TSTP Solution File: SET724^4 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SET724^4 : TPTP v8.1.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n017.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 04:55:16 EDT 2022
% Result : Theorem 2.07s 2.64s
% Output : Proof 2.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 23
% Syntax : Number of formulae : 62 ( 25 unt; 0 typ; 8 def)
% Number of atoms : 152 ( 34 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 174 ( 59 ~; 31 |; 0 &; 69 @)
% ( 0 <=>; 14 =>; 1 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 24 con; 0-2 aty)
% Number of variables : 58 ( 22 ^ 36 !; 0 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(def_fun_image,definition,
( fun_image
= ( ^ [X1: $i > $i,X2: $i > $o,X3: $i] :
~ ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3
!= ( X1 @ X4 ) ) ) ) ) ).
thf(def_fun_composition,definition,
( fun_composition
= ( ^ [X1: $i > $i,X2: $i > $i,X3: $i] : ( X2 @ ( X1 @ X3 ) ) ) ) ).
thf(def_fun_inv_image,definition,
( fun_inv_image
= ( ^ [X1: $i > $i,X2: $i > $o,X3: $i] :
~ ! [X4: $i] :
( ( X2 @ X4 )
=> ( X4
!= ( X1 @ X3 ) ) ) ) ) ).
thf(def_fun_injective,definition,
( fun_injective
= ( ^ [X1: $i > $i] :
! [X2: $i,X3: $i] :
( ( ( X1 @ X2 )
= ( X1 @ X3 ) )
=> ( X2 = X3 ) ) ) ) ).
thf(def_fun_surjective,definition,
( fun_surjective
= ( ^ [X1: $i > $i] :
! [X2: $i] :
~ ! [X3: $i] :
( X2
!= ( X1 @ X3 ) ) ) ) ).
thf(def_fun_bijective,definition,
( fun_bijective
= ( ^ [X1: $i > $i] :
~ ( ( fun_injective @ X1 )
=> ~ ( fun_surjective @ X1 ) ) ) ) ).
thf(def_fun_decreasing,definition,
( fun_decreasing
= ( ^ [X1: $i > $i,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X2 @ ( X1 @ X4 ) @ ( X1 @ X3 ) ) ) ) ) ).
thf(def_fun_increasing,definition,
( fun_increasing
= ( ^ [X1: $i > $i,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X2 @ ( X1 @ X3 ) @ ( X1 @ X4 ) ) ) ) ) ).
thf(thm,conjecture,
! [X1: $i > $i,X2: $i > $i,X3: $i > $i] :
( ~ ( ( ( ^ [X4: $i] : ( X2 @ ( X1 @ X4 ) ) )
= ( ^ [X4: $i] : ( X3 @ ( X1 @ X4 ) ) ) )
=> ~ ! [X4: $i] :
~ ! [X5: $i] :
( X4
!= ( X1 @ X5 ) ) )
=> ( X2 = X3 ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $i,X2: $i > $i,X3: $i > $i] :
( ~ ( ( ( ^ [X4: $i] : ( X2 @ ( X1 @ X4 ) ) )
= ( ^ [X4: $i] : ( X3 @ ( X1 @ X4 ) ) ) )
=> ~ ! [X4: $i] :
~ ! [X5: $i] :
( X4
!= ( X1 @ X5 ) ) )
=> ( X2 = X3 ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(ax2197,axiom,
( p1
| ~ p2 ),
file('<stdin>',ax2197) ).
thf(ax2198,axiom,
~ p1,
file('<stdin>',ax2198) ).
thf(ax2196,axiom,
( p2
| ~ p3 ),
file('<stdin>',ax2196) ).
thf(ax2195,axiom,
( p3
| ~ p4 ),
file('<stdin>',ax2195) ).
thf(ax2194,axiom,
( p4
| ~ p5 ),
file('<stdin>',ax2194) ).
thf(ax2154,axiom,
( ~ p21
| p40 ),
file('<stdin>',ax2154) ).
thf(ax2176,axiom,
( p5
| p21 ),
file('<stdin>',ax2176) ).
thf(pax40,axiom,
( p40
=> ! [X1: $i] :
( ( f__1 @ ( f__0 @ X1 ) )
= ( f__2 @ ( f__0 @ X1 ) ) ) ),
file('<stdin>',pax40) ).
thf(pax22,axiom,
( p22
=> ! [X1: $i] :
~ ! [X2: $i] :
( X1
!= ( f__0 @ X2 ) ) ),
file('<stdin>',pax22) ).
thf(ax2175,axiom,
( p5
| p22 ),
file('<stdin>',ax2175) ).
thf(ax2193,axiom,
( p4
| ~ p6 ),
file('<stdin>',ax2193) ).
