%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU932^5 : 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 : n011.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 02:52:59 PM UTC 2025
% Result : Theorem 19.21s 18.93s
% Output : Proof 19.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 25
% Syntax : Number of formulae : 91 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 204 ( 21 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 210 ( 88 ~; 69 |; 0 &; 39 @)
% ( 0 <=>; 13 =>; 1 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 25 con; 0-2 aty)
% Number of variables : 21 ( 6 ^; 15 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(cTHM141_pme,conjecture,
! [X1: $i > $i] :
( ~ ! [X2: $i > $i] :
( ( ( ^ [X3: $i] : ( X1 @ ( X2 @ X3 ) ) )
= ( ^ [X3: $i] : ( X2 @ ( X1 @ X3 ) ) ) )
=> ! [X3: $i] :
( ( ( X2 @ X3 )
= X3 )
=> ~ ! [X4: $i] :
( ( ( X2 @ X4 )
= X4 )
=> ( X4 = X3 ) ) ) )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
!= X2 ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $i] :
( ~ ! [X2: $i > $i] :
( ( ( ^ [X3: $i] : ( X1 @ ( X2 @ X3 ) ) )
= ( ^ [X3: $i] : ( X2 @ ( X1 @ X3 ) ) ) )
=> ! [X3: $i] :
( ( ( X2 @ X3 )
= X3 )
=> ~ ! [X4: $i] :
( ( ( X2 @ X4 )
= X4 )
=> ( X4 = X3 ) ) ) )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
!= X2 ) ),
inference(assume_negation,[status(cth)],[cTHM141_pme]) ).
thf(ax1153,axiom,
( p1
| ~ p2 ),
file('<stdin>',ax1153) ).
thf(ax1154,axiom,
~ p1,
file('<stdin>',ax1154) ).
thf(ax1152,axiom,
( p2
| ~ p3 ),
file('<stdin>',ax1152) ).
thf(ax1150,axiom,
( p3
| ~ p5 ),
file('<stdin>',ax1150) ).
thf(ax1066,axiom,
( ~ p44
| p84 ),
file('<stdin>',ax1066) ).
thf(ax1148,axiom,
( p5
| ~ p7 ),
file('<stdin>',ax1148) ).
thf(ax779,axiom,
( ~ p84
| p354 ),
file('<stdin>',ax779) ).
thf(ax1111,axiom,
p44,
file('<stdin>',ax1111) ).
thf(ax1139,axiom,
( ~ p6
| p15 ),
file('<stdin>',ax1139) ).
thf(ax1149,axiom,
( p5
| p6 ),
file('<stdin>',ax1149) ).
thf(ax1138,axiom,
( p7
| ~ p16 ),
file('<stdin>',ax1138) ).
thf(ax778,axiom,
( ~ p354
| ~ p207
| p353 ),
file('<stdin>',ax778) ).
thf(ax940,axiom,
( ~ p15
| p207 ),
file('<stdin>',ax940) ).
thf(ax939,axiom,
( ~ p4
| ~ p208 ),
file('<stdin>',ax939) ).
thf(ax1151,axiom,
( p2
| p4 ),
file('<stdin>',ax1151) ).
thf(ax759,axiom,
( ~ p209
| ~ p366
| p208 ),
file('<stdin>',ax759) ).
thf(ax938,axiom,
( ~ p27
| p209 ),
file('<stdin>',ax938) ).
thf(ax1126,axiom,
( p16
| p27 ),
file('<stdin>',ax1126) ).
thf(ax776,axiom,
( ~ p352
| ~ p26
| p351 ),
file('<stdin>',ax776) ).
thf(ax1127,axiom,
( p16
| p26 ),
file('<stdin>',ax1127) ).
thf(ax777,axiom,
( ~ p353
| p352 ),
file('<stdin>',ax777) ).
thf(pax351,axiom,
( p351
=> ( ( f__0 @ f__3 )
= ( f__1 @ ( f__0 @ f__3 ) ) ) ),
file('<stdin>',pax351) ).
thf(nax366,axiom,
( p366
<= ( ( f__1 @ ( f__0 @ f__3 ) )
= ( f__0 @ f__3 ) ) ),
file('<stdin>',nax366) ).
thf(c_0_23,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax1153]) ).
thf(c_0_24,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1154]) ).
thf(c_0_25,plain,
( p2
| ~ p3 ),
inference(fof_simplification,[status(thm)],[ax1152]) ).
thf(c_0_26,plain,
( p1
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_27,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_28,plain,
( p3
| ~ p5 ),
inference(fof_simplification,[status(thm)],[ax1150]) ).
thf(c_0_29,plain,
( p2
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_30,plain,
~ p2,
inference(sr,[status(thm)],[c_0_26,c_0_27]) ).
thf(c_0_31,plain,
( ~ p44
| p84 ),
inference(fof_simplification,[status(thm)],[ax1066]) ).
thf(c_0_32,plain,
( p3
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_33,plain,
~ p3,
inference(sr,[status(thm)],[c_0_29,c_0_30]) ).
thf(c_0_34,plain,
( p5
| ~ p7 ),
inference(fof_simplification,[status(thm)],[ax1148]) ).
thf(c_0_35,plain,
( ~ p84
| p354 ),
inference(fof_simplification,[status(thm)],[ax779]) ).
thf(c_0_36,plain,
( p84
| ~ p44 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_37,plain,
p44,
inference(split_conjunct,[status(thm)],[ax1111]) ).
thf(c_0_38,plain,
( ~ p6
| p15 ),
inference(fof_simplification,[status(thm)],[ax1139]) ).
thf(c_0_39,plain,
( p5
| p6 ),
inference(split_conjunct,[status(thm)],[ax1149]) ).
