%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP067^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 Sep 30 08:04:15 AM UTC 2026
% Result : Theorem 0.65s 0.41s
% Output : CNFRefutation 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 120 ( 37 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 1108 ( 45 ~; 39 |; 14 &; 991 @)
% ( 1 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 9 con; 0-3 aty)
% Number of variables : 96 ( 0 ^; 96 !; 0 ?; 96 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
tree_a: $tType ).
thf(decl_sort2,type,
a: $tType ).
thf(decl_27,type,
heapIm1140443833left_a: tree_a > tree_a ).
thf(decl_28,type,
heapIm1257206334ight_a: tree_a > tree_a ).
thf(decl_29,type,
heapIm1091024090Down_a: tree_a > tree_a ).
thf(decl_31,type,
t_a: a > tree_a > tree_a > tree_a ).
thf(decl_34,type,
in_tree_a: a > tree_a > $o ).
thf(decl_37,type,
val_a: tree_a > a ).
thf(decl_49,type,
ord_less_eq_a: a > a > $o ).
thf(decl_57,type,
l1: tree_a ).
thf(decl_58,type,
l2: tree_a ).
thf(decl_59,type,
r1: tree_a ).
thf(decl_60,type,
r2: tree_a ).
thf(decl_62,type,
v: a ).
thf(decl_63,type,
v1: a ).
thf(decl_64,type,
v2: a ).
thf(decl_65,type,
v3: a ).
thf(fact_15_siftDown_Osimps_I6_J,axiom,
! [X24: a,X25: tree_a,X26: tree_a,X27: a,X28: tree_a,X29: tree_a,X7: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X24 @ X25 @ X26 ) ) @ ( val_a @ ( t_a @ X27 @ X28 @ X29 ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X27 @ X28 @ X29 ) ) @ X7 )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X7 @ ( t_a @ X27 @ X28 @ X29 ) @ ( t_a @ X24 @ X25 @ X26 ) ) )
= ( t_a @ X7 @ ( t_a @ X27 @ X28 @ X29 ) @ ( t_a @ X24 @ X25 @ X26 ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X27 @ X28 @ X29 ) ) @ X7 )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X7 @ ( t_a @ X27 @ X28 @ X29 ) @ ( t_a @ X24 @ X25 @ X26 ) ) )
= ( t_a @ ( val_a @ ( t_a @ X27 @ X28 @ X29 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ X7 @ ( heapIm1140443833left_a @ ( t_a @ X27 @ X28 @ X29 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X27 @ X28 @ X29 ) ) ) ) @ ( t_a @ X24 @ X25 @ X26 ) ) ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X24 @ X25 @ X26 ) ) @ ( val_a @ ( t_a @ X27 @ X28 @ X29 ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X24 @ X25 @ X26 ) ) @ X7 )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X7 @ ( t_a @ X27 @ X28 @ X29 ) @ ( t_a @ X24 @ X25 @ X26 ) ) )
= ( t_a @ X7 @ ( t_a @ X27 @ X28 @ X29 ) @ ( t_a @ X24 @ X25 @ X26 ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X24 @ X25 @ X26 ) ) @ X7 )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X7 @ ( t_a @ X27 @ X28 @ X29 ) @ ( t_a @ X24 @ X25 @ X26 ) ) )
= ( t_a @ ( val_a @ ( t_a @ X24 @ X25 @ X26 ) ) @ ( t_a @ X27 @ X28 @ X29 ) @ ( heapIm1091024090Down_a @ ( t_a @ X7 @ ( heapIm1140443833left_a @ ( t_a @ X24 @ X25 @ X26 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X24 @ X25 @ X26 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2u5ArlhE4A/E---3.1_1220184.p',fact_15_siftDown_Osimps_I6_J) ).
thf(conj_0,conjecture,
in_tree_a @ v @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.2u5ArlhE4A/E---3.1_1220184.p',conj_0) ).
