%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG283^5 : 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 : n001.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 18.65s 19.05s
% Output : Proof 18.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 41 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 186 ( 37 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 229 ( 43 ~; 20 |; 3 &; 148 @)
% ( 0 <=>; 14 =>; 1 <=; 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 : 16 ( 14 usr; 15 con; 0-2 aty)
% Number of variables : 65 ( 0 ^; 65 !; 0 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
thf(cTHM20_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 @ X1 @ X3 )
!= 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 @ X1 @ X3 )
!= X2 ) ),
inference(assume_negation,[status(cth)],[cTHM20_pme]) ).
thf(ax1071,axiom,
( p1
| ~ p2 ),
file('<stdin>',ax1071) ).
thf(ax1072,axiom,
~ p1,
file('<stdin>',ax1072) ).
thf(ax1069,axiom,
( p2
| ~ p4 ),
file('<stdin>',ax1069) ).
thf(pax7,axiom,
( p7
=> ! [X1: a,X2: a,X3: a] :
( ( fcP @ ( fcP @ X1 @ X2 ) @ X3 )
= ( fcP @ X1 @ ( fcP @ X2 @ X3 ) ) ) ),
file('<stdin>',pax7) ).
thf(ax1066,axiom,
( p4
| p7 ),
file('<stdin>',ax1066) ).
thf(pax5,axiom,
( p5
=> ! [X1: a] :
( ( fcP @ ( fcJ @ X1 ) @ X1 )
= fcE ) ),
file('<stdin>',pax5) ).
thf(ax1068,axiom,
( p2
| p5 ),
file('<stdin>',ax1068) ).
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 @ X1 @ X3 )
!= X2 ) ) ),
file('<stdin>',nax1) ).
thf(c_0_8,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax1071]) ).
thf(c_0_9,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1072]) ).
thf(c_0_10,plain,
( p2
| ~ p4 ),
inference(fof_simplification,[status(thm)],[ax1069]) ).
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,
( p2
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_14,plain,
~ p2,
inference(sr,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_15,plain,
! [X1683: a,X1684: a,X1685: a] :
( ~ p7
| ( ( fcP @ ( fcP @ X1683 @ X1684 ) @ X1685 )
= ( fcP @ X1683 @ ( fcP @ X1684 @ X1685 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax7])])]) ).
thf(c_0_16,plain,
( p4
| p7 ),
inference(split_conjunct,[status(thm)],[ax1066]) ).
thf(c_0_17,plain,
~ p4,
inference(sr,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_18,plain,
! [X1693: a] :
( ~ p5
| ( ( fcP @ ( fcJ @ X1693 ) @ X1693 )
= fcE ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax5])])]) ).
thf(c_0_19,plain,
( p2
| p5 ),
inference(split_conjunct,[status(thm)],[ax1068]) ).
thf(c_0_20,plain,
! [X1727: a,X1728: a,X1729: a,X1730: a,X1731: a,X1734: a] :
( ( ( ( fcP @ ( fcP @ X1727 @ X1728 ) @ X1729 )
= ( fcP @ X1727 @ ( fcP @ X1728 @ X1729 ) ) )
| p1 )
& ( ( ( fcP @ fcE @ X1730 )
= X1730 )
| p1 )
& ( ( ( fcP @ ( fcJ @ X1731 ) @ X1731 )
= fcE )
| p1 )
& ( ( ( fcP @ esk864_0 @ X1734 )
!= esk865_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_21,plain,
! [X1: a,X2: a,X3: a] :
( ( ( fcP @ ( fcP @ X1 @ X2 ) @ X3 )
= ( fcP @ X1 @ ( fcP @ X2 @ X3 ) ) )
| ~ p7 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_22,plain,
p7,
inference(sr,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_23,plain,
! [X1: a] :
( ( ( fcP @ ( fcJ @ X1 ) @ X1 )
= fcE )
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_24,plain,
p5,
inference(sr,[status(thm)],[c_0_19,c_0_14]) ).
thf(c_0_25,plain,
! [X1: a] :
( ( ( fcP @ fcE @ X1 )
= X1 )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_26,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_21,c_0_22])]) ).
thf(c_0_27,plain,
! [X1: a] :
( ( fcP @ ( fcJ @ X1 ) @ X1 )
= fcE ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]) ).
thf(c_0_28,plain,
! [X1: a] :
( ( fcP @ fcE @ X1 )
= X1 ),
inference(sr,[status(thm)],[c_0_25,c_0_12]) ).
thf(c_0_29,plain,
! [X1: a,X2: a] :
( ( fcP @ ( fcJ @ X1 ) @ ( fcP @ X1 @ X2 ) )
= X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
thf(c_0_30,plain,
! [X1: a] :
( ( fcP @ ( fcJ @ ( fcJ @ X1 ) ) @ fcE )
= X1 ),
inference(spm,[status(thm)],[c_0_29,c_0_27]) ).
thf(c_0_31,plain,
! [X1: a] :
( ( fcP @ ( fcJ @ ( fcJ @ ( fcJ @ X1 ) ) ) @ X1 )
= fcE ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
thf(c_0_32,plain,
! [X1: a] :
( p1
| ( ( fcP @ esk864_0 @ X1 )
!= esk865_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_33,plain,
! [X1: a] :
( ( fcJ @ ( fcJ @ X1 ) )
= X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_31]),c_0_30]) ).
thf(c_0_34,plain,
! [X1: a] :
( ( fcP @ esk864_0 @ X1 )
!= esk865_0 ),
inference(sr,[status(thm)],[c_0_32,c_0_12]) ).
thf(c_0_35,plain,
! [X1: a,X2: a] :
( ( fcP @ X1 @ ( fcP @ ( fcJ @ X1 ) @ X2 ) )
= X2 ),
inference(spm,[status(thm)],[c_0_29,c_0_33]) ).
thf(c_0_36,plain,
$false,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35])]),
[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 @ X1 @ X3 )
!= X2 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ALG283^5 : TPTP v9.2.0. Released v4.0.0.
% 0.03/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n001.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 8 23:27:08 EDT 2025
% 0.13/0.36 % CPUTime :
% 18.65/19.05 % SZS status Theorem
% 18.65/19.05 % Mode: mode485
% 18.65/19.05 % Inferences: 42
% 18.65/19.05 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------