%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV513^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n027.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 : Wed Feb 25 09:41:25 AM UTC 2026
% Result : Theorem 1.40s 1.19s
% Output : Refutation 1.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV513^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.35 % Computer : n027.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Feb 24 12:48:37 EST 2026
% 0.15/0.35 % CPUTime :
% 0.15/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SEV513^1 : TPTP v9.2.1. Released v7.0.0.
% 0.19/0.45 % Domain : Analysis
% 0.19/0.45 % Problem : SUM_CASES
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English :
% 0.19/0.45
% 0.19/0.45 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Kal16]
% 0.19/0.45 % Names : SUM_CASES_.p [Kal16]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.00 v7.5.0, 0.33 v7.2.0, 0.25 v7.1.0
% 0.19/0.45 % Syntax : Number of formulae : 14 ( 2 unt; 10 typ; 1 def)
% 0.19/0.45 % Number of atoms : 19 ( 3 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 3 ( 4 avg)
% 0.19/0.45 % Number of connectives : 103 ( 2 ~; 0 |; 4 &; 94 @)
% 0.19/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 12 ( 7 avg)
% 0.19/0.45 % Number of types : 2 ( 1 usr)
% 0.19/0.45 % Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 10 ( 9 usr; 0 con; 2-5 aty)
% 0.19/0.45 % Number of variables : 32 ( 6 ^; 13 !; 4 ?; 32 :)
% 0.19/0.45 % ( 9 !>; 0 ?*; 0 @-; 0 @+)
% 0.19/0.45 % SPC : TH1_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : Exported from core HOL Light.
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf('thf_type_type/realax/real',type,
% 0.19/0.45 'type/realax/real': $tType ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/sets/SETSPEC',type,
% 0.19/0.45 'const/sets/SETSPEC':
% 0.19/0.45 !>[A: $tType] : ( A > $o > A > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/sets/IN',type,
% 0.19/0.45 'const/sets/IN':
% 0.19/0.45 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/sets/GSPEC',type,
% 0.19/0.45 'const/sets/GSPEC':
% 0.19/0.45 !>[A: $tType] : ( ( A > $o ) > A > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/sets/FINITE',type,
% 0.19/0.45 'const/sets/FINITE':
% 0.19/0.45 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/realax/real_add',type,
% 0.19/0.45 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/iterate/sum',type,
% 0.19/0.45 'const/iterate/sum':
% 0.19/0.45 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/iterate/monoidal',type,
% 0.19/0.45 'const/iterate/monoidal':
% 0.19/0.45 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/iterate/iterate',type,
% 0.19/0.45 'const/iterate/iterate':
% 0.19/0.45 !>[A: $tType,A0: $tType] : ( ( A0 > A0 > A0 ) > ( A > $o ) > ( A > A0 ) > A0 ) ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/class/COND',type,
% 0.19/0.45 'const/class/COND':
% 0.19/0.45 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.19/0.45
% 0.19/0.45 thf('thm/iterate/ITERATE_CASES_',axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,A0: B > B > B] :
% 0.19/0.45 ( ( 'const/iterate/monoidal' @ B @ A0 )
% 0.19/0.45 => ! [A1: A > $o,P: A > $o,A2: A > B,A3: A > B] :
% 0.19/0.45 ( ( 'const/sets/FINITE' @ A @ A1 )
% 0.19/0.45 => ( ( 'const/iterate/iterate' @ A @ B @ A0 @ A1
% 0.19/0.45 @ ^ [A4: A] : ( 'const/class/COND' @ B @ ( P @ A4 ) @ ( A2 @ A4 ) @ ( A3 @ A4 ) ) )
% 0.19/0.45 = ( A0
% 0.19/0.45 @ ( 'const/iterate/iterate' @ A @ B @ A0
% 0.19/0.45 @ ( 'const/sets/GSPEC' @ A
% 0.19/0.45 @ ^ [A4: A] :
% 0.19/0.45 ? [A5: A] :
% 0.19/0.45 ( 'const/sets/SETSPEC' @ A @ A4
% 0.19/0.45 @ ( ( 'const/sets/IN' @ A @ A5 @ A1 )
% 0.19/0.45 & ( P @ A5 ) )
% 0.19/0.45 @ A5 ) )
% 0.19/0.45 @ A2 )
% 0.19/0.45 @ ( 'const/iterate/iterate' @ A @ B @ A0
% 0.19/0.45 @ ( 'const/sets/GSPEC' @ A
% 0.19/0.45 @ ^ [A4: A] :
% 0.19/0.45 ? [A5: A] :
% 0.19/0.45 ( 'const/sets/SETSPEC' @ A @ A4
% 0.19/0.45 @ ( ( 'const/sets/IN' @ A @ A5 @ A1 )
% 0.19/0.45 & ~ ( P @ A5 ) )
% 0.19/0.45 @ A5 ) )
% 0.19/0.45 @ A3 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf('thm/iterate/MONOIDAL_REAL_ADD_',axiom,
% 0.19/0.45 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' ).
