TSTP Solution File: ITP067^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : ITP067^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n014.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 : 300s
% DateTime : Sat May 4 08:06:50 EDT 2024
% Result : Theorem 0.48s 0.66s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 34
% Syntax : Number of formulae : 86 ( 35 unt; 21 typ; 0 def)
% Number of atoms : 161 ( 75 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 1261 ( 64 ~; 55 |; 19 &;1101 @)
% ( 2 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 10 con; 0-3 aty)
% Number of variables : 164 ( 0 ^ 164 !; 0 ?; 164 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
tree_a: $tType ).
thf(decl_sort2,type,
a: $tType ).
thf(decl_26,type,
heapIm1140443833left_a: tree_a > tree_a ).
thf(decl_27,type,
heapIm1257206334ight_a: tree_a > tree_a ).
thf(decl_28,type,
heapIm1091024090Down_a: tree_a > tree_a ).
thf(decl_29,type,
e_a: tree_a ).
thf(decl_30,type,
t_a: a > tree_a > tree_a > tree_a ).
thf(decl_33,type,
in_tree_a: a > tree_a > $o ).
thf(decl_36,type,
val_a: tree_a > a ).
thf(decl_48,type,
ord_less_eq_a: a > a > $o ).
thf(decl_56,type,
l1: tree_a ).
thf(decl_57,type,
l2: tree_a ).
thf(decl_58,type,
r1: tree_a ).
thf(decl_59,type,
r2: tree_a ).
thf(decl_61,type,
v: a ).
thf(decl_62,type,
v1: a ).
thf(decl_63,type,
v2: a ).
thf(decl_64,type,
v3: a ).
thf(decl_97,type,
esk33_1: tree_a > a ).
thf(decl_98,type,
esk34_1: tree_a > tree_a ).
thf(decl_99,type,
esk35_1: tree_a > tree_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/sandbox/tmp/tmp.hpc935L0JX/E---3.1_15094.p',fact_15_siftDown_Osimps_I6_J) ).
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/sandbox/tmp/tmp.hpc935L0JX/E---3.1_15094.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/sandbox/tmp/tmp.hpc935L0JX/E---3.1_15094.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/sandbox/tmp/tmp.hpc935L0JX/E---3.1_15094.p',fact_9_right_Osimps) ).
thf(conj_0,conjecture,
in_tree_a @ v @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ),
file('/export/starexec/sandbox/tmp/tmp.hpc935L0JX/E---3.1_15094.p',conj_0) ).
thf(fact_25_Tree_Oexhaust,axiom,
! [X37: tree_a] :
( ( X37 != e_a )
=> ~ ! [X38: a,X39: tree_a,X40: tree_a] :
( X37
!= ( t_a @ X38 @ X39 @ X40 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.hpc935L0JX/E---3.1_15094.p',fact_25_Tree_Oexhaust) ).
thf(fact_27_Tree_Odistinct_I1_J,axiom,
! [X1: a,X2: tree_a,X3: tree_a] :
( e_a
!= ( t_a @ X1 @ X2 @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.hpc935L0JX/E---3.1_15094.p',fact_27_Tree_Odistinct_I1_J) ).
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/sandbox/tmp/tmp.hpc935L0JX/E---3.1_15094.p',fact_7__C5__1_Ohyps_C_I1_J) ).
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/sandbox/tmp/tmp.hpc935L0JX/E---3.1_15094.p',fact_5_in__tree_Osimps_I2_J) ).
thf(fact_2_True,axiom,
ord_less_eq_a @ v2 @ v1,
file('/export/starexec/sandbox/tmp/tmp.hpc935L0JX/E---3.1_15094.p',fact_2_True) ).
