%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : GRP001^5 : 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 : n019.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 01:36:30 PM UTC 2025
% Result : Theorem 1.10s 1.65s
% Output : Proof 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 19
% Syntax : Number of formulae : 75 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 364 ( 47 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 371 ( 72 ~; 48 |; 4 &; 226 @)
% ( 0 <=>; 19 =>; 2 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 21 con; 0-2 aty)
% Number of variables : 52 ( 0 ^; 52 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(cGRP_COMM2,conjecture,
( ~ ( ~ ( ~ ( ! [X1: $i] :
( ( cP @ e @ X1 )
= X1 )
=> ~ ! [X1: $i] :
( ( cP @ X1 @ e )
= X1 ) )
=> ~ ! [X1: $i] :
( ( cP @ X1 @ X1 )
= e ) )
=> ~ ! [X1: $i,X2: $i,X3: $i] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ! [X1: $i,X2: $i] :
( ( cP @ X1 @ X2 )
= ( cP @ X2 @ X1 ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
( ( cP @ e @ X1 )
= X1 )
=> ~ ! [X1: $i] :
( ( cP @ X1 @ e )
= X1 ) )
=> ~ ! [X1: $i] :
( ( cP @ X1 @ X1 )
= e ) )
=> ~ ! [X1: $i,X2: $i,X3: $i] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ! [X1: $i,X2: $i] :
( ( cP @ X1 @ X2 )
= ( cP @ X2 @ X1 ) ) ),
inference(assume_negation,[status(cth)],[cGRP_COMM2]) ).
thf(ax1945,axiom,
( p1
| ~ p2 ),
file('<stdin>',ax1945) ).
thf(ax1946,axiom,
~ p1,
file('<stdin>',ax1946) ).
thf(ax1922,axiom,
( ~ p19
| p23 ),
file('<stdin>',ax1922) ).
thf(ax1926,axiom,
( p2
| p19 ),
file('<stdin>',ax1926) ).
thf(ax1944,axiom,
( p1
| ~ p3 ),
file('<stdin>',ax1944) ).
thf(ax1925,axiom,
( ~ p19
| p20 ),
file('<stdin>',ax1925) ).
thf(nax1,axiom,
( p1
<= ( ~ ( ~ ( ~ ( ! [X1: $i] :
( ( fcP @ fe @ X1 )
= X1 )
=> ~ ! [X1: $i] :
( ( fcP @ X1 @ fe )
= X1 ) )
=> ~ ! [X1: $i] :
( ( fcP @ X1 @ X1 )
= fe ) )
=> ~ ! [X1: $i,X2: $i,X3: $i] :
( ( fcP @ ( fcP @ X1 @ X2 ) @ X3 )
= ( fcP @ X1 @ ( fcP @ X2 @ X3 ) ) ) )
=> ! [X1: $i,X2: $i] :
( ( fcP @ X1 @ X2 )
= ( fcP @ X2 @ X1 ) ) ) ),
file('<stdin>',nax1) ).
thf(ax1918,axiom,
( ~ p23
| p27 ),
file('<stdin>',ax1918) ).
thf(ax1920,axiom,
( ~ p23
| p25 ),
file('<stdin>',ax1920) ).
thf(ax1943,axiom,
( p3
| ~ p4 ),
file('<stdin>',ax1943) ).
thf(ax107,axiom,
( ~ p20
| p916 ),
file('<stdin>',ax107) ).
thf(pax27,axiom,
( p27
=> ! [X1: $i] :
( ( fcP @ ( fcP @ f__0 @ f__0 ) @ X1 )
= ( fcP @ f__0 @ ( fcP @ f__0 @ X1 ) ) ) ),
file('<stdin>',pax27) ).
thf(ax153,axiom,
( ~ p25
| p870 ),
file('<stdin>',ax153) ).
thf(ax1942,axiom,
( p4
| ~ p5 ),
file('<stdin>',ax1942) ).
thf(pax916,axiom,
( p916
=> ! [X1: $i] :
( ( fcP @ ( fcP @ f__1 @ f__1 ) @ X1 )
= ( fcP @ f__1 @ ( fcP @ f__1 @ X1 ) ) ) ),
file('<stdin>',pax916) ).