% 0.19/0.45
% 0.19/0.45 thf('thm/iterate/sum_',definition,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( 'const/iterate/sum' @ A )
% 0.19/0.45 = ( 'const/iterate/iterate' @ A @ 'type/realax/real' @ 'const/realax/real_add' ) ) ).
% 0.19/0.45
% 0.19/0.45 thf('thm/iterate/SUM_CASES_',conjecture,
% 0.19/0.45 ! [A: $tType,A0: A > $o,P: A > $o,A1: A > 'type/realax/real',A2: A > 'type/realax/real'] :
% 0.19/0.45 ( ( 'const/sets/FINITE' @ A @ A0 )
% 0.19/0.45 => ( ( 'const/iterate/sum' @ A @ A0
% 0.19/0.45 @ ^ [A3: A] : ( 'const/class/COND' @ 'type/realax/real' @ ( P @ A3 ) @ ( A1 @ A3 ) @ ( A2 @ A3 ) ) )
% 0.19/0.45 = ( 'const/realax/real_add'
% 0.19/0.45 @ ( 'const/iterate/sum' @ A
% 0.19/0.45 @ ( 'const/sets/GSPEC' @ A
% 0.19/0.45 @ ^ [A3: A] :
% 0.19/0.45 ? [A4: A] :
% 0.19/0.45 ( 'const/sets/SETSPEC' @ A @ A3
% 0.19/0.45 @ ( ( 'const/sets/IN' @ A @ A4 @ A0 )
% 0.19/0.45 & ( P @ A4 ) )
% 0.19/0.45 @ A4 ) )
% 0.19/0.45 @ A1 )
% 0.19/0.45 @ ( 'const/iterate/sum' @ A
% 0.19/0.45 @ ( 'const/sets/GSPEC' @ A
% 0.19/0.45 @ ^ [A3: A] :
% 0.19/0.45 ? [A4: A] :
% 0.19/0.45 ( 'const/sets/SETSPEC' @ A @ A3
% 0.19/0.45 @ ( ( 'const/sets/IN' @ A @ A4 @ A0 )
% 0.19/0.45 & ~ ( P @ A4 ) )
% 0.19/0.45 @ A4 ) )
% 0.19/0.45 @ A2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.40/1.16 ---- Embedded in THF ---
% 1.40/1.16 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.40/1.16 %%% Generated on Tue Feb 24 12:48:38 EST 2026
% 1.40/1.16 %%% using '$$dhol' embedding, version 1.3.0.
% 1.40/1.16 %%% Logic specification used:
% 1.40/1.16 %%% thf(spec, logic, $$dhol).
% 1.40/1.16
% 1.40/1.16 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.TpSpnsJgFg/DTF2DTF12183.p
% 1.40/1.16 thf('thf_type_type/realax/real', type, 'type/realax/real': $tType).
% 1.40/1.16 thf('thf_const_const/sets/SETSPEC', type, 'const/sets/SETSPEC': (!> [A:$tType]: ((A > ($o > (A > $o)))))).
% 1.40/1.16 thf('thf_const_const/sets/IN', type, 'const/sets/IN': (!> [A:$tType]: ((A > ((A > $o) > $o))))).
% 1.40/1.16 thf('thf_const_const/sets/GSPEC', type, 'const/sets/GSPEC': (!> [A:$tType]: (((A > $o) > (A > $o))))).
% 1.40/1.16 thf('thf_const_const/sets/FINITE', type, 'const/sets/FINITE': (!> [A:$tType]: (((A > $o) > $o)))).
% 1.40/1.16 thf('thf_const_const/realax/real_add', type, 'const/realax/real_add': ('type/realax/real' > ('type/realax/real' > 'type/realax/real'))).
% 1.40/1.16 thf('thf_const_const/iterate/sum', type, 'const/iterate/sum': (!> [A:$tType]: (((A > $o) > ((A > 'type/realax/real') > 'type/realax/real'))))).
% 1.40/1.16 thf('thf_const_const/iterate/monoidal', type, 'const/iterate/monoidal': (!> [A:$tType]: (((A > (A > A)) > $o)))).
% 1.40/1.16 thf('thf_const_const/iterate/iterate', type, 'const/iterate/iterate': (!> [A:$tType,A0:$tType]: (((A0 > (A0 > A0)) > ((A > $o) > ((A > A0) > A0)))))).
% 1.40/1.16 thf('thf_const_const/class/COND', type, 'const/class/COND': (!> [A:$tType]: (($o > (A > (A > A)))))).
% 1.40/1.16 thf('thm/iterate/ITERATE_CASES_', axiom, (! [A:$tType,B:$tType,A0:(B > (B > B))]: (((('const/iterate/monoidal' @ B) @ A0) => (! [A1:(A > $o),P:(A > $o),A2:(A > B),A3:(A > B)]: (((('const/sets/FINITE' @ A) @ A1) => (((((('const/iterate/iterate' @ A) @ B) @ A0) @ A1) @ (^ [A4:A]: ((((('const/class/COND' @ B) @ (P @ A4)) @ (A2 @ A4)) @ (A3 @ A4))))) = ((A0 @ ((((('const/iterate/iterate' @ A) @ B) @ A0) @ (('const/sets/GSPEC' @ A) @ (^ [A4:A]: ((? [A5:A]: ((((('const/sets/SETSPEC' @ A) @ A4) @ (((('const/sets/IN' @ A) @ A5) @ A1) & (P @ A5))) @ A5))))))) @ A2)) @ ((((('const/iterate/iterate' @ A) @ B) @ A0) @ (('const/sets/GSPEC' @ A) @ (^ [A4:A]: ((? [A5:A]: ((((('const/sets/SETSPEC' @ A) @ A4) @ (((('const/sets/IN' @ A) @ A5) @ A1) & (~ ((P @ A5))))) @ A5))))))) @ A3)))))))))).