thf(ax2185,axiom,
( p6
| ~ p13 ),
file('<stdin>',ax2185) ).
thf(nax13,axiom,
( p13
<= ! [X1: $i] :
( ( f__1 @ X1 )
= ( f__2 @ X1 ) ) ),
file('<stdin>',nax13) ).
thf(c_0_13,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax2197]) ).
thf(c_0_14,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax2198]) ).
thf(c_0_15,plain,
( p2
| ~ p3 ),
inference(fof_simplification,[status(thm)],[ax2196]) ).
thf(c_0_16,plain,
( p1
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_17,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_18,plain,
( p3
| ~ p4 ),
inference(fof_simplification,[status(thm)],[ax2195]) ).
thf(c_0_19,plain,
( p2
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_20,plain,
~ p2,
inference(sr,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_21,plain,
( p4
| ~ p5 ),
inference(fof_simplification,[status(thm)],[ax2194]) ).
thf(c_0_22,plain,
( p3
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_23,plain,
~ p3,
inference(sr,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_24,plain,
( p4
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_25,plain,
~ p4,
inference(sr,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_26,plain,
( ~ p21
| p40 ),
inference(fof_simplification,[status(thm)],[ax2154]) ).
thf(c_0_27,plain,
( p5
| p21 ),
inference(split_conjunct,[status(thm)],[ax2176]) ).
thf(c_0_28,plain,
~ p5,
inference(sr,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_29,plain,
! [X895: $i] :
( ~ p40
| ( ( f__1 @ ( f__0 @ X895 ) )
= ( f__2 @ ( f__0 @ X895 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax40])])]) ).
thf(c_0_30,plain,
( p40
| ~ p21 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_31,plain,
p21,
inference(sr,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_32,plain,
! [X905: $i] :
( ~ p22
| ( X905
= ( f__0 @ ( esk451_1 @ X905 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax22])])])])]) ).
thf(c_0_33,plain,
( p5
| p22 ),
inference(split_conjunct,[status(thm)],[ax2175]) ).
thf(c_0_34,plain,
( p4
| ~ p6 ),
inference(fof_simplification,[status(thm)],[ax2193]) ).
thf(c_0_35,plain,
! [X1: $i] :
( ( ( f__1 @ ( f__0 @ X1 ) )
= ( f__2 @ ( f__0 @ X1 ) ) )
| ~ p40 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_36,plain,
p40,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).
thf(c_0_37,plain,
! [X1: $i] :
( ( X1
= ( f__0 @ ( esk451_1 @ X1 ) ) )
| ~ p22 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_38,plain,
p22,
inference(sr,[status(thm)],[c_0_33,c_0_28]) ).
thf(c_0_39,plain,
( p6
| ~ p13 ),
inference(fof_simplification,[status(thm)],[ax2185]) ).
thf(c_0_40,plain,
( p4
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_41,plain,
( ( ( f__1 @ esk457_0 )
!= ( f__2 @ esk457_0 ) )
| p13 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax13])])])]) ).
thf(c_0_42,plain,
! [X1: $i] :
( ( f__1 @ ( f__0 @ X1 ) )
= ( f__2 @ ( f__0 @ X1 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
thf(c_0_43,plain,
! [X1: $i] :
( ( f__0 @ ( esk451_1 @ X1 ) )
= X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
thf(c_0_44,plain,
( p6
| ~ p13 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_45,plain,
~ p6,
inference(sr,[status(thm)],[c_0_40,c_0_25]) ).
thf(c_0_46,plain,
( p13
| ( ( f__1 @ esk457_0 )
!= ( f__2 @ esk457_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_47,plain,
! [X1: $i] :
( ( f__1 @ X1 )
= ( f__2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
thf(c_0_48,plain,
~ p13,
inference(sr,[status(thm)],[c_0_44,c_0_45]) ).
thf(c_0_49,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]),c_0_48]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],]) ).
thf(0,theorem,
! [X1: $i > $i,X2: $i > $i,X3: $i > $i] :
( ~ ( ( ( ^ [X4: $i] : ( X2 @ ( X1 @ X4 ) ) )
= ( ^ [X4: $i] : ( X3 @ ( X1 @ X4 ) ) ) )
=> ~ ! [X4: $i] :
~ ! [X5: $i] :
( X4
!= ( X1 @ X5 ) ) )
=> ( X2 = X3 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET724^4 : TPTP v8.1.0. Released v3.6.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jul 11 07:02:48 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.07/2.64 % SZS status Theorem
% 2.07/2.64 % Mode: mode506
% 2.07/2.64 % Inferences: 20745
% 2.07/2.64 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------