%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP065^1 : TPTP v9.3.1. Released v7.5.0.
% 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 : 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 10:23:56 AM UTC 2026
% Result : Theorem 0.08s 0.23s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 79 ( 42 unt; 0 typ; 0 def)
% Number of atoms : 346 ( 185 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 492 ( 101 ~; 88 |; 0 &; 288 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 3 con; 0-3 aty)
% Number of variables : 169 ( 4 ^; 165 !; 0 ?; 169 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_b,type,
b: $tType ).
thf(tp_tree_b,type,
tree_b: $tType ).
thf(tp_e_b,type,
e_b: tree_b ).
thf(tp_heapIm1140443834left_b,type,
heapIm1140443834left_b: tree_b > tree_b ).
thf(tp_heapIm1257206335ight_b,type,
heapIm1257206335ight_b: tree_b > tree_b ).
thf(tp_heapIm229596387mpty_b,type,
heapIm229596387mpty_b: tree_b > $o ).
thf(tp_in_tree_b,type,
in_tree_b: b > tree_b > $o ).
thf(tp_ord_less_eq_Tree_b_o,type,
ord_less_eq_Tree_b_o: ( tree_b > $o ) > ( tree_b > $o ) > $o ).
thf(tp_ord_less_eq_b_o,type,
ord_less_eq_b_o: ( b > $o ) > ( b > $o ) > $o ).
thf(tp_pred_Tree_b,type,
pred_Tree_b: ( b > $o ) > tree_b > $o ).
thf(tp_sK1_SY17,type,
sK1_SY17: tree_b > b ).
thf(tp_sK2_SY28,type,
sK2_SY28: tree_b > tree_b ).
thf(tp_sK3_SY21,type,
sK3_SY21: tree_b > ( tree_b > $o ) > b ).
thf(tp_sK4_SY30,type,
sK4_SY30: tree_b > tree_b ).
thf(tp_sK5_SY31,type,
sK5_SY31: tree_b > ( tree_b > $o ) > tree_b ).
thf(tp_sK6_SY33,type,
sK6_SY33: tree_b > ( tree_b > $o ) > tree_b ).
thf(tp_t_b,type,
t_b: b > tree_b > tree_b > tree_b ).
thf(tp_val_b,type,
val_b: tree_b > b ).
thf(5,axiom,
! [X21: b,X22: tree_b,X23: tree_b] :
( e_b
!= ( t_b @ X21 @ X22 @ X23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_Tree_Odistinct_I1_J) ).
thf(6,axiom,
! [P: tree_b > $o,Tree: tree_b] :
( ( P @ e_b )
=> ( ! [X1: b,X2: tree_b,X3: tree_b] :
( ( P @ X2 )
=> ( ( P @ X3 )
=> ( P @ ( t_b @ X1 @ X2 @ X3 ) ) ) )
=> ( P @ Tree ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_Tree_Oinduct) ).
thf(7,axiom,
! [Y: tree_b] :
( ( Y != e_b )
=> ~ ! [X212: b,X222: tree_b,X232: tree_b] :
( Y
!= ( t_b @ X212 @ X222 @ X232 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_Tree_Oexhaust) ).
thf(11,axiom,
! [P: b > $o] : ( pred_Tree_b @ P @ e_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_Tree_Opred__inject_I1_J) ).
thf(12,axiom,
! [V: b] :
~ ( in_tree_b @ V @ e_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_in__tree_Osimps_I1_J) ).
thf(13,axiom,
( heapIm229596387mpty_b
= ( ^ [T: tree_b] : ( T = e_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_hs__is__empty__def) ).
thf(14,conjecture,
heapIm229596387mpty_b @ e_b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(15,negated_conjecture,
( ( heapIm229596387mpty_b @ e_b )
= $false ),
inference(negate_conjecture,[status(cth)],[14]) ).
thf(16,plain,
( ( heapIm229596387mpty_b @ e_b )
= $false ),
inference(unfold_def,[status(thm)],[15]) ).