% 1.40/1.16 thf('thm/iterate/MONOIDAL_REAL_ADD_', axiom, (('const/iterate/monoidal' @ 'type/realax/real') @ 'const/realax/real_add')).
% 1.40/1.16 thf('thm/iterate/sum_', definition, (! [A:$tType]: ((('const/iterate/sum' @ A) = ((('const/iterate/iterate' @ A) @ 'type/realax/real') @ 'const/realax/real_add'))))).
% 1.40/1.16 thf('thm/iterate/SUM_CASES_', conjecture, (! [A:$tType,A0:(A > $o),P:(A > $o),A1:(A > 'type/realax/real'),A2:(A > 'type/realax/real')]: (((('const/sets/FINITE' @ A) @ A0) => (((('const/iterate/sum' @ A) @ A0) @ (^ [A3:A]: ((((('const/class/COND' @ 'type/realax/real') @ (P @ A3)) @ (A1 @ A3)) @ (A2 @ A3))))) = (('const/realax/real_add' @ ((('const/iterate/sum' @ A) @ (('const/sets/GSPEC' @ A) @ (^ [A3:A]: ((? [A4:A]: ((((('const/sets/SETSPEC' @ A) @ A3) @ (((('const/sets/IN' @ A) @ A4) @ A0) & (P @ A4))) @ A4))))))) @ A1)) @ ((('const/iterate/sum' @ A) @ (('const/sets/GSPEC' @ A) @ (^ [A3:A]: ((? [A4:A]: ((((('const/sets/SETSPEC' @ A) @ A3) @ (((('const/sets/IN' @ A) @ A4) @ A0) & (~ ((P @ A4))))) @ A4))))))) @ A2))))))).
% 1.40/1.16 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.TpSpnsJgFg/DTF2DTF12183.p
% 1.40/1.16 ------------------------
% 1.40/1.17 ---- Cleaned THF ---
% 1.40/1.17 thf('thf_type_type/realax/real',type,
% 1.40/1.17 'type/realax/real': $tType ).
% 1.40/1.17
% 1.40/1.17 thf('thf_const_const/sets/SETSPEC',type,
% 1.40/1.17 'const/sets/SETSPEC':
% 1.40/1.17 !>[A: $tType] : ( A > $o > A > $o ) ).
% 1.40/1.17
% 1.40/1.17 thf('thf_const_const/sets/IN',type,
% 1.40/1.17 'const/sets/IN':
% 1.40/1.17 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.40/1.17
% 1.40/1.17 thf('thf_const_const/sets/GSPEC',type,
% 1.40/1.17 'const/sets/GSPEC':
% 1.40/1.17 !>[A: $tType] : ( ( A > $o ) > A > $o ) ).
% 1.40/1.17
% 1.40/1.17 thf('thf_const_const/sets/FINITE',type,
% 1.40/1.17 'const/sets/FINITE':
% 1.40/1.17 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 1.40/1.17
% 1.40/1.17 thf('thf_const_const/realax/real_add',type,
% 1.40/1.17 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 1.40/1.17
% 1.40/1.17 thf('thf_const_const/iterate/sum',type,
% 1.40/1.17 'const/iterate/sum':
% 1.40/1.17 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 1.40/1.17
% 1.40/1.17 thf('thf_const_const/iterate/monoidal',type,
% 1.40/1.17 'const/iterate/monoidal':
% 1.40/1.17 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 1.40/1.17
% 1.40/1.17 thf('thf_const_const/iterate/iterate',type,
% 1.40/1.17 'const/iterate/iterate':
% 1.40/1.17 !>[A: $tType,A0: $tType] : ( ( A0 > A0 > A0 ) > ( A > $o ) > ( A > A0 ) > A0 ) ).
% 1.40/1.17
% 1.40/1.17 thf('thf_const_const/class/COND',type,
% 1.40/1.17 'const/class/COND':
% 1.40/1.17 !>[A: $tType] : ( $o > A > A > A ) ).
