%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU996^5 : 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 : n012.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 02:53:04 PM UTC 2025
% Result : Theorem 19.14s 19.25s
% Output : Proof 19.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 21
% Syntax : Number of formulae : 81 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 383 ( 80 equ; 0 cnn)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 685 ( 137 ~; 69 |; 12 &; 418 @)
% ( 0 <=>; 48 =>; 1 <=; 0 <~>)
% Maximal formula depth : 36 ( 4 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 26 con; 0-2 aty)
% Number of variables : 142 ( 0 ^; 142 !; 0 ?; 142 :)
% Comments :
%------------------------------------------------------------------------------
thf(cMODULAR_THM_pme,conjecture,
! [X1: a > a > a,X2: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X3: a] :
( ( X1 @ X3 @ X3 )
= X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 @ X3 )
= X3 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
= ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X2 @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ X3 @ ( X2 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ X3 @ X4 )
= ( X1 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ X3 @ X4 )
= ( X2 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ ( X2 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ ( X1 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X1 @ X3 @ ( X2 @ X4 @ X5 ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ ( X1 @ X3 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X2 @ X3 @ ( X1 @ X4 @ X5 ) )
= ( X1 @ ( X2 @ X3 @ X4 ) @ ( X2 @ X3 @ X5 ) ) ) )
=> ! [X3: a,X4: a,X5: a] :
( ( ( X1 @ X3 @ X5 )
= X5 )
=> ( ( X1 @ X3 @ ( X2 @ X4 @ X5 ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ X5 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > a > a,X2: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X3: a] :
( ( X1 @ X3 @ X3 )
= X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 @ X3 )
= X3 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
= ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X2 @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ X3 @ ( X2 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ X3 @ X4 )
= ( X1 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ X3 @ X4 )
= ( X2 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ ( X2 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ ( X1 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X1 @ X3 @ ( X2 @ X4 @ X5 ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ ( X1 @ X3 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X2 @ X3 @ ( X1 @ X4 @ X5 ) )
= ( X1 @ ( X2 @ X3 @ X4 ) @ ( X2 @ X3 @ X5 ) ) ) )
=> ! [X3: a,X4: a,X5: a] :
( ( ( X1 @ X3 @ X5 )
= X5 )
=> ( ( X1 @ X3 @ ( X2 @ X4 @ X5 ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ X5 ) ) ) ),
inference(assume_negation,[status(cth)],[cMODULAR_THM_pme]) ).
thf(ax1060,axiom,
( p1
| ~ p2 ),
file('<stdin>',ax1060) ).
thf(ax1061,axiom,
~ p1,
file('<stdin>',ax1061) ).
thf(ax1059,axiom,
( p2
| ~ p3 ),
file('<stdin>',ax1059) ).
thf(ax1057,axiom,
( p3
| ~ p5 ),
file('<stdin>',ax1057) ).
thf(ax1054,axiom,
( p5
| ~ p8 ),
file('<stdin>',ax1054) ).
thf(ax832,axiom,
( ~ p230
| p231 ),
file('<stdin>',ax832) ).
thf(ax1051,axiom,
( p8
| ~ p11 ),
file('<stdin>',ax1051) ).
thf(ax831,axiom,
( ~ p231
| p232 ),
file('<stdin>',ax831) ).
thf(ax833,axiom,
p230,
file('<stdin>',ax833) ).
thf(ax1046,axiom,
( p11
| ~ p16 ),
file('<stdin>',ax1046) ).
thf(ax1007,axiom,
( ~ p42
| p60 ),
file('<stdin>',ax1007) ).
thf(ax830,axiom,
( ~ p232
| ~ p31
| p229 ),
file('<stdin>',ax830) ).
thf(ax951,axiom,
( ~ p60
| p114 ),
file('<stdin>',ax951) ).
thf(ax1026,axiom,
p42,
file('<stdin>',ax1026) ).
thf(ax1031,axiom,
( p16
| p31 ),
file('<stdin>',ax1031) ).