thf(17,plain,
( ( ! [X21: b,X22: tree_b,X23: tree_b] :
( e_b
!= ( t_b @ X21 @ X22 @ X23 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(18,plain,
( ( ! [P: tree_b > $o,Tree: tree_b] :
( ( P @ e_b )
=> ( ! [X1: b,X2: tree_b,X3: tree_b] :
( ( P @ X2 )
=> ( ( P @ X3 )
=> ( P @ ( t_b @ X1 @ X2 @ X3 ) ) ) )
=> ( P @ Tree ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(19,plain,
( ( ! [Y: tree_b] :
( ( Y != e_b )
=> ~ ! [X212: b,X222: tree_b,X232: tree_b] :
( Y
!= ( t_b @ X212 @ X222 @ X232 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(20,plain,
( ( ! [P: b > $o] : ( pred_Tree_b @ P @ e_b ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(21,plain,
( ( ! [V: b] :
~ ( in_tree_b @ V @ e_b ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(22,plain,
( ( heapIm229596387mpty_b
= ( ^ [T: tree_b] : ( T = e_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(23,plain,
( ( ~ ( heapIm229596387mpty_b @ e_b ) )
= $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(24,plain,
( ( heapIm229596387mpty_b
= ( ^ [T: tree_b] : ( T = e_b ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(25,plain,
( ( ! [V: b] :
~ ( in_tree_b @ V @ e_b ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(26,plain,
( ( ! [P: b > $o] : ( pred_Tree_b @ P @ e_b ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(27,plain,
( ( ! [Y: tree_b] :
( ( Y != e_b )
=> ~ ! [X212: b,X222: tree_b,X232: tree_b] :
( Y
!= ( t_b @ X212 @ X222 @ X232 ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(28,plain,
( ( ! [P: tree_b > $o,Tree: tree_b] :
( ( P @ e_b )
=> ( ! [X1: b,X2: tree_b,X3: tree_b] :
( ( P @ X2 )
=> ( ( P @ X3 )
=> ( P @ ( t_b @ X1 @ X2 @ X3 ) ) ) )
=> ( P @ Tree ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(29,plain,
( ( ! [X21: b,X22: tree_b,X23: tree_b] :
( e_b
!= ( t_b @ X21 @ X22 @ X23 ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(30,plain,
( ( ~ ( heapIm229596387mpty_b @ e_b ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(31,plain,
( ( ! [SX0: b,SX1: tree_b,SX2: tree_b] :
( e_b
!= ( t_b @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(32,plain,
( ( ! [SX0: tree_b] :
( ~ ( ( SX0 != e_b ) )
| ~ ! [SX1: b,SX2: tree_b,SX3: tree_b] :
( SX0
!= ( t_b @ SX1 @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(33,plain,
( ( ! [SX0: tree_b > $o,SX1: tree_b] :
( ~ ( SX0 @ e_b )
| ~ ! [SX2: b,SX3: tree_b,SX4: tree_b] :
( ~ ( SX0 @ SX3 )
| ~ ( SX0 @ SX4 )
| ( SX0 @ ( t_b @ SX2 @ SX3 @ SX4 ) ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(34,plain,
( ( ! [SV1: tree_b] :
( ( heapIm229596387mpty_b @ SV1 )
= ( SV1 = e_b ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[24]) ).
thf(35,plain,
( ( heapIm229596387mpty_b
= ( ^ [T: tree_b] : ( T = e_b ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[24]) ).
thf(36,plain,
! [SV2: b] :
( ( ~ ( in_tree_b @ SV2 @ e_b ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(37,plain,
! [SV3: b > $o] :
( ( pred_Tree_b @ SV3 @ e_b )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(38,plain,
( ( heapIm229596387mpty_b @ e_b )
= $false ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(39,plain,
! [SV4: b] :
( ( ! [SY15: tree_b,SY16: tree_b] :
( e_b
!= ( t_b @ SV4 @ SY15 @ SY16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(40,plain,
! [SV5: tree_b] :
( ( ~ ( ( SV5 != e_b ) )
| ~ ! [SY17: b,SY18: tree_b,SY19: tree_b] :
( SV5
!= ( t_b @ SY17 @ SY18 @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(41,plain,
! [SV6: tree_b > $o] :
( ( ! [SY20: tree_b] :
( ~ ( SV6 @ e_b )
| ~ ! [SY21: b,SY22: tree_b,SY23: tree_b] :
( ~ ( SV6 @ SY22 )
| ~ ( SV6 @ SY23 )
| ( SV6 @ ( t_b @ SY21 @ SY22 @ SY23 ) ) )
| ( SV6 @ SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(42,plain,
! [SV7: tree_b] :
( ( ( heapIm229596387mpty_b @ SV7 )
= ( SV7 = e_b ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(43,plain,
! [SV2: b] :
( ( in_tree_b @ SV2 @ e_b )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(44,plain,
! [SV8: tree_b,SV4: b] :
( ( ! [SY24: tree_b] :
( e_b
!= ( t_b @ SV4 @ SV8 @ SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(45,plain,
! [SV5: tree_b] :
( ( ( ~ ( ( SV5 != e_b ) ) )
= $true )
| ( ( ~ ! [SY17: b,SY18: tree_b,SY19: tree_b] :
( SV5
!= ( t_b @ SY17 @ SY18 @ SY19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(46,plain,
! [SV9: tree_b,SV6: tree_b > $o] :
( ( ~ ( SV6 @ e_b )
| ~ ! [SY21: b,SY22: tree_b,SY23: tree_b] :
( ~ ( SV6 @ SY22 )
| ~ ( SV6 @ SY23 )
| ( SV6 @ ( t_b @ SY21 @ SY22 @ SY23 ) ) )
| ( SV6 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(47,plain,
! [SV7: tree_b] :
( ( ~ ( ( heapIm229596387mpty_b @ SV7 )
| ( SV7 = e_b ) )
| ~ ( ~ ( heapIm229596387mpty_b @ SV7 )
| ( SV7 != e_b ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[42]) ).