% 1.40/1.17
% 1.40/1.17 thf('thm/iterate/ITERATE_CASES_',axiom,
% 1.40/1.17 ! [A: $tType,B: $tType,A0: B > B > B] :
% 1.40/1.17 ( ( 'const/iterate/monoidal' @ B @ A0 )
% 1.40/1.17 => ! [A1: A > $o,P: A > $o,A2: A > B,A3: A > B] :
% 1.40/1.17 ( ( 'const/sets/FINITE' @ A @ A1 )
% 1.40/1.17 => ( ( 'const/iterate/iterate' @ A @ B @ A0 @ A1
% 1.40/1.17 @ ^ [A4: A] : ( 'const/class/COND' @ B @ ( P @ A4 ) @ ( A2 @ A4 ) @ ( A3 @ A4 ) ) )
% 1.40/1.17 = ( A0
% 1.40/1.17 @ ( 'const/iterate/iterate' @ A @ B @ A0
% 1.40/1.17 @ ( 'const/sets/GSPEC' @ A
% 1.40/1.17 @ ^ [A4: A] :
% 1.40/1.17 ? [A5: A] :
% 1.40/1.17 ( 'const/sets/SETSPEC' @ A @ A4
% 1.40/1.17 @ ( ( 'const/sets/IN' @ A @ A5 @ A1 )
% 1.40/1.17 & ( P @ A5 ) )
% 1.40/1.17 @ A5 ) )
% 1.40/1.17 @ A2 )
% 1.40/1.17 @ ( 'const/iterate/iterate' @ A @ B @ A0
% 1.40/1.17 @ ( 'const/sets/GSPEC' @ A
% 1.40/1.17 @ ^ [A4: A] :
% 1.40/1.17 ? [A5: A] :
% 1.40/1.17 ( 'const/sets/SETSPEC' @ A @ A4
% 1.40/1.17 @ ( ( 'const/sets/IN' @ A @ A5 @ A1 )
% 1.40/1.17 & ~ ( P @ A5 ) )
% 1.40/1.17 @ A5 ) )
% 1.40/1.17 @ A3 ) ) ) ) ) ).
% 1.40/1.17
% 1.40/1.17 thf('thm/iterate/MONOIDAL_REAL_ADD_',axiom,
% 1.40/1.17 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' ).
% 1.40/1.17
% 1.40/1.17 thf('thm/iterate/sum_',definition,
% 1.40/1.17 ! [A: $tType] :
% 1.40/1.17 ( ( 'const/iterate/sum' @ A )
% 1.40/1.17 = ( 'const/iterate/iterate' @ A @ 'type/realax/real' @ 'const/realax/real_add' ) ) ).
% 1.40/1.17
% 1.40/1.17 thf('thm/iterate/SUM_CASES_',conjecture,
% 1.40/1.17 ! [A: $tType,A0: A > $o,P: A > $o,A1: A > 'type/realax/real',A2: A > 'type/realax/real'] :
% 1.40/1.17 ( ( 'const/sets/FINITE' @ A @ A0 )
% 1.40/1.17 => ( ( 'const/iterate/sum' @ A @ A0
% 1.40/1.17 @ ^ [A3: A] : ( 'const/class/COND' @ 'type/realax/real' @ ( P @ A3 ) @ ( A1 @ A3 ) @ ( A2 @ A3 ) ) )
% 1.40/1.17 = ( 'const/realax/real_add'
% 1.40/1.17 @ ( 'const/iterate/sum' @ A
% 1.40/1.17 @ ( 'const/sets/GSPEC' @ A
% 1.40/1.17 @ ^ [A3: A] :
% 1.40/1.17 ? [A4: A] :
% 1.40/1.17 ( 'const/sets/SETSPEC' @ A @ A3
% 1.40/1.17 @ ( ( 'const/sets/IN' @ A @ A4 @ A0 )
% 1.40/1.17 & ( P @ A4 ) )
% 1.40/1.17 @ A4 ) )
% 1.40/1.17 @ A1 )
% 1.40/1.17 @ ( 'const/iterate/sum' @ A
% 1.40/1.17 @ ( 'const/sets/GSPEC' @ A
% 1.40/1.17 @ ^ [A3: A] :
% 1.40/1.17 ? [A4: A] :
% 1.40/1.17 ( 'const/sets/SETSPEC' @ A @ A3
% 1.40/1.17 @ ( ( 'const/sets/IN' @ A @ A4 @ A0 )
% 1.40/1.17 & ~ ( P @ A4 ) )
% 1.40/1.17 @ A4 ) )
% 1.40/1.17 @ A2 ) ) ) ) ).
% 1.40/1.17 ------------------------
% 1.40/1.18 % (12284)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_12183 for (2999ds/27Mi)
% 1.40/1.18 % (12282)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12183 for (2999ds/183Mi)
% 1.40/1.18 % (12284)Refutation not found, incomplete strategy
% 1.40/1.18 % (12284)------------------------------
% 1.40/1.18 % (12284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.40/1.18 % (12284)Termination reason: Refutation not found, incomplete strategy
% 1.40/1.18
% 1.40/1.18
% 1.40/1.18 % (12284)Memory used [KB]: 5628
% 1.40/1.18 % (12284)Time elapsed: 0.006 s
% 1.40/1.18 % (12284)Instructions burned: 13 (million)
% 1.40/1.18 % (12284)------------------------------
% 1.40/1.18 % (12284)------------------------------
% 1.40/1.19 % (12285)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12183 for (2999ds/2Mi)
% 1.40/1.19 % (12288)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12183 for (2999ds/18Mi)
% 1.40/1.19 % (12286)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_12183 for (2999ds/2Mi)
% 1.40/1.19 % (12287)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_12183 for (2999ds/275Mi)
% 1.40/1.19 % Exception at run slice level
% 1.40/1.19 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.40/1.19 % (12285)Instruction limit reached!