thf(nax3,axiom,
( p3
<= ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: a] :
( ( f__0 @ X1 @ X1 )
= X1 )
=> ~ ! [X1: a] :
( ( f__1 @ X1 @ X1 )
= X1 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( f__1 @ ( f__1 @ X1 @ X2 ) @ X3 )
= ( f__1 @ X1 @ ( f__1 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a] :
( ( f__0 @ X1 @ X2 )
= ( f__0 @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a] :
( ( f__1 @ X1 @ X2 )
= ( f__1 @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a] :
( ( f__0 @ ( f__1 @ X1 @ X2 ) @ X2 )
= X2 ) )
=> ~ ! [X1: a,X2: a] :
( ( f__1 @ ( f__0 @ X1 @ X2 ) @ X2 )
= X2 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( f__0 @ X1 @ ( f__1 @ X2 @ X3 ) )
= ( f__1 @ ( f__0 @ X1 @ X2 ) @ ( f__0 @ X1 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( f__1 @ X1 @ ( f__0 @ X2 @ X3 ) )
= ( f__0 @ ( f__1 @ X1 @ X2 ) @ ( f__1 @ X1 @ X3 ) ) ) )
=> ! [X1: a,X2: a,X3: a] :
( ( ( f__0 @ X1 @ X3 )
= X3 )
=> ( ( f__0 @ X1 @ ( f__1 @ X2 @ X3 ) )
= ( f__1 @ ( f__0 @ X1 @ X2 ) @ X3 ) ) ) ) ),
file('<stdin>',nax3) ).
thf(ax950,axiom,
( ~ p114
| p16
| p113 ),
file('<stdin>',ax950) ).
thf(pax229,axiom,
( p229
=> ( f__5
= ( f__0 @ f__2 @ f__5 ) ) ),
file('<stdin>',pax229) ).
thf(pax113,axiom,
( p113
=> ! [X1: a] :
( ( X1 = f__5 )
=> ~ ( ( ( f__0 @ f__2 @ f__5 )
= f__5 )
=> ( ( f__0 @ f__2 @ ( f__1 @ f__3 @ f__5 ) )
= ( f__1 @ ( f__0 @ f__2 @ f__3 ) @ X1 ) ) ) ) ),
file('<stdin>',pax113) ).
thf(c_0_19,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax1060]) ).
thf(c_0_20,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1061]) ).
thf(c_0_21,plain,
( p2
| ~ p3 ),
inference(fof_simplification,[status(thm)],[ax1059]) ).
thf(c_0_22,plain,
( p1
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_23,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_24,plain,
( p3
| ~ p5 ),
inference(fof_simplification,[status(thm)],[ax1057]) ).
thf(c_0_25,plain,
( p2
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_26,plain,
~ p2,
inference(sr,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_27,plain,
( p5
| ~ p8 ),
inference(fof_simplification,[status(thm)],[ax1054]) ).
thf(c_0_28,plain,
( p3
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_29,plain,
~ p3,
inference(sr,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_30,plain,
( ~ p230
| p231 ),
inference(fof_simplification,[status(thm)],[ax832]) ).
thf(c_0_31,plain,
( p8
| ~ p11 ),
inference(fof_simplification,[status(thm)],[ax1051]) ).
thf(c_0_32,plain,
( p5
| ~ p8 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_33,plain,
~ p5,
inference(sr,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_34,plain,
( ~ p231
| p232 ),
inference(fof_simplification,[status(thm)],[ax831]) ).
thf(c_0_35,plain,
( p231
| ~ p230 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_36,plain,
p230,
inference(split_conjunct,[status(thm)],[ax833]) ).
thf(c_0_37,plain,
( p11
| ~ p16 ),
inference(fof_simplification,[status(thm)],[ax1046]) ).
thf(c_0_38,plain,
( p8
| ~ p11 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_39,plain,
~ p8,
inference(sr,[status(thm)],[c_0_32,c_0_33]) ).
thf(c_0_40,plain,
( ~ p42
| p60 ),
inference(fof_simplification,[status(thm)],[ax1007]) ).
thf(c_0_41,plain,
( ~ p232
| ~ p31
| p229 ),
inference(fof_simplification,[status(thm)],[ax830]) ).
thf(c_0_42,plain,
( p232
| ~ p231 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_43,plain,
p231,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
thf(c_0_44,plain,
( p11
| ~ p16 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_45,plain,
~ p11,
inference(sr,[status(thm)],[c_0_38,c_0_39]) ).