thf(fact_29_val_Osimps,axiom,
! [X7: a,X46: tree_a,X47: tree_a] :
( ( val_a @ ( t_a @ X7 @ X46 @ X47 ) )
= X7 ),
file('/export/starexec/sandbox2/tmp/tmp.2u5ArlhE4A/E---3.1_1220184.p',fact_29_val_Osimps) ).
thf(fact_8_left_Osimps,axiom,
! [X7: a,X9: tree_a,X10: tree_a] :
( ( heapIm1140443833left_a @ ( t_a @ X7 @ X9 @ X10 ) )
= X9 ),
file('/export/starexec/sandbox2/tmp/tmp.2u5ArlhE4A/E---3.1_1220184.p',fact_8_left_Osimps) ).
thf(fact_9_right_Osimps,axiom,
! [X7: a,X9: tree_a,X10: tree_a] :
( ( heapIm1257206334ight_a @ ( t_a @ X7 @ X9 @ X10 ) )
= X10 ),
file('/export/starexec/sandbox2/tmp/tmp.2u5ArlhE4A/E---3.1_1220184.p',fact_9_right_Osimps) ).
thf(fact_7__C5__1_Ohyps_C_I1_J,axiom,
( ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
=> ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ v3 )
=> ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) )
=> ( in_tree_a @ v @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2u5ArlhE4A/E---3.1_1220184.p',fact_7__C5__1_Ohyps_C_I1_J) ).
thf(fact_3__C5__1_Oprems_C,axiom,
in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2u5ArlhE4A/E---3.1_1220184.p',fact_3__C5__1_Oprems_C) ).
thf(fact_2_True,axiom,
ord_less_eq_a @ v2 @ v1,
file('/export/starexec/sandbox2/tmp/tmp.2u5ArlhE4A/E---3.1_1220184.p',fact_2_True) ).
thf(fact_5_in__tree_Osimps_I2_J,axiom,
! [X7: a,X8: a,X9: tree_a,X10: tree_a] :
( ( in_tree_a @ X7 @ ( t_a @ X8 @ X9 @ X10 ) )
<=> ( ( X7 = X8 )
| ( in_tree_a @ X7 @ X9 )
| ( in_tree_a @ X7 @ X10 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2u5ArlhE4A/E---3.1_1220184.p',fact_5_in__tree_Osimps_I2_J) ).
thf(fact_0_False,axiom,
~ ( ( v = v3 )
| ( v = v1 )
| ( v = v2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.2u5ArlhE4A/E---3.1_1220184.p',fact_0_False) ).
thf(c_0_10,plain,
! [X24: a,X25: tree_a,X26: tree_a,X27: a,X28: tree_a,X29: tree_a,X7: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X24 @ X25 @ X26 ) ) @ ( val_a @ ( t_a @ X27 @ X28 @ X29 ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X27 @ X28 @ X29 ) ) @ X7 )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X7 @ ( t_a @ X27 @ X28 @ X29 ) @ ( t_a @ X24 @ X25 @ X26 ) ) )
= ( t_a @ X7 @ ( t_a @ X27 @ X28 @ X29 ) @ ( t_a @ X24 @ X25 @ X26 ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X27 @ X28 @ X29 ) ) @ X7 )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X7 @ ( t_a @ X27 @ X28 @ X29 ) @ ( t_a @ X24 @ X25 @ X26 ) ) )
= ( t_a @ ( val_a @ ( t_a @ X27 @ X28 @ X29 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ X7 @ ( heapIm1140443833left_a @ ( t_a @ X27 @ X28 @ X29 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X27 @ X28 @ X29 ) ) ) ) @ ( t_a @ X24 @ X25 @ X26 ) ) ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X24 @ X25 @ X26 ) ) @ ( val_a @ ( t_a @ X27 @ X28 @ X29 ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X24 @ X25 @ X26 ) ) @ X7 )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X7 @ ( t_a @ X27 @ X28 @ X29 ) @ ( t_a @ X24 @ X25 @ X26 ) ) )
= ( t_a @ X7 @ ( t_a @ X27 @ X28 @ X29 ) @ ( t_a @ X24 @ X25 @ X26 ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X24 @ X25 @ X26 ) ) @ X7 )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X7 @ ( t_a @ X27 @ X28 @ X29 ) @ ( t_a @ X24 @ X25 @ X26 ) ) )
= ( t_a @ ( val_a @ ( t_a @ X24 @ X25 @ X26 ) ) @ ( t_a @ X27 @ X28 @ X29 ) @ ( heapIm1091024090Down_a @ ( t_a @ X7 @ ( heapIm1140443833left_a @ ( t_a @ X24 @ X25 @ X26 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X24 @ X25 @ X26 ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_15_siftDown_Osimps_I6_J]) ).
