%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA100^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n029.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 08:38:52 AM UTC 2026
% Result : Theorem 1.66s 1.42s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 26 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 246 ( 20 ~; 7 |; 0 &; 218 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 2 con; 0-5 aty)
% Number of variables : 61 ( 16 ^; 37 !; 8 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/realax/real': $tType ).
thf(type_def_7,type,
sK0: $tType ).
thf(func_def_0,type,
'type/realax/real': $tType ).
thf(func_def_1,type,
'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_2,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_8,type,
sK1: sK0 > 'type/realax/real' ).
thf(func_def_9,type,
sK2: 'type/realax/real' ).
thf(func_def_10,type,
sK3: sK0 > $o ).
thf(func_def_12,type,
ph5:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
sK6:
!>[X0: $tType] : ( 'type/realax/real' > 'type/realax/real' > ( X0 > 'type/realax/real' ) > ( X0 > 'type/realax/real' ) > X0 ) ).
thf(func_def_14,type,
sK7: 'type/realax/real' > ( sK0 > 'type/realax/real' ) > sK0 ).
thf(f28,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f25,f13]) ).
thf(f13,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ X0 @ X1 )
= ( 'const/realax/real_mul' @ X1 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ X0 @ X1 )
= ( 'const/realax/real_mul' @ X1 @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.ar4cLvm9z5/DTF2THF_29524.p','thm/realax/REAL_MUL_SYM_') ).
thf(f25,plain,
( ( 'const/realax/real_mul' @ sK2 @ ( sK1 @ ( sK7 @ sK2 @ sK1 ) ) )
!= ( 'const/realax/real_mul' @ ( sK1 @ ( sK7 @ sK2 @ sK1 ) ) @ sK2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( 'const/realax/real_mul' @ sK2 @ ( sK1 @ ( sK7 @ sK2 @ sK1 ) ) )
!= ( 'const/realax/real_mul' @ ( sK1 @ ( sK7 @ sK2 @ sK1 ) ) @ sK2 ) )
| ( sK3 != sK3 ) ),
inference(equality_resolution,[status(thm)],[f20]) ).
thf(f20,plain,
! [X2: sK0 > 'type/realax/real',X0: sK0 > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_mul' @ X1 @ ( 'const/iterate/sum' @ sK0 @ X0 @ X2 ) )
!= ( 'const/realax/real_mul' @ sK2 @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK1 ) ) )
| ( sK3 != X0 )
| ( ( 'const/realax/real_mul' @ ( sK1 @ ( sK7 @ X1 @ X2 ) ) @ sK2 )
!= ( 'const/realax/real_mul' @ X1 @ ( X2 @ ( sK7 @ X1 @ X2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
! [X2: sK0 > 'type/realax/real',X0: sK0 > $o,X1: 'type/realax/real'] :
( ( ( ^ [Y0: sK0] : ( 'const/realax/real_mul' @ ( sK1 @ Y0 ) @ sK2 )
@ ( sK7 @ X1 @ X2 ) )
!= ( ^ [Y0: sK0] : ( 'const/realax/real_mul' @ X1 @ ( X2 @ Y0 ) )
@ ( sK7 @ X1 @ X2 ) ) )
| ( ( 'const/realax/real_mul' @ X1 @ ( 'const/iterate/sum' @ sK0 @ X0 @ X2 ) )
!= ( 'const/realax/real_mul' @ sK2 @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK1 ) ) )
| ( sK3 != X0 ) ),
inference(negative_extensionality,[status(thm)],[f16]) ).
thf(f16,plain,
! [X2: sK0 > 'type/realax/real',X0: sK0 > $o,X1: 'type/realax/real'] :
( ( ( ^ [Y0: sK0] : ( 'const/realax/real_mul' @ X1 @ ( X2 @ Y0 ) ) )
!= ( ^ [Y0: sK0] : ( 'const/realax/real_mul' @ ( sK1 @ Y0 ) @ sK2 ) ) )
| ( ( 'const/realax/real_mul' @ X1 @ ( 'const/iterate/sum' @ sK0 @ X0 @ X2 ) )
!= ( 'const/realax/real_mul' @ sK2 @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK1 ) ) )
| ( sK3 != X0 ) ),
inference(constrained_superposition,[status(thm)],[f14,f12]) ).