% 1.40/1.19 % (12285)------------------------------
% 1.40/1.19 % (12285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.40/1.19 % (12285)Termination reason: Unknown
% 1.40/1.19 % (12285)Termination phase: Preprocessing 3
% 1.40/1.19
% 1.40/1.19 % (12285)Memory used [KB]: 1023
% 1.40/1.19 % (12285)Time elapsed: 0.003 s
% 1.40/1.19 % (12285)Instructions burned: 3 (million)
% 1.40/1.19 % (12285)------------------------------
% 1.40/1.19 % (12285)------------------------------
% 1.40/1.19 % (12287)First to succeed.
% 1.40/1.19 % (12287)Refutation found. Thanks to Tanya!
% 1.40/1.19 % SZS status Theorem for DTF2THF_12183
% 1.40/1.19 % SZS output start Proof for DTF2THF_12183
% 1.40/1.19 thf(type_def_6, type, 'type/realax/real': $tType).
% 1.40/1.19 thf(type_def_7, type, sK0: $tType).
% 1.40/1.19 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.40/1.19 thf(func_def_1, type, 'const/sets/SETSPEC': !>[X0: $tType]:(X0 > $o > X0 > $o)).
% 1.40/1.19 thf(func_def_2, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.40/1.19 thf(func_def_3, type, 'const/sets/GSPEC': !>[X0: $tType]:((X0 > $o) > X0 > $o)).
% 1.40/1.19 thf(func_def_4, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 1.40/1.19 thf(func_def_5, type, 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real').
% 1.40/1.19 thf(func_def_6, type, 'const/iterate/sum': !>[X0: $tType]:((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real')).
% 1.40/1.19 thf(func_def_7, type, 'const/iterate/monoidal': !>[X0: $tType]:((X0 > X0 > X0) > $o)).
% 1.40/1.19 thf(func_def_8, type, 'const/iterate/iterate': !>[X0: $tType, X1: $tType]:((X1 > X1 > X1) > (X0 > $o) > (X0 > X1) > X1)).
% 1.40/1.19 thf(func_def_9, type, 'const/class/COND': !>[X0: $tType]:($o > X0 > X0 > X0)).
% 1.40/1.19 thf(func_def_19, type, sK1: sK0 > $o).
% 1.40/1.19 thf(func_def_20, type, sK2: sK0 > $o).
% 1.40/1.19 thf(func_def_21, type, sK3: sK0 > 'type/realax/real').
% 1.40/1.19 thf(func_def_22, type, sK4: sK0 > 'type/realax/real').
% 1.40/1.19 thf(func_def_24, type, ph6: !>[X0: $tType]:(X0)).
% 1.40/1.19 thf(f26,plain,(
% 1.40/1.19 $false),
% 1.40/1.19 inference(subsumption_resolution,[status(thm)],[f25,f20])).
% 1.40/1.19 thf(f20,plain,(
% 1.40/1.19 (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') = $true)),
% 1.40/1.19 inference(cnf_transformation,[status(thm)],[f10])).
% 1.40/1.19 thf(f10,plain,(
% 1.40/1.19 (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') = $true)),
% 1.40/1.19 inference(fool_elimination,[status(thm)],[f9])).
% 1.40/1.19 thf(f9,plain,(
% 1.40/1.19 ('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')),
% 1.40/1.19 inference(rectify,[status(thm)],[f2])).
% 1.40/1.19 thf(f2,axiom,(
% 1.40/1.19 ('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')),
% 1.40/1.19 file('/export/starexec/sandbox2/tmp/tmp.TpSpnsJgFg/DTF2THF_12183.p','thm/iterate/MONOIDAL_REAL_ADD_')).
% 1.40/1.19 thf(f25,plain,(
% 1.40/1.19 (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') != $true)),
% 1.40/1.19 inference(subsumption_resolution,[status(thm)],[f24,f19])).
% 1.40/1.19 thf(f19,plain,(
% 1.40/1.19 ($true = ('const/sets/FINITE' @ sK0 @ sK1))),
% 1.40/1.19 inference(cnf_transformation,[status(thm)],[f16])).
% 1.40/1.19 thf(f16,plain,(
% 1.40/1.19 ($true = ('const/sets/FINITE' @ sK0 @ sK1)) & (('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ ((sK2 @ Y1) & ('const/sets/IN' @ sK0 @ Y1 @ sK1)) @ Y1))))) @ sK3) @ ('const/iterate/sum' @ sK0 @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ ((~ (sK2 @ Y1)) & ('const/sets/IN' @ sK0 @ Y1 @ sK1)) @ Y1))))) @ sK4)) != ('const/iterate/sum' @ sK0 @ sK1 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (sK2 @ Y0) @ (sK3 @ Y0) @ (sK4 @ Y0)))))),
% 1.40/1.19 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f13,f15])).