thf(c_0_46,plain,
( ~ p60
| p114 ),
inference(fof_simplification,[status(thm)],[ax951]) ).
thf(c_0_47,plain,
( p60
| ~ p42 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_48,plain,
p42,
inference(split_conjunct,[status(thm)],[ax1026]) ).
thf(c_0_49,plain,
( p229
| ~ p232
| ~ p31 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_50,plain,
p232,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]) ).
thf(c_0_51,plain,
( p16
| p31 ),
inference(split_conjunct,[status(thm)],[ax1031]) ).
thf(c_0_52,plain,
~ p16,
inference(sr,[status(thm)],[c_0_44,c_0_45]) ).
thf(c_0_53,plain,
! [X1539: a,X1540: a,X1541: a,X1542: a,X1543: a,X1544: a,X1545: a,X1546: a,X1547: a,X1548: a,X1549: a,X1550: a,X1551: a,X1552: a,X1553: a,X1554: a,X1555: a,X1556: a,X1557: a,X1558: a,X1559: a,X1560: a] :
( ( ( ( f__0 @ X1539 @ X1539 )
= X1539 )
| p3 )
& ( ( ( f__1 @ X1540 @ X1540 )
= X1540 )
| p3 )
& ( ( ( f__0 @ ( f__0 @ X1541 @ X1542 ) @ X1543 )
= ( f__0 @ X1541 @ ( f__0 @ X1542 @ X1543 ) ) )
| p3 )
& ( ( ( f__1 @ ( f__1 @ X1544 @ X1545 ) @ X1546 )
= ( f__1 @ X1544 @ ( f__1 @ X1545 @ X1546 ) ) )
| p3 )
& ( ( ( f__0 @ X1547 @ X1548 )
= ( f__0 @ X1548 @ X1547 ) )
| p3 )
& ( ( ( f__1 @ X1549 @ X1550 )
= ( f__1 @ X1550 @ X1549 ) )
| p3 )
& ( ( ( f__0 @ ( f__1 @ X1551 @ X1552 ) @ X1552 )
= X1552 )
| p3 )
& ( ( ( f__1 @ ( f__0 @ X1553 @ X1554 ) @ X1554 )
= X1554 )
| p3 )
& ( ( ( f__0 @ X1555 @ ( f__1 @ X1556 @ X1557 ) )
= ( f__1 @ ( f__0 @ X1555 @ X1556 ) @ ( f__0 @ X1555 @ X1557 ) ) )
| p3 )
& ( ( ( f__1 @ X1558 @ ( f__0 @ X1559 @ X1560 ) )
= ( f__0 @ ( f__1 @ X1558 @ X1559 ) @ ( f__1 @ X1558 @ X1560 ) ) )
| p3 )
& ( ( ( f__0 @ esk776_0 @ esk778_0 )
= esk778_0 )
| p3 )
& ( ( ( f__0 @ esk776_0 @ ( f__1 @ esk777_0 @ esk778_0 ) )
!= ( f__1 @ ( f__0 @ esk776_0 @ esk777_0 ) @ esk778_0 ) )
| p3 ) ),
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)],[nax3])])])])])]) ).
thf(c_0_54,plain,
( ~ p114
| p16
| p113 ),
inference(fof_simplification,[status(thm)],[ax950]) ).
thf(c_0_55,plain,
( p114
| ~ p60 ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_56,plain,
p60,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]) ).
thf(c_0_57,plain,
( ~ p229
| ( f__5
= ( f__0 @ f__2 @ f__5 ) ) ),
inference(fof_nnf,[status(thm)],[pax229]) ).
thf(c_0_58,plain,
( p229
| ~ p31 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]) ).
thf(c_0_59,plain,
p31,
inference(sr,[status(thm)],[c_0_51,c_0_52]) ).
thf(c_0_60,plain,
! [X1198: a] :
( ( ( ( f__0 @ f__2 @ f__5 )
= f__5 )
| ( X1198 != f__5 )
| ~ p113 )
& ( ( ( f__0 @ f__2 @ ( f__1 @ f__3 @ f__5 ) )
!= ( f__1 @ ( f__0 @ f__2 @ f__3 ) @ X1198 ) )
| ( X1198 != f__5 )
| ~ p113 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax113])])])]) ).