thf(f12,plain,
! [X0: $tType,X2: 'type/realax/real',X3: X0 > $o,X1: X0 > 'type/realax/real'] :
( ( 'const/realax/real_mul' @ X2 @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) )
= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [Y0: X0] : ( 'const/realax/real_mul' @ X2 @ ( X1 @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: 'type/realax/real',X3: X0 > $o] :
( ( 'const/realax/real_mul' @ X2 @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) )
= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [Y0: X0] : ( 'const/realax/real_mul' @ X2 @ ( X1 @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: 'type/realax/real',X3: X0 > $o] :
( ( 'const/realax/real_mul' @ X2 @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) )
= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [X4: X0] : ( 'const/realax/real_mul' @ X2 @ ( X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ar4cLvm9z5/DTF2THF_29524.p','thm/iterate/SUM_LMUL_') ).
thf(f14,plain,
( ( 'const/iterate/sum' @ sK0 @ sK3
@ ^ [Y0: sK0] : ( 'const/realax/real_mul' @ ( sK1 @ Y0 ) @ sK2 ) )
!= ( 'const/realax/real_mul' @ sK2 @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK1 ) ) ),
inference(backward_demodulation,[status(thm)],[f11,f13]) ).
thf(f11,plain,
( ( 'const/iterate/sum' @ sK0 @ sK3
@ ^ [Y0: sK0] : ( 'const/realax/real_mul' @ ( sK1 @ Y0 ) @ sK2 ) )
!= ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK1 ) @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( 'const/iterate/sum' @ sK0 @ sK3
@ ^ [Y0: sK0] : ( 'const/realax/real_mul' @ ( sK1 @ Y0 ) @ sK2 ) )
!= ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK1 ) @ sK2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f9]) ).
thf(f9,plain,
( ? [X0: $tType,X1: X0 > 'type/realax/real',X2: 'type/realax/real',X3: X0 > $o] :
( ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ X2 )
!= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [Y0: X0] : ( 'const/realax/real_mul' @ ( X1 @ Y0 ) @ X2 ) ) )
=> ( ( 'const/iterate/sum' @ sK0 @ sK3
@ ^ [Y0: sK0] : ( 'const/realax/real_mul' @ ( sK1 @ Y0 ) @ sK2 ) )
!= ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK1 ) @ sK2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: $tType,X1: X0 > 'type/realax/real',X2: 'type/realax/real',X3: X0 > $o] :
( ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ X2 )
!= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [Y0: X0] : ( 'const/realax/real_mul' @ ( X1 @ Y0 ) @ X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: $tType,X1: X0 > 'type/realax/real',X2: 'type/realax/real',X3: X0 > $o] :
( ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ X2 )
= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [Y0: X0] : ( 'const/realax/real_mul' @ ( X1 @ Y0 ) @ X2 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X1: X0 > 'type/realax/real',X2: 'type/realax/real',X3: X0 > $o] :
( ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ X2 )
= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [X4: X0] : ( 'const/realax/real_mul' @ ( X1 @ X4 ) @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: 'type/realax/real',X3: X0 > $o] :
( ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ X2 )
= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [X4: X0] : ( 'const/realax/real_mul' @ ( X1 @ X4 ) @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ar4cLvm9z5/DTF2THF_29524.p','thm/iterate/SUM_RMUL_') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA100^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n029.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 03:50:29 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : ANA100^1 : TPTP v9.2.1. Released v7.0.0.
% 0.19/0.46 % Domain : Analysis
% 0.19/0.46 % Problem : SUM_RMUL
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Kal16]
% 0.19/0.46 % Names : SUM_RMUL_.p [Kal16]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.33 v8.1.0, 0.25 v7.5.0, 0.00 v7.1.0
% 0.19/0.46 % Syntax : Number of formulae : 6 ( 3 unt; 3 typ; 0 def)
% 0.19/0.46 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.19/0.46 % Number of connectives : 26 ( 0 ~; 0 |; 0 &; 26 @)
% 0.19/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 5 ( 4 avg)
% 0.19/0.46 % Number of types : 2 ( 1 usr)
% 0.19/0.46 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 3 ( 2 usr; 0 con; 2-3 aty)
% 0.19/0.46 % Number of variables : 13 ( 2 ^; 10 !; 0 ?; 13 :)
% 0.19/0.46 % ( 1 !>; 0 ?*; 0 @-; 0 @+)
% 0.19/0.46 % SPC : TH1_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : Exported from core HOL Light.
