%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM696^1 : 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 : 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 : 300s
% DateTime : Thu Oct 9 02:11:50 PM UTC 2025
% Result : Theorem 23.92s 23.94s
% Output : Proof 23.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 49 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 234 ( 45 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 213 ( 39 ~; 21 |; 1 &; 140 @)
% ( 0 <=>; 10 =>; 2 <=; 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 : 20 ( 18 usr; 19 con; 0-2 aty)
% Number of variables : 42 ( 0 ^; 42 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(satz25,conjecture,
( ! [X1: nat] :
( y
!= ( pl @ ( pl @ x @ n_1 ) @ X1 ) )
=> ( y
= ( pl @ x @ n_1 ) ) ) ).
thf(h0,negated_conjecture,
~ ( ! [X1: nat] :
( y
!= ( pl @ ( pl @ x @ n_1 ) @ X1 ) )
=> ( y
= ( pl @ x @ n_1 ) ) ),
inference(assume_negation,[status(cth)],[satz25]) ).
thf(ax7,axiom,
~ p1,
file('<stdin>',ax7) ).
thf(pax7,axiom,
( p7
=> ! [X1: nat] :
( fy
!= ( fpl @ ( fpl @ fx @ fn_1 ) @ X1 ) ) ),
file('<stdin>',pax7) ).
thf(ax1,axiom,
( p1
| p7 ),
file('<stdin>',ax1) ).
thf(pax6,axiom,
( p6
=> ! [X1: nat,X2: nat] :
( ( fpl @ X1 @ X2 )
= ( fpl @ X2 @ X1 ) ) ),
file('<stdin>',pax6) ).
thf(ax2,axiom,
p6,
file('<stdin>',ax2) ).
thf(pax5,axiom,
( p5
=> ! [X1: nat,X2: nat,X3: nat] :
( ~ ! [X4: nat] :
( X1
!= ( fpl @ X2 @ X4 ) )
=> ~ ! [X4: nat] :
( ( fpl @ X1 @ X3 )
!= ( fpl @ ( fpl @ X2 @ X3 ) @ X4 ) ) ) ),
file('<stdin>',pax5) ).
thf(ax3,axiom,
p5,
file('<stdin>',ax3) ).
thf(pax4,axiom,
( p4
=> ! [X1: nat] :
( ! [X2: nat] :
( X1
!= ( fpl @ fn_1 @ X2 ) )
=> ( X1 = fn_1 ) ) ),
file('<stdin>',pax4) ).
thf(ax4,axiom,
p4,
file('<stdin>',ax4) ).
thf(nax2,axiom,
( p2
<= ! [X1: nat] :
( fy
!= ( fpl @ fx @ X1 ) ) ),
file('<stdin>',nax2) ).
thf(ax6,axiom,
~ p2,
file('<stdin>',ax6) ).
thf(nax1,axiom,
( p1
<= ( ! [X1: nat] :
( fy
!= ( fpl @ ( fpl @ fx @ fn_1 ) @ X1 ) )
=> ( fy
= ( fpl @ fx @ fn_1 ) ) ) ),
file('<stdin>',nax1) ).
thf(c_0_12,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax7]) ).
thf(c_0_13,plain,
! [X11: nat] :
( ~ p7
| ( fy
!= ( fpl @ ( fpl @ fx @ fn_1 ) @ X11 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax7])])])]) ).
thf(c_0_14,plain,
( p1
| p7 ),
inference(split_conjunct,[status(thm)],[ax1]) ).
thf(c_0_15,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_16,plain,
! [X13: nat,X14: nat] :
( ~ p6
| ( ( fpl @ X13 @ X14 )
= ( fpl @ X14 @ X13 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax6])])]) ).
thf(c_0_17,plain,
! [X1: nat] :
( ~ p7
| ( fy
!= ( fpl @ ( fpl @ fx @ fn_1 ) @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_18,plain,
p7,
inference(sr,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_19,plain,
! [X2: nat,X1: nat] :
( ( ( fpl @ X1 @ X2 )
= ( fpl @ X2 @ X1 ) )
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_20,plain,
p6,
inference(split_conjunct,[status(thm)],[ax2]) ).
thf(c_0_21,plain,
! [X17: nat,X18: nat,X19: nat,X20: nat] :
( ~ p5
| ( X17
!= ( fpl @ X18 @ X19 ) )
| ( ( fpl @ X17 @ X20 )
= ( fpl @ ( fpl @ X18 @ X20 ) @ ( esk7_3 @ X17 @ X18 @ X20 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax5])])])])])]) ).
