%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP092^1 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n018.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 01:46:56 PM UTC 2025
% Result : Theorem 165.97s 164.36s
% Output : Proof 165.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of formulae : 59 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 218 ( 17 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 251 ( 46 ~; 34 |; 0 &; 168 @)
% ( 0 <=>; 2 =>; 1 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 50 ( 0 ^; 50 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(conj_0,conjecture,
! [X1: list_P1467822637od_a_a,X2: a,X3: a,X4: list_P1467822637od_a_a] :
( es
!= ( append1574001858od_a_a @ X1 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X2 @ X3 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X3 @ X2 ) @ X4 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: list_P1467822637od_a_a,X2: a,X3: a,X4: list_P1467822637od_a_a] :
( es
!= ( append1574001858od_a_a @ X1 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X2 @ X3 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X3 @ X2 ) @ X4 ) ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(ax32,axiom,
( ~ p33
| p32 ),
file('<stdin>',ax32) ).
thf(ax34,axiom,
( ~ p18
| p26 ),
file('<stdin>',ax34) ).
thf(ax31,axiom,
( ~ p32
| p31 ),
file('<stdin>',ax31) ).
thf(ax33,axiom,
p33,
file('<stdin>',ax33) ).
thf(ax27,axiom,
( ~ p26
| p28 ),
file('<stdin>',ax27) ).
thf(ax43,axiom,
p18,
file('<stdin>',ax43) ).
thf(ax30,axiom,
( ~ p31
| ~ p19
| p30 ),
file('<stdin>',ax30) ).
thf(ax28,axiom,
( ~ p29
| ~ p28
| p27 ),
file('<stdin>',ax28) ).
thf(ax29,axiom,
( ~ p30
| p29 ),
file('<stdin>',ax29) ).
thf(ax42,axiom,
p19,
file('<stdin>',ax42) ).
thf(pax27,axiom,
( p27
=> ! [X6: list_P1467822637od_a_a,X4: a,X7: a,X8: list_P1467822637od_a_a] :
( ( fcons_P1921020637od_a_a @ fe @ fes )
!= ( fappend1574001858od_a_a @ X6 @ ( fcons_P1921020637od_a_a @ ( fproduct_Pair_a_a @ X4 @ X7 ) @ ( fcons_P1921020637od_a_a @ ( fproduct_Pair_a_a @ X7 @ X4 ) @ X8 ) ) ) ) ),
file('<stdin>',pax27) ).
thf(pax11,axiom,
( p11
=> ! [X11: product_prod_a_a,X9: list_P1467822637od_a_a,X10: list_P1467822637od_a_a] :
( ( fappend1574001858od_a_a @ ( fcons_P1921020637od_a_a @ X11 @ X9 ) @ X10 )
= ( fcons_P1921020637od_a_a @ X11 @ ( fappend1574001858od_a_a @ X9 @ X10 ) ) ) ),
file('<stdin>',pax11) ).
thf(ax50,axiom,
p11,
file('<stdin>',ax50) ).
thf(nax1,axiom,
( p1
<= ! [X20: list_P1467822637od_a_a,X21: a,X16: a,X22: list_P1467822637od_a_a] :
( fes
!= ( fappend1574001858od_a_a @ X20 @ ( fcons_P1921020637od_a_a @ ( fproduct_Pair_a_a @ X21 @ X16 ) @ ( fcons_P1921020637od_a_a @ ( fproduct_Pair_a_a @ X16 @ X21 ) @ X22 ) ) ) ) ),
file('<stdin>',nax1) ).
thf(ax60,axiom,
~ p1,
file('<stdin>',ax60) ).
thf(c_0_15,plain,
( ~ p33
| p32 ),
inference(fof_simplification,[status(thm)],[ax32]) ).
thf(c_0_16,plain,
( ~ p18
| p26 ),
inference(fof_simplification,[status(thm)],[ax34]) ).
thf(c_0_17,plain,
( ~ p32
| p31 ),
inference(fof_simplification,[status(thm)],[ax31]) ).