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/sandbox/tmp/tmp.hpc935L0JX/E---3.1_15094.p',fact_3__C5__1_Oprems_C) ).
thf(fact_4_Tree_Oinject,axiom,
! [X1: a,X2: tree_a,X3: tree_a,X4: a,X5: tree_a,X6: tree_a] :
( ( ( t_a @ X1 @ X2 @ X3 )
= ( t_a @ X4 @ X5 @ X6 ) )
<=> ( ( X1 = X4 )
& ( X2 = X5 )
& ( X3 = X6 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.hpc935L0JX/E---3.1_15094.p',fact_4_Tree_Oinject) ).
thf(fact_0_False,axiom,
~ ( ( v = v3 )
| ( v = v1 )
| ( v = v2 ) ),
file('/export/starexec/sandbox/tmp/tmp.hpc935L0JX/E---3.1_15094.p',fact_0_False) ).
thf(c_0_13,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_14,plain,
! [X651: a,X652: tree_a,X653: tree_a,X654: a,X655: tree_a,X656: tree_a,X657: a] :
( ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X654 @ X655 @ X656 ) ) @ X657 )
| ( ( heapIm1091024090Down_a @ ( t_a @ X657 @ ( t_a @ X654 @ X655 @ X656 ) @ ( t_a @ X651 @ X652 @ X653 ) ) )
= ( t_a @ X657 @ ( t_a @ X654 @ X655 @ X656 ) @ ( t_a @ X651 @ X652 @ X653 ) ) )
| ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X651 @ X652 @ X653 ) ) @ ( val_a @ ( t_a @ X654 @ X655 @ X656 ) ) ) )
& ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X654 @ X655 @ X656 ) ) @ X657 )
| ( ( heapIm1091024090Down_a @ ( t_a @ X657 @ ( t_a @ X654 @ X655 @ X656 ) @ ( t_a @ X651 @ X652 @ X653 ) ) )
= ( t_a @ ( val_a @ ( t_a @ X654 @ X655 @ X656 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ X657 @ ( heapIm1140443833left_a @ ( t_a @ X654 @ X655 @ X656 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X654 @ X655 @ X656 ) ) ) ) @ ( t_a @ X651 @ X652 @ X653 ) ) )
| ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X651 @ X652 @ X653 ) ) @ ( val_a @ ( t_a @ X654 @ X655 @ X656 ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X651 @ X652 @ X653 ) ) @ X657 )
| ( ( heapIm1091024090Down_a @ ( t_a @ X657 @ ( t_a @ X654 @ X655 @ X656 ) @ ( t_a @ X651 @ X652 @ X653 ) ) )
= ( t_a @ X657 @ ( t_a @ X654 @ X655 @ X656 ) @ ( t_a @ X651 @ X652 @ X653 ) ) )
| ( ord_less_eq_a @ ( val_a @ ( t_a @ X651 @ X652 @ X653 ) ) @ ( val_a @ ( t_a @ X654 @ X655 @ X656 ) ) ) )
& ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X651 @ X652 @ X653 ) ) @ X657 )
| ( ( heapIm1091024090Down_a @ ( t_a @ X657 @ ( t_a @ X654 @ X655 @ X656 ) @ ( t_a @ X651 @ X652 @ X653 ) ) )
= ( t_a @ ( val_a @ ( t_a @ X651 @ X652 @ X653 ) ) @ ( t_a @ X654 @ X655 @ X656 ) @ ( heapIm1091024090Down_a @ ( t_a @ X657 @ ( heapIm1140443833left_a @ ( t_a @ X651 @ X652 @ X653 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X651 @ X652 @ X653 ) ) ) ) ) )
| ( ord_less_eq_a @ ( val_a @ ( t_a @ X651 @ X652 @ X653 ) ) @ ( val_a @ ( t_a @ X654 @ X655 @ X656 ) ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
thf(c_0_15,plain,
! [X541: a,X542: tree_a,X543: tree_a] :
( ( val_a @ ( t_a @ X541 @ X542 @ X543 ) )
= X541 ),
inference(variable_rename,[status(thm)],[fact_29_val_Osimps]) ).
thf(c_0_16,plain,
! [X673: a,X674: tree_a,X675: tree_a] :
( ( heapIm1140443833left_a @ ( t_a @ X673 @ X674 @ X675 ) )
= X674 ),
inference(variable_rename,[status(thm)],[fact_8_left_Osimps]) ).
