%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO171+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 10:18:07 AM UTC 2026
% Result : Theorem 0.08s 0.12s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 61 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 268 ( 67 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 366 ( 29 ~; 56 |; 0 &; 264 @)
% ( 0 <=>; 17 =>; 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; 4 con; 0-2 aty)
% Number of variables : 123 ( 0 ^; 123 !; 0 ?; 123 :)
% 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_sK1_X,type,
sK1_X: $i ).
thf(tp_sK2_SY15,type,
sK2_SY15: $i ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ( distinct_lines @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq3) ).
thf(2,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( apart_point_and_line @ X @ Y )
=> ( ( distinct_lines @ Y @ Z )
| ( apart_point_and_line @ X @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq2) ).
thf(7,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart6) ).
thf(8,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( distinct_lines @ X @ Y )
=> ( ( distinct_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart5) ).
thf(10,axiom,
! [X: $i] :
~ ( convergent_lines @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart3) ).
thf(11,axiom,
! [X: $i] :
~ ( distinct_lines @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart2) ).
thf(13,conjecture,
! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ( distinct_lines @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(14,negated_conjecture,
( ( ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ( distinct_lines @ X @ Y ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[13]) ).
thf(15,plain,
( ( ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ( distinct_lines @ X @ Y ) ) )
= $false ),
inference(unfold_def,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ( distinct_lines @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apart_point_and_line @ X @ Y )
=> ( ( distinct_lines @ Y @ Z )
| ( apart_point_and_line @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(18,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)],[7]) ).
thf(19,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( distinct_lines @ X @ Y )
=> ( ( distinct_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(20,plain,
( ( ! [X: $i] :
~ ( convergent_lines @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(21,plain,
( ( ! [X: $i] :
~ ( distinct_lines @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(22,plain,
( ( ! [SY15: $i] :
( ( convergent_lines @ sK1_X @ SY15 )
=> ( distinct_lines @ sK1_X @ SY15 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(23,plain,
( ( ( convergent_lines @ sK1_X @ sK2_SY15 )
=> ( distinct_lines @ sK1_X @ sK2_SY15 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[22]) ).
thf(24,plain,
( ( convergent_lines @ sK1_X @ sK2_SY15 )
= $true ),
inference(standard_cnf,[status(thm)],[23]) ).
thf(25,plain,
( ( distinct_lines @ sK1_X @ sK2_SY15 )
= $false ),
inference(standard_cnf,[status(thm)],[23]) ).
thf(26,plain,
( ( ~ ( distinct_lines @ sK1_X @ sK2_SY15 ) )
= $true ),
inference(polarity_switch,[status(thm)],[25]) ).
thf(27,plain,
( ( ! [X: $i] :
~ ( distinct_lines @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(28,plain,
( ( ! [X: $i] :
~ ( convergent_lines @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( distinct_lines @ X @ Y )
=> ( ( distinct_lines @ X @ Z )
| ( distinct_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(30,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(31,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apart_point_and_line @ X @ Y )
=> ( ( distinct_lines @ Y @ Z )
| ( apart_point_and_line @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(32,plain,
( ( ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ( distinct_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(33,plain,
( ( convergent_lines @ sK1_X @ sK2_SY15 )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(34,plain,
( ( ~ ( distinct_lines @ sK1_X @ sK2_SY15 ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(35,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( distinct_lines @ SX0 @ SX1 )
| ( distinct_lines @ SX0 @ SX2 )
| ( distinct_lines @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(36,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( apart_point_and_line @ SX0 @ SX1 )
| ( distinct_lines @ SX1 @ SX2 )
| ( apart_point_and_line @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(37,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)],[30]) ).
thf(38,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( distinct_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(39,plain,
! [SV1: $i] :
( ( ~ ( distinct_lines @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(40,plain,
! [SV2: $i] :
( ( ~ ( convergent_lines @ SV2 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(41,plain,
( ( distinct_lines @ sK1_X @ sK2_SY15 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(42,plain,
! [SV3: $i] :
( ( ! [SY16: $i,SY17: $i] :
( ~ ( distinct_lines @ SV3 @ SY16 )
| ( distinct_lines @ SV3 @ SY17 )
| ( distinct_lines @ SY16 @ SY17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(43,plain,
! [SV4: $i] :
( ( ! [SY18: $i,SY19: $i] :
( ~ ( apart_point_and_line @ SV4 @ SY18 )
| ( distinct_lines @ SY18 @ SY19 )
