%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM662^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n015.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 02:11:41 PM UTC 2025
% Result : Theorem 1.09s 1.61s
% Output : Proof 1.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 43 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 148 ( 20 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 111 ( 29 ~; 16 |; 0 &; 62 @)
% ( 0 <=>; 3 =>; 1 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 18 con; 0-2 aty)
% Number of variables : 13 ( 0 ^; 13 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
thf(satz15,conjecture,
~ ! [X1: nat] :
( z
!= ( pl @ x @ X1 ) ) ).
thf(h0,negated_conjecture,
! [X1: nat] :
( z
!= ( pl @ x @ X1 ) ),
inference(assume_negation,[status(cth)],[satz15]) ).
thf(ax1806,axiom,
~ p2,
file('<stdin>',ax1806) ).
thf(ax1733,axiom,
( ~ p5
| p64 ),
file('<stdin>',ax1733) ).
thf(pax19,axiom,
( p19
=> ( fy
= ( fpl @ fx @ f__2 ) ) ),
file('<stdin>',pax19) ).
thf(ax1788,axiom,
( p2
| p19 ),
file('<stdin>',ax1788) ).
thf(ax986,axiom,
( ~ p64
| p542 ),
file('<stdin>',ax986) ).
thf(ax1803,axiom,
p5,
file('<stdin>',ax1803) ).
thf(pax1,axiom,
( p1
=> ! [X1: nat] :
( fz
!= ( fpl @ fx @ X1 ) ) ),
file('<stdin>',pax1) ).
thf(pax542,axiom,
( p542
=> ! [X1: nat] :
( ( fpl @ ( fpl @ fx @ f__2 ) @ X1 )
= ( fpl @ fx @ ( fpl @ f__2 @ X1 ) ) ) ),
file('<stdin>',pax542) ).
thf(nax3,axiom,
( p3
<= ! [X1: nat] :
( fz
!= ( fpl @ fy @ X1 ) ) ),
file('<stdin>',nax3) ).
thf(ax1805,axiom,
~ p3,
file('<stdin>',ax1805) ).
thf(ax1807,axiom,
p1,
file('<stdin>',ax1807) ).
thf(c_0_11,plain,
~ p2,
inference(fof_simplification,[status(thm)],[ax1806]) ).
thf(c_0_12,plain,
( ~ p5
| p64 ),
inference(fof_simplification,[status(thm)],[ax1733]) ).
thf(c_0_13,plain,
( ~ p19
| ( fy
= ( fpl @ fx @ f__2 ) ) ),
inference(fof_nnf,[status(thm)],[pax19]) ).
thf(c_0_14,plain,
( p2
| p19 ),
inference(split_conjunct,[status(thm)],[ax1788]) ).
thf(c_0_15,plain,
~ p2,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_16,plain,
( ~ p64
| p542 ),
inference(fof_simplification,[status(thm)],[ax986]) ).
thf(c_0_17,plain,
( p64
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_18,plain,
p5,
inference(split_conjunct,[status(thm)],[ax1803]) ).
thf(c_0_19,plain,
! [X648: nat] :
( ~ p1
| ( fz
!= ( fpl @ fx @ X648 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax1])])])]) ).
thf(c_0_20,plain,
! [X292: nat] :
( ~ p542
| ( ( fpl @ ( fpl @ fx @ f__2 ) @ X292 )
= ( fpl @ fx @ ( fpl @ f__2 @ X292 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax542])])]) ).
thf(c_0_21,plain,
( ( fy
= ( fpl @ fx @ f__2 ) )
| ~ p19 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_22,plain,
p19,
inference(sr,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_23,plain,
( p542
| ~ p64 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_24,plain,
p64,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).
thf(c_0_25,plain,
( ( fz
= ( fpl @ fy @ esk321_0 ) )
| p3 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax3])])])]) ).
thf(c_0_26,plain,
~ p3,
inference(fof_simplification,[status(thm)],[ax1805]) ).
thf(c_0_27,plain,
! [X1: nat] :
( ~ p1
| ( fz
!= ( fpl @ fx @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_28,plain,
p1,
inference(split_conjunct,[status(thm)],[ax1807]) ).
thf(c_0_29,plain,
! [X1: nat] :
( ( ( fpl @ ( fpl @ fx @ f__2 ) @ X1 )
= ( fpl @ fx @ ( fpl @ f__2 @ X1 ) ) )
| ~ p542 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_30,plain,
( ( fpl @ fx @ f__2 )
= fy ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]) ).
thf(c_0_31,plain,
p542,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]) ).
thf(c_0_32,plain,
( ( fz
= ( fpl @ fy @ esk321_0 ) )
| p3 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_33,plain,
~ p3,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_34,plain,
! [X1: nat] :
( ( fpl @ fx @ X1 )
!= fz ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
thf(c_0_35,plain,
! [X1: nat] :
( ( fpl @ fx @ ( fpl @ f__2 @ X1 ) )
= ( fpl @ fy @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
thf(c_0_36,plain,
( ( fpl @ fy @ esk321_0 )
= fz ),
inference(sr,[status(thm)],[c_0_32,c_0_33]) ).
thf(c_0_37,plain,
! [X1: nat] :
( ( fpl @ fy @ X1 )
!= fz ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_38,plain,
$false,
inference(sr,[status(thm)],[c_0_36,c_0_37]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],[]) ).
thf(0,theorem,
~ ! [X1: nat] :
( z
!= ( pl @ x @ X1 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM662^1 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 8 22:40:53 EDT 2025
% 0.12/0.34 % CPUTime :
% 1.09/1.61 % SZS status Theorem
% 1.09/1.61 % Mode: mode506
% 1.09/1.61 % Inferences: 40327
% 1.09/1.61 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------