TSTP Solution File: SEU972^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU972^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n020.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 : 600s
% DateTime : Tue Jul 19 14:11:05 EDT 2022
% Result : Theorem 36.83s 37.36s
% Output : Proof 36.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 73 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 457 ( 83 equ; 0 cnn)
% Maximal formula atoms : 26 ( 6 avg)
% Number of connectives : 504 ( 143 ~; 68 |; 5 &; 229 @)
% ( 0 <=>; 57 =>; 2 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 26 usr; 27 con; 0-2 aty)
% Number of variables : 56 ( 0 ^ 56 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(cPU_LEM2E_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 ) ) ) ) )
=> ~ ! [X1: a > $o] :
( ! [X2: a,X3: a] :
( ( X1 @ ( cP @ X2 @ X3 ) )
=> ~ ( ~ ( ( ( X2 = cZ )
= ( X3 = cZ ) )
=> ~ ( X1 @ ( cP @ ( cL @ X2 ) @ ( cL @ X3 ) ) ) )
=> ~ ( X1 @ ( cP @ ( cR @ X2 ) @ ( cR @ X3 ) ) ) ) )
=> ! [X2: a,X3: a] :
( ( X1 @ ( cP @ X2 @ X3 ) )
=> ( X2 = X3 ) ) ) )
=> ! [X1: a] :
~ ! [X2: a > $o] :
( ( X2 @ ( cP @ cZ @ X1 ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ ( cP @ X3 @ X4 ) )
=> ~ ( ~ ( ( ( X4 = cZ )
=> ( X3 = cZ ) )
=> ~ ( X2 @ ( cP @ ( cL @ X3 ) @ ( cL @ X4 ) ) ) )
=> ~ ( X2 @ ( cP @ ( cR @ X3 ) @ ( cR @ X4 ) ) ) ) ) ) ) ).
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 ) ) ) ) )
=> ~ ! [X1: a > $o] :
( ! [X2: a,X3: a] :
( ( X1 @ ( cP @ X2 @ X3 ) )
=> ~ ( ~ ( ( ( X2 = cZ )
= ( X3 = cZ ) )
=> ~ ( X1 @ ( cP @ ( cL @ X2 ) @ ( cL @ X3 ) ) ) )
=> ~ ( X1 @ ( cP @ ( cR @ X2 ) @ ( cR @ X3 ) ) ) ) )
=> ! [X2: a,X3: a] :
( ( X1 @ ( cP @ X2 @ X3 ) )
=> ( X2 = X3 ) ) ) )
=> ! [X1: a] :
~ ! [X2: a > $o] :
( ( X2 @ ( cP @ cZ @ X1 ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ ( cP @ X3 @ X4 ) )
=> ~ ( ~ ( ( ( X4 = cZ )
=> ( X3 = cZ ) )
=> ~ ( X2 @ ( cP @ ( cL @ X3 ) @ ( cL @ X4 ) ) ) )
=> ~ ( X2 @ ( cP @ ( cR @ X3 ) @ ( cR @ X4 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cPU_LEM2E_pme]) ).
thf(ax1912,axiom,
( p1
| ~ p3 ),
file('<stdin>',ax1912) ).
thf(ax1914,axiom,
~ p1,
file('<stdin>',ax1914) ).
thf(ax987,axiom,
( ~ p455
| p906 ),
file('<stdin>',ax987) ).
thf(ax1913,axiom,
( p1
| ~ p2 ),
file('<stdin>',ax1913) ).
thf(ax1847,axiom,
( ~ p6
| p67 ),
file('<stdin>',ax1847) ).
thf(ax1909,axiom,
( p3
| p6 ),
file('<stdin>',ax1909) ).
thf(ax986,axiom,
( ~ p906
| p905 ),
file('<stdin>',ax986) ).
thf(ax1464,axiom,
p455,
file('<stdin>',ax1464) ).
thf(ax1911,axiom,
( p2
| ~ p4 ),
file('<stdin>',ax1911) ).
thf(ax985,axiom,
( ~ p905
| ~ p67
| p904 ),
file('<stdin>',ax985) ).
thf(ax1908,axiom,
( p4
| ~ p7 ),
file('<stdin>',ax1908) ).
thf(ax984,axiom,
( ~ p904
| p903 ),
file('<stdin>',ax984) ).
thf(nax7,axiom,
( p7
<= ( ~ ( ~ ( ( ( 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>',nax7) ).
thf(ax983,axiom,
( ~ p903
| ~ p902
| p901 ),
file('<stdin>',ax983) ).
thf(nax902,axiom,
( p902
<= ( ( fcL @ ( fcP @ fcZ @ f__0 ) )
= fcZ ) ),
file('<stdin>',nax902) ).
