TSTP Solution File: GEO002-4 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GEO002-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 05:05:52 EDT 2022
% Result : Unsatisfiable 0.20s 0.45s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 92 ( 54 unt; 7 typ; 0 def)
% Number of atoms : 412 ( 109 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 938 ( 90 ~; 109 |; 0 &; 739 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-5 aty)
% Number of variables : 309 ( 0 ^ 309 !; 0 ?; 309 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_between,type,
between: $i > $i > $i > $o ).
thf(tp_equalish,type,
equalish: $i > $i > $o ).
thf(tp_equidistant,type,
equidistant: $i > $i > $i > $i > $o ).
thf(tp_extension,type,
extension: $i > $i > $i > $i > $i ).
thf(tp_outer_pasch,type,
outer_pasch: $i > $i > $i > $i > $i > $i ).
thf(1,axiom,
! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( between @ W @ Z @ X )
| ( between @ W @ Z @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_substitution3) ).
thf(2,axiom,
! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).
thf(3,axiom,
! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction1) ).
thf(4,axiom,
! [X: $i,W: $i,V: $i,Y: $i,Z: $i] :
( ~ ( between @ X @ W @ V )
| ~ ( between @ Y @ V @ Z )
| ( between @ Z @ W @ ( outer_pasch @ W @ X @ Y @ Z @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_pasch2) ).
thf(5,axiom,
! [X: $i,W: $i,V: $i,Y: $i,Z: $i] :
( ~ ( between @ X @ W @ V )
| ~ ( between @ Y @ V @ Z )
| ( between @ X @ ( outer_pasch @ W @ X @ Y @ Z @ V ) @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_pasch1) ).
thf(6,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( equalish @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
thf(7,axiom,
! [X: $i,Y: $i,V: $i,Z: $i] :
( ~ ( between @ X @ Y @ V )
| ~ ( between @ Y @ Z @ V )
| ( between @ X @ Y @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_for_betweeness) ).
thf(8,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(9,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[8]) ).
thf(10,negated_conjecture,
~ ( between @ a @ a @ b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_between_a_and_b) ).
thf(11,plain,
$false = $false,
inference(unfold_def,[status(thm)],[9]) ).
thf(12,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( between @ W @ Z @ X )
| ( between @ W @ Z @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(13,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(14,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [X: $i,W: $i,V: $i,Y: $i,Z: $i] :
( ~ ( between @ X @ W @ V )
| ~ ( between @ Y @ V @ Z )
| ( between @ Z @ W @ ( outer_pasch @ W @ X @ Y @ Z @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(16,plain,
( ( ! [X: $i,W: $i,V: $i,Y: $i,Z: $i] :
( ~ ( between @ X @ W @ V )
| ~ ( between @ Y @ V @ Z )
| ( between @ X @ ( outer_pasch @ W @ X @ Y @ Z @ V ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( equalish @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(18,plain,
( ( ! [X: $i,Y: $i,V: $i,Z: $i] :
( ~ ( between @ X @ Y @ V )
| ~ ( between @ Y @ Z @ V )
| ( between @ X @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(19,plain,
( ( ~ ( between @ a @ a @ b ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(20,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(21,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i,Z: $i] :
( ~ ( between @ W @ Z @ X )
| ( between @ W @ Z @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(22,plain,
( ( ! [X: $i,W: $i,V: $i] :
( ~ ( between @ X @ W @ V )
| ! [Y: $i,Z: $i] :
