%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO207+2 : TPTP v9.3.1. Released v3.3.0.
% 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 : 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 : Wed Oct 7 10:18:24 AM UTC 2026
% Result : Theorem 0.07s 0.22s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 139 ( 37 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 188 ( 22 ~; 22 |; 0 &; 138 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 66 ( 0 ^; 66 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apart_point_and_line,type,
apart_point_and_line: $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_intersection_point,type,
intersection_point: $i > $i > $i ).
thf(tp_line_connecting,type,
line_connecting: $i > $i > $i ).
thf(tp_parallel_through_point,type,
parallel_through_point: $i > $i > $i ).
thf(tp_sK1_X,type,
sK1_X: $i ).
thf(3,axiom,
! [X: $i,Y: $i] :
~ ( convergent_lines @ ( parallel_through_point @ Y @ X ) @ Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp1) ).
thf(4,axiom,
! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ( distinct_lines @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq3) ).
thf(10,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart6) ).
thf(13,axiom,
! [X: $i] :
~ ( convergent_lines @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart3) ).
thf(16,conjecture,
! [X: $i] :
~ ( convergent_lines @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(17,negated_conjecture,
( ( ! [X: $i] :
~ ( convergent_lines @ X @ X ) )
= $false ),
inference(negate_conjecture,[status(cth)],[16]) ).
thf(18,plain,
( ( ! [X: $i] :
~ ( convergent_lines @ X @ X ) )
= $false ),
inference(unfold_def,[status(thm)],[17]) ).
thf(19,plain,
( ( ! [X: $i,Y: $i] :
~ ( convergent_lines @ ( parallel_through_point @ Y @ X ) @ Y ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ( distinct_lines @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(21,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(22,plain,
( ( ! [X: $i] :
~ ( convergent_lines @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(23,plain,
( ( ~ ( convergent_lines @ sK1_X @ sK1_X ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(24,plain,
( ( convergent_lines @ sK1_X @ sK1_X )
= $true ),
inference(polarity_switch,[status(thm)],[23]) ).
thf(25,plain,
( ( ! [X: $i] :
~ ( convergent_lines @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(26,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ( distinct_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(28,plain,
( ( ! [X: $i,Y: $i] :
~ ( convergent_lines @ ( parallel_through_point @ Y @ X ) @ Y ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(29,plain,
( ( convergent_lines @ sK1_X @ sK1_X )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(30,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( convergent_lines @ SX0 @ SX2 )
| ( convergent_lines @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(31,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( distinct_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(32,plain,
! [SV1: $i] :
( ( ~ ( convergent_lines @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(33,plain,
! [SV2: $i] :
( ( ! [SY9: $i] :
~ ( convergent_lines @ ( parallel_through_point @ SY9 @ SV2 ) @ SY9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(34,plain,
! [SV3: $i] :
( ( ! [SY10: $i,SY11: $i] :
( ~ ( convergent_lines @ SV3 @ SY10 )
| ( convergent_lines @ SV3 @ SY11 )
| ( convergent_lines @ SY10 @ SY11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV4: $i] :
( ( ! [SY12: $i] :
( ~ ( convergent_lines @ SV4 @ SY12 )
| ( distinct_lines @ SV4 @ SY12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV1: $i] :
( ( convergent_lines @ SV1 @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV2: $i,SV5: $i] :
( ( ~ ( convergent_lines @ ( parallel_through_point @ SV5 @ SV2 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV6: $i,SV3: $i] :
( ( ! [SY13: $i] :
( ~ ( convergent_lines @ SV3 @ SV6 )
| ( convergent_lines @ SV3 @ SY13 )
| ( convergent_lines @ SV6 @ SY13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV7: $i,SV4: $i] :
( ( ~ ( convergent_lines @ SV4 @ SV7 )
| ( distinct_lines @ SV4 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV2: $i,SV5: $i] :
( ( convergent_lines @ ( parallel_through_point @ SV5 @ SV2 ) @ SV5 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ~ ( convergent_lines @ SV3 @ SV6 )
| ( convergent_lines @ SV3 @ SV8 )
| ( convergent_lines @ SV6 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV7: $i,SV4: $i] :
( ( ( ~ ( convergent_lines @ SV4 @ SV7 ) )
= $true )
| ( ( distinct_lines @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( convergent_lines @ SV3 @ SV6 ) )
= $true )
| ( ( ( convergent_lines @ SV3 @ SV8 )
| ( convergent_lines @ SV6 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(44,plain,
! [SV7: $i,SV4: $i] :
( ( ( convergent_lines @ SV4 @ SV7 )
= $false )
| ( ( distinct_lines @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(45,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ( convergent_lines @ SV3 @ SV6 )
= $false )
| ( ( ( convergent_lines @ SV3 @ SV8 )
| ( convergent_lines @ SV6 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(46,plain,
! [SV6: $i,SV8: $i,SV3: $i] :
( ( ( convergent_lines @ SV3 @ SV8 )
= $true )
| ( ( convergent_lines @ SV6 @ SV8 )
= $true )
| ( ( convergent_lines @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(47,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[29,46,44,40,36]) ).
thf(48,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO207+2 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.07/0.18 % Computer : n007.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 10:07:15 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.22
% 0.07/0.22 No.of.Axioms: 4
% 0.07/0.22
% 0.07/0.22 Length.of.Defs: 0
% 0.07/0.22
% 0.07/0.22 Contains.Choice.Funs: false
% 0.07/0.22
% 0.07/0.22 ********************************
% 0.07/0.22 * All subproblems solved! *
% 0.07/0.22 ********************************
% 0.07/0.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:4,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:47,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.22
% 0.07/0.22 %**** Beginning of derivation protocol ****
% 0.07/0.22 % SZS output start CNFRefutation
% See solution above
% 0.07/0.22
% 0.07/0.22 %**** End of derivation protocol ****
% 0.07/0.22 %**** no. of clauses in derivation: 37 ****
% 0.07/0.22 %**** clause counter: 47 ****
% 0.07/0.22
% 0.07/0.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:4,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:47,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------