% 1.40/1.19 thf(f15,plain,(
% 1.40/1.19 ? [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/realax/real',X4 : X0 > 'type/realax/real'] : ((('const/sets/FINITE' @ X0 @ X1) = $true) & (('const/iterate/sum' @ X0 @ X1 @ (^[Y0 : X0]: ('const/class/COND' @ 'type/realax/real' @ (X2 @ Y0) @ (X3 @ Y0) @ (X4 @ Y0)))) != ('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((X2 @ Y1) & ('const/sets/IN' @ X0 @ Y1 @ X1)) @ Y1))))) @ X3) @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((~ (X2 @ Y1)) & ('const/sets/IN' @ X0 @ Y1 @ X1)) @ Y1))))) @ X4)))) => (($true = ('const/sets/FINITE' @ sK0 @ sK1)) & (('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ ((sK2 @ Y1) & ('const/sets/IN' @ sK0 @ Y1 @ sK1)) @ Y1))))) @ sK3) @ ('const/iterate/sum' @ sK0 @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ ((~ (sK2 @ Y1)) & ('const/sets/IN' @ sK0 @ Y1 @ sK1)) @ Y1))))) @ sK4)) != ('const/iterate/sum' @ sK0 @ sK1 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (sK2 @ Y0) @ (sK3 @ Y0) @ (sK4 @ Y0))))))),
% 1.40/1.19 introduced(definition,[],[choice_axiom])).
% 1.40/1.19 thf(f13,plain,(
% 1.40/1.19 ? [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/realax/real',X4 : X0 > 'type/realax/real'] : ((('const/sets/FINITE' @ X0 @ X1) = $true) & (('const/iterate/sum' @ X0 @ X1 @ (^[Y0 : X0]: ('const/class/COND' @ 'type/realax/real' @ (X2 @ Y0) @ (X3 @ Y0) @ (X4 @ Y0)))) != ('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((X2 @ Y1) & ('const/sets/IN' @ X0 @ Y1 @ X1)) @ Y1))))) @ X3) @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((~ (X2 @ Y1)) & ('const/sets/IN' @ X0 @ Y1 @ X1)) @ Y1))))) @ X4))))),
% 1.40/1.19 inference(ennf_transformation,[status(thm)],[f8])).
% 1.40/1.19 thf(f8,plain,(
% 1.40/1.19 ~! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/realax/real',X4 : X0 > 'type/realax/real'] : ((('const/sets/FINITE' @ X0 @ X1) = $true) => (('const/iterate/sum' @ X0 @ X1 @ (^[Y0 : X0]: ('const/class/COND' @ 'type/realax/real' @ (X2 @ Y0) @ (X3 @ Y0) @ (X4 @ Y0)))) = ('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((X2 @ Y1) & ('const/sets/IN' @ X0 @ Y1 @ X1)) @ Y1))))) @ X3) @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((~ (X2 @ Y1)) & ('const/sets/IN' @ X0 @ Y1 @ X1)) @ Y1))))) @ X4))))),
% 1.40/1.19 inference(fool_elimination,[status(thm)],[f7])).
% 1.40/1.19 thf(f7,plain,(
% 1.40/1.19 ~! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/realax/real',X4 : X0 > 'type/realax/real'] : (('const/sets/FINITE' @ X0 @ X1) => (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X5 : X0] : (? [X6 : X0] : ('const/sets/SETSPEC' @ X0 @ X5 @ ('const/sets/IN' @ X0 @ X6 @ X1) & (X2 @ X6) @ X6)))) @ X3) @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X7 : X0] : (? [X8 : X0] : ('const/sets/SETSPEC' @ X0 @ X7 @ ('const/sets/IN' @ X0 @ X8 @ X1) & ~(X2 @ X8) @ X8)))) @ X4)) = ('const/iterate/sum' @ X0 @ X1 @ (^[X9 : X0] : ('const/class/COND' @ 'type/realax/real' @ (X2 @ X9) @ (X3 @ X9) @ (X4 @ X9))))))),
% 1.40/1.19 inference(rectify,[status(thm)],[f5])).
% 1.40/1.19 thf(f5,negated_conjecture,(
% 1.40/1.19 ~! [X0 : $tType,X1 : X0 > $o,X4 : X0 > $o,X3 : X0 > 'type/realax/real',X5 : X0 > 'type/realax/real'] : (('const/sets/FINITE' @ X0 @ X1) => (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X6 : X0] : (? [X7 : X0] : ('const/sets/SETSPEC' @ X0 @ X6 @ ('const/sets/IN' @ X0 @ X7 @ X1) & (X4 @ X7) @ X7)))) @ X3) @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X6 : X0] : (? [X7 : X0] : ('const/sets/SETSPEC' @ X0 @ X6 @ ('const/sets/IN' @ X0 @ X7 @ X1) & ~(X4 @ X7) @ X7)))) @ X5)) = ('const/iterate/sum' @ X0 @ X1 @ (^[X6 : X0] : ('const/class/COND' @ 'type/realax/real' @ (X4 @ X6) @ (X3 @ X6) @ (X5 @ X6))))))),
% 1.40/1.19 inference(negated_conjecture,[status(cth)],[f4])).