( ~ ( between @ Y @ V @ Z )
| ( between @ Z @ W @ ( outer_pasch @ W @ X @ Y @ Z @ V ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(23,plain,
( ( ! [X: $i,W: $i,V: $i] :
( ~ ( between @ X @ W @ V )
| ! [Y: $i,Z: $i] :
( ~ ( between @ Y @ V @ Z )
| ( between @ X @ ( outer_pasch @ W @ X @ Y @ Z @ V ) @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(24,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
~ ( equidistant @ X @ Y @ Z @ Z )
| ( equalish @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(25,plain,
( ( ! [X: $i,Y: $i,V: $i] :
( ~ ( between @ X @ Y @ V )
| ! [Z: $i] :
( ~ ( between @ Y @ Z @ V )
| ( between @ X @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(26,plain,
( ( ~ ( between @ a @ a @ b ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i,V: $i] :
( ~ ( between @ X @ Y @ V )
| ! [Z: $i] :
( ~ ( between @ Y @ Z @ V )
| ( between @ X @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(28,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
~ ( equidistant @ X @ Y @ Z @ Z )
| ( equalish @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(29,plain,
( ( ! [X: $i,W: $i,V: $i] :
( ~ ( between @ X @ W @ V )
| ! [Y: $i,Z: $i] :
( ~ ( between @ Y @ V @ Z )
| ( between @ X @ ( outer_pasch @ W @ X @ Y @ Z @ V ) @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(30,plain,
( ( ! [X: $i,W: $i,V: $i] :
( ~ ( between @ X @ W @ V )
| ! [Y: $i,Z: $i] :
( ~ ( between @ Y @ V @ Z )
| ( between @ Z @ W @ ( outer_pasch @ W @ X @ Y @ Z @ V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(31,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(32,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(33,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i,Z: $i] :
( ~ ( between @ W @ Z @ X )
| ( between @ W @ Z @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(34,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(35,plain,
( ( between @ a @ a @ b )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(36,plain,
! [SV1: $i] :
( ( ! [SY29: $i,SY30: $i] :
( ~ ( between @ SV1 @ SY29 @ SY30 )
| ! [SY31: $i] :
( ~ ( between @ SY29 @ SY31 @ SY30 )
| ( between @ SV1 @ SY29 @ SY31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(37,plain,
! [SV2: $i] :
( ( ! [SY32: $i] :
( ! [SY33: $i] :
~ ( equidistant @ SV2 @ SY32 @ SY33 @ SY33 )
| ( equalish @ SV2 @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(38,plain,
! [SV3: $i] :
( ( ! [SY34: $i,SY35: $i] :
( ~ ( between @ SV3 @ SY34 @ SY35 )
| ! [SY36: $i,SY37: $i] :
( ~ ( between @ SY36 @ SY35 @ SY37 )
| ( between @ SV3 @ ( outer_pasch @ SY34 @ SV3 @ SY36 @ SY37 @ SY35 ) @ SY36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(39,plain,
! [SV4: $i] :
( ( ! [SY38: $i,SY39: $i] :
( ~ ( between @ SV4 @ SY38 @ SY39 )
| ! [SY40: $i,SY41: $i] :
( ~ ( between @ SY40 @ SY39 @ SY41 )
| ( between @ SY41 @ SY38 @ ( outer_pasch @ SY38 @ SV4 @ SY40 @ SY41 @ SY39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(40,plain,
! [SV5: $i] :
( ( ! [SY42: $i,SY43: $i,SY44: $i] : ( between @ SV5 @ SY42 @ ( extension @ SV5 @ SY42 @ SY43 @ SY44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(41,plain,
! [SV6: $i] :
( ( ! [SY45: $i,SY46: $i,SY47: $i] : ( equidistant @ SV6 @ ( extension @ SY45 @ SV6 @ SY46 @ SY47 ) @ SY46 @ SY47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(42,plain,
! [SV7: $i] :
( ( ! [SY48: $i] :
( ~ ( equalish @ SV7 @ SY48 )
| ! [SY49: $i,SY50: $i] :
( ~ ( between @ SY49 @ SY50 @ SV7 )
| ( between @ SY49 @ SY50 @ SY48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(43,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(44,plain,