thf(c_0_40,plain,
~ p5,
inference(sr,[status(thm)],[c_0_32,c_0_33]) ).
thf(c_0_41,plain,
( p7
| ~ p16 ),
inference(fof_simplification,[status(thm)],[ax1138]) ).
thf(c_0_42,plain,
( p5
| ~ p7 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_43,plain,
( ~ p354
| ~ p207
| p353 ),
inference(fof_simplification,[status(thm)],[ax778]) ).
thf(c_0_44,plain,
( p354
| ~ p84 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_45,plain,
p84,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]) ).
thf(c_0_46,plain,
( ~ p15
| p207 ),
inference(fof_simplification,[status(thm)],[ax940]) ).
thf(c_0_47,plain,
( p15
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_48,plain,
p6,
inference(sr,[status(thm)],[c_0_39,c_0_40]) ).
thf(c_0_49,plain,
( ~ p4
| ~ p208 ),
inference(fof_simplification,[status(thm)],[ax939]) ).
thf(c_0_50,plain,
( p2
| p4 ),
inference(split_conjunct,[status(thm)],[ax1151]) ).
thf(c_0_51,plain,
( p7
| ~ p16 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_52,plain,
~ p7,
inference(sr,[status(thm)],[c_0_42,c_0_40]) ).
thf(c_0_53,plain,
( p353
| ~ p354
| ~ p207 ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_54,plain,
p354,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]) ).
thf(c_0_55,plain,
( p207
| ~ p15 ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_56,plain,
p15,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]) ).
thf(c_0_57,plain,
( ~ p209
| ~ p366
| p208 ),
inference(fof_simplification,[status(thm)],[ax759]) ).
thf(c_0_58,plain,
( ~ p4
| ~ p208 ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
thf(c_0_59,plain,
p4,
inference(sr,[status(thm)],[c_0_50,c_0_30]) ).
thf(c_0_60,plain,
( ~ p27
| p209 ),
inference(fof_simplification,[status(thm)],[ax938]) ).
thf(c_0_61,plain,
( p16
| p27 ),
inference(split_conjunct,[status(thm)],[ax1126]) ).
thf(c_0_62,plain,
~ p16,
inference(sr,[status(thm)],[c_0_51,c_0_52]) ).
thf(c_0_63,plain,
( ~ p352
| ~ p26
| p351 ),
inference(fof_simplification,[status(thm)],[ax776]) ).
thf(c_0_64,plain,
( p16
| p26 ),
inference(split_conjunct,[status(thm)],[ax1127]) ).
thf(c_0_65,plain,
( ~ p353
| p352 ),
inference(fof_simplification,[status(thm)],[ax777]) ).
thf(c_0_66,plain,
( p353
| ~ p207 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54])]) ).
thf(c_0_67,plain,
p207,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56])]) ).
thf(c_0_68,plain,
( p208
| ~ p209
| ~ p366 ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
thf(c_0_69,plain,
~ p208,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]) ).
thf(c_0_70,plain,
( p209
| ~ p27 ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
thf(c_0_71,plain,
p27,
inference(sr,[status(thm)],[c_0_61,c_0_62]) ).
thf(c_0_72,plain,
( p351
| ~ p352
| ~ p26 ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_73,plain,
p26,
inference(sr,[status(thm)],[c_0_64,c_0_62]) ).
thf(c_0_74,plain,
( p352
| ~ p353 ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
thf(c_0_75,plain,
p353,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67])]) ).
thf(c_0_76,plain,
( ~ p351
| ( ( f__0 @ f__3 )
= ( f__1 @ ( f__0 @ f__3 ) ) ) ),
inference(fof_nnf,[status(thm)],[pax351]) ).
thf(c_0_77,plain,
( ( ( f__1 @ ( f__0 @ f__3 ) )
!= ( f__0 @ f__3 ) )
| p366 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax366])]) ).
thf(c_0_78,plain,
( ~ p209
| ~ p366 ),
inference(sr,[status(thm)],[c_0_68,c_0_69]) ).
thf(c_0_79,plain,
p209,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_71])]) ).
thf(c_0_80,plain,
( p351
| ~ p352 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73])]) ).
thf(c_0_81,plain,
p352,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75])]) ).
thf(c_0_82,plain,
( ( ( f__0 @ f__3 )
= ( f__1 @ ( f__0 @ f__3 ) ) )
| ~ p351 ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
thf(c_0_83,plain,
( p366
| ( ( f__1 @ ( f__0 @ f__3 ) )
!= ( f__0 @ f__3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
thf(c_0_84,plain,
~ p366,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_79])]) ).
thf(c_0_85,plain,
p351,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81])]) ).
thf(c_0_86,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_82,c_0_83,c_0_84,c_0_85]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],[]) ).
thf(0,theorem,
! [X1: $i > $i] :
( ~ ! [X2: $i > $i] :
( ( ( ^ [X3: $i] : ( X1 @ ( X2 @ X3 ) ) )
= ( ^ [X3: $i] : ( X2 @ ( X1 @ X3 ) ) ) )
=> ! [X3: $i] :
( ( ( X2 @ X3 )
= X3 )
=> ~ ! [X4: $i] :
( ( ( X2 @ X4 )
= X4 )
=> ( X4 = X3 ) ) ) )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
!= X2 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU932^5 : TPTP v9.2.0. Released v4.0.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.32 % Computer : n011.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Oct 8 20:57:23 EDT 2025
% 0.11/0.32 % CPUTime :
% 5.29/4.95 slave returned with unknown status
% 19.21/18.93 % SZS status Theorem
% 19.21/18.93 % Mode: mode485
% 19.21/18.93 % Inferences: 58
% 19.21/18.93 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------