% 1.40/1.19 thf(f4,conjecture,(
% 1.40/1.19 ! [X0 : $tType,X1 : X0 > $o,X4 : X0 > $o,X3 : X0 > 'type/realax/real',X5 : X0 > 'type/realax/real'] : (('const/sets/FINITE' @ X0 @ X1) => (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X6 : X0] : (? [X7 : X0] : ('const/sets/SETSPEC' @ X0 @ X6 @ ('const/sets/IN' @ X0 @ X7 @ X1) & (X4 @ X7) @ X7)))) @ X3) @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X6 : X0] : (? [X7 : X0] : ('const/sets/SETSPEC' @ X0 @ X6 @ ('const/sets/IN' @ X0 @ X7 @ X1) & ~(X4 @ X7) @ X7)))) @ X5)) = ('const/iterate/sum' @ X0 @ X1 @ (^[X6 : X0] : ('const/class/COND' @ 'type/realax/real' @ (X4 @ X6) @ (X3 @ X6) @ (X5 @ X6))))))),
% 1.40/1.19 file('/export/starexec/sandbox2/tmp/tmp.TpSpnsJgFg/DTF2THF_12183.p','thm/iterate/SUM_CASES_')).
% 1.40/1.19 thf(f24,plain,(
% 1.40/1.19 ($true != ('const/sets/FINITE' @ sK0 @ sK1)) | (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') != $true)),
% 1.40/1.19 inference(trivial_inequality_removal,[status(thm)],[f23])).
% 1.40/1.19 thf(f23,plain,(
% 1.40/1.19 (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') != $true) | ($true != ('const/sets/FINITE' @ sK0 @ sK1)) | (('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (sK2 @ Y0) @ (sK3 @ Y0) @ (sK4 @ Y0)))) != ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (sK2 @ Y0) @ (sK3 @ Y0) @ (sK4 @ Y0)))))),
% 1.40/1.19 inference(superposition,[status(thm)],[f22,f17])).
% 1.40/1.19 thf(f17,plain,(
% 1.40/1.19 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X1 > X1,X3 : X0 > $o,X6 : X0 > X1,X4 : X0 > $o,X5 : X0 > X1] : ((('const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ (^[Y0 : X0]: ('const/class/COND' @ X1 @ (X4 @ Y0) @ (X5 @ Y0) @ (X6 @ Y0)))) = (X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((X4 @ Y1) & ('const/sets/IN' @ X0 @ Y1 @ X3)) @ Y1))))) @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((~ (X4 @ Y1)) & ('const/sets/IN' @ X0 @ Y1 @ X3)) @ Y1))))) @ X6))) | (('const/sets/FINITE' @ X0 @ X3) != $true) | (('const/iterate/monoidal' @ X1 @ X2) != $true)) )),
% 1.40/1.19 inference(cnf_transformation,[status(thm)],[f14])).
% 1.40/1.19 thf(f14,plain,(
% 1.40/1.19 ! [X0 : $tType,X1 : $tType,X2 : X1 > X1 > X1] : (! [X3 : X0 > $o,X4 : X0 > $o,X5 : X0 > X1,X6 : X0 > X1] : ((('const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ (^[Y0 : X0]: ('const/class/COND' @ X1 @ (X4 @ Y0) @ (X5 @ Y0) @ (X6 @ Y0)))) = (X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((X4 @ Y1) & ('const/sets/IN' @ X0 @ Y1 @ X3)) @ Y1))))) @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((~ (X4 @ Y1)) & ('const/sets/IN' @ X0 @ Y1 @ X3)) @ Y1))))) @ X6))) | (('const/sets/FINITE' @ X0 @ X3) != $true)) | (('const/iterate/monoidal' @ X1 @ X2) != $true))),
% 1.40/1.19 inference(ennf_transformation,[status(thm)],[f12])).
% 1.40/1.19 thf(f12,plain,(
% 1.40/1.19 ! [X0 : $tType,X1 : $tType,X2 : X1 > X1 > X1] : ((('const/iterate/monoidal' @ X1 @ X2) = $true) => ! [X3 : X0 > $o,X4 : X0 > $o,X5 : X0 > X1,X6 : X0 > X1] : ((('const/sets/FINITE' @ X0 @ X3) = $true) => (('const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ (^[Y0 : X0]: ('const/class/COND' @ X1 @ (X4 @ Y0) @ (X5 @ Y0) @ (X6 @ Y0)))) = (X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((X4 @ Y1) & ('const/sets/IN' @ X0 @ Y1 @ X3)) @ Y1))))) @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ ((~ (X4 @ Y1)) & ('const/sets/IN' @ X0 @ Y1 @ X3)) @ Y1))))) @ X6)))))),
% 1.40/1.19 inference(fool_elimination,[status(thm)],[f11])).