! [SV8: $i,SV1: $i] :
( ( ! [SY51: $i] :
( ~ ( between @ SV1 @ SV8 @ SY51 )
| ! [SY52: $i] :
( ~ ( between @ SV8 @ SY52 @ SY51 )
| ( between @ SV1 @ SV8 @ SY52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(45,plain,
! [SV9: $i,SV2: $i] :
( ( ! [SY53: $i] :
~ ( equidistant @ SV2 @ SV9 @ SY53 @ SY53 )
| ( equalish @ SV2 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(46,plain,
! [SV10: $i,SV3: $i] :
( ( ! [SY54: $i] :
( ~ ( between @ SV3 @ SV10 @ SY54 )
| ! [SY55: $i,SY56: $i] :
( ~ ( between @ SY55 @ SY54 @ SY56 )
| ( between @ SV3 @ ( outer_pasch @ SV10 @ SV3 @ SY55 @ SY56 @ SY54 ) @ SY55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(47,plain,
! [SV11: $i,SV4: $i] :
( ( ! [SY57: $i] :
( ~ ( between @ SV4 @ SV11 @ SY57 )
| ! [SY58: $i,SY59: $i] :
( ~ ( between @ SY58 @ SY57 @ SY59 )
| ( between @ SY59 @ SV11 @ ( outer_pasch @ SV11 @ SV4 @ SY58 @ SY59 @ SY57 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(48,plain,
! [SV12: $i,SV5: $i] :
( ( ! [SY60: $i,SY61: $i] : ( between @ SV5 @ SV12 @ ( extension @ SV5 @ SV12 @ SY60 @ SY61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(49,plain,
! [SV13: $i,SV6: $i] :
( ( ! [SY62: $i,SY63: $i] : ( equidistant @ SV6 @ ( extension @ SV13 @ SV6 @ SY62 @ SY63 ) @ SY62 @ SY63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(50,plain,
! [SV14: $i,SV7: $i] :
( ( ~ ( equalish @ SV7 @ SV14 )
| ! [SY64: $i,SY65: $i] :
( ~ ( between @ SY64 @ SY65 @ SV7 )
| ( between @ SY64 @ SY65 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(51,plain,
! [SV15: $i,SV8: $i,SV1: $i] :
( ( ~ ( between @ SV1 @ SV8 @ SV15 )
| ! [SY66: $i] :
( ~ ( between @ SV8 @ SY66 @ SV15 )
| ( between @ SV1 @ SV8 @ SY66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(52,plain,
! [SV9: $i,SV2: $i] :
( ( ( ! [SY53: $i] :
~ ( equidistant @ SV2 @ SV9 @ SY53 @ SY53 ) )
= $true )
| ( ( equalish @ SV2 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(53,plain,
! [SV16: $i,SV10: $i,SV3: $i] :
( ( ~ ( between @ SV3 @ SV10 @ SV16 )
| ! [SY67: $i,SY68: $i] :
( ~ ( between @ SY67 @ SV16 @ SY68 )
| ( between @ SV3 @ ( outer_pasch @ SV10 @ SV3 @ SY67 @ SY68 @ SV16 ) @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(54,plain,
! [SV17: $i,SV11: $i,SV4: $i] :
( ( ~ ( between @ SV4 @ SV11 @ SV17 )
| ! [SY69: $i,SY70: $i] :
( ~ ( between @ SY69 @ SV17 @ SY70 )
| ( between @ SY70 @ SV11 @ ( outer_pasch @ SV11 @ SV4 @ SY69 @ SY70 @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(55,plain,
! [SV18: $i,SV12: $i,SV5: $i] :
( ( ! [SY71: $i] : ( between @ SV5 @ SV12 @ ( extension @ SV5 @ SV12 @ SV18 @ SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(56,plain,
! [SV19: $i,SV13: $i,SV6: $i] :
( ( ! [SY72: $i] : ( equidistant @ SV6 @ ( extension @ SV13 @ SV6 @ SV19 @ SY72 ) @ SV19 @ SY72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(57,plain,
! [SV14: $i,SV7: $i] :
( ( ( ~ ( equalish @ SV7 @ SV14 ) )
= $true )
| ( ( ! [SY64: $i,SY65: $i] :
( ~ ( between @ SY64 @ SY65 @ SV7 )
| ( between @ SY64 @ SY65 @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(58,plain,
! [SV15: $i,SV8: $i,SV1: $i] :
( ( ( ~ ( between @ SV1 @ SV8 @ SV15 ) )
= $true )
| ( ( ! [SY66: $i] :
( ~ ( between @ SV8 @ SY66 @ SV15 )
| ( between @ SV1 @ SV8 @ SY66 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(59,plain,
! [SV20: $i,SV9: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV9 @ SV20 @ SV20 ) )
= $true )
| ( ( equalish @ SV2 @ SV9 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(60,plain,
! [SV16: $i,SV10: $i,SV3: $i] :
( ( ( ~ ( between @ SV3 @ SV10 @ SV16 ) )