thf(c_0_22,plain,
! [X1: nat] :
( ( fpl @ ( fpl @ fx @ fn_1 ) @ X1 )
!= fy ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).
thf(c_0_23,plain,
! [X2: nat,X1: nat] :
( ( fpl @ X1 @ X2 )
= ( fpl @ X2 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]) ).
thf(c_0_24,plain,
! [X1: nat,X2: nat,X4: nat,X3: nat] :
( ( ( fpl @ X1 @ X4 )
= ( fpl @ ( fpl @ X2 @ X4 ) @ ( esk7_3 @ X1 @ X2 @ X4 ) ) )
| ~ p5
| ( X1
!= ( fpl @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_25,plain,
p5,
inference(split_conjunct,[status(thm)],[ax3]) ).
thf(c_0_26,plain,
! [X27: nat] :
( ~ p4
| ( X27
= ( fpl @ fn_1 @ ( esk12_1 @ X27 ) ) )
| ( X27 = fn_1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax4])])])])]) ).
thf(c_0_27,plain,
! [X1: nat] :
( ( fpl @ ( fpl @ fn_1 @ fx ) @ X1 )
!= fy ),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_28,plain,
! [X1: nat,X3: nat,X2: nat] :
( ( fpl @ ( fpl @ X1 @ X2 ) @ ( esk7_3 @ ( fpl @ X1 @ X3 ) @ X1 @ X2 ) )
= ( fpl @ ( fpl @ X1 @ X3 ) @ X2 ) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])])]) ).
thf(c_0_29,plain,
! [X1: nat] :
( ( X1
= ( fpl @ fn_1 @ ( esk12_1 @ X1 ) ) )
| ( X1 = fn_1 )
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_30,plain,
p4,
inference(split_conjunct,[status(thm)],[ax4]) ).
thf(c_0_31,plain,
( ( fy
= ( fpl @ fx @ esk14_0 ) )
| p2 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax2])])])]) ).
thf(c_0_32,plain,
~ p2,
inference(fof_simplification,[status(thm)],[ax6]) ).
thf(c_0_33,plain,
! [X34: nat] :
( ( ( fy
!= ( fpl @ ( fpl @ fx @ fn_1 ) @ X34 ) )
| p1 )
& ( ( fy
!= ( fpl @ fx @ fn_1 ) )
| p1 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])])])]) ).
thf(c_0_34,plain,
! [X1: nat] :
( ( fpl @ fx @ ( fpl @ fn_1 @ X1 ) )
!= fy ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_23]) ).
thf(c_0_35,plain,
! [X1: nat] :
( ( ( fpl @ fn_1 @ ( esk12_1 @ X1 ) )
= X1 )
| ( X1 = fn_1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).
thf(c_0_36,plain,
( ( fy
= ( fpl @ fx @ esk14_0 ) )
| p2 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_37,plain,
~ p2,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_38,plain,
( p1
| ( fy
!= ( fpl @ fx @ fn_1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_39,plain,
! [X1: nat] :
( ( X1 = fn_1 )
| ( ( fpl @ fx @ X1 )
!= fy ) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_40,plain,
( ( fpl @ fx @ esk14_0 )
= fy ),
inference(sr,[status(thm)],[c_0_36,c_0_37]) ).
thf(c_0_41,plain,
( ( fpl @ fx @ fn_1 )
!= fy ),
inference(sr,[status(thm)],[c_0_38,c_0_15]) ).
thf(c_0_42,plain,
esk14_0 = fn_1,
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
thf(c_0_43,plain,
( ( fpl @ fn_1 @ fx )
!= fy ),
inference(rw,[status(thm)],[c_0_41,c_0_23]) ).
thf(c_0_44,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_42]),c_0_23]),c_0_43]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],[]) ).
thf(0,theorem,
( ! [X1: nat] :
( y
!= ( pl @ ( pl @ x @ n_1 ) @ X1 ) )
=> ( y
= ( pl @ x @ n_1 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM696^1 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 8 22:55:38 EDT 2025
% 0.14/0.36 % CPUTime :
% 23.92/23.94 % SZS status Theorem
% 23.92/23.94 % Mode: mode371
% 23.92/23.94 % Inferences: 3
% 23.92/23.94 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------