thf(c_0_61,plain,
! [X2: a,X1: a] :
( ( ( f__1 @ X1 @ X2 )
= ( f__1 @ X2 @ X1 ) )
| p3 ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_62,plain,
( p16
| p113
| ~ p114 ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
thf(c_0_63,plain,
p114,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56])]) ).
thf(c_0_64,plain,
! [X1: a,X2: a,X3: a] :
( ( ( f__0 @ X1 @ ( f__1 @ X2 @ X3 ) )
= ( f__1 @ ( f__0 @ X1 @ X2 ) @ ( f__0 @ X1 @ X3 ) ) )
| p3 ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_65,plain,
( ( f__5
= ( f__0 @ f__2 @ f__5 ) )
| ~ p229 ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
thf(c_0_66,plain,
p229,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]) ).
thf(c_0_67,plain,
! [X1: a] :
( ( ( f__0 @ f__2 @ ( f__1 @ f__3 @ f__5 ) )
!= ( f__1 @ ( f__0 @ f__2 @ f__3 ) @ X1 ) )
| ( X1 != f__5 )
| ~ p113 ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
thf(c_0_68,plain,
! [X2: a,X1: a] :
( ( f__1 @ X1 @ X2 )
= ( f__1 @ X2 @ X1 ) ),
inference(sr,[status(thm)],[c_0_61,c_0_29]) ).
thf(c_0_69,plain,
( p113
| p16 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63])]) ).
thf(c_0_70,plain,
! [X1: a,X2: a,X3: a] :
( ( f__1 @ ( f__0 @ X1 @ X2 ) @ ( f__0 @ X1 @ X3 ) )
= ( f__0 @ X1 @ ( f__1 @ X2 @ X3 ) ) ),
inference(sr,[status(thm)],[c_0_64,c_0_29]) ).
thf(c_0_71,plain,
( ( f__0 @ f__2 @ f__5 )
= f__5 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66])]) ).
thf(c_0_72,plain,
( ( ( f__1 @ f__5 @ ( f__0 @ f__2 @ f__3 ) )
!= ( f__0 @ f__2 @ ( f__1 @ f__5 @ f__3 ) ) )
| ~ p113 ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]),c_0_68]) ).
thf(c_0_73,plain,
p113,
inference(sr,[status(thm)],[c_0_69,c_0_52]) ).
thf(c_0_74,plain,
! [X1: a] :
( ( f__1 @ f__5 @ ( f__0 @ f__2 @ X1 ) )
= ( f__0 @ f__2 @ ( f__1 @ f__5 @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
thf(c_0_75,plain,
( ( f__1 @ f__5 @ ( f__0 @ f__2 @ f__3 ) )
!= ( f__0 @ f__2 @ ( f__1 @ f__5 @ f__3 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73])]) ).
thf(c_0_76,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_74,c_0_75]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],[]) ).
thf(0,theorem,
! [X1: a > a > a,X2: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X3: a] :
( ( X1 @ X3 @ X3 )
= X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 @ X3 )
= X3 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
= ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X2 @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ X3 @ ( X2 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ X3 @ X4 )
= ( X1 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ X3 @ X4 )
= ( X2 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ ( X2 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ ( X1 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X1 @ X3 @ ( X2 @ X4 @ X5 ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ ( X1 @ X3 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X2 @ X3 @ ( X1 @ X4 @ X5 ) )
= ( X1 @ ( X2 @ X3 @ X4 ) @ ( X2 @ X3 @ X5 ) ) ) )
=> ! [X3: a,X4: a,X5: a] :
( ( ( X1 @ X3 @ X5 )
= X5 )
=> ( ( X1 @ X3 @ ( X2 @ X4 @ X5 ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ X5 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU996^5 : TPTP v9.2.0. Released v4.0.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.34 % CPULimit : 300
% 0.20/0.34 % WCLimit : 300
% 0.20/0.34 % DateTime : Wed Oct 8 20:37:23 EDT 2025
% 0.20/0.34 % CPUTime :
% 19.14/19.25 % SZS status Theorem
% 19.14/19.25 % Mode: mode485
% 19.14/19.25 % Inferences: 34
% 19.14/19.25 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------