thf(c_0_11,negated_conjecture,
~ ( in_tree_a @ v @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_12,plain,
! [X864: a,X865: tree_a,X866: tree_a,X867: a,X868: tree_a,X869: tree_a,X870: a] :
( ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X867 @ X868 @ X869 ) ) @ X870 )
| ( ( heapIm1091024090Down_a @ ( t_a @ X870 @ ( t_a @ X867 @ X868 @ X869 ) @ ( t_a @ X864 @ X865 @ X866 ) ) )
= ( t_a @ X870 @ ( t_a @ X867 @ X868 @ X869 ) @ ( t_a @ X864 @ X865 @ X866 ) ) )
| ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X864 @ X865 @ X866 ) ) @ ( val_a @ ( t_a @ X867 @ X868 @ X869 ) ) ) )
& ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X867 @ X868 @ X869 ) ) @ X870 )
| ( ( heapIm1091024090Down_a @ ( t_a @ X870 @ ( t_a @ X867 @ X868 @ X869 ) @ ( t_a @ X864 @ X865 @ X866 ) ) )
= ( t_a @ ( val_a @ ( t_a @ X867 @ X868 @ X869 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ X870 @ ( heapIm1140443833left_a @ ( t_a @ X867 @ X868 @ X869 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X867 @ X868 @ X869 ) ) ) ) @ ( t_a @ X864 @ X865 @ X866 ) ) )
| ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X864 @ X865 @ X866 ) ) @ ( val_a @ ( t_a @ X867 @ X868 @ X869 ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X864 @ X865 @ X866 ) ) @ X870 )
| ( ( heapIm1091024090Down_a @ ( t_a @ X870 @ ( t_a @ X867 @ X868 @ X869 ) @ ( t_a @ X864 @ X865 @ X866 ) ) )
= ( t_a @ X870 @ ( t_a @ X867 @ X868 @ X869 ) @ ( t_a @ X864 @ X865 @ X866 ) ) )
| ( ord_less_eq_a @ ( val_a @ ( t_a @ X864 @ X865 @ X866 ) ) @ ( val_a @ ( t_a @ X867 @ X868 @ X869 ) ) ) )
& ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X864 @ X865 @ X866 ) ) @ X870 )
| ( ( heapIm1091024090Down_a @ ( t_a @ X870 @ ( t_a @ X867 @ X868 @ X869 ) @ ( t_a @ X864 @ X865 @ X866 ) ) )
= ( t_a @ ( val_a @ ( t_a @ X864 @ X865 @ X866 ) ) @ ( t_a @ X867 @ X868 @ X869 ) @ ( heapIm1091024090Down_a @ ( t_a @ X870 @ ( heapIm1140443833left_a @ ( t_a @ X864 @ X865 @ X866 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X864 @ X865 @ X866 ) ) ) ) ) )
| ( ord_less_eq_a @ ( val_a @ ( t_a @ X864 @ X865 @ X866 ) ) @ ( val_a @ ( t_a @ X867 @ X868 @ X869 ) ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
thf(c_0_13,plain,
! [X933: a,X934: tree_a,X935: tree_a] :
( ( val_a @ ( t_a @ X933 @ X934 @ X935 ) )
= X933 ),
inference(variable_rename,[status(thm)],[fact_29_val_Osimps]) ).
