TSTP Solution File: ALG265^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG265^2 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n019.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 : Thu Jul 14 17:57:50 EDT 2022
% Result : Theorem 1.03s 1.24s
% Output : Proof 1.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 21
% Syntax : Number of formulae : 62 ( 22 unt; 0 typ; 5 def)
% Number of atoms : 342 ( 28 equ; 0 cnn)
% Maximal formula atoms : 27 ( 5 avg)
% Number of connectives : 466 ( 38 ~; 37 |; 0 &; 356 @)
% ( 0 <=>; 34 =>; 1 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 32 usr; 33 con; 0-2 aty)
% Number of variables : 85 ( 2 ^ 83 !; 0 ?; 85 :)
% Comments :
%------------------------------------------------------------------------------
thf(def_axclos,definition,
( axclos
= ( ! [X1: term,X2: subst,X3: subst] :
( ( sub @ ( sub @ X1 @ X2 ) @ X3 )
= ( sub @ X1 @ ( comp @ X2 @ X3 ) ) ) ) ) ).
thf(def_axmap,definition,
( axmap
= ( ! [X1: term,X2: subst,X3: subst] :
( ( comp @ ( push @ X1 @ X2 ) @ X3 )
= ( push @ ( sub @ X1 @ X3 ) @ ( comp @ X2 @ X3 ) ) ) ) ) ).
thf(def_hoaslam,definition,
( hoaslam
= ( ^ [X1: subst,X2: subst > term > term] : ( lam @ ( X2 @ sh @ one ) ) ) ) ).
thf(def_hoasinduction_lem3aa,definition,
( hoasinduction_lem3aa
= ( ! [X1: subst > term > subst > $o] :
( ! [X2: subst > term > term] :
( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
=> ( X1 @ id @ ( hoaslam @ id @ X2 ) @ id ) ) )
=> ! [X2: term] :
( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ) ).
thf(def_hoasinduction_lem3aa_lthm,definition,
( hoasinduction_lem3aa_lthm
= ( axclos
=> ( axmap
=> hoasinduction_lem3aa ) ) ) ).
thf(thm,conjecture,
( ! [X1: term,X2: subst,X3: subst] :
( ( sub @ ( sub @ X1 @ X2 ) @ X3 )
= ( sub @ X1 @ ( comp @ X2 @ X3 ) ) )
=> ( ! [X1: term,X2: subst,X3: subst] :
( ( comp @ ( push @ X1 @ X2 ) @ X3 )
= ( push @ ( sub @ X1 @ X3 ) @ ( comp @ X2 @ X3 ) ) )
=> ! [X1: subst > term > subst > $o] :
( ! [X2: subst > term > term] :
( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) )
=> ! [X2: term] :
( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( ! [X1: term,X2: subst,X3: subst] :
( ( sub @ ( sub @ X1 @ X2 ) @ X3 )
= ( sub @ X1 @ ( comp @ X2 @ X3 ) ) )
=> ( ! [X1: term,X2: subst,X3: subst] :
( ( comp @ ( push @ X1 @ X2 ) @ X3 )
= ( push @ ( sub @ X1 @ X3 ) @ ( comp @ X2 @ X3 ) ) )
=> ! [X1: subst > term > subst > $o] :
( ! [X2: subst > term > term] :
( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) )
=> ! [X2: term] :
( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(ax1151,axiom,
( p1
| ~ p3 ),
file('<stdin>',ax1151) ).
thf(ax1153,axiom,
~ p1,
file('<stdin>',ax1153) ).
thf(ax1149,axiom,
( p3
| ~ p5 ),
file('<stdin>',ax1149) ).
thf(ax1146,axiom,
( p5
| ~ p8 ),
file('<stdin>',ax1146) ).
thf(ax1093,axiom,
( ~ p9
| p61 ),
file('<stdin>',ax1093) ).
thf(ax1145,axiom,
( p8
| p9 ),
file('<stdin>',ax1145) ).
thf(pax4,axiom,
( p4
=> ! [X130: term,X129: subst,X131: subst] :
( ( fcomp @ ( fpush @ X130 @ X129 ) @ X131 )
= ( fpush @ ( fsub @ X130 @ X131 ) @ ( fcomp @ X129 @ X131 ) ) ) ),
file('<stdin>',pax4) ).
thf(ax1150,axiom,
( p3
| p4 ),
file('<stdin>',ax1150) ).
thf(pax2,axiom,
( p2
=> ! [X130: term,X129: subst,X131: subst] :
( ( fsub @ ( fsub @ X130 @ X129 ) @ X131 )
= ( fsub @ X130 @ ( fcomp @ X129 @ X131 ) ) ) ),
file('<stdin>',pax2) ).
thf(ax1152,axiom,
( p1
| p2 ),
file('<stdin>',ax1152) ).
thf(ax1082,axiom,
( ~ p61
| ~ p73
| p14 ),
file('<stdin>',ax1082) ).
thf(nax73,axiom,
( p73
<= ! [X82: subst,X78: term,X60: subst] :
( ( fsub @ ( fsub @ f__3 @ ( fpush @ X78 @ X82 ) ) @ X60 )
= ( fsub @ f__3 @ ( fpush @ ( fsub @ X78 @ X60 ) @ ( fcomp @ X82 @ X60 ) ) ) ) ),
file('<stdin>',nax73) ).
thf(ax1140,axiom,
( p10
| ~ p14 ),
file('<stdin>',ax1140) ).
thf(ax1144,axiom,
( p8
| ~ p10 ),
file('<stdin>',ax1144) ).
thf(c_0_14,plain,
( p1
| ~ p3 ),
inference(fof_simplification,[status(thm)],[ax1151]) ).