thf(c_0_17,plain,
! [X648: a,X649: tree_a,X650: tree_a] :
( ( heapIm1257206334ight_a @ ( t_a @ X648 @ X649 @ X650 ) )
= X650 ),
inference(variable_rename,[status(thm)],[fact_9_right_Osimps]) ).
thf(c_0_18,negated_conjecture,
~ ( in_tree_a @ v @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
thf(c_0_19,plain,
! [X37: tree_a] :
( ( X37 != e_a )
=> ~ ! [X38: a,X39: tree_a,X40: tree_a] :
( X37
!= ( t_a @ X38 @ X39 @ X40 ) ) ),
inference(fof_simplification,[status(thm)],[fact_25_Tree_Oexhaust]) ).
thf(c_0_20,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_14]) ).
thf(c_0_21,plain,
! [X3: tree_a,X2: tree_a,X1: a] :
( ( val_a @ ( t_a @ X1 @ X2 @ X3 ) )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
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_16]) ).
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_17]) ).
thf(c_0_24,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_14]) ).
thf(c_0_25,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_18]) ).
thf(c_0_26,plain,
! [X1: a,X2: tree_a,X3: tree_a] :
( e_a
!= ( t_a @ X1 @ X2 @ X3 ) ),
inference(fof_simplification,[status(thm)],[fact_27_Tree_Odistinct_I1_J]) ).
thf(c_0_27,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_28,plain,
! [X481: a,X482: a,X483: tree_a,X484: tree_a] :
( ( ~ ( in_tree_a @ X481 @ ( t_a @ X482 @ X483 @ X484 ) )
| ( X481 = X482 )
| ( in_tree_a @ X481 @ X483 )
| ( in_tree_a @ X481 @ X484 ) )
& ( ( X481 != X482 )
| ( in_tree_a @ X481 @ ( t_a @ X482 @ X483 @ X484 ) ) )
& ( ~ ( in_tree_a @ X481 @ X483 )
| ( in_tree_a @ X481 @ ( t_a @ X482 @ X483 @ X484 ) ) )
& ( ~ ( in_tree_a @ X481 @ X484 )
| ( in_tree_a @ X481 @ ( t_a @ X482 @ X483 @ X484 ) ) ) ),
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,
! [X529: tree_a] :
( ( X529 = e_a )
| ( X529
= ( t_a @ ( esk33_1 @ X529 ) @ ( esk34_1 @ X529 ) @ ( esk35_1 @ X529 ) ) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
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_20,c_0_21]),c_0_22]),c_0_23]),c_0_21]),c_0_21]),c_0_21]) ).
thf(c_0_31,plain,
ord_less_eq_a @ v2 @ v1,
inference(split_conjunct,[status(thm)],[fact_2_True]) ).
thf(c_0_32,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_33,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_24,c_0_21]),c_0_21]),c_0_21]) ).
thf(c_0_34,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_25]) ).
thf(c_0_35,plain,
! [X489: a,X490: tree_a,X491: tree_a,X492: a,X493: tree_a,X494: tree_a] :
( ( ( X489 = X492 )
| ( ( t_a @ X489 @ X490 @ X491 )
!= ( t_a @ X492 @ X493 @ X494 ) ) )
& ( ( X490 = X493 )
| ( ( t_a @ X489 @ X490 @ X491 )
!= ( t_a @ X492 @ X493 @ X494 ) ) )
& ( ( X491 = X494 )
| ( ( t_a @ X489 @ X490 @ X491 )
!= ( t_a @ X492 @ X493 @ X494 ) ) )
& ( ( X489 != X492 )
| ( X490 != X493 )
| ( X491 != X494 )
| ( ( t_a @ X489 @ X490 @ X491 )
= ( t_a @ X492 @ X493 @ X494 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_4_Tree_Oinject])])])]) ).
thf(c_0_36,plain,
! [X538: a,X539: tree_a,X540: tree_a] :
( e_a
!= ( t_a @ X538 @ X539 @ X540 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_26])]) ).
thf(c_0_37,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_27])]) ).