thf(c_0_14,negated_conjecture,
~ ( in_tree_a @ v @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
thf(c_0_15,plain,
! [X831: a,X832: tree_a,X833: tree_a] :
( ( heapIm1140443833left_a @ ( t_a @ X831 @ X832 @ X833 ) )
= X832 ),
inference(variable_rename,[status(thm)],[fact_8_left_Osimps]) ).
thf(c_0_16,plain,
! [X834: a,X835: tree_a,X836: tree_a] :
( ( heapIm1257206334ight_a @ ( t_a @ X834 @ X835 @ X836 ) )
= X836 ),
inference(variable_rename,[status(thm)],[fact_9_right_Osimps]) ).
thf(c_0_17,plain,
! [X1: a,X2: tree_a,X4: a,X7: a,X6: tree_a,X5: tree_a,X3: tree_a] :
( ( ( heapIm1091024090Down_a @ ( t_a @ X4 @ ( t_a @ X1 @ X2 @ X3 ) @ ( t_a @ X7 @ X5 @ X6 ) ) )
= ( t_a @ X4 @ ( t_a @ X1 @ X2 @ X3 ) @ ( t_a @ X7 @ X5 @ X6 ) ) )
| ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X1 @ X2 @ X3 ) ) @ X4 )
| ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X7 @ X5 @ X6 ) ) @ ( val_a @ ( t_a @ X1 @ X2 @ X3 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_18,plain,
! [X3: tree_a,X2: tree_a,X1: a] :
( ( val_a @ ( t_a @ X1 @ X2 @ X3 ) )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_19,negated_conjecture,
~ ( in_tree_a @ v @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ),
inference(fof_nnf,[status(thm)],[c_0_14]) ).
thf(c_0_20,plain,
( ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
=> ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ v3 )
=> ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) )
=> ( in_tree_a @ v @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_7__C5__1_Ohyps_C_I1_J]) ).
thf(c_0_21,plain,
! [X1: a,X2: tree_a,X4: a,X7: a,X6: tree_a,X5: tree_a,X3: tree_a] :
( ( ord_less_eq_a @ ( val_a @ ( t_a @ X1 @ X2 @ X3 ) ) @ X4 )
| ( ( heapIm1091024090Down_a @ ( t_a @ X4 @ ( t_a @ X1 @ X2 @ X3 ) @ ( t_a @ X7 @ X5 @ X6 ) ) )
= ( t_a @ ( val_a @ ( t_a @ X1 @ X2 @ X3 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ X4 @ ( heapIm1140443833left_a @ ( t_a @ X1 @ X2 @ X3 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X1 @ X2 @ X3 ) ) ) ) @ ( t_a @ X7 @ X5 @ X6 ) ) )
| ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X7 @ X5 @ X6 ) ) @ ( val_a @ ( t_a @ X1 @ X2 @ X3 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_22,plain,
! [X1: a,X3: tree_a,X2: tree_a] :
( ( heapIm1140443833left_a @ ( t_a @ X1 @ X2 @ X3 ) )
= X2 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_23,plain,
! [X1: a,X2: tree_a,X3: tree_a] :
( ( heapIm1257206334ight_a @ ( t_a @ X1 @ X2 @ X3 ) )
= X3 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_24,plain,
in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ),
inference(split_conjunct,[status(thm)],[fact_3__C5__1_Oprems_C]) ).
thf(c_0_25,plain,
! [X2: tree_a,X1: a,X3: tree_a,X6: tree_a,X5: tree_a,X7: a,X4: a] :
( ( ( heapIm1091024090Down_a @ ( t_a @ X1 @ ( t_a @ X4 @ X2 @ X3 ) @ ( t_a @ X7 @ X5 @ X6 ) ) )
= ( t_a @ X1 @ ( t_a @ X4 @ X2 @ X3 ) @ ( t_a @ X7 @ X5 @ X6 ) ) )
| ~ ( ord_less_eq_a @ X4 @ X1 )
| ~ ( ord_less_eq_a @ X7 @ X4 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_18]),c_0_18]) ).