thf(c_0_18,plain,
( p32
| ~ p33 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_19,plain,
p33,
inference(split_conjunct,[status(thm)],[ax33]) ).
thf(c_0_20,plain,
( ~ p26
| p28 ),
inference(fof_simplification,[status(thm)],[ax27]) ).
thf(c_0_21,plain,
( p26
| ~ p18 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_22,plain,
p18,
inference(split_conjunct,[status(thm)],[ax43]) ).
thf(c_0_23,plain,
( ~ p31
| ~ p19
| p30 ),
inference(fof_simplification,[status(thm)],[ax30]) ).
thf(c_0_24,plain,
( p31
| ~ p32 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_25,plain,
p32,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]) ).
thf(c_0_26,plain,
( ~ p29
| ~ p28
| p27 ),
inference(fof_simplification,[status(thm)],[ax28]) ).
thf(c_0_27,plain,
( p28
| ~ p26 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_28,plain,
p26,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]) ).
thf(c_0_29,plain,
( ~ p30
| p29 ),
inference(fof_simplification,[status(thm)],[ax29]) ).
thf(c_0_30,plain,
( p30
| ~ p31
| ~ p19 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_31,plain,
p19,
inference(split_conjunct,[status(thm)],[ax42]) ).
thf(c_0_32,plain,
p31,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
thf(c_0_33,plain,
( p27
| ~ p29
| ~ p28 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_34,plain,
p28,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
thf(c_0_35,plain,
( p29
| ~ p30 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_36,plain,
p30,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
thf(c_0_37,plain,
! [X41: list_P1467822637od_a_a,X42: a,X43: a,X44: list_P1467822637od_a_a] :
( ~ p27
| ( ( fcons_P1921020637od_a_a @ fe @ fes )
!= ( fappend1574001858od_a_a @ X41 @ ( fcons_P1921020637od_a_a @ ( fproduct_Pair_a_a @ X42 @ X43 ) @ ( fcons_P1921020637od_a_a @ ( fproduct_Pair_a_a @ X43 @ X42 ) @ X44 ) ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax27])])])]) ).
thf(c_0_38,plain,
( p27
| ~ p29 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]) ).
thf(c_0_39,plain,
p29,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
thf(c_0_40,plain,
! [X65: product_prod_a_a,X66: list_P1467822637od_a_a,X67: list_P1467822637od_a_a] :
( ~ p11
| ( ( fappend1574001858od_a_a @ ( fcons_P1921020637od_a_a @ X65 @ X66 ) @ X67 )
= ( fcons_P1921020637od_a_a @ X65 @ ( fappend1574001858od_a_a @ X66 @ X67 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax11])])]) ).
thf(c_0_41,plain,
! [X1: list_P1467822637od_a_a,X4: a,X3: a,X2: list_P1467822637od_a_a] :
( ~ p27
| ( ( fcons_P1921020637od_a_a @ fe @ fes )
!= ( fappend1574001858od_a_a @ X1 @ ( fcons_P1921020637od_a_a @ ( fproduct_Pair_a_a @ X3 @ X4 ) @ ( fcons_P1921020637od_a_a @ ( fproduct_Pair_a_a @ X4 @ X3 ) @ X2 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_42,plain,
p27,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]) ).
thf(c_0_43,plain,
! [X1: list_P1467822637od_a_a,X11: product_prod_a_a,X2: list_P1467822637od_a_a] :
( ( ( fappend1574001858od_a_a @ ( fcons_P1921020637od_a_a @ X11 @ X1 ) @ X2 )
= ( fcons_P1921020637od_a_a @ X11 @ ( fappend1574001858od_a_a @ X1 @ X2 ) ) )
| ~ p11 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_44,plain,
p11,
inference(split_conjunct,[status(thm)],[ax50]) ).