= $true )
| ( ( ! [SY67: $i,SY68: $i] :
( ~ ( between @ SY67 @ SV16 @ SY68 )
| ( between @ SV3 @ ( outer_pasch @ SV10 @ SV3 @ SY67 @ SY68 @ SV16 ) @ SY67 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(61,plain,
! [SV17: $i,SV11: $i,SV4: $i] :
( ( ( ~ ( between @ SV4 @ SV11 @ SV17 ) )
= $true )
| ( ( ! [SY69: $i,SY70: $i] :
( ~ ( between @ SY69 @ SV17 @ SY70 )
| ( between @ SY70 @ SV11 @ ( outer_pasch @ SV11 @ SV4 @ SY69 @ SY70 @ SV17 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(62,plain,
! [SV21: $i,SV18: $i,SV12: $i,SV5: $i] :
( ( between @ SV5 @ SV12 @ ( extension @ SV5 @ SV12 @ SV18 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(63,plain,
! [SV22: $i,SV19: $i,SV13: $i,SV6: $i] :
( ( equidistant @ SV6 @ ( extension @ SV13 @ SV6 @ SV19 @ SV22 ) @ SV19 @ SV22 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(64,plain,
! [SV14: $i,SV7: $i] :
( ( ( equalish @ SV7 @ SV14 )
= $false )
| ( ( ! [SY64: $i,SY65: $i] :
( ~ ( between @ SY64 @ SY65 @ SV7 )
| ( between @ SY64 @ SY65 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(65,plain,
! [SV15: $i,SV8: $i,SV1: $i] :
( ( ( between @ SV1 @ SV8 @ SV15 )
= $false )
| ( ( ! [SY66: $i] :
( ~ ( between @ SV8 @ SY66 @ SV15 )
| ( between @ SV1 @ SV8 @ SY66 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(66,plain,
! [SV20: $i,SV9: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV9 @ SV20 @ SV20 )
= $false )
| ( ( equalish @ SV2 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(67,plain,
! [SV16: $i,SV10: $i,SV3: $i] :
( ( ( between @ SV3 @ SV10 @ SV16 )
= $false )
| ( ( ! [SY67: $i,SY68: $i] :
( ~ ( between @ SY67 @ SV16 @ SY68 )
| ( between @ SV3 @ ( outer_pasch @ SV10 @ SV3 @ SY67 @ SY68 @ SV16 ) @ SY67 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(68,plain,
! [SV17: $i,SV11: $i,SV4: $i] :
( ( ( between @ SV4 @ SV11 @ SV17 )
= $false )
| ( ( ! [SY69: $i,SY70: $i] :
( ~ ( between @ SY69 @ SV17 @ SY70 )
| ( between @ SY70 @ SV11 @ ( outer_pasch @ SV11 @ SV4 @ SY69 @ SY70 @ SV17 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(69,plain,
! [SV14: $i,SV7: $i,SV23: $i] :
( ( ( ! [SY73: $i] :
( ~ ( between @ SV23 @ SY73 @ SV7 )
| ( between @ SV23 @ SY73 @ SV14 ) ) )
= $true )
| ( ( equalish @ SV7 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(70,plain,
! [SV1: $i,SV15: $i,SV24: $i,SV8: $i] :
( ( ( ~ ( between @ SV8 @ SV24 @ SV15 )
| ( between @ SV1 @ SV8 @ SV24 ) )
= $true )
| ( ( between @ SV1 @ SV8 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(71,plain,
! [SV10: $i,SV3: $i,SV16: $i,SV25: $i] :
( ( ( ! [SY74: $i] :
( ~ ( between @ SV25 @ SV16 @ SY74 )
| ( between @ SV3 @ ( outer_pasch @ SV10 @ SV3 @ SV25 @ SY74 @ SV16 ) @ SV25 ) ) )
= $true )
| ( ( between @ SV3 @ SV10 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(72,plain,
! [SV4: $i,SV11: $i,SV17: $i,SV26: $i] :
( ( ( ! [SY75: $i] :
( ~ ( between @ SV26 @ SV17 @ SY75 )
| ( between @ SY75 @ SV11 @ ( outer_pasch @ SV11 @ SV4 @ SV26 @ SY75 @ SV17 ) ) ) )
= $true )
| ( ( between @ SV4 @ SV11 @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(73,plain,
! [SV14: $i,SV7: $i,SV27: $i,SV23: $i] :
( ( ( ~ ( between @ SV23 @ SV27 @ SV7 )
| ( between @ SV23 @ SV27 @ SV14 ) )
= $true )
| ( ( equalish @ SV7 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(74,plain,
! [SV1: $i,SV15: $i,SV24: $i,SV8: $i] :
( ( ( ~ ( between @ SV8 @ SV24 @ SV15 ) )
= $true )
| ( ( between @ SV1 @ SV8 @ SV24 )
= $true )
| ( ( between @ SV1 @ SV8 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(75,plain,
! [SV10: $i,SV3: $i,SV28: $i,SV16: $i,SV25: $i] :
( ( ( ~ ( between @ SV25 @ SV16 @ SV28 )