thf(c_0_38,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_39,plain,
! [X2: tree_a] :
( ( X2 = e_a )
| ( X2
= ( t_a @ ( esk33_1 @ X2 ) @ ( esk34_1 @ X2 ) @ ( esk35_1 @ X2 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_40,plain,
! [X3: tree_a,X2: tree_a,X6: tree_a,X5: tree_a,X1: a] :
( ( ( heapIm1091024090Down_a @ ( t_a @ X1 @ ( t_a @ v1 @ X2 @ X3 ) @ ( t_a @ v2 @ X5 @ X6 ) ) )
= ( t_a @ v1 @ ( heapIm1091024090Down_a @ ( t_a @ X1 @ X2 @ X3 ) ) @ ( t_a @ v2 @ X5 @ X6 ) ) )
| ( ord_less_eq_a @ v1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_41,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_32,c_0_33]),c_0_31])]),c_0_34]) ).
thf(c_0_42,plain,
! [X1: a,X2: tree_a,X3: tree_a,X4: a,X5: tree_a,X6: tree_a] :
( ( X1 = X4 )
| ( ( t_a @ X1 @ X2 @ X3 )
!= ( t_a @ X4 @ X5 @ X6 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_43,plain,
! [X1: a,X2: tree_a,X3: tree_a] :
( e_a
!= ( t_a @ X1 @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_44,plain,
! [X1: a,X2: tree_a,X3: tree_a,X4: a,X5: tree_a,X6: tree_a] :
( ( X2 = X3 )
| ( ( t_a @ X1 @ X2 @ X5 )
!= ( t_a @ X4 @ X3 @ X6 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_45,plain,
! [X1: a,X2: tree_a,X4: a,X6: tree_a,X5: tree_a,X3: tree_a] :
( ( X2 = X3 )
| ( ( t_a @ X1 @ X5 @ X2 )
!= ( t_a @ X4 @ X6 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_46,plain,
( ( v != v3 )
& ( v != v1 )
& ( v != v2 ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_0_False])]) ).
thf(c_0_47,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_48,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_37]) ).
thf(c_0_49,plain,
! [X1: a,X2: tree_a] :
( ( X1
= ( esk33_1 @ X2 ) )
| ( X2 = e_a )
| ( in_tree_a @ X1 @ ( esk34_1 @ X2 ) )
| ( in_tree_a @ X1 @ ( esk35_1 @ X2 ) )
| ~ ( in_tree_a @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
thf(c_0_50,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(spm,[status(thm)],[c_0_32,c_0_40]),c_0_41]) ).
thf(c_0_51,plain,
! [X3: tree_a,X2: tree_a,X1: a] :
( ( esk33_1 @ ( t_a @ X1 @ X2 @ X3 ) )
= X1 ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_39])]),c_0_43]) ).
thf(c_0_52,plain,
! [X1: a,X3: tree_a,X2: tree_a] :
( ( esk34_1 @ ( t_a @ X1 @ X2 @ X3 ) )
= X2 ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_39])]),c_0_43]) ).
thf(c_0_53,plain,
! [X1: a,X2: tree_a,X3: tree_a] :
( ( esk35_1 @ ( t_a @ X1 @ X2 @ X3 ) )
= X3 ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_39])]),c_0_43]) ).
thf(c_0_54,plain,
v != v1,
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_55,negated_conjecture,
~ ( in_tree_a @ v @ ( t_a @ v2 @ l2 @ r2 ) ),
inference(spm,[status(thm)],[c_0_34,c_0_47]) ).
thf(c_0_56,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_57,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_48,c_0_21]),c_0_22]),c_0_23]),c_0_21]),c_0_21]),c_0_31]),c_0_22]),c_0_23])]) ).
thf(c_0_58,plain,
in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ l1 @ r1 ) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_52]),c_0_53]),c_0_54]),c_0_43]),c_0_55]) ).
thf(c_0_59,negated_conjecture,
~ ( in_tree_a @ v @ ( t_a @ v1 @ l1 @ r1 ) ),
inference(spm,[status(thm)],[c_0_34,c_0_56]) ).
thf(c_0_60,plain,
in_tree_a @ v @ ( t_a @ v3 @ l1 @ r1 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]),c_0_41]) ).
thf(c_0_61,plain,
v != v3,
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_62,negated_conjecture,
~ ( in_tree_a @ v @ l1 ),
inference(spm,[status(thm)],[c_0_59,c_0_56]) ).
thf(c_0_63,negated_conjecture,
~ ( in_tree_a @ v @ r1 ),
inference(spm,[status(thm)],[c_0_59,c_0_47]) ).
thf(c_0_64,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_60]),c_0_51]),c_0_52]),c_0_53]),c_0_61]),c_0_43]),c_0_62]),c_0_63]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.16 % Problem : ITP067^1 : TPTP v8.1.2. Released v7.5.0.
