TSTP Solution File: ITP118^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP118^1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n024.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 : Sun Jul 17 00:29:10 EDT 2022
% Result : Theorem 2.59s 2.84s
% Output : Proof 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 25
% Syntax : Number of formulae : 52 ( 26 unt; 11 typ; 0 def)
% Number of atoms : 223 ( 27 equ; 0 cnn)
% Maximal formula atoms : 2 ( 5 avg)
% Number of connectives : 214 ( 17 ~; 10 |; 0 &; 182 @)
% ( 0 <=>; 4 =>; 1 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 4 ( 4 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 27 usr; 25 con; 0-2 aty)
% Number of variables : 17 ( 0 ^ 17 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_finite1489363574real_n,type,
finite1489363574real_n: $tType ).
thf(ty_n,type,
n: $tType ).
thf(ty_int,type,
int: $tType ).
thf(ty_real,type,
real: $tType ).
thf(ty_minus_minus_real,type,
minus_minus_real: real > real > real ).
thf(ty_eigen__0,type,
eigen__0: int ).
thf(ty_y,type,
y: finite1489363574real_n ).
thf(ty_i,type,
i: n ).
thf(ty_finite772340589real_n,type,
finite772340589real_n: finite1489363574real_n > n > real ).
thf(ty_x,type,
x: finite1489363574real_n ).
thf(ty_ring_1_of_int_real,type,
ring_1_of_int_real: int > real ).
thf(conj_0,conjecture,
( ( ring_1_of_int_real @ ( abs_abs_int @ m ) )
= ( abs_abs_real @ ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ i ) ) ) ).
thf(h0,negated_conjecture,
( ring_1_of_int_real @ ( abs_abs_int @ m ) )
!= ( abs_abs_real @ ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ i ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
( ( ring_1_of_int_real @ eigen__0 )
= ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) ) ),
introduced(assumption,[]) ).
thf(pax4,axiom,
( p4
=> ( ( fring_1_of_int_real @ f__0 )
= ( fminus_minus_real @ ( ffinite772340589real_n @ fx @ fi ) @ ( ffinite772340589real_n @ fy @ fi ) ) ) ),
file('<stdin>',pax4) ).
thf(pax3,axiom,
( p3
=> ( ( fring_1_of_int_real @ fm )
= ( fminus_minus_real @ ( ffinite772340589real_n @ fx @ fi ) @ ( ffinite772340589real_n @ fy @ fi ) ) ) ),
file('<stdin>',pax3) ).
thf(ax106,axiom,
p4,
file('<stdin>',ax106) ).
thf(pax7,axiom,
( p7
=> ! [X92: int] :
( ( fring_1_of_int_real @ ( fabs_abs_int @ X92 ) )
= ( fabs_abs_real @ ( fring_1_of_int_real @ X92 ) ) ) ),
file('<stdin>',pax7) ).
thf(ax107,axiom,
p3,
file('<stdin>',ax107) ).
thf(pax5,axiom,
( p5
=> ! [X94: finite1489363574real_n,X95: finite1489363574real_n,X96: n] :
( ( ffinite772340589real_n @ ( fminus_1037315151real_n @ X94 @ X95 ) @ X96 )
= ( fminus_minus_real @ ( ffinite772340589real_n @ X94 @ X96 ) @ ( ffinite772340589real_n @ X95 @ X96 ) ) ) ),
file('<stdin>',pax5) ).
thf(nax110,axiom,
( p110
<= ( ( fring_1_of_int_real @ ( fabs_abs_int @ fm ) )
= ( fabs_abs_real @ ( ffinite772340589real_n @ ( fminus_1037315151real_n @ fx @ fy ) @ fi ) ) ) ),
file('<stdin>',nax110) ).
thf(ax103,axiom,
p7,
file('<stdin>',ax103) ).
thf(ax0,axiom,
~ p110,
file('<stdin>',ax0) ).
thf(ax105,axiom,
p5,
file('<stdin>',ax105) ).
thf(c_0_10,plain,
( ~ p4
| ( ( fring_1_of_int_real @ f__0 )
= ( fminus_minus_real @ ( ffinite772340589real_n @ fx @ fi ) @ ( ffinite772340589real_n @ fy @ fi ) ) ) ),
inference(fof_nnf,[status(thm)],[pax4]) ).
thf(c_0_11,plain,
( ~ p3
| ( ( fring_1_of_int_real @ fm )
= ( fminus_minus_real @ ( ffinite772340589real_n @ fx @ fi ) @ ( ffinite772340589real_n @ fy @ fi ) ) ) ),
inference(fof_nnf,[status(thm)],[pax3]) ).
thf(c_0_12,plain,
( ( ( fring_1_of_int_real @ f__0 )
= ( fminus_minus_real @ ( ffinite772340589real_n @ fx @ fi ) @ ( ffinite772340589real_n @ fy @ fi ) ) )
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_13,plain,
p4,
inference(split_conjunct,[status(thm)],[ax106]) ).
thf(c_0_14,plain,
! [X345: int] :
( ~ p7
| ( ( fring_1_of_int_real @ ( fabs_abs_int @ X345 ) )
= ( fabs_abs_real @ ( fring_1_of_int_real @ X345 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax7])])]) ).