thf(c_0_15,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1153]) ).
thf(c_0_16,plain,
( p3
| ~ p5 ),
inference(fof_simplification,[status(thm)],[ax1149]) ).
thf(c_0_17,plain,
( p1
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_18,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_19,plain,
( p5
| ~ p8 ),
inference(fof_simplification,[status(thm)],[ax1146]) ).
thf(c_0_20,plain,
( p3
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_21,plain,
~ p3,
inference(sr,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_22,plain,
( p5
| ~ p8 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_23,plain,
~ p5,
inference(sr,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_24,plain,
( ~ p9
| p61 ),
inference(fof_simplification,[status(thm)],[ax1093]) ).
thf(c_0_25,plain,
( p8
| p9 ),
inference(split_conjunct,[status(thm)],[ax1145]) ).
thf(c_0_26,plain,
~ p8,
inference(sr,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_27,plain,
! [X1080: term,X1081: subst,X1082: subst] :
( ~ p4
| ( ( fcomp @ ( fpush @ X1080 @ X1081 ) @ X1082 )
= ( fpush @ ( fsub @ X1080 @ X1082 ) @ ( fcomp @ X1081 @ X1082 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax4])])]) ).
thf(c_0_28,plain,
( p3
| p4 ),
inference(split_conjunct,[status(thm)],[ax1150]) ).
thf(c_0_29,plain,
! [X1086: term,X1087: subst,X1088: subst] :
( ~ p2
| ( ( fsub @ ( fsub @ X1086 @ X1087 ) @ X1088 )
= ( fsub @ X1086 @ ( fcomp @ X1087 @ X1088 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax2])])]) ).
thf(c_0_30,plain,
( p1
| p2 ),
inference(split_conjunct,[status(thm)],[ax1152]) ).
thf(c_0_31,plain,
( ~ p61
| ~ p73
| p14 ),
inference(fof_simplification,[status(thm)],[ax1082]) ).
thf(c_0_32,plain,
( p61
| ~ p9 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_33,plain,
p9,
inference(sr,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_34,plain,
( ( ( fsub @ ( fsub @ f__3 @ ( fpush @ esk412_0 @ esk411_0 ) ) @ esk413_0 )
!= ( fsub @ f__3 @ ( fpush @ ( fsub @ esk412_0 @ esk413_0 ) @ ( fcomp @ esk411_0 @ esk413_0 ) ) ) )
| p73 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax73])])])]) ).
thf(c_0_35,plain,
! [X1: subst,X2: term,X3: subst] :
( ( ( fcomp @ ( fpush @ X2 @ X1 ) @ X3 )
= ( fpush @ ( fsub @ X2 @ X3 ) @ ( fcomp @ X1 @ X3 ) ) )
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_36,plain,
p4,
inference(sr,[status(thm)],[c_0_28,c_0_21]) ).
thf(c_0_37,plain,
! [X1: subst,X2: term,X3: subst] :
( ( ( fsub @ ( fsub @ X2 @ X1 ) @ X3 )
= ( fsub @ X2 @ ( fcomp @ X1 @ X3 ) ) )
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_38,plain,
p2,
inference(sr,[status(thm)],[c_0_30,c_0_18]) ).
thf(c_0_39,plain,
( p14
| ~ p61
| ~ p73 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_40,plain,
p61,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]) ).
thf(c_0_41,plain,
( p73
| ( ( fsub @ ( fsub @ f__3 @ ( fpush @ esk412_0 @ esk411_0 ) ) @ esk413_0 )
!= ( fsub @ f__3 @ ( fpush @ ( fsub @ esk412_0 @ esk413_0 ) @ ( fcomp @ esk411_0 @ esk413_0 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_42,plain,
! [X3: subst,X2: term,X1: subst] :
( ( fpush @ ( fsub @ X2 @ X1 ) @ ( fcomp @ X3 @ X1 ) )
= ( fcomp @ ( fpush @ X2 @ X3 ) @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
thf(c_0_43,plain,
! [X1: subst,X2: term,X3: subst] :
( ( fsub @ X2 @ ( fcomp @ X1 @ X3 ) )
= ( fsub @ ( fsub @ X2 @ X1 ) @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
thf(c_0_44,plain,
( p10
| ~ p14 ),
inference(fof_simplification,[status(thm)],[ax1140]) ).
thf(c_0_45,plain,
( p14
| ~ p73 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40])]) ).
thf(c_0_46,plain,
p73,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).
thf(c_0_47,plain,
( p8
| ~ p10 ),
inference(fof_simplification,[status(thm)],[ax1144]) ).
thf(c_0_48,plain,
( p10
| ~ p14 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
thf(c_0_49,plain,
p14,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]) ).
thf(c_0_50,plain,
( p8
| ~ p10 ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_51,plain,
p10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]) ).
thf(c_0_52,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51])]),c_0_26]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],]) ).
thf(0,theorem,
( ! [X1: term,X2: subst,X3: subst] :
( ( sub @ ( sub @ X1 @ X2 ) @ X3 )
= ( sub @ X1 @ ( comp @ X2 @ X3 ) ) )
=> ( ! [X1: term,X2: subst,X3: subst] :
( ( comp @ ( push @ X1 @ X2 ) @ X3 )
= ( push @ ( sub @ X1 @ X3 ) @ ( comp @ X2 @ X3 ) ) )
=> ! [X1: subst > term > subst > $o] :
( ! [X2: subst > term > term] :
( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) )
=> ! [X2: term] :
( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ALG265^2 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.04/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 9 05:20:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.03/1.24 % SZS status Theorem
% 1.03/1.24 % Mode: mode485:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 1.03/1.24 % Inferences: 275
% 1.03/1.24 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------