% 0.08/0.17 % Command : run_E %s %d THM
% 0.18/0.38 % Computer : n014.cluster.edu
% 0.18/0.38 % Model : x86_64 x86_64
% 0.18/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.38 % Memory : 8042.1875MB
% 0.18/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.38 % CPULimit : 300
% 0.18/0.38 % WCLimit : 300
% 0.18/0.38 % DateTime : Fri May 3 12:28:17 EDT 2024
% 0.18/0.39 % CPUTime :
% 0.24/0.56 Running higher-order theorem proving
% 0.24/0.56 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.hpc935L0JX/E---3.1_15094.p
% 0.48/0.66 # Version: 3.1.0-ho
% 0.48/0.66 # Preprocessing class: HSLSSMSMSSSCHFA.
% 0.48/0.66 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.48/0.66 # Starting lpo5_fix with 1500s (5) cores
% 0.48/0.66 # Starting lpo6_lambda_fix with 300s (1) cores
% 0.48/0.66 # Starting post_as_ho8 with 300s (1) cores
% 0.48/0.66 # Starting lpo5_rw_fix with 300s (1) cores
% 0.48/0.66 # lpo5_rw_fix with pid 15188 completed with status 0
% 0.48/0.66 # Result found by lpo5_rw_fix
% 0.48/0.66 # Preprocessing class: HSLSSMSMSSSCHFA.
% 0.48/0.66 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.48/0.66 # Starting lpo5_fix with 1500s (5) cores
% 0.48/0.66 # Starting lpo6_lambda_fix with 300s (1) cores
% 0.48/0.66 # Starting post_as_ho8 with 300s (1) cores
% 0.48/0.66 # Starting lpo5_rw_fix with 300s (1) cores
% 0.48/0.66 # SinE strategy is gf120_gu_RUU_F100_L01000
% 0.48/0.66 # Search class: HGUSM-FSLS31-MHFFFFBN
% 0.48/0.66 # partial match(2): HGHSM-FSLM31-MHFFFFBN
% 0.48/0.66 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.48/0.66 # Starting new_ho_11 with 163s (1) cores
% 0.48/0.66 # new_ho_11 with pid 15190 completed with status 0
% 0.48/0.66 # Result found by new_ho_11
% 0.48/0.66 # Preprocessing class: HSLSSMSMSSSCHFA.
% 0.48/0.66 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.48/0.66 # Starting lpo5_fix with 1500s (5) cores
% 0.48/0.66 # Starting lpo6_lambda_fix with 300s (1) cores
% 0.48/0.66 # Starting post_as_ho8 with 300s (1) cores
% 0.48/0.66 # Starting lpo5_rw_fix with 300s (1) cores
% 0.48/0.66 # SinE strategy is gf120_gu_RUU_F100_L01000
% 0.48/0.66 # Search class: HGUSM-FSLS31-MHFFFFBN
% 0.48/0.66 # partial match(2): HGHSM-FSLM31-MHFFFFBN
% 0.48/0.66 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.48/0.66 # Starting new_ho_11 with 163s (1) cores
% 0.48/0.66 # Preprocessing time : 0.005 s
% 0.48/0.66 # Presaturation interreduction done
% 0.48/0.66
% 0.48/0.66 # Proof found!