| ( apart_point_and_line @ SV4 @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(44,plain,
! [SV5: $i] :
( ( ! [SY20: $i,SY21: $i] :
( ~ ( convergent_lines @ SV5 @ SY20 )
| ( convergent_lines @ SV5 @ SY21 )
| ( convergent_lines @ SY20 @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(45,plain,
! [SV6: $i] :
( ( ! [SY22: $i] :
( ~ ( convergent_lines @ SV6 @ SY22 )
| ( distinct_lines @ SV6 @ SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(46,plain,
! [SV1: $i] :
( ( distinct_lines @ SV1 @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(47,plain,
! [SV2: $i] :
( ( convergent_lines @ SV2 @ SV2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(48,plain,
! [SV7: $i,SV3: $i] :
( ( ! [SY23: $i] :
( ~ ( distinct_lines @ SV3 @ SV7 )
| ( distinct_lines @ SV3 @ SY23 )
| ( distinct_lines @ SV7 @ SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(49,plain,
! [SV8: $i,SV4: $i] :
( ( ! [SY24: $i] :
( ~ ( apart_point_and_line @ SV4 @ SV8 )
| ( distinct_lines @ SV8 @ SY24 )
| ( apart_point_and_line @ SV4 @ SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(50,plain,
! [SV9: $i,SV5: $i] :
( ( ! [SY25: $i] :
( ~ ( convergent_lines @ SV5 @ SV9 )
| ( convergent_lines @ SV5 @ SY25 )
| ( convergent_lines @ SV9 @ SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(51,plain,
! [SV10: $i,SV6: $i] :
( ( ~ ( convergent_lines @ SV6 @ SV10 )
| ( distinct_lines @ SV6 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(52,plain,
! [SV11: $i,SV7: $i,SV3: $i] :
( ( ~ ( distinct_lines @ SV3 @ SV7 )
| ( distinct_lines @ SV3 @ SV11 )
| ( distinct_lines @ SV7 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV12: $i,SV8: $i,SV4: $i] :
( ( ~ ( apart_point_and_line @ SV4 @ SV8 )
| ( distinct_lines @ SV8 @ SV12 )
| ( apart_point_and_line @ SV4 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(54,plain,
! [SV13: $i,SV9: $i,SV5: $i] :
( ( ~ ( convergent_lines @ SV5 @ SV9 )
| ( convergent_lines @ SV5 @ SV13 )
| ( convergent_lines @ SV9 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV10: $i,SV6: $i] :
( ( ( ~ ( convergent_lines @ SV6 @ SV10 ) )
= $true )
| ( ( distinct_lines @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(56,plain,
! [SV11: $i,SV7: $i,SV3: $i] :
( ( ( ~ ( distinct_lines @ SV3 @ SV7 ) )
= $true )
| ( ( ( distinct_lines @ SV3 @ SV11 )
| ( distinct_lines @ SV7 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(57,plain,
! [SV12: $i,SV8: $i,SV4: $i] :
( ( ( ~ ( apart_point_and_line @ SV4 @ SV8 ) )
= $true )
| ( ( ( distinct_lines @ SV8 @ SV12 )
| ( apart_point_and_line @ SV4 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(58,plain,
! [SV13: $i,SV9: $i,SV5: $i] :
( ( ( ~ ( convergent_lines @ SV5 @ SV9 ) )
= $true )
| ( ( ( convergent_lines @ SV5 @ SV13 )
| ( convergent_lines @ SV9 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(59,plain,
! [SV10: $i,SV6: $i] :
( ( ( convergent_lines @ SV6 @ SV10 )
= $false )
| ( ( distinct_lines @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(60,plain,
! [SV11: $i,SV7: $i,SV3: $i] :
( ( ( distinct_lines @ SV3 @ SV7 )
= $false )
| ( ( ( distinct_lines @ SV3 @ SV11 )
| ( distinct_lines @ SV7 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(61,plain,
! [SV12: $i,SV8: $i,SV4: $i] :
( ( ( apart_point_and_line @ SV4 @ SV8 )
= $false )
| ( ( ( distinct_lines @ SV8 @ SV12 )
| ( apart_point_and_line @ SV4 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(62,plain,
! [SV13: $i,SV9: $i,SV5: $i] :
( ( ( convergent_lines @ SV5 @ SV9 )
= $false )
| ( ( ( convergent_lines @ SV5 @ SV13 )
| ( convergent_lines @ SV9 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV7: $i,SV11: $i,SV3: $i] :
( ( ( distinct_lines @ SV3 @ SV11 )
= $true )
| ( ( distinct_lines @ SV7 @ SV11 )
= $true )
| ( ( distinct_lines @ SV3 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(64,plain,
! [SV4: $i,SV12: $i,SV8: $i] :
( ( ( distinct_lines @ SV8 @ SV12 )
= $true )
| ( ( apart_point_and_line @ SV4 @ SV12 )
= $true )
| ( ( apart_point_and_line @ SV4 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(65,plain,
! [SV9: $i,SV13: $i,SV5: $i] :
( ( ( convergent_lines @ SV5 @ SV13 )
= $true )
| ( ( convergent_lines @ SV9 @ SV13 )
= $true )
| ( ( convergent_lines @ SV5 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(66,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[33,65,64,63,59,47,46,41]) ).
thf(67,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO171+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Oct 6 10:06:01 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.12
% 0.08/0.12 No.of.Axioms: 6
% 0.08/0.12
% 0.08/0.12 Length.of.Defs: 0
% 0.08/0.12
% 0.08/0.12 Contains.Choice.Funs: false
% 0.08/0.12 .
% 0.08/0.12
% 0.08/0.12 ********************************
% 0.08/0.12 * All subproblems solved! *
% 0.08/0.12 ********************************
% 0.08/0.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:7,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:66,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.12
% 0.08/0.12 %**** Beginning of derivation protocol ****
% 0.08/0.12 % SZS output start CNFRefutation
% See solution above
% 0.08/0.13
% 0.08/0.13 %**** End of derivation protocol ****
% 0.08/0.13 %**** no. of clauses in derivation: 61 ****
% 0.08/0.13 %**** clause counter: 66 ****
% 0.08/0.13
% 0.08/0.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:7,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:66,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------