thf(48,plain,
! [SV7: tree_b] :
( ( ( heapIm229596387mpty_b @ SV7 )
= ( SV7 = e_b ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[42]) ).
thf(49,plain,
! [SV10: tree_b,SV8: tree_b,SV4: b] :
( ( e_b
!= ( t_b @ SV4 @ SV8 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(50,plain,
! [SV5: tree_b] :
( ( ( SV5 != e_b )
= $false )
| ( ( ~ ! [SY17: b,SY18: tree_b,SY19: tree_b] :
( SV5
!= ( t_b @ SY17 @ SY18 @ SY19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(51,plain,
! [SV9: tree_b,SV6: tree_b > $o] :
( ( ( ~ ( SV6 @ e_b ) )
= $true )
| ( ( ~ ! [SY21: b,SY22: tree_b,SY23: tree_b] :
( ~ ( SV6 @ SY22 )
| ~ ( SV6 @ SY23 )
| ( SV6 @ ( t_b @ SY21 @ SY22 @ SY23 ) ) )
| ( SV6 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(52,plain,
! [SV7: tree_b] :
( ( ( ~ ( ( heapIm229596387mpty_b @ SV7 )
| ( SV7 = e_b ) ) )
= $true )
| ( ( ~ ( ~ ( heapIm229596387mpty_b @ SV7 )
| ( SV7 != e_b ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(53,plain,
! [SV10: tree_b,SV8: tree_b,SV4: b] :
( ( e_b
= ( t_b @ SV4 @ SV8 @ SV10 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(54,plain,
! [SV5: tree_b] :
( ( ( SV5 = e_b )
= $true )
| ( ( ~ ! [SY17: b,SY18: tree_b,SY19: tree_b] :
( SV5
!= ( t_b @ SY17 @ SY18 @ SY19 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(55,plain,
! [SV9: tree_b,SV6: tree_b > $o] :
( ( ( SV6 @ e_b )
= $false )
| ( ( ~ ! [SY21: b,SY22: tree_b,SY23: tree_b] :
( ~ ( SV6 @ SY22 )
| ~ ( SV6 @ SY23 )
| ( SV6 @ ( t_b @ SY21 @ SY22 @ SY23 ) ) )
| ( SV6 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(56,plain,
! [SV7: tree_b] :
( ( ( ( heapIm229596387mpty_b @ SV7 )
| ( SV7 = e_b ) )
= $false )
| ( ( ~ ( ~ ( heapIm229596387mpty_b @ SV7 )
| ( SV7 != e_b ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(57,plain,
! [SV5: tree_b] :
( ( ( ! [SY17: b,SY18: tree_b,SY19: tree_b] :
( SV5
!= ( t_b @ SY17 @ SY18 @ SY19 ) ) )
= $false )
| ( ( SV5 = e_b )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(58,plain,
! [SV9: tree_b,SV6: tree_b > $o] :
( ( ( ~ ! [SY21: b,SY22: tree_b,SY23: tree_b] :
( ~ ( SV6 @ SY22 )
| ~ ( SV6 @ SY23 )
| ( SV6 @ ( t_b @ SY21 @ SY22 @ SY23 ) ) ) )
= $true )
| ( ( SV6 @ SV9 )
= $true )
| ( ( SV6 @ e_b )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(59,plain,
! [SV7: tree_b] :
( ( ( heapIm229596387mpty_b @ SV7 )
= $false )
| ( ( ~ ( ~ ( heapIm229596387mpty_b @ SV7 )
| ( SV7 != e_b ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(60,plain,
! [SV7: tree_b] :
( ( ( SV7 = e_b )
= $false )
| ( ( ~ ( ~ ( heapIm229596387mpty_b @ SV7 )
| ( SV7 != e_b ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(61,plain,
! [SV5: tree_b] :
( ( ( ! [SY28: tree_b,SY29: tree_b] :
( SV5
!= ( t_b @ ( sK1_SY17 @ SV5 ) @ SY28 @ SY29 ) ) )
= $false )
| ( ( SV5 = e_b )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[57]) ).
