%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG287^5 : TPTP v9.2.0. Released v4.0.0.
% 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 01:12:19 PM UTC 2025
% Result : Theorem 2.43s 2.61s
% Output : Proof 2.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 40 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 264 ( 61 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 224 ( 68 ~; 26 |; 4 &; 96 @)
% ( 0 <=>; 28 =>; 2 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 23 con; 0-2 aty)
% Number of variables : 31 ( 0 ^; 31 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(cPU_P_INJ_pme,conjecture,
( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( X1 != cZ )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
=> ( ( ( cP @ x @ u )
= ( cP @ y @ v ) )
=> ~ ( ( x = y )
=> ( u != v ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( X1 != cZ )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
=> ( ( ( cP @ x @ u )
= ( cP @ y @ v ) )
=> ~ ( ( x = y )
=> ( u != v ) ) ) ),
inference(assume_negation,[status(cth)],[cPU_P_INJ_pme]) ).
thf(ax4182,axiom,
( p1
| ~ p2 ),
file('<stdin>',ax4182) ).
thf(ax4183,axiom,
~ p1,
file('<stdin>',ax4183) ).
thf(ax4158,axiom,
( p2
| ~ p24 ),
file('<stdin>',ax4158) ).
thf(ax4181,axiom,
( p1
| ~ p3 ),
file('<stdin>',ax4181) ).
thf(nax24,axiom,
( p24
<= ( ~ ( ~ ( ( ( fcL @ fcZ )
= fcZ )
=> ( ( fcR @ fcZ )
!= fcZ ) )
=> ~ ! [X1: a,X2: a] :
( ( fcL @ ( fcP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( fcR @ ( fcP @ X1 @ X2 ) )
= X2 ) ) ),
file('<stdin>',nax24) ).
thf(nax3,axiom,
( p3
<= ( ( ( fcP @ fx @ fu )
= ( fcP @ fy @ fv ) )
=> ~ ( ( fx = fy )
=> ( fu != fv ) ) ) ),
file('<stdin>',nax3) ).
thf(pax5,axiom,
( p5
=> ( ( fx = fy )
=> ( fu != fv ) ) ),
file('<stdin>',pax5) ).
thf(ax4179,axiom,
( p3
| p5 ),
file('<stdin>',ax4179) ).
thf(c_0_8,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax4182]) ).
thf(c_0_9,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax4183]) ).
thf(c_0_10,plain,
( p2
| ~ p24 ),
inference(fof_simplification,[status(thm)],[ax4158]) ).
thf(c_0_11,plain,
( p1
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,plain,
( p1
| ~ p3 ),
inference(fof_simplification,[status(thm)],[ax4181]) ).
thf(c_0_14,plain,
! [X973: a,X974: a,X975: a,X976: a] :
( ( ( ( fcL @ fcZ )
= fcZ )
| p24 )
& ( ( ( fcR @ fcZ )
= fcZ )
| p24 )
& ( ( ( fcL @ ( fcP @ X973 @ X974 ) )
= X973 )
| p24 )
& ( ( ( fcR @ ( fcP @ X975 @ X976 ) )
= X976 )
| p24 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax24])])])])]) ).
thf(c_0_15,plain,
( p2
| ~ p24 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_16,plain,
~ p2,
inference(sr,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_17,plain,
( ( ( ( fcP @ fx @ fu )
= ( fcP @ fy @ fv ) )
| p3 )
& ( ( fx != fy )
| ( fu != fv )
| p3 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax3])])]) ).
thf(c_0_18,plain,
( p1
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_19,plain,
! [X2: a,X1: a] :
( ( ( fcL @ ( fcP @ X1 @ X2 ) )
= X1 )
| p24 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_20,plain,
~ p24,
inference(sr,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_21,plain,
( ( ( fcP @ fx @ fu )
= ( fcP @ fy @ fv ) )
| p3 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_22,plain,
~ p3,
inference(sr,[status(thm)],[c_0_18,c_0_12]) ).
thf(c_0_23,plain,
( ~ p5
| ( fx != fy )
| ( fu != fv ) ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax5])]) ).
thf(c_0_24,plain,
( p3
| p5 ),
inference(split_conjunct,[status(thm)],[ax4179]) ).
thf(c_0_25,plain,
! [X2: a,X1: a] :
( ( fcL @ ( fcP @ X1 @ X2 ) )
= X1 ),
inference(sr,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_26,plain,
( ( fcP @ fy @ fv )
= ( fcP @ fx @ fu ) ),
inference(sr,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_27,plain,
( ~ p5
| ( fx != fy )
| ( fu != fv ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_28,plain,
p5,
inference(sr,[status(thm)],[c_0_24,c_0_22]) ).
thf(c_0_29,plain,
! [X1: a,X2: a] :
( ( ( fcR @ ( fcP @ X1 @ X2 ) )
= X2 )
| p24 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_30,plain,
fy = fx,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_25]) ).
thf(c_0_31,plain,
( ( fv != fu )
| ( fy != fx ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
thf(c_0_32,plain,
! [X1: a,X2: a] :
( ( fcR @ ( fcP @ X1 @ X2 ) )
= X2 ),
inference(sr,[status(thm)],[c_0_29,c_0_20]) ).
thf(c_0_33,plain,
( ( fcP @ fx @ fv )
= ( fcP @ fx @ fu ) ),
inference(rw,[status(thm)],[c_0_26,c_0_30]) ).
thf(c_0_34,plain,
fv != fu,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_30])]) ).
thf(c_0_35,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_32]),c_0_34]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],[]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( X1 != cZ )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
=> ( ( ( cP @ x @ u )
= ( cP @ y @ v ) )
=> ~ ( ( x = y )
=> ( u != v ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ALG287^5 : TPTP v9.2.0. Released v4.0.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Oct 8 23:33:38 EDT 2025
% 0.13/0.33 % CPUTime :
% 2.43/2.61 % SZS status Theorem
% 2.43/2.61 % Mode: mode506
% 2.43/2.61 % Inferences: 38595
% 2.43/2.61 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------