ sK2_SY12 @ sK3_SY14 )
= $false ),
inference(standard_cnf,[status(thm)],[41]) ).
thf(45,plain,
( ( ~ ( left_apart_point @ sK2_SY12 @ sK3_SY14 ) )
= $true ),
inference(polarity_switch,[status(thm)],[44]) ).
thf(46,plain,
( ( ! [A: $i,L: $i] :
~ ( ( left_apart_point @ A @ L )
| ( left_apart_point @ A @ ( reverse_line @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(47,plain,
( ( ! [A: $i,L: $i] :
~ ( apart_point_and_line @ A @ ( parallel_through_point @ L @ A ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(48,plain,
( ( ! [A: $i,L: $i] :
~ ( unequally_directed_lines @ ( parallel_through_point @ L @ A ) @ L ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(49,plain,
( ( ! [A: $i,B: $i,L: $i] :
( ( left_apart_point @ A @ L )
=> ( ( distinct_points @ A @ B )
| ( left_apart_point @ B @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(50,plain,
( ( left_apart_point @ sK2_SY12 @ ( parallel_through_point @ sK3_SY14 @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(51,plain,
( ( left_apart_point @ sK1_A @ sK3_SY14 )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(52,plain,
( ( ~ ( left_apart_point @ sK2_SY12 @ sK3_SY14 ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(53,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( left_apart_point @ SX0 @ SX2 )
| ( distinct_points @ SX0 @ SX1 )
| ( left_apart_point @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(54,plain,
! [SV1: $i] :
( ( ! [SY15: $i] :
~ ( ( left_apart_point @ SV1 @ SY15 )
| ( left_apart_point @ SV1 @ ( reverse_line @ SY15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(55,plain,
! [SV2: $i] :
( ( ! [SY16: $i] :
~ ( apart_point_and_line @ SV2 @ ( parallel_through_point @ SY16 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(56,plain,
! [SV3: $i] :
( ( ! [SY17: $i] :
~ ( unequally_directed_lines @ ( parallel_through_point @ SY17 @ SV3 ) @ SY17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(57,plain,
( ( left_apart_point @ sK2_SY12 @ sK3_SY14 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV4: $i] :
( ( ! [SY18: $i,SY19: $i] :
( ~ ( left_apart_point @ SV4 @ SY19 )
| ( distinct_points @ SV4 @ SY18 )
| ( left_apart_point @ SY18 @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(59,plain,
! [SV5: $i,SV1: $i] :
( ( ~ ( ( left_apart_point @ SV1 @ SV5 )
| ( left_apart_point @ SV1 @ ( reverse_line @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV6: $i,SV2: $i] :
( ( ~ ( apart_point_and_line @ SV2 @ ( parallel_through_point @ SV6 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(61,plain,
! [SV3: $i,SV7: $i] :
( ( ~ ( unequally_directed_lines @ ( parallel_through_point @ SV7 @ SV3 ) @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(62,plain,
! [SV8: $i,SV4: $i] :
( ( ! [SY20: $i] :
( ~ ( left_apart_point @ SV4 @ SY20 )
| ( distinct_points @ SV4 @ SV8 )
| ( left_apart_point @ SV8 @ SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV5: $i,SV1: $i] :
( ( ( left_apart_point @ SV1 @ SV5 )
| ( left_apart_point @ SV1 @ ( reverse_line @ SV5 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(64,plain,
! [SV6: $i,SV2: $i] :
( ( apart_point_and_line @ SV2 @ ( parallel_through_point @ SV6 @ SV2 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(65,plain,
! [SV3: $i,SV7: $i] :
( ( unequally_directed_lines @ ( parallel_through_point @ SV7 @ SV3 ) @ SV7 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV8: $i,SV9: $i,SV4: $i] :
( ( ~ ( left_apart_point @ SV4 @ SV9 )
| ( distinct_points @ SV4 @ SV8 )
| ( left_apart_point @ SV8 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV5: $i,SV1: $i] :
( ( left_apart_point @ SV1 @ SV5 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(68,plain,
! [SV5: $i,SV1: $i] :
( ( left_apart_point @ SV1 @ ( reverse_line @ SV5 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(69,plain,
! [SV8: $i,SV9: $i,SV4: $i] :
( ( ( ~ ( left_apart_point @ SV4 @ SV9 ) )
= $true )
| ( ( ( distinct_points @ SV4 @ SV8 )
| ( left_apart_point @ SV8 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(70,plain,
! [SV8: $i,SV9: $i,SV4: $i] :
( ( ( left_apart_point @ SV4 @ SV9 )
= $false )
| ( ( ( distinct_points @ SV4 @ SV8 )
| ( left_apart_point @ SV8 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(71,plain,
! [SV9: $i,SV8: $i,SV4: $i] :
( ( ( distinct_points @ SV4 @ SV8 )
= $true )
| ( ( left_apart_point @ SV8 @ SV9 )
= $true )
| ( ( left_apart_point @ SV4 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(72,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[50,71,68,67,65,64,57,51]) ).
thf(73,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO248+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.17 % Computer : n015.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 10:16:12 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.21
% 0.09/0.21 No.of.Axioms: 4
% 0.09/0.21
% 0.09/0.21 Length.of.Defs: 0
% 0.09/0.21
% 0.09/0.21 Contains.Choice.Funs: false
% 0.09/0.21 .
% 0.09/0.21
% 0.09/0.21 ********************************
% 0.09/0.21 * All subproblems solved! *
% 0.09/0.21 ********************************
% 0.09/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:6,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:72,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.21
% 0.09/0.21 %**** Beginning of derivation protocol ****
% 0.09/0.21 % SZS output start CNFRefutation
% See solution above
% 0.09/0.21
% 0.09/0.21 %**** End of derivation protocol ****
% 0.09/0.21 %**** no. of clauses in derivation: 46 ****
% 0.09/0.21 %**** clause counter: 72 ****
% 0.09/0.21
% 0.09/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:6,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:72,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------