thf(62,plain,
! [SV9: tree_b,SV6: tree_b > $o] :
( ( ( ! [SY21: b,SY22: tree_b,SY23: tree_b] :
( ~ ( SV6 @ SY22 )
| ~ ( SV6 @ SY23 )
| ( SV6 @ ( t_b @ SY21 @ SY22 @ SY23 ) ) ) )
= $false )
| ( ( SV6 @ SV9 )
= $true )
| ( ( SV6 @ e_b )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV7: tree_b] :
( ( ( ~ ( heapIm229596387mpty_b @ SV7 )
| ( SV7 != e_b ) )
= $false )
| ( ( heapIm229596387mpty_b @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(64,plain,
! [SV7: tree_b] :
( ( ( ~ ( heapIm229596387mpty_b @ SV7 )
| ( SV7 != e_b ) )
= $false )
| ( ( SV7 = e_b )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(65,plain,
! [SV5: tree_b] :
( ( ( ! [SY30: tree_b] :
( SV5
!= ( t_b @ ( sK1_SY17 @ SV5 ) @ ( sK2_SY28 @ SV5 ) @ SY30 ) ) )
= $false )
| ( ( SV5 = e_b )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[61]) ).
thf(66,plain,
! [SV9: tree_b,SV6: tree_b > $o] :
( ( ( ! [SY31: tree_b,SY32: tree_b] :
( ~ ( SV6 @ SY31 )
| ~ ( SV6 @ SY32 )
| ( SV6 @ ( t_b @ ( sK3_SY21 @ SV9 @ SV6 ) @ SY31 @ SY32 ) ) ) )
= $false )
| ( ( SV6 @ SV9 )
= $true )
| ( ( SV6 @ e_b )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[62]) ).
thf(67,plain,
! [SV7: tree_b] :
( ( ( ~ ( heapIm229596387mpty_b @ SV7 ) )
= $false )
| ( ( heapIm229596387mpty_b @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(68,plain,
! [SV7: tree_b] :
( ( ( SV7 != e_b )
= $false )
| ( ( heapIm229596387mpty_b @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(69,plain,
! [SV7: tree_b] :
( ( ( ~ ( heapIm229596387mpty_b @ SV7 ) )
= $false )
| ( ( SV7 = e_b )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(70,plain,
! [SV7: tree_b] :
( ( ( SV7 != e_b )
= $false )
| ( ( SV7 = e_b )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(71,plain,
! [SV5: tree_b] :
( ( ( SV5
!= ( t_b @ ( sK1_SY17 @ SV5 ) @ ( sK2_SY28 @ SV5 ) @ ( sK4_SY30 @ SV5 ) ) )
= $false )
| ( ( SV5 = e_b )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[65]) ).
thf(72,plain,
! [SV9: tree_b,SV6: tree_b > $o] :
( ( ( ! [SY33: tree_b] :
( ~ ( SV6 @ ( sK5_SY31 @ SV9 @ SV6 ) )
| ~ ( SV6 @ SY33 )
| ( SV6 @ ( t_b @ ( sK3_SY21 @ SV9 @ SV6 ) @ ( sK5_SY31 @ SV9 @ SV6 ) @ SY33 ) ) ) )
= $false )
| ( ( SV6 @ SV9 )
= $true )
| ( ( SV6 @ e_b )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[66]) ).
