%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG285^5 : 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 : n008.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 1.77s 1.96s
% Output : Proof 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 48 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 271 ( 55 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 346 ( 69 ~; 29 |; 3 &; 221 @)
% ( 0 <=>; 23 =>; 1 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 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 : 91 ( 0 ^; 91 !; 0 ?; 91 :)
% Comments :
%------------------------------------------------------------------------------
thf(cTHM22_pme,conjecture,
( ~ ( ~ ( ! [X1: a,X2: a,X3: a] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) )
=> ~ ! [X1: a] :
( ( cP @ cE @ X1 )
= X1 ) )
=> ~ ! [X1: a] :
( ( cP @ ( cJ @ X1 ) @ X1 )
= cE ) )
=> ~ ( ! [X1: a,X2: a,X3: a] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) )
=> ~ ! [X1: a,X2: a] :
~ ( ~ ! [X3: a] :
( ( cP @ X1 @ X3 )
!= X2 )
=> ! [X3: a] :
( ( cP @ X3 @ X1 )
!= X2 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ! [X1: a,X2: a,X3: a] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) )
=> ~ ! [X1: a] :
( ( cP @ cE @ X1 )
= X1 ) )
=> ~ ! [X1: a] :
( ( cP @ ( cJ @ X1 ) @ X1 )
= cE ) )
=> ~ ( ! [X1: a,X2: a,X3: a] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) )
=> ~ ! [X1: a,X2: a] :
~ ( ~ ! [X3: a] :
( ( cP @ X1 @ X3 )
!= X2 )
=> ! [X3: a] :
( ( cP @ X3 @ X1 )
!= X2 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM22_pme]) ).
thf(ax1185,axiom,
( p1
| ~ p2 ),
file('<stdin>',ax1185) ).
thf(ax1186,axiom,
~ p1,
file('<stdin>',ax1186) ).
thf(ax1177,axiom,
( p2
| ~ p12 ),
file('<stdin>',ax1177) ).
thf(pax4,axiom,
( p4
=> ! [X1: a,X2: a,X3: a] :
( ( fcP @ ( fcP @ X1 @ X2 ) @ X3 )
= ( fcP @ X1 @ ( fcP @ X2 @ X3 ) ) ) ),
file('<stdin>',pax4) ).
thf(ax1148,axiom,
( p12
| p4 ),
file('<stdin>',ax1148) ).
thf(pax13,axiom,
( p13
=> ! [X1: a] :
( ( fcP @ ( fcJ @ X1 ) @ X1 )
= fcE ) ),
file('<stdin>',pax13) ).
thf(ax1176,axiom,
( p2
| p13 ),
file('<stdin>',ax1176) ).
thf(pax39,axiom,
( p39
=> ! [X1: a] :
( ( fcP @ fcE @ X1 )
= X1 ) ),
file('<stdin>',pax39) ).
thf(ax1147,axiom,
( p12
| p39 ),
file('<stdin>',ax1147) ).
thf(nax1,axiom,
( p1
<= ( ~ ( ~ ( ! [X1: a,X2: a,X3: a] :
( ( fcP @ ( fcP @ X1 @ X2 ) @ X3 )
= ( fcP @ X1 @ ( fcP @ X2 @ X3 ) ) )
=> ~ ! [X1: a] :
( ( fcP @ fcE @ X1 )
= X1 ) )
=> ~ ! [X1: a] :
( ( fcP @ ( fcJ @ X1 ) @ X1 )
= fcE ) )
=> ~ ( ! [X1: a,X2: a,X3: a] :
( ( fcP @ ( fcP @ X1 @ X2 ) @ X3 )
= ( fcP @ X1 @ ( fcP @ X2 @ X3 ) ) )
=> ~ ! [X1: a,X2: a] :
~ ( ~ ! [X3: a] :
( ( fcP @ X1 @ X3 )
!= X2 )
=> ! [X3: a] :
( ( fcP @ X3 @ X1 )
!= X2 ) ) ) ) ),
file('<stdin>',nax1) ).
thf(c_0_10,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax1185]) ).
thf(c_0_11,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1186]) ).
thf(c_0_12,plain,
( p2
| ~ p12 ),
inference(fof_simplification,[status(thm)],[ax1177]) ).
thf(c_0_13,plain,
( p1
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_14,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_15,plain,
( p2
| ~ p12 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_16,plain,
~ p2,
inference(sr,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_17,plain,
! [X1784: a,X1785: a,X1786: a] :
( ~ p4
| ( ( fcP @ ( fcP @ X1784 @ X1785 ) @ X1786 )
= ( fcP @ X1784 @ ( fcP @ X1785 @ X1786 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax4])])]) ).
thf(c_0_18,plain,
( p12
| p4 ),
inference(split_conjunct,[status(thm)],[ax1148]) ).
thf(c_0_19,plain,
~ p12,
inference(sr,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_20,plain,
! [X1749: a] :
( ~ p13
| ( ( fcP @ ( fcJ @ X1749 ) @ X1749 )
= fcE ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax13])])]) ).
thf(c_0_21,plain,
( p2
| p13 ),
inference(split_conjunct,[status(thm)],[ax1176]) ).
thf(c_0_22,plain,
! [X1727: a] :
( ~ p39
| ( ( fcP @ fcE @ X1727 )
= X1727 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax39])])]) ).
thf(c_0_23,plain,
( p12
| p39 ),
inference(split_conjunct,[status(thm)],[ax1147]) ).