thf(c_0_26,plain,
ord_less_eq_a @ v2 @ v1,
inference(split_conjunct,[status(thm)],[fact_2_True]) ).
thf(c_0_27,negated_conjecture,
~ ( in_tree_a @ v @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_28,plain,
! [X827: a,X828: a,X829: tree_a,X830: tree_a] :
( ( ~ ( in_tree_a @ X827 @ ( t_a @ X828 @ X829 @ X830 ) )
| ( X827 = X828 )
| ( in_tree_a @ X827 @ X829 )
| ( in_tree_a @ X827 @ X830 ) )
& ( ( X827 != X828 )
| ( in_tree_a @ X827 @ ( t_a @ X828 @ X829 @ X830 ) ) )
& ( ~ ( in_tree_a @ X827 @ X829 )
| ( in_tree_a @ X827 @ ( t_a @ X828 @ X829 @ X830 ) ) )
& ( ~ ( in_tree_a @ X827 @ X830 )
| ( in_tree_a @ X827 @ ( t_a @ X828 @ X829 @ X830 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_5_in__tree_Osimps_I2_J])])])]) ).
thf(c_0_29,plain,
( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
| ( ord_less_eq_a @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ v3 )
| ~ ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) )
| ( in_tree_a @ v @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])]) ).
thf(c_0_30,plain,
! [X2: tree_a,X1: a,X3: tree_a,X6: tree_a,X5: tree_a,X7: a,X4: a] :
( ( ( heapIm1091024090Down_a @ ( t_a @ X1 @ ( t_a @ X4 @ X2 @ X3 ) @ ( t_a @ X7 @ X5 @ X6 ) ) )
= ( t_a @ X4 @ ( heapIm1091024090Down_a @ ( t_a @ X1 @ X2 @ X3 ) ) @ ( t_a @ X7 @ X5 @ X6 ) ) )
| ( ord_less_eq_a @ X4 @ X1 )
| ~ ( ord_less_eq_a @ X7 @ X4 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_18]),c_0_22]),c_0_23]),c_0_18]),c_0_18]),c_0_18]) ).
thf(c_0_31,plain,
~ ( ord_less_eq_a @ v1 @ v3 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]),c_0_27]) ).
thf(c_0_32,plain,
( ( v != v3 )
& ( v != v1 )
& ( v != v2 ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_0_False])]) ).
thf(c_0_33,plain,
! [X1: a,X4: a,X3: tree_a,X2: tree_a] :
( ( in_tree_a @ X1 @ ( t_a @ X4 @ X3 @ X2 ) )
| ~ ( in_tree_a @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_34,plain,
( ( ord_less_eq_a @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ v3 )
| ( in_tree_a @ v @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) )
| ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
| ~ ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_35,plain,
! [X1: a,X2: tree_a,X4: a,X3: tree_a] :
( ( X1 = X4 )
| ( in_tree_a @ X1 @ X2 )
| ( in_tree_a @ X1 @ X3 )
| ~ ( in_tree_a @ X1 @ ( t_a @ X4 @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_36,plain,
in_tree_a @ v @ ( t_a @ v1 @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ l1 @ r1 ) ) @ ( t_a @ v2 @ l2 @ r2 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_30]),c_0_26])]),c_0_31]) ).
thf(c_0_37,plain,
v != v1,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_38,negated_conjecture,
~ ( in_tree_a @ v @ ( t_a @ v2 @ l2 @ r2 ) ),
inference(spm,[status(thm)],[c_0_27,c_0_33]) ).
thf(c_0_39,plain,
! [X1: a,X4: a,X3: tree_a,X2: tree_a] :
( ( in_tree_a @ X1 @ ( t_a @ X4 @ X2 @ X3 ) )
| ~ ( in_tree_a @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_40,plain,
( ( in_tree_a @ v @ ( t_a @ v3 @ l1 @ r1 ) )
| ( ord_less_eq_a @ v1 @ v3 )
| ~ ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ l1 @ r1 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_22]),c_0_23]),c_0_18]),c_0_22]),c_0_23]),c_0_18]),c_0_18]),c_0_26])]) ).
