TSTP Solution File: ITP066^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP066^1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n022.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 : Sun Jul 17 00:28:58 EDT 2022
% Result : Theorem 3.27s 3.47s
% Output : Proof 3.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 12
% Syntax : Number of formulae : 37 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 280 ( 24 equ; 0 cnn)
% Maximal formula atoms : 2 ( 7 avg)
% Number of connectives : 290 ( 15 ~; 10 |; 0 &; 260 @)
% ( 0 <=>; 4 =>; 1 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 28 usr; 29 con; 0-2 aty)
% Number of variables : 36 ( 0 ^ 36 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(conj_0,conjecture,
( v_a
= ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) ).
thf(h0,negated_conjecture,
v_a
!= ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v1 @ l1 @ r1 ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(pax5,axiom,
( p5
=> ! [X49: a,X51: a,X48: tree_a,X26: tree_a,X52: a,X53: tree_a,X30: tree_a] :
( ( fheapIm837449470Leaf_a @ ( ft_a @ X49 @ ( ft_a @ X51 @ X48 @ X26 ) @ ( ft_a @ X52 @ X53 @ X30 ) ) )
= ( fproduc686083979Tree_a @ ( fproduct_fst_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ X51 @ X48 @ X26 ) ) ) @ ( ft_a @ X49 @ ( fproduct_snd_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ X51 @ X48 @ X26 ) ) ) @ ( ft_a @ X52 @ X53 @ X30 ) ) ) ) ),
file('<stdin>',pax5) ).
thf(pax3,axiom,
( p3
=> ( ft_a2
= ( ft_a @ fv3 @ ( fproduct_snd_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ fv1 @ fl1 @ fr1 ) ) ) @ ( ft_a @ fv2 @ fl2 @ fr2 ) ) ) ),
file('<stdin>',pax3) ).
thf(pax1,axiom,
( p1
=> ( ( fproduc686083979Tree_a @ fv_a @ ft_a2 )
= ( fheapIm837449470Leaf_a @ ( ft_a @ fv3 @ ( ft_a @ fv1 @ fl1 @ fr1 ) @ ( ft_a @ fv2 @ fl2 @ fr2 ) ) ) ) ),
file('<stdin>',pax1) ).
thf(pax10,axiom,
( p10
=> ! [X44: a,X41: tree_a] :
( ( fproduct_fst_a_Tree_a @ ( fproduc686083979Tree_a @ X44 @ X41 ) )
= X44 ) ),
file('<stdin>',pax10) ).
thf(ax45,axiom,
p5,
file('<stdin>',ax45) ).
thf(ax47,axiom,
p3,
file('<stdin>',ax47) ).
thf(ax49,axiom,
p1,
file('<stdin>',ax49) ).
thf(nax46,axiom,
( p46
<= ( fv_a
= ( fproduct_fst_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ fv1 @ fl1 @ fr1 ) ) ) ) ),
file('<stdin>',nax46) ).
thf(ax4,axiom,
~ p46,
file('<stdin>',ax4) ).
thf(ax40,axiom,
p10,
file('<stdin>',ax40) ).
thf(c_0_10,plain,
! [X304: a,X305: a,X306: tree_a,X307: tree_a,X308: a,X309: tree_a,X310: tree_a] :
( ~ p5
| ( ( fheapIm837449470Leaf_a @ ( ft_a @ X304 @ ( ft_a @ X305 @ X306 @ X307 ) @ ( ft_a @ X308 @ X309 @ X310 ) ) )
= ( fproduc686083979Tree_a @ ( fproduct_fst_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ X305 @ X306 @ X307 ) ) ) @ ( ft_a @ X304 @ ( fproduct_snd_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ X305 @ X306 @ X307 ) ) ) @ ( ft_a @ X308 @ X309 @ X310 ) ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax5])])]) ).
thf(c_0_11,plain,
( ~ p3
| ( ft_a2
= ( ft_a @ fv3 @ ( fproduct_snd_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ fv1 @ fl1 @ fr1 ) ) ) @ ( ft_a @ fv2 @ fl2 @ fr2 ) ) ) ),
inference(fof_nnf,[status(thm)],[pax3]) ).
thf(c_0_12,plain,
( ~ p1
| ( ( fproduc686083979Tree_a @ fv_a @ ft_a2 )
= ( fheapIm837449470Leaf_a @ ( ft_a @ fv3 @ ( ft_a @ fv1 @ fl1 @ fr1 ) @ ( ft_a @ fv2 @ fl2 @ fr2 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[pax1]) ).
thf(c_0_13,plain,
! [X282: a,X283: tree_a] :
( ~ p10
| ( ( fproduct_fst_a_Tree_a @ ( fproduc686083979Tree_a @ X282 @ X283 ) )
= X282 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax10])])]) ).