| ( between @ SV3 @ ( outer_pasch @ SV10 @ SV3 @ SV25 @ SV28 @ SV16 ) @ SV25 ) )
= $true )
| ( ( between @ SV3 @ SV10 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(76,plain,
! [SV4: $i,SV11: $i,SV29: $i,SV17: $i,SV26: $i] :
( ( ( ~ ( between @ SV26 @ SV17 @ SV29 )
| ( between @ SV29 @ SV11 @ ( outer_pasch @ SV11 @ SV4 @ SV26 @ SV29 @ SV17 ) ) )
= $true )
| ( ( between @ SV4 @ SV11 @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(77,plain,
! [SV14: $i,SV7: $i,SV27: $i,SV23: $i] :
( ( ( ~ ( between @ SV23 @ SV27 @ SV7 ) )
= $true )
| ( ( between @ SV23 @ SV27 @ SV14 )
= $true )
| ( ( equalish @ SV7 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(78,plain,
! [SV1: $i,SV15: $i,SV24: $i,SV8: $i] :
( ( ( between @ SV8 @ SV24 @ SV15 )
= $false )
| ( ( between @ SV1 @ SV8 @ SV24 )
= $true )
| ( ( between @ SV1 @ SV8 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(79,plain,
! [SV10: $i,SV3: $i,SV28: $i,SV16: $i,SV25: $i] :
( ( ( ~ ( between @ SV25 @ SV16 @ SV28 ) )
= $true )
| ( ( between @ SV3 @ ( outer_pasch @ SV10 @ SV3 @ SV25 @ SV28 @ SV16 ) @ SV25 )
= $true )
| ( ( between @ SV3 @ SV10 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(80,plain,
! [SV4: $i,SV11: $i,SV29: $i,SV17: $i,SV26: $i] :
( ( ( ~ ( between @ SV26 @ SV17 @ SV29 ) )
= $true )
| ( ( between @ SV29 @ SV11 @ ( outer_pasch @ SV11 @ SV4 @ SV26 @ SV29 @ SV17 ) )
= $true )
| ( ( between @ SV4 @ SV11 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(81,plain,
! [SV14: $i,SV7: $i,SV27: $i,SV23: $i] :
( ( ( between @ SV23 @ SV27 @ SV7 )
= $false )
| ( ( between @ SV23 @ SV27 @ SV14 )
= $true )
| ( ( equalish @ SV7 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(82,plain,
! [SV10: $i,SV3: $i,SV28: $i,SV16: $i,SV25: $i] :
( ( ( between @ SV25 @ SV16 @ SV28 )
= $false )
| ( ( between @ SV3 @ ( outer_pasch @ SV10 @ SV3 @ SV25 @ SV28 @ SV16 ) @ SV25 )
= $true )
| ( ( between @ SV3 @ SV10 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(83,plain,
! [SV4: $i,SV11: $i,SV29: $i,SV17: $i,SV26: $i] :
( ( ( between @ SV26 @ SV17 @ SV29 )
= $false )
| ( ( between @ SV29 @ SV11 @ ( outer_pasch @ SV11 @ SV4 @ SV26 @ SV29 @ SV17 ) )
= $true )
| ( ( between @ SV4 @ SV11 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(84,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[35,83,82,81,78,66,63,62,43]) ).
thf(85,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO002-4 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jun 18 09:06:53 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 8
% 0.13/0.36
% 0.13/0.36 Length.of.Defs: 0
% 0.13/0.36
% 0.13/0.36 Contains.Choice.Funs: false
% 0.13/0.37 (rf:0,axioms:8,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:10,loop_count:0,foatp_calls:0,translation:fof_full).....
% 0.20/0.45
% 0.20/0.45 ********************************
% 0.20/0.45 * All subproblems solved! *
% 0.20/0.45 ********************************
% 0.20/0.45 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:8,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:84,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.46
% 0.20/0.46 %**** Beginning of derivation protocol ****
% 0.20/0.46 % SZS output start CNFRefutation
% See solution above
% 0.20/0.46
% 0.20/0.46 %**** End of derivation protocol ****
% 0.20/0.46 %**** no. of clauses in derivation: 85 ****
% 0.20/0.46 %**** clause counter: 84 ****
% 0.20/0.46
% 0.20/0.46 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:8,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:84,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------