thf(pax870,axiom,
( p870
=> ( ( fcP @ ( fcP @ f__0 @ ( fcP @ f__0 @ f__1 ) ) @ ( fcP @ f__0 @ f__1 ) )
= ( fcP @ f__0 @ ( fcP @ ( fcP @ f__0 @ f__1 ) @ ( fcP @ f__0 @ f__1 ) ) ) ) ),
file('<stdin>',pax870) ).
thf(nax5,axiom,
( p5
<= ( ( fcP @ f__0 @ f__1 )
= ( fcP @ f__1 @ f__0 ) ) ),
file('<stdin>',nax5) ).
thf(c_0_17,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax1945]) ).
thf(c_0_18,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1946]) ).
thf(c_0_19,plain,
( p1
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_21,plain,
( ~ p19
| p23 ),
inference(fof_simplification,[status(thm)],[ax1922]) ).
thf(c_0_22,plain,
( p2
| p19 ),
inference(split_conjunct,[status(thm)],[ax1926]) ).
thf(c_0_23,plain,
~ p2,
inference(sr,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_24,plain,
( p1
| ~ p3 ),
inference(fof_simplification,[status(thm)],[ax1944]) ).
thf(c_0_25,plain,
( ~ p19
| p20 ),
inference(fof_simplification,[status(thm)],[ax1925]) ).
thf(c_0_26,plain,
! [X1324: $i,X1325: $i,X1326: $i,X1327: $i,X1328: $i,X1329: $i] :
( ( ( ( fcP @ fe @ X1324 )
= X1324 )
| p1 )
& ( ( ( fcP @ X1325 @ fe )
= X1325 )
| p1 )
& ( ( ( fcP @ X1326 @ X1326 )
= fe )
| p1 )
& ( ( ( fcP @ ( fcP @ X1327 @ X1328 ) @ X1329 )
= ( fcP @ X1327 @ ( fcP @ X1328 @ X1329 ) ) )
| p1 )
& ( ( ( fcP @ esk663_0 @ esk664_0 )
!= ( fcP @ esk664_0 @ esk663_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_27,plain,
( ~ p23
| p27 ),
inference(fof_simplification,[status(thm)],[ax1918]) ).
thf(c_0_28,plain,
( p23
| ~ p19 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_29,plain,
p19,
inference(sr,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_30,plain,
( ~ p23
| p25 ),
inference(fof_simplification,[status(thm)],[ax1920]) ).
thf(c_0_31,plain,
( p3
| ~ p4 ),
inference(fof_simplification,[status(thm)],[ax1943]) ).
thf(c_0_32,plain,
( p1
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_33,plain,
( ~ p20
| p916 ),
inference(fof_simplification,[status(thm)],[ax107]) ).
thf(c_0_34,plain,
( p20
| ~ p19 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_35,plain,
! [X1250: $i] :
( ~ p27
| ( ( fcP @ ( fcP @ f__0 @ f__0 ) @ X1250 )
= ( fcP @ f__0 @ ( fcP @ f__0 @ X1250 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax27])])]) ).
thf(c_0_36,plain,
! [X1: $i] :
( ( ( fcP @ X1 @ X1 )
= fe )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_37,plain,
! [X1: $i] :
( ( ( fcP @ fe @ X1 )
= X1 )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_38,plain,
( p27
| ~ p23 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_39,plain,
p23,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).
thf(c_0_40,plain,
( ~ p25
| p870 ),
inference(fof_simplification,[status(thm)],[ax153]) ).
thf(c_0_41,plain,
( p25
| ~ p23 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_42,plain,
( p4
| ~ p5 ),
inference(fof_simplification,[status(thm)],[ax1942]) ).
thf(c_0_43,plain,
( p3
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_44,plain,
~ p3,
inference(sr,[status(thm)],[c_0_32,c_0_20]) ).
thf(c_0_45,plain,
! [X240: $i] :
( ~ p916
| ( ( fcP @ ( fcP @ f__1 @ f__1 ) @ X240 )
= ( fcP @ f__1 @ ( fcP @ f__1 @ X240 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax916])])]) ).
thf(c_0_46,plain,
( p916
| ~ p20 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_47,plain,
p20,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_29])]) ).
thf(c_0_48,plain,
( ~ p870
| ( ( fcP @ ( fcP @ f__0 @ ( fcP @ f__0 @ f__1 ) ) @ ( fcP @ f__0 @ f__1 ) )
= ( fcP @ f__0 @ ( fcP @ ( fcP @ f__0 @ f__1 ) @ ( fcP @ f__0 @ f__1 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[pax870]) ).