thf(c_0_14,plain,
! [X1: a,X2: a,X3: tree_a,X4: tree_a,X5: tree_a,X6: a,X8: tree_a] :
( ( ( fheapIm837449470Leaf_a @ ( ft_a @ X1 @ ( ft_a @ X2 @ X3 @ X4 ) @ ( ft_a @ X6 @ X5 @ X8 ) ) )
= ( fproduc686083979Tree_a @ ( fproduct_fst_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ X2 @ X3 @ X4 ) ) ) @ ( ft_a @ X1 @ ( fproduct_snd_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ X2 @ X3 @ X4 ) ) ) @ ( ft_a @ X6 @ X5 @ X8 ) ) ) )
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,plain,
p5,
inference(split_conjunct,[status(thm)],[ax45]) ).
thf(c_0_16,plain,
( ( ft_a2
= ( ft_a @ fv3 @ ( fproduct_snd_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ fv1 @ fl1 @ fr1 ) ) ) @ ( ft_a @ fv2 @ fl2 @ fr2 ) ) )
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_17,plain,
p3,
inference(split_conjunct,[status(thm)],[ax47]) ).
thf(c_0_18,plain,
( ( ( fproduc686083979Tree_a @ fv_a @ ft_a2 )
= ( fheapIm837449470Leaf_a @ ( ft_a @ fv3 @ ( ft_a @ fv1 @ fl1 @ fr1 ) @ ( ft_a @ fv2 @ fl2 @ fr2 ) ) ) )
| ~ p1 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_19,plain,
p1,
inference(split_conjunct,[status(thm)],[ax49]) ).
thf(c_0_20,plain,
( ( fv_a
!= ( fproduct_fst_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ fv1 @ fl1 @ fr1 ) ) ) )
| p46 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax46])]) ).
thf(c_0_21,plain,
~ p46,
inference(fof_simplification,[status(thm)],[ax4]) ).
thf(c_0_22,plain,
! [X3: tree_a,X1: a] :
( ( ( fproduct_fst_a_Tree_a @ ( fproduc686083979Tree_a @ X1 @ X3 ) )
= X1 )
| ~ p10 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_23,plain,
p10,
inference(split_conjunct,[status(thm)],[ax40]) ).
thf(c_0_24,plain,
! [X1: a,X2: a,X3: tree_a,X4: tree_a,X5: tree_a,X6: a,X8: tree_a] :
( ( fproduc686083979Tree_a @ ( fproduct_fst_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ X1 @ X3 @ X4 ) ) ) @ ( ft_a @ X2 @ ( fproduct_snd_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ X1 @ X3 @ X4 ) ) ) @ ( ft_a @ X6 @ X5 @ X8 ) ) )
= ( fheapIm837449470Leaf_a @ ( ft_a @ X2 @ ( ft_a @ X1 @ X3 @ X4 ) @ ( ft_a @ X6 @ X5 @ X8 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]) ).
thf(c_0_25,plain,
( ( ft_a @ fv3 @ ( fproduct_snd_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ fv1 @ fl1 @ fr1 ) ) ) @ ( ft_a @ fv2 @ fl2 @ fr2 ) )
= ft_a2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]) ).
thf(c_0_26,plain,
( ( fheapIm837449470Leaf_a @ ( ft_a @ fv3 @ ( ft_a @ fv1 @ fl1 @ fr1 ) @ ( ft_a @ fv2 @ fl2 @ fr2 ) ) )
= ( fproduc686083979Tree_a @ fv_a @ ft_a2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]) ).
thf(c_0_27,plain,
( p46
| ( fv_a
!= ( fproduct_fst_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ fv1 @ fl1 @ fr1 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_28,plain,
~ p46,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_29,plain,
! [X3: tree_a,X1: a] :
( ( fproduct_fst_a_Tree_a @ ( fproduc686083979Tree_a @ X1 @ X3 ) )
= X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
thf(c_0_30,plain,
( ( fproduc686083979Tree_a @ ( fproduct_fst_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ fv1 @ fl1 @ fr1 ) ) ) @ ft_a2 )
= ( fproduc686083979Tree_a @ fv_a @ ft_a2 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
thf(c_0_31,plain,
( fproduct_fst_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ fv1 @ fl1 @ fr1 ) ) )
!= fv_a,
inference(sr,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_32,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_29]),c_0_31]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],]) ).
thf(0,theorem,
( v_a
= ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP066^1 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n022.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 : Thu Jun 2 16:42:06 EDT 2022
% 0.13/0.35 % CPUTime :
% 3.27/3.47 % SZS status Theorem
% 3.27/3.47 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 3.27/3.47 % Inferences: 1
% 3.27/3.47 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------