thf(c_0_41,plain,
in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ l1 @ r1 ) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_38]) ).
thf(c_0_42,negated_conjecture,
~ ( in_tree_a @ v @ ( t_a @ v1 @ l1 @ r1 ) ),
inference(spm,[status(thm)],[c_0_27,c_0_39]) ).
thf(c_0_43,plain,
in_tree_a @ v @ ( t_a @ v3 @ l1 @ r1 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]),c_0_31]) ).
thf(c_0_44,plain,
v != v3,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_45,negated_conjecture,
~ ( in_tree_a @ v @ r1 ),
inference(spm,[status(thm)],[c_0_42,c_0_33]) ).
thf(c_0_46,negated_conjecture,
~ ( in_tree_a @ v @ l1 ),
inference(spm,[status(thm)],[c_0_42,c_0_39]) ).
thf(c_0_47,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_43]),c_0_44]),c_0_45]),c_0_46]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP067^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.19 % Computer : n006.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Tue Sep 29 19:45:54 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.26 Running higher-order theorem proving
% 0.12/0.29 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.2u5ArlhE4A/E---3.1_1220184.p
% 0.65/0.41 % Version: 3.5.1-ho
% 0.65/0.41 % Preprocessing class: HSLSSMSMSSSCHFA.
% 0.65/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.65/0.41 % Starting lpo5_fix with 1500s (5) cores
% 0.65/0.41 % Starting lpo6_lambda_fix with 300s (1) cores
% 0.65/0.41 % Starting post_as_ho8 with 300s (1) cores
% 0.65/0.41 % Starting lpo5_rw_fix with 300s (1) cores
% 0.65/0.41 % lpo5_fix with pid 1220200 completed with status 0
% 0.65/0.41 % Result found by lpo5_fix
% 0.65/0.41 % Preprocessing class: HSLSSMSMSSSCHFA.
% 0.65/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.65/0.41 % Starting lpo5_fix with 1500s (5) cores
% 0.65/0.41 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.65/0.41 % No SInE strategy applied
% 0.65/0.41 % Search class: HGHSM-FSLM32-MHFFFSBN
% 0.65/0.41 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.65/0.41 % Starting SubtermCWHack with 136s (1) cores
% 0.65/0.41 % Starting lpo5_fix with 151s (1) cores
% 0.65/0.41 % Starting post_as_ho6 with 136s (1) cores
% 0.65/0.41 % Starting almost_fo_1 with 136s (1) cores
% 0.65/0.41 % Starting lpo6_lambda_fix with 136s (1) cores
% 0.65/0.41 % post_as_ho6 with pid 1220214 completed with status 0
% 0.65/0.41 % Result found by post_as_ho6
% 0.65/0.41 % Preprocessing class: HSLSSMSMSSSCHFA.
% 0.65/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.65/0.41 % Starting lpo5_fix with 1500s (5) cores
% 0.65/0.41 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.65/0.41 % No SInE strategy applied
% 0.65/0.41 % Search class: HGHSM-FSLM32-MHFFFSBN
% 0.65/0.41 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.65/0.41 % Starting SubtermCWHack with 136s (1) cores
% 0.65/0.41 % Starting lpo5_fix with 151s (1) cores
% 0.65/0.41 % Starting post_as_ho6 with 136s (1) cores
% 0.65/0.41 % Preprocessing time : 0.005 s
% 0.65/0.41 % Presaturation interreduction done
% 0.65/0.41
% 0.65/0.41 % Proof found!