thf(73,plain,
! [SV7: tree_b] :
( ( ( heapIm229596387mpty_b @ SV7 )
= $true )
| ( ( heapIm229596387mpty_b @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(74,plain,
! [SV7: tree_b] :
( ( ( SV7 = e_b )
= $true )
| ( ( heapIm229596387mpty_b @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(75,plain,
! [SV7: tree_b] :
( ( ( heapIm229596387mpty_b @ SV7 )
= $true )
| ( ( SV7 = e_b )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(76,plain,
! [SV7: tree_b] :
( ( ( SV7 = e_b )
= $true )
| ( ( SV7 = e_b )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(77,plain,
! [SV5: tree_b] :
( ( ( SV5
= ( t_b @ ( sK1_SY17 @ SV5 ) @ ( sK2_SY28 @ SV5 ) @ ( sK4_SY30 @ SV5 ) ) )
= $true )
| ( ( SV5 = e_b )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(78,plain,
! [SV9: tree_b,SV6: tree_b > $o] :
( ( ( ~ ( SV6 @ ( sK5_SY31 @ SV9 @ SV6 ) )
| ~ ( SV6 @ ( sK6_SY33 @ SV9 @ SV6 ) )
| ( SV6 @ ( t_b @ ( sK3_SY21 @ SV9 @ SV6 ) @ ( sK5_SY31 @ SV9 @ SV6 ) @ ( sK6_SY33 @ SV9 @ SV6 ) ) ) )
= $false )
| ( ( SV6 @ SV9 )
= $true )
| ( ( SV6 @ e_b )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[72]) ).
thf(79,plain,
! [SV9: tree_b,SV6: tree_b > $o] :
( ( ( ~ ( SV6 @ ( sK5_SY31 @ SV9 @ SV6 ) ) )
= $false )
| ( ( SV6 @ SV9 )
= $true )
| ( ( SV6 @ e_b )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(80,plain,
! [SV9: tree_b,SV6: tree_b > $o] :
( ( ( ~ ( SV6 @ ( sK6_SY33 @ SV9 @ SV6 ) )
| ( SV6 @ ( t_b @ ( sK3_SY21 @ SV9 @ SV6 ) @ ( sK5_SY31 @ SV9 @ SV6 ) @ ( sK6_SY33 @ SV9 @ SV6 ) ) ) )
= $false )
| ( ( SV6 @ SV9 )
= $true )
| ( ( SV6 @ e_b )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(81,plain,
! [SV9: tree_b,SV6: tree_b > $o] :
( ( ( SV6 @ ( sK5_SY31 @ SV9 @ SV6 ) )
= $true )
| ( ( SV6 @ SV9 )
= $true )
| ( ( SV6 @ e_b )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(82,plain,
! [SV9: tree_b,SV6: tree_b > $o] :
( ( ( ~ ( SV6 @ ( sK6_SY33 @ SV9 @ SV6 ) ) )
= $false )
| ( ( SV6 @ SV9 )
= $true )
| ( ( SV6 @ e_b )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(83,plain,
! [SV9: tree_b,SV6: tree_b > $o] :
( ( ( SV6 @ ( t_b @ ( sK3_SY21 @ SV9 @ SV6 ) @ ( sK5_SY31 @ SV9 @ SV6 ) @ ( sK6_SY33 @ SV9 @ SV6 ) ) )
= $false )
| ( ( SV6 @ SV9 )
= $true )
| ( ( SV6 @ e_b )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(84,plain,
! [SV9: tree_b,SV6: tree_b > $o] :
( ( ( SV6 @ ( sK6_SY33 @ SV9 @ SV6 ) )
= $true )
| ( ( SV6 @ SV9 )
= $true )
| ( ( SV6 @ e_b )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(85,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[35,84,83,81,77,76,75,74,73,53,48,43,38,37]) ).
thf(86,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP065^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n007.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 11:13:15 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.23
% 0.08/0.23 No.of.Axioms: 6
% 0.08/0.23
% 0.08/0.23 Length.of.Defs: 0
% 0.08/0.23
% 0.08/0.23 Contains.Choice.Funs: false
% 0.08/0.23 .
% 0.08/0.23
% 0.08/0.23 ********************************
% 0.08/0.23 * All subproblems solved! *
% 0.08/0.23 ********************************
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox2/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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:85,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.23
% 0.08/0.23 %**** Beginning of derivation protocol ****
% 0.08/0.23 % SZS output start CNFRefutation
% See solution above
% 0.08/0.23
% 0.08/0.23 %**** End of derivation protocol ****
% 0.08/0.23 %**** no. of clauses in derivation: 79 ****
% 0.08/0.23 %**** clause counter: 85 ****
% 0.08/0.23
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox2/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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:85,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------