%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG256^2 : TPTP v9.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n028.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 : Thu Oct 9 01:12:13 PM UTC 2025
% Result : Theorem 0.46s 0.96s
% Output : Proof 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 46 ( 18 unt; 0 typ; 5 def)
% Number of atoms : 205 ( 47 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 189 ( 27 ~; 25 |; 1 &; 115 @)
% ( 0 <=>; 20 =>; 1 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 24 con; 0-2 aty)
% Number of variables : 64 ( 3 ^; 61 !; 0 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(def_axvarid,definition,
( axvarid
= ( ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ) ) ).
thf(def_apinj1,definition,
( apinj1
= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) ).
thf(def_hoasap,definition,
( hoasap
= ( ^ [X1: subst,X2: term,X3: subst] : ( ap @ ( sub @ X2 @ X3 ) ) ) ) ).
thf(def_hoasapinj1,definition,
( hoasapinj1
= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( hoasap @ id @ X1 @ id @ X3 )
= ( hoasap @ id @ X2 @ id @ X4 ) )
=> ( X1 = X2 ) ) ) ) ).
thf(def_hoasapinj1_lthm,definition,
( hoasapinj1_lthm
= ( axvarid
=> ( apinj1
=> hoasapinj1 ) ) ) ).
thf(thm,conjecture,
( ! [X1: term] :
( ( sub @ X1 @ id )
= X1 )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( ! [X1: term] :
( ( sub @ X1 @ id )
= X1 )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(ax1034,axiom,
( p1
| ~ p3 ),
file('<stdin>',ax1034) ).
thf(ax1036,axiom,
~ p1,
file('<stdin>',ax1036) ).
thf(ax1032,axiom,
( p3
| ~ p5 ),
file('<stdin>',ax1032) ).
thf(pax2,axiom,
( p2
=> ! [X1: term] :
( ( fsub @ X1 @ fid )
= X1 ) ),
file('<stdin>',pax2) ).
thf(ax1035,axiom,
( p1
| p2 ),
file('<stdin>',ax1035) ).
thf(ax1029,axiom,
( p5
| ~ p8 ),
file('<stdin>',ax1029) ).
thf(pax4,axiom,
( p4
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( fap @ X1 @ X3 )
= ( fap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ),
file('<stdin>',pax4) ).
thf(ax1033,axiom,
( p3
| p4 ),
file('<stdin>',ax1033) ).
thf(nax8,axiom,
( p8
<= ! [X1: term,X2: term,X3: term] :
( ( ( fap @ ( fsub @ f__1 @ fid ) @ X2 )
= ( fap @ ( fsub @ X1 @ fid ) @ X3 ) )
=> ( f__1 = X1 ) ) ),
file('<stdin>',nax8) ).
thf(c_0_9,plain,
( p1
| ~ p3 ),
inference(fof_simplification,[status(thm)],[ax1034]) ).
thf(c_0_10,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1036]) ).
thf(c_0_11,plain,
( p3
| ~ p5 ),
inference(fof_simplification,[status(thm)],[ax1032]) ).
thf(c_0_12,plain,
( p1
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_14,plain,
! [X2979: term] :
( ~ p2
| ( ( fsub @ X2979 @ fid )
= X2979 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax2])])]) ).
thf(c_0_15,plain,
( p1
| p2 ),
inference(split_conjunct,[status(thm)],[ax1035]) ).
thf(c_0_16,plain,
( p5
| ~ p8 ),
inference(fof_simplification,[status(thm)],[ax1029]) ).
thf(c_0_17,plain,
( p3
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_18,plain,
~ p3,
inference(sr,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_19,plain,
! [X2955: term,X2956: term,X2957: term,X2958: term] :
( ~ p4
| ( ( fap @ X2955 @ X2957 )
!= ( fap @ X2956 @ X2958 ) )
| ( X2955 = X2956 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax4])])]) ).
thf(c_0_20,plain,
( p3
| p4 ),
inference(split_conjunct,[status(thm)],[ax1033]) ).
thf(c_0_21,plain,
( ( ( ( fap @ ( fsub @ f__1 @ fid ) @ esk1467_0 )
= ( fap @ ( fsub @ esk1466_0 @ fid ) @ esk1468_0 ) )
| p8 )
& ( ( f__1 != esk1466_0 )
| p8 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax8])])])])]) ).
thf(c_0_22,plain,
! [X1: term] :
( ( ( fsub @ X1 @ fid )
= X1 )
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_23,plain,
p2,
inference(sr,[status(thm)],[c_0_15,c_0_13]) ).
thf(c_0_24,plain,
( p5
| ~ p8 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_25,plain,
~ p5,
inference(sr,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_26,plain,
! [X1: term,X2: term,X3: term,X4: term] :
( ( X1 = X3 )
| ~ p4
| ( ( fap @ X1 @ X2 )
!= ( fap @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_27,plain,
p4,
inference(sr,[status(thm)],[c_0_20,c_0_18]) ).
thf(c_0_28,plain,
( ( ( fap @ ( fsub @ f__1 @ fid ) @ esk1467_0 )
= ( fap @ ( fsub @ esk1466_0 @ fid ) @ esk1468_0 ) )
| p8 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_29,plain,
! [X1: term] :
( ( fsub @ X1 @ fid )
= X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
thf(c_0_30,plain,
~ p8,
inference(sr,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_31,plain,
! [X1: term,X2: term,X3: term,X4: term] :
( ( X1 = X2 )
| ( ( fap @ X1 @ X3 )
!= ( fap @ X2 @ X4 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]) ).
thf(c_0_32,plain,
( ( fap @ esk1466_0 @ esk1468_0 )
= ( fap @ f__1 @ esk1467_0 ) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),c_0_29]),c_0_30]) ).
thf(c_0_33,plain,
( p8
| ( f__1 != esk1466_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_34,plain,
! [X1: term,X2: term] :
( ( X1 = esk1466_0 )
| ( ( fap @ X1 @ X2 )
!= ( fap @ f__1 @ esk1467_0 ) ) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
thf(c_0_35,plain,
esk1466_0 != f__1,
inference(sr,[status(thm)],[c_0_33,c_0_30]) ).
thf(c_0_36,plain,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_34]),c_0_35]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],[]) ).
thf(0,theorem,
( ! [X1: term] :
( ( sub @ X1 @ id )
= X1 )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG256^2 : TPTP v9.2.0. Bugfixed v5.2.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n028.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 : 300
% 0.13/0.34 % DateTime : Wed Oct 8 23:34:08 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.46/0.96 % SZS status Theorem
% 0.46/0.96 % Mode: mode485:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 0.46/0.96 % Inferences: 35
% 0.46/0.96 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------