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf('thf_type_type/realax/real',type,
% 0.19/0.46 'type/realax/real': $tType ).
% 0.19/0.46
% 0.19/0.46 thf('thf_const_const/realax/real_mul',type,
% 0.19/0.46 'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 0.19/0.46
% 0.19/0.46 thf('thf_const_const/iterate/sum',type,
% 0.19/0.46 'const/iterate/sum':
% 0.19/0.46 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 0.19/0.46
% 0.19/0.46 thf('thm/iterate/SUM_LMUL_',axiom,
% 0.19/0.46 ! [A: $tType,A0: A > 'type/realax/real',A1: 'type/realax/real',A2: A > $o] :
% 0.19/0.46 ( ( 'const/iterate/sum' @ A @ A2
% 0.19/0.46 @ ^ [A3: A] : ( 'const/realax/real_mul' @ A1 @ ( A0 @ A3 ) ) )
% 0.19/0.46 = ( 'const/realax/real_mul' @ A1 @ ( 'const/iterate/sum' @ A @ A2 @ A0 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf('thm/realax/REAL_MUL_SYM_',axiom,
% 0.19/0.46 ! [A: 'type/realax/real',A0: 'type/realax/real'] :
% 0.19/0.46 ( ( 'const/realax/real_mul' @ A @ A0 )
% 0.19/0.46 = ( 'const/realax/real_mul' @ A0 @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf('thm/iterate/SUM_RMUL_',conjecture,
% 0.19/0.46 ! [A: $tType,A0: A > 'type/realax/real',A1: 'type/realax/real',A2: A > $o] :
% 0.19/0.46 ( ( 'const/iterate/sum' @ A @ A2
% 0.19/0.46 @ ^ [A3: A] : ( 'const/realax/real_mul' @ ( A0 @ A3 ) @ A1 ) )
% 0.19/0.46 = ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ A @ A2 @ A0 ) @ A1 ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.49/1.38 ---- Embedded in THF ---
% 1.49/1.38 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.38 %%% Generated on Tue Feb 24 03:50:30 EST 2026
% 1.49/1.38 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.38 %%% Logic specification used:
% 1.49/1.38 %%% thf(spec, logic, $$dhol).
% 1.49/1.38
% 1.49/1.38 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ar4cLvm9z5/DTF2DTF29524.p
% See solution above
% 1.49/1.38 ------------------------
% 1.49/1.39 ---- Cleaned THF ---
% 1.49/1.39 thf('thf_type_type/realax/real',type,
% 1.49/1.39 'type/realax/real': $tType ).
% 1.49/1.39
% 1.49/1.39 thf('thf_const_const/realax/real_mul',type,
% 1.49/1.39 'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 1.49/1.39
% 1.49/1.39 thf('thf_const_const/iterate/sum',type,
% 1.49/1.39 'const/iterate/sum':
% 1.49/1.39 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 1.49/1.39
% 1.49/1.39 thf('thm/iterate/SUM_LMUL_',axiom,
% 1.49/1.39 ! [A: $tType,A0: A > 'type/realax/real',A1: 'type/realax/real',A2: A > $o] :
% 1.49/1.39 ( ( 'const/iterate/sum' @ A @ A2
% 1.49/1.39 @ ^ [A3: A] : ( 'const/realax/real_mul' @ A1 @ ( A0 @ A3 ) ) )
% 1.49/1.39 = ( 'const/realax/real_mul' @ A1 @ ( 'const/iterate/sum' @ A @ A2 @ A0 ) ) ) ).
% 1.49/1.39
% 1.49/1.39 thf('thm/realax/REAL_MUL_SYM_',axiom,
% 1.49/1.39 ! [A: 'type/realax/real',A0: 'type/realax/real'] :
% 1.49/1.39 ( ( 'const/realax/real_mul' @ A @ A0 )
% 1.49/1.39 = ( 'const/realax/real_mul' @ A0 @ A ) ) ).