% 0.65/0.41 % SZS status Theorem
% 0.65/0.41 % SZS output start CNFRefutation
% See solution above
% 0.65/0.41 % Parsed axioms : 216
% 0.65/0.41 % Removed by relevancy pruning/SinE : 0
% 0.65/0.41 % Initial clauses : 531
% 0.65/0.41 % Removed in clause preprocessing : 130
% 0.65/0.41 % Initial clauses in saturation : 401
% 0.65/0.41 % Processed clauses : 771
% 0.65/0.41 % ...of these trivial : 5
% 0.65/0.41 % ...subsumed : 211
% 0.65/0.41 % ...remaining for further processing : 555
% 0.65/0.41 % Other redundant clauses eliminated : 106
% 0.65/0.41 % Clauses deleted for lack of memory : 0
% 0.65/0.41 % Backward-subsumed : 2
% 0.65/0.41 % Backward-rewritten : 5
% 0.65/0.41 % Generated clauses : 1225
% 0.65/0.41 % ...of the previous two non-redundant : 1033
% 0.65/0.41 % ...aggressively subsumed : 0
% 0.65/0.41 % Contextual simplify-reflections : 4
% 0.65/0.41 % Paramodulations : 1068
% 0.65/0.41 % Factorizations : 4
% 0.65/0.41 % NegExts : 0
% 0.65/0.41 % Equation resolutions : 110
% 0.65/0.41 % Disequality decompositions : 0
% 0.65/0.41 % Total rewrite steps : 202
% 0.65/0.41 % ...of those cached : 151
% 0.65/0.41 % Propositional unsat checks : 0
% 0.65/0.41 % Propositional check models : 0
% 0.65/0.41 % Propositional check unsatisfiable : 0
% 0.65/0.41 % Propositional clauses : 0
% 0.65/0.41 % Propositional clauses after purity: 0
% 0.65/0.41 % Propositional unsat core size : 0
% 0.65/0.41 % Propositional preprocessing time : 0.000
% 0.65/0.41 % Propositional encoding time : 0.000
% 0.65/0.41 % Propositional solver time : 0.000
% 0.65/0.41 % Success case prop preproc time : 0.000
% 0.65/0.41 % Success case prop encoding time : 0.000
% 0.65/0.41 % Success case prop solver time : 0.000
% 0.65/0.41 % Current number of processed clauses : 266
% 0.65/0.41 % Positive orientable unit clauses : 40
% 0.65/0.41 % Positive unorientable unit clauses: 0
% 0.65/0.41 % Negative unit clauses : 22
% 0.65/0.41 % Non-unit-clauses : 204
% 0.65/0.41 % Current number of unprocessed clauses: 894
% 0.65/0.41 % ...number of literals in the above : 3389
% 0.65/0.41 % Current number of archived formulas : 0
% 0.65/0.41 % Current number of archived clauses : 238
% 0.65/0.41 % Clause-clause subsumption calls (NU) : 16108
% 0.65/0.41 % Rec. Clause-clause subsumption calls : 8999
% 0.65/0.41 % Non-unit clause-clause subsumptions : 199
% 0.65/0.41 % Unit Clause-clause subsumption calls : 577
% 0.65/0.41 % Rewrite failures with RHS unbound : 0
% 0.65/0.41 % BW rewrite match attempts : 30
% 0.65/0.41 % BW rewrite match successes : 5
% 0.65/0.41 % Condensation attempts : 771
% 0.65/0.41 % Condensation successes : 17
% 0.65/0.41 % Termbank termtop insertions : 61789
% 0.65/0.41 % Search garbage collected termcells : 9418
% 0.65/0.41
% 0.65/0.41 % -------------------------------------------------
% 0.65/0.41 % User time : 0.076 s
% 0.65/0.41 % System time : 0.009 s
% 0.65/0.41 % Total time : 0.085 s
% 0.65/0.41 % Maximum resident set size: 5612 pages
% 0.65/0.41
% 0.65/0.41 % -------------------------------------------------
% 0.65/0.41 % User time : 0.280 s
% 0.65/0.41 % System time : 0.030 s
% 0.65/0.41 % Total time : 0.310 s
% 0.65/0.41 % Maximum resident set size: 5376 pages
% 0.65/0.41 % E exiting
%------------------------------------------------------------------------------