% 0.48/0.66 # SZS status Theorem
% 0.48/0.66 # SZS output start CNFRefutation
% See solution above
% 0.48/0.66 # Parsed axioms : 216
% 0.48/0.66 # Removed by relevancy pruning/SinE : 160
% 0.48/0.66 # Initial clauses : 164
% 0.48/0.66 # Removed in clause preprocessing : 4
% 0.48/0.66 # Initial clauses in saturation : 160
% 0.48/0.66 # Processed clauses : 430
% 0.48/0.66 # ...of these trivial : 6
% 0.48/0.66 # ...subsumed : 174
% 0.48/0.66 # ...remaining for further processing : 250
% 0.48/0.66 # Other redundant clauses eliminated : 44
% 0.48/0.66 # Clauses deleted for lack of memory : 0
% 0.48/0.66 # Backward-subsumed : 2
% 0.48/0.66 # Backward-rewritten : 6
% 0.48/0.66 # Generated clauses : 1540
% 0.48/0.66 # ...of the previous two non-redundant : 1326
% 0.48/0.66 # ...aggressively subsumed : 0
% 0.48/0.66 # Contextual simplify-reflections : 1
% 0.48/0.66 # Paramodulations : 1469
% 0.48/0.66 # Factorizations : 24
% 0.48/0.66 # NegExts : 0
% 0.48/0.66 # Equation resolutions : 47
% 0.48/0.66 # Disequality decompositions : 0
% 0.48/0.66 # Total rewrite steps : 497
% 0.48/0.66 # ...of those cached : 375
% 0.48/0.66 # Propositional unsat checks : 0
% 0.48/0.66 # Propositional check models : 0
% 0.48/0.66 # Propositional check unsatisfiable : 0
% 0.48/0.66 # Propositional clauses : 0
% 0.48/0.66 # Propositional clauses after purity: 0
% 0.48/0.66 # Propositional unsat core size : 0
% 0.48/0.66 # Propositional preprocessing time : 0.000
% 0.48/0.66 # Propositional encoding time : 0.000
% 0.48/0.66 # Propositional solver time : 0.000
% 0.48/0.66 # Success case prop preproc time : 0.000
% 0.48/0.66 # Success case prop encoding time : 0.000
% 0.48/0.66 # Success case prop solver time : 0.000
% 0.48/0.66 # Current number of processed clauses : 160
% 0.48/0.66 # Positive orientable unit clauses : 24
% 0.48/0.66 # Positive unorientable unit clauses: 0
% 0.48/0.66 # Negative unit clauses : 20
% 0.48/0.66 # Non-unit-clauses : 116
% 0.48/0.66 # Current number of unprocessed clauses: 1074
% 0.48/0.66 # ...number of literals in the above : 4096
% 0.48/0.66 # Current number of archived formulas : 0
% 0.48/0.66 # Current number of archived clauses : 76
% 0.48/0.66 # Clause-clause subsumption calls (NU) : 2260
% 0.48/0.66 # Rec. Clause-clause subsumption calls : 1460
% 0.48/0.66 # Non-unit clause-clause subsumptions : 131
% 0.48/0.66 # Unit Clause-clause subsumption calls : 170
% 0.48/0.66 # Rewrite failures with RHS unbound : 0
% 0.48/0.66 # BW rewrite match attempts : 13
% 0.48/0.66 # BW rewrite match successes : 5
% 0.48/0.66 # Condensation attempts : 0
% 0.48/0.66 # Condensation successes : 0
% 0.48/0.66 # Termbank termtop insertions : 38013
% 0.48/0.66 # Search garbage collected termcells : 3951
% 0.48/0.66
% 0.48/0.66 # -------------------------------------------------
% 0.48/0.66 # User time : 0.067 s
% 0.48/0.66 # System time : 0.010 s
% 0.48/0.66 # Total time : 0.077 s
% 0.48/0.66 # Maximum resident set size: 2736 pages
% 0.48/0.66
% 0.48/0.66 # -------------------------------------------------
% 0.48/0.66 # User time : 0.075 s
% 0.48/0.66 # System time : 0.012 s
% 0.48/0.66 # Total time : 0.088 s
% 0.48/0.66 # Maximum resident set size: 2216 pages
% 0.48/0.66 % E---3.1 exiting
% 0.48/0.66 % E exiting
%------------------------------------------------------------------------------