% 1.40/1.19 thf(f11,plain,(
% 1.40/1.19 ! [X0 : $tType,X1 : $tType,X2 : X1 > X1 > X1] : (('const/iterate/monoidal' @ X1 @ X2) => ! [X3 : X0 > $o,X4 : X0 > $o,X5 : X0 > X1,X6 : X0 > X1] : (('const/sets/FINITE' @ X0 @ X3) => (('const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ (^[X7 : X0] : ('const/class/COND' @ X1 @ (X4 @ X7) @ (X5 @ X7) @ (X6 @ X7)))) = (X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[X8 : X0] : (? [X9 : X0] : ('const/sets/SETSPEC' @ X0 @ X8 @ ('const/sets/IN' @ X0 @ X9 @ X3) & (X4 @ X9) @ X9)))) @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[X10 : X0] : (? [X11 : X0] : ('const/sets/SETSPEC' @ X0 @ X10 @ ('const/sets/IN' @ X0 @ X11 @ X3) & ~(X4 @ X11) @ X11)))) @ X6)))))),
% 1.40/1.19 inference(rectify,[status(thm)],[f1])).
% 1.40/1.19 thf(f1,axiom,(
% 1.40/1.19 ! [X0 : $tType,X2 : $tType,X1 : X2 > X2 > X2] : (('const/iterate/monoidal' @ X2 @ X1) => ! [X3 : X0 > $o,X4 : X0 > $o,X5 : X0 > X2,X6 : X0 > X2] : (('const/sets/FINITE' @ X0 @ X3) => (('const/iterate/iterate' @ X0 @ X2 @ X1 @ X3 @ (^[X7 : X0] : ('const/class/COND' @ X2 @ (X4 @ X7) @ (X5 @ X7) @ (X6 @ X7)))) = (X1 @ ('const/iterate/iterate' @ X0 @ X2 @ X1 @ ('const/sets/GSPEC' @ X0 @ (^[X7 : X0] : (? [X8 : X0] : ('const/sets/SETSPEC' @ X0 @ X7 @ ('const/sets/IN' @ X0 @ X8 @ X3) & (X4 @ X8) @ X8)))) @ X5) @ ('const/iterate/iterate' @ X0 @ X2 @ X1 @ ('const/sets/GSPEC' @ X0 @ (^[X7 : X0] : (? [X8 : X0] : ('const/sets/SETSPEC' @ X0 @ X7 @ ('const/sets/IN' @ X0 @ X8 @ X3) & ~(X4 @ X8) @ X8)))) @ X6)))))),
% 1.40/1.19 file('/export/starexec/sandbox2/tmp/tmp.TpSpnsJgFg/DTF2THF_12183.p','thm/iterate/ITERATE_CASES_')).
% 1.40/1.19 thf(f22,plain,(
% 1.40/1.19 (('const/realax/real_add' @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ ((sK2 @ Y1) & ('const/sets/IN' @ sK0 @ Y1 @ sK1)) @ Y1))))) @ sK3) @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ ((~ (sK2 @ Y1)) & ('const/sets/IN' @ sK0 @ Y1 @ sK1)) @ Y1))))) @ sK4)) != ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (sK2 @ Y0) @ (sK3 @ Y0) @ (sK4 @ Y0)))))),
% 1.40/1.19 inference(definition_unfolding,[status(thm)],[f18,f21,f21,f21])).
% 1.40/1.19 thf(f21,plain,(
% 1.40/1.19 ( ! [X0 : $tType] : (('const/iterate/sum' @ X0 = ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add'))) )),
% 1.40/1.19 inference(cnf_transformation,[status(thm)],[f3])).
% 1.40/1.19 thf(f3,axiom,(
% 1.40/1.19 ! [X0 : $tType] : ('const/iterate/sum' @ X0 = ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add'))),
% 1.40/1.19 file('/export/starexec/sandbox2/tmp/tmp.TpSpnsJgFg/DTF2THF_12183.p','thm/iterate/sum_')).
% 1.40/1.19 thf(f18,plain,(
% 1.40/1.19 (('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ ((sK2 @ Y1) & ('const/sets/IN' @ sK0 @ Y1 @ sK1)) @ Y1))))) @ sK3) @ ('const/iterate/sum' @ sK0 @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ ((~ (sK2 @ Y1)) & ('const/sets/IN' @ sK0 @ Y1 @ sK1)) @ Y1))))) @ sK4)) != ('const/iterate/sum' @ sK0 @ sK1 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (sK2 @ Y0) @ (sK3 @ Y0) @ (sK4 @ Y0)))))),
% 1.40/1.19 inference(cnf_transformation,[status(thm)],[f16])).
% 1.40/1.19 % SZS output end Proof for DTF2THF_12183
% 1.40/1.19 % (12287)------------------------------
% 1.40/1.19 % (12287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.40/1.19 % (12287)Termination reason: Refutation
% 1.40/1.19
% 1.40/1.19 % (12287)Memory used [KB]: 5628
% 1.40/1.19 % (12287)Time elapsed: 0.008 s
% 1.40/1.19 % (12287)Instructions burned: 6 (million)
% 1.40/1.19 % (12287)------------------------------
% 1.40/1.19 % (12287)------------------------------
% 1.40/1.19 % (12281)Success in time 0.023 s
%------------------------------------------------------------------------------