thf(c_0_45,plain,
( ( fes
= ( fappend1574001858od_a_a @ esk40_0 @ ( fcons_P1921020637od_a_a @ ( fproduct_Pair_a_a @ esk41_0 @ esk42_0 ) @ ( fcons_P1921020637od_a_a @ ( fproduct_Pair_a_a @ esk42_0 @ esk41_0 ) @ esk43_0 ) ) ) )
| p1 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])])]) ).
thf(c_0_46,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax60]) ).
thf(c_0_47,plain,
! [X1: list_P1467822637od_a_a,X4: a,X3: a,X2: list_P1467822637od_a_a] :
( ( fappend1574001858od_a_a @ X1 @ ( fcons_P1921020637od_a_a @ ( fproduct_Pair_a_a @ X3 @ X4 ) @ ( fcons_P1921020637od_a_a @ ( fproduct_Pair_a_a @ X4 @ X3 ) @ X2 ) ) )
!= ( fcons_P1921020637od_a_a @ fe @ fes ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]) ).
thf(c_0_48,plain,
! [X1: list_P1467822637od_a_a,X11: product_prod_a_a,X2: list_P1467822637od_a_a] :
( ( fappend1574001858od_a_a @ ( fcons_P1921020637od_a_a @ X11 @ X1 ) @ X2 )
= ( fcons_P1921020637od_a_a @ X11 @ ( fappend1574001858od_a_a @ X1 @ X2 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]) ).
thf(c_0_49,plain,
( ( fes
= ( fappend1574001858od_a_a @ esk40_0 @ ( fcons_P1921020637od_a_a @ ( fproduct_Pair_a_a @ esk41_0 @ esk42_0 ) @ ( fcons_P1921020637od_a_a @ ( fproduct_Pair_a_a @ esk42_0 @ esk41_0 ) @ esk43_0 ) ) ) )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
thf(c_0_50,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_51,plain,
! [X1: list_P1467822637od_a_a,X11: product_prod_a_a,X4: a,X3: a,X2: list_P1467822637od_a_a] :
( ( fcons_P1921020637od_a_a @ X11 @ ( fappend1574001858od_a_a @ X1 @ ( fcons_P1921020637od_a_a @ ( fproduct_Pair_a_a @ X3 @ X4 ) @ ( fcons_P1921020637od_a_a @ ( fproduct_Pair_a_a @ X4 @ X3 ) @ X2 ) ) ) )
!= ( fcons_P1921020637od_a_a @ fe @ fes ) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
thf(c_0_52,plain,
( ( fappend1574001858od_a_a @ esk40_0 @ ( fcons_P1921020637od_a_a @ ( fproduct_Pair_a_a @ esk41_0 @ esk42_0 ) @ ( fcons_P1921020637od_a_a @ ( fproduct_Pair_a_a @ esk42_0 @ esk41_0 ) @ esk43_0 ) ) )
= fes ),
inference(sr,[status(thm)],[c_0_49,c_0_50]) ).
thf(c_0_53,plain,
! [X11: product_prod_a_a] :
( ( fcons_P1921020637od_a_a @ X11 @ fes )
!= ( fcons_P1921020637od_a_a @ fe @ fes ) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
thf(c_0_54,plain,
$false,
inference(er,[status(thm)],[c_0_53]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],[]) ).
thf(0,theorem,
! [X1: list_P1467822637od_a_a,X2: a,X3: a,X4: list_P1467822637od_a_a] :
( es
!= ( append1574001858od_a_a @ X1 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X2 @ X3 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X3 @ X2 ) @ X4 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : ITP092^1 : TPTP v9.2.0. Released v7.5.0.
% 0.04/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n018.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Oct 8 17:55:08 EDT 2025
% 0.14/0.36 % CPUTime :
% 61.58/60.25 slave returned with unknown status
% 165.97/164.36 % SZS status Theorem
% 165.97/164.36 % Mode: mode500:USE_SINE=true:SINE_TOLERANCE=1.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=2.:SINE_DEPTH=0
% 165.97/164.36 % Inferences: 9
% 165.97/164.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------