thf(c_0_15,plain,
( ( ( fring_1_of_int_real @ fm )
= ( fminus_minus_real @ ( ffinite772340589real_n @ fx @ fi ) @ ( ffinite772340589real_n @ fy @ fi ) ) )
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_16,plain,
( ( fminus_minus_real @ ( ffinite772340589real_n @ fx @ fi ) @ ( ffinite772340589real_n @ fy @ fi ) )
= ( fring_1_of_int_real @ f__0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13])]) ).
thf(c_0_17,plain,
p3,
inference(split_conjunct,[status(thm)],[ax107]) ).
thf(c_0_18,plain,
! [X349: finite1489363574real_n,X350: finite1489363574real_n,X351: n] :
( ~ p5
| ( ( ffinite772340589real_n @ ( fminus_1037315151real_n @ X349 @ X350 ) @ X351 )
= ( fminus_minus_real @ ( ffinite772340589real_n @ X349 @ X351 ) @ ( ffinite772340589real_n @ X350 @ X351 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax5])])]) ).
thf(c_0_19,plain,
( ( ( fring_1_of_int_real @ ( fabs_abs_int @ fm ) )
!= ( fabs_abs_real @ ( ffinite772340589real_n @ ( fminus_1037315151real_n @ fx @ fy ) @ fi ) ) )
| p110 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax110])]) ).
thf(c_0_20,plain,
! [X3: int] :
( ( ( fring_1_of_int_real @ ( fabs_abs_int @ X3 ) )
= ( fabs_abs_real @ ( fring_1_of_int_real @ X3 ) ) )
| ~ p7 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_21,plain,
p7,
inference(split_conjunct,[status(thm)],[ax103]) ).
thf(c_0_22,plain,
~ p110,
inference(fof_simplification,[status(thm)],[ax0]) ).
thf(c_0_23,plain,
( ( fring_1_of_int_real @ f__0 )
= ( fring_1_of_int_real @ fm ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
thf(c_0_24,plain,
! [X9: finite1489363574real_n,X10: finite1489363574real_n,X11: n] :
( ( ( ffinite772340589real_n @ ( fminus_1037315151real_n @ X9 @ X10 ) @ X11 )
= ( fminus_minus_real @ ( ffinite772340589real_n @ X9 @ X11 ) @ ( ffinite772340589real_n @ X10 @ X11 ) ) )
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_25,plain,
p5,
inference(split_conjunct,[status(thm)],[ax105]) ).
thf(c_0_26,plain,
( p110
| ( ( fring_1_of_int_real @ ( fabs_abs_int @ fm ) )
!= ( fabs_abs_real @ ( ffinite772340589real_n @ ( fminus_1037315151real_n @ fx @ fy ) @ fi ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_27,plain,
! [X3: int] :
( ( fring_1_of_int_real @ ( fabs_abs_int @ X3 ) )
= ( fabs_abs_real @ ( fring_1_of_int_real @ X3 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]) ).
thf(c_0_28,plain,
~ p110,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_29,plain,
( ( fminus_minus_real @ ( ffinite772340589real_n @ fx @ fi ) @ ( ffinite772340589real_n @ fy @ fi ) )
= ( fring_1_of_int_real @ fm ) ),
inference(rw,[status(thm)],[c_0_16,c_0_23]) ).
thf(c_0_30,plain,
! [X9: finite1489363574real_n,X10: finite1489363574real_n,X11: n] :
( ( fminus_minus_real @ ( ffinite772340589real_n @ X9 @ X11 ) @ ( ffinite772340589real_n @ X10 @ X11 ) )
= ( ffinite772340589real_n @ ( fminus_1037315151real_n @ X9 @ X10 ) @ X11 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
thf(c_0_31,plain,
( fabs_abs_real @ ( ffinite772340589real_n @ ( fminus_1037315151real_n @ fx @ fy ) @ fi ) )
!= ( fabs_abs_real @ ( fring_1_of_int_real @ fm ) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
thf(c_0_32,plain,
( ( ffinite772340589real_n @ ( fminus_1037315151real_n @ fx @ fy ) @ fi )
= ( fring_1_of_int_real @ fm ) ),
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
thf(c_0_33,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h1,h0])],]) ).
thf(fact_3__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_Areal__of__int_Am_A_061_Ax_A_E_Ai_A_N_Ay_A_E_Ai_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
~ ! [X1: int] :
( ( ring_1_of_int_real @ X1 )
!= ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) ) ) ).
thf(2,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_3__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_Areal__of__int_Am_A_061_Ax_A_E_Ai_A_N_Ay_A_E_Ai_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,1,h1]) ).
thf(0,theorem,
( ( ring_1_of_int_real @ ( abs_abs_int @ m ) )
= ( abs_abs_real @ ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ i ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[2,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP118^1 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n024.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 : Thu Jun 2 21:42:50 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.59/2.84 % SZS status Theorem
% 2.59/2.84 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 2.59/2.84 % Inferences: 1
% 2.59/2.84 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------