thf(pax901,axiom,
( p901
=> ( ( fcZ = fcZ )
=> ~ ! [X1: a,X2: a] :
( ( ( fcL @ ( fcP @ X1 @ X2 ) )
= fcZ )
=> ~ ( ~ ( ( ( X2 = fcZ )
=> ( X1 = fcZ ) )
=> ( ( fcL @ ( fcP @ ( fcL @ X1 ) @ ( fcL @ X2 ) ) )
!= fcZ ) )
=> ( ( fcL @ ( fcP @ ( fcR @ X1 ) @ ( fcR @ X2 ) ) )
!= fcZ ) ) ) ) ),
file('<stdin>',pax901) ).
thf(c_0_16,plain,
( p1
| ~ p3 ),
inference(fof_simplification,[status(thm)],[ax1912]) ).
thf(c_0_17,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1914]) ).
thf(c_0_18,plain,
( p1
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_19,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,plain,
( ~ p455
| p906 ),
inference(fof_simplification,[status(thm)],[ax987]) ).
thf(c_0_21,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax1913]) ).
thf(c_0_22,plain,
( ~ p6
| p67 ),
inference(fof_simplification,[status(thm)],[ax1847]) ).
thf(c_0_23,plain,
( p3
| p6 ),
inference(split_conjunct,[status(thm)],[ax1909]) ).
thf(c_0_24,plain,
~ p3,
inference(sr,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_25,plain,
( ~ p906
| p905 ),
inference(fof_simplification,[status(thm)],[ax986]) ).
thf(c_0_26,plain,
( p906
| ~ p455 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_27,plain,
p455,
inference(split_conjunct,[status(thm)],[ax1464]) ).
thf(c_0_28,plain,
( p2
| ~ p4 ),
inference(fof_simplification,[status(thm)],[ax1911]) ).
thf(c_0_29,plain,
( p1
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_30,plain,
( ~ p905
| ~ p67
| p904 ),
inference(fof_simplification,[status(thm)],[ax985]) ).
thf(c_0_31,plain,
( p67
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_32,plain,
p6,
inference(sr,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_33,plain,
( p905
| ~ p906 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_34,plain,
p906,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]) ).
thf(c_0_35,plain,
( p4
| ~ p7 ),
inference(fof_simplification,[status(thm)],[ax1908]) ).
thf(c_0_36,plain,
( p2
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_37,plain,
~ p2,
inference(sr,[status(thm)],[c_0_29,c_0_19]) ).
thf(c_0_38,plain,
( ~ p904
| p903 ),
inference(fof_simplification,[status(thm)],[ax984]) ).
thf(c_0_39,plain,
( p904
| ~ p905
| ~ p67 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_40,plain,
p67,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).
thf(c_0_41,plain,
p905,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]) ).
thf(c_0_42,plain,
! [X2378: a,X2379: a,X2380: a,X2381: a] :
( ( ( ( fcL @ fcZ )
= fcZ )
| p7 )
& ( ( ( fcR @ fcZ )
= fcZ )
| p7 )
& ( ( ( fcL @ ( fcP @ X2378 @ X2379 ) )
= X2378 )
| p7 )
& ( ( ( fcR @ ( fcP @ X2380 @ X2381 ) )
= X2381 )
| p7 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax7])])])])]) ).
thf(c_0_43,plain,
( p4
| ~ p7 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_44,plain,
~ p4,
inference(sr,[status(thm)],[c_0_36,c_0_37]) ).
thf(c_0_45,plain,
( ~ p903
| ~ p902
| p901 ),
inference(fof_simplification,[status(thm)],[ax983]) ).
thf(c_0_46,plain,
( p903
| ~ p904 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_47,plain,
p904,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).
thf(c_0_48,plain,
( ( ( fcL @ ( fcP @ fcZ @ f__0 ) )
!= fcZ )
| p902 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax902])]) ).
thf(c_0_49,plain,
! [X2: a,X1: a] :
( ( ( fcL @ ( fcP @ X1 @ X2 ) )
= X1 )
| p7 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_50,plain,
~ p7,
inference(sr,[status(thm)],[c_0_43,c_0_44]) ).
thf(c_0_51,plain,
( ( ( ( fcL @ ( fcP @ esk454_0 @ esk455_0 ) )
= fcZ )
| ( fcZ != fcZ )
| ~ p901 )
& ( ( esk455_0 = fcZ )
| ( ( fcL @ ( fcP @ ( fcL @ esk454_0 ) @ ( fcL @ esk455_0 ) ) )
!= fcZ )
| ( ( fcL @ ( fcP @ ( fcR @ esk454_0 ) @ ( fcR @ esk455_0 ) ) )
!= fcZ )
| ( fcZ != fcZ )
| ~ p901 )
& ( ( esk454_0 != fcZ )
| ( ( fcL @ ( fcP @ ( fcL @ esk454_0 ) @ ( fcL @ esk455_0 ) ) )
!= fcZ )
| ( ( fcL @ ( fcP @ ( fcR @ esk454_0 ) @ ( fcR @ esk455_0 ) ) )
!= fcZ )
| ( fcZ != fcZ )
| ~ p901 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax901])])])])]) ).