thf(c_0_49,plain,
! [X1: $i] :
( ( ( fcP @ ( fcP @ f__0 @ f__0 ) @ X1 )
= ( fcP @ f__0 @ ( fcP @ f__0 @ X1 ) ) )
| ~ p27 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_50,plain,
! [X1: $i] :
( ( fcP @ X1 @ X1 )
= fe ),
inference(sr,[status(thm)],[c_0_36,c_0_20]) ).
thf(c_0_51,plain,
! [X1: $i] :
( ( fcP @ fe @ X1 )
= X1 ),
inference(sr,[status(thm)],[c_0_37,c_0_20]) ).
thf(c_0_52,plain,
p27,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]) ).
thf(c_0_53,plain,
! [X1: $i] :
( ( ( fcP @ X1 @ fe )
= X1 )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_54,plain,
( p870
| ~ p25 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_55,plain,
p25,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_39])]) ).
thf(c_0_56,plain,
( ( ( fcP @ f__0 @ f__1 )
!= ( fcP @ f__1 @ f__0 ) )
| p5 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax5])]) ).
thf(c_0_57,plain,
( p4
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_58,plain,
~ p4,
inference(sr,[status(thm)],[c_0_43,c_0_44]) ).
thf(c_0_59,plain,
! [X1: $i] :
( ( ( fcP @ ( fcP @ f__1 @ f__1 ) @ X1 )
= ( fcP @ f__1 @ ( fcP @ f__1 @ X1 ) ) )
| ~ p916 ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
thf(c_0_60,plain,
p916,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).
thf(c_0_61,plain,
( ( ( fcP @ ( fcP @ f__0 @ ( fcP @ f__0 @ f__1 ) ) @ ( fcP @ f__0 @ f__1 ) )
= ( fcP @ f__0 @ ( fcP @ ( fcP @ f__0 @ f__1 ) @ ( fcP @ f__0 @ f__1 ) ) ) )
| ~ p870 ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
thf(c_0_62,plain,
! [X1: $i] :
( ( fcP @ f__0 @ ( fcP @ f__0 @ X1 ) )
= X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_52])]) ).
thf(c_0_63,plain,
! [X1: $i] :
( ( fcP @ X1 @ fe )
= X1 ),
inference(sr,[status(thm)],[c_0_53,c_0_20]) ).
thf(c_0_64,plain,
p870,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).
thf(c_0_65,plain,
( p5
| ( ( fcP @ f__0 @ f__1 )
!= ( fcP @ f__1 @ f__0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
thf(c_0_66,plain,
~ p5,
inference(sr,[status(thm)],[c_0_57,c_0_58]) ).
thf(c_0_67,plain,
! [X1: $i] :
( ( fcP @ f__1 @ ( fcP @ f__1 @ X1 ) )
= X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_50]),c_0_51]),c_0_60])]) ).
thf(c_0_68,plain,
( ( fcP @ f__1 @ ( fcP @ f__0 @ f__1 ) )
= f__0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62]),c_0_50]),c_0_63]),c_0_64])]) ).
thf(c_0_69,plain,
( ( fcP @ f__1 @ f__0 )
!= ( fcP @ f__0 @ f__1 ) ),
inference(sr,[status(thm)],[c_0_65,c_0_66]) ).
thf(c_0_70,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],[]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( ! [X1: $i] :
( ( cP @ e @ X1 )
= X1 )
=> ~ ! [X1: $i] :
( ( cP @ X1 @ e )
= X1 ) )
=> ~ ! [X1: $i] :
( ( cP @ X1 @ X1 )
= e ) )
=> ~ ! [X1: $i,X2: $i,X3: $i] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ! [X1: $i,X2: $i] :
( ( cP @ X1 @ X2 )
= ( cP @ X2 @ X1 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP001^5 : TPTP v9.2.0. Released v4.0.0.
% 0.14/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Oct 8 16:26:38 EDT 2025
% 0.14/0.35 % CPUTime :
% 1.10/1.65 % SZS status Theorem
% 1.10/1.65 % Mode: mode506
% 1.10/1.65 % Inferences: 20830
% 1.10/1.65 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------