thf(c_0_24,plain,
! [X1: a,X2: a,X3: a] :
( ( ( fcP @ ( fcP @ X1 @ X2 ) @ X3 )
= ( fcP @ X1 @ ( fcP @ X2 @ X3 ) ) )
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_25,plain,
p4,
inference(sr,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_26,plain,
! [X1: a] :
( ( ( fcP @ ( fcJ @ X1 ) @ X1 )
= fcE )
| ~ p13 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_27,plain,
p13,
inference(sr,[status(thm)],[c_0_21,c_0_16]) ).
thf(c_0_28,plain,
! [X1: a] :
( ( ( fcP @ fcE @ X1 )
= X1 )
| ~ p39 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_29,plain,
p39,
inference(sr,[status(thm)],[c_0_23,c_0_19]) ).
thf(c_0_30,plain,
! [X1: a,X2: a,X3: a] :
( ( fcP @ ( fcP @ X1 @ X2 ) @ X3 )
= ( fcP @ X1 @ ( fcP @ X2 @ X3 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
thf(c_0_31,plain,
! [X1: a] :
( ( fcP @ ( fcJ @ X1 ) @ X1 )
= fcE ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]) ).
thf(c_0_32,plain,
! [X1: a] :
( ( fcP @ fcE @ X1 )
= X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).
thf(c_0_33,plain,
! [X1830: a,X1831: a,X1832: a,X1833: a,X1834: a,X1840: a,X1841: a] :
( ( ( ( fcP @ ( fcP @ X1830 @ X1831 ) @ X1832 )
= ( fcP @ X1830 @ ( fcP @ X1831 @ X1832 ) ) )
| p1 )
& ( ( ( fcP @ fcE @ X1833 )
= X1833 )
| p1 )
& ( ( ( fcP @ ( fcJ @ X1834 ) @ X1834 )
= fcE )
| p1 )
& ( ( ( fcP @ ( fcP @ esk908_0 @ esk909_0 ) @ esk910_0 )
!= ( fcP @ esk908_0 @ ( fcP @ esk909_0 @ esk910_0 ) ) )
| ( ( fcP @ esk911_0 @ X1840 )
!= esk912_0 )
| ( ( fcP @ X1841 @ esk911_0 )
!= esk912_0 )
| p1 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])])])])]) ).
thf(c_0_34,plain,
! [X1: a,X2: a] :
( ( fcP @ ( fcJ @ X1 ) @ ( fcP @ X1 @ X2 ) )
= X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
thf(c_0_35,plain,
! [X1: a,X2: a] :
( p1
| ( ( fcP @ ( fcP @ esk908_0 @ esk909_0 ) @ esk910_0 )
!= ( fcP @ esk908_0 @ ( fcP @ esk909_0 @ esk910_0 ) ) )
| ( ( fcP @ esk911_0 @ X1 )
!= esk912_0 )
| ( ( fcP @ X2 @ esk911_0 )
!= esk912_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_36,plain,
! [X1: a,X2: a] :
( ( fcP @ ( fcJ @ ( fcJ @ X1 ) ) @ X2 )
= ( fcP @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_34,c_0_34]) ).
thf(c_0_37,plain,
! [X1: a,X2: a] :
( ( ( fcP @ X1 @ esk911_0 )
!= esk912_0 )
| ( ( fcP @ esk911_0 @ X2 )
!= esk912_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_30])]),c_0_14]) ).
thf(c_0_38,plain,
! [X1: a] :
( ( fcP @ X1 @ fcE )
= X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_31]),c_0_36]) ).
thf(c_0_39,plain,
! [X1: a,X2: a,X3: a] :
( ( ( fcP @ X1 @ ( fcP @ X2 @ esk911_0 ) )
!= esk912_0 )
| ( ( fcP @ esk911_0 @ X3 )
!= esk912_0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_30]) ).
thf(c_0_40,plain,
! [X1: a] :
( ( fcJ @ ( fcJ @ X1 ) )
= X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_38]),c_0_38]) ).
thf(c_0_41,plain,
! [X1: a] :
( ( fcP @ esk911_0 @ X1 )
!= esk912_0 ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_31]),c_0_38])]) ).
thf(c_0_42,plain,
! [X1: a,X2: a] :
( ( fcP @ X1 @ ( fcP @ ( fcJ @ X1 ) @ X2 ) )
= X2 ),
inference(spm,[status(thm)],[c_0_34,c_0_40]) ).
thf(c_0_43,plain,
$false,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42])]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],[]) ).
thf(0,theorem,
( ~ ( ~ ( ! [X1: a,X2: a,X3: a] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) )
=> ~ ! [X1: a] :
( ( cP @ cE @ X1 )
= X1 ) )
=> ~ ! [X1: a] :
( ( cP @ ( cJ @ X1 ) @ X1 )
= cE ) )
=> ~ ( ! [X1: a,X2: a,X3: a] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) )
=> ~ ! [X1: a,X2: a] :
~ ( ~ ! [X3: a] :
( ( cP @ X1 @ X3 )
!= X2 )
=> ! [X3: a] :
( ( cP @ X3 @ X1 )
!= X2 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : ALG285^5 : TPTP v9.2.0. Released v4.0.0.
% 0.09/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n008.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 23:24:53 EDT 2025
% 0.14/0.35 % CPUTime :
% 1.77/1.96 % SZS status Theorem
% 1.77/1.96 % Mode: mode506
% 1.77/1.96 % Inferences: 38931
% 1.77/1.96 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------