thf(c_0_52,plain,
( p901
| ~ p903
| ~ p902 ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
thf(c_0_53,plain,
p903,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).
thf(c_0_54,plain,
( p902
| ( ( fcL @ ( fcP @ fcZ @ f__0 ) )
!= fcZ ) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
thf(c_0_55,plain,
! [X2: a,X1: a] :
( ( fcL @ ( fcP @ X1 @ X2 ) )
= X1 ),
inference(sr,[status(thm)],[c_0_49,c_0_50]) ).
thf(c_0_56,plain,
( ( ( fcL @ ( fcP @ esk454_0 @ esk455_0 ) )
= fcZ )
| ( fcZ != fcZ )
| ~ p901 ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
thf(c_0_57,plain,
( p901
| ~ p902 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_53])]) ).
thf(c_0_58,plain,
p902,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).
thf(c_0_59,plain,
( ( esk454_0 != fcZ )
| ( ( fcL @ ( fcP @ ( fcL @ esk454_0 ) @ ( fcL @ esk455_0 ) ) )
!= fcZ )
| ( ( fcL @ ( fcP @ ( fcR @ esk454_0 ) @ ( fcR @ esk455_0 ) ) )
!= fcZ )
| ( fcZ != fcZ )
| ~ p901 ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
thf(c_0_60,plain,
( ( ( fcL @ ( fcP @ esk454_0 @ esk455_0 ) )
= fcZ )
| ~ p901 ),
inference(cn,[status(thm)],[c_0_56]) ).
thf(c_0_61,plain,
p901,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]) ).
thf(c_0_62,plain,
( ( ( fcL @ fcZ )
= fcZ )
| p7 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_63,plain,
( ( ( fcR @ fcZ )
= fcZ )
| p7 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_64,plain,
( ( esk454_0 != fcZ )
| ( ( fcL @ ( fcP @ ( fcL @ esk454_0 ) @ ( fcL @ esk455_0 ) ) )
!= fcZ )
| ( ( fcL @ ( fcP @ ( fcR @ esk454_0 ) @ ( fcR @ esk455_0 ) ) )
!= fcZ )
| ~ p901 ),
inference(cn,[status(thm)],[c_0_59]) ).
thf(c_0_65,plain,
esk454_0 = fcZ,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_55]),c_0_61])]) ).
thf(c_0_66,plain,
( ( fcL @ fcZ )
= fcZ ),
inference(sr,[status(thm)],[c_0_62,c_0_50]) ).
thf(c_0_67,plain,
( ( fcR @ fcZ )
= fcZ ),
inference(sr,[status(thm)],[c_0_63,c_0_50]) ).
thf(c_0_68,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65]),c_0_65]),c_0_66]),c_0_55]),c_0_65]),c_0_67]),c_0_55]),c_0_61])]),
[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 ) ) ) ) )
=> ~ ! [X1: a > $o] :
( ! [X2: a,X3: a] :
( ( X1 @ ( cP @ X2 @ X3 ) )
=> ~ ( ~ ( ( ( X2 = cZ )
= ( X3 = cZ ) )
=> ~ ( X1 @ ( cP @ ( cL @ X2 ) @ ( cL @ X3 ) ) ) )
=> ~ ( X1 @ ( cP @ ( cR @ X2 ) @ ( cR @ X3 ) ) ) ) )
=> ! [X2: a,X3: a] :
( ( X1 @ ( cP @ X2 @ X3 ) )
=> ( X2 = X3 ) ) ) )
=> ! [X1: a] :
~ ! [X2: a > $o] :
( ( X2 @ ( cP @ cZ @ X1 ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ ( cP @ X3 @ X4 ) )
=> ~ ( ~ ( ( ( X4 = cZ )
=> ( X3 = cZ ) )
=> ~ ( X2 @ ( cP @ ( cL @ X3 ) @ ( cL @ X4 ) ) ) )
=> ~ ( X2 @ ( cP @ ( cR @ X3 ) @ ( cR @ X4 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SEU972^5 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n020.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 : 600
% 0.12/0.34 % DateTime : Sun Jun 19 09:33:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 36.83/37.36 % SZS status Theorem
% 36.83/37.36 % Mode: mode485
% 36.83/37.36 % Inferences: 39
% 36.83/37.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------