% 1.49/1.39
% 1.49/1.39 thf('thm/iterate/SUM_RMUL_',conjecture,
% 1.49/1.39 ! [A: $tType,A0: A > 'type/realax/real',A1: 'type/realax/real',A2: A > $o] :
% 1.49/1.39 ( ( 'const/iterate/sum' @ A @ A2
% 1.49/1.39 @ ^ [A3: A] : ( 'const/realax/real_mul' @ ( A0 @ A3 ) @ A1 ) )
% 1.49/1.39 = ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ A @ A2 @ A0 ) @ A1 ) ) ).
% 1.49/1.39 ------------------------
% 1.66/1.41 % (29624)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_29524 for (2999ds/27Mi)
% 1.66/1.41 % (29623)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_29524 for (2999ds/4Mi)
% 1.66/1.41 % (29622)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29524 for (2999ds/183Mi)
% 1.66/1.41 % (29625)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29524 for (2999ds/2Mi)
% 1.66/1.41 % (29626)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_29524 for (2999ds/2Mi)
% 1.66/1.41 % (29627)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_29524 for (2999ds/275Mi)
% 1.66/1.41 % (29628)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29524 for (2999ds/18Mi)
% 1.66/1.41 % Exception at run slice level
% 1.66/1.41 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
% 1.66/1.41 % (29625)Instruction limit reached!
% 1.66/1.41 % (29625)------------------------------
% 1.66/1.41 % (29625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.41 % (29625)Termination reason: Unknown
% 1.66/1.41 % (29625)Termination phase: Saturation
% 1.66/1.41
% 1.66/1.41 % (29625)Memory used [KB]: 5500
% 1.66/1.41 % (29625)Time elapsed: 0.003 s
% 1.66/1.41 % (29625)Instructions burned: 2 (million)
% 1.66/1.41 % (29625)------------------------------
% 1.66/1.41 % (29625)------------------------------
% 1.66/1.41 % (29627)Refutation not found, incomplete strategy
% 1.66/1.41 % (29627)------------------------------
% 1.66/1.41 % (29627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.41 % (29627)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.41
% 1.66/1.41
% 1.66/1.41 % (29627)Memory used [KB]: 5500
% 1.66/1.41 % (29627)Time elapsed: 0.003 s
% 1.66/1.41 % (29627)Instructions burned: 2 (million)
% 1.66/1.41 % (29627)------------------------------
% 1.66/1.41 % (29627)------------------------------
% 1.66/1.41 % (29624)Refutation not found, incomplete strategy
% 1.66/1.41 % (29624)------------------------------
% 1.66/1.41 % (29624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.41 % (29623)Instruction limit reached!
% 1.66/1.41 % (29623)------------------------------
% 1.66/1.41 % (29623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.41 % (29624)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.41
% 1.66/1.41
% 1.66/1.41 % (29624)Memory used [KB]: 5500
% 1.66/1.41 % (29624)Time elapsed: 0.003 s
% 1.66/1.41 % (29624)Instructions burned: 2 (million)
% 1.66/1.41 % (29624)------------------------------
% 1.66/1.41 % (29624)------------------------------
% 1.66/1.41 % (29623)Termination reason: Unknown
% 1.66/1.41 % (29623)Termination phase: Saturation
% 1.66/1.41
% 1.66/1.41 % (29623)Memory used [KB]: 5500
% 1.66/1.41 % (29623)Time elapsed: 0.004 s
% 1.66/1.41 % (29623)Instructions burned: 4 (million)
% 1.66/1.41 % (29623)------------------------------
% 1.66/1.41 % (29623)------------------------------
% 1.66/1.42 % (29628)First to succeed.
% 1.66/1.42 % (29628)Refutation found. Thanks to Tanya!
% 1.66/1.42 % SZS status Theorem for DTF2THF_29524
% 1.66/1.42 % SZS output start Proof for DTF2THF_29524
% 1.66/1.42 thf(type_def_5, type, 'type/realax/real': $tType).
% 1.66/1.42 thf(type_def_7, type, sK0: $tType).
% 1.66/1.42 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.66/1.42 thf(func_def_1, type, 'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real').
% 1.66/1.42 thf(func_def_2, type, 'const/iterate/sum': !>[X0: $tType]:((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real')).
% 1.66/1.42 thf(func_def_8, type, sK1: sK0 > 'type/realax/real').
% 1.66/1.42 thf(func_def_9, type, sK2: 'type/realax/real').
% 1.66/1.42 thf(func_def_10, type, sK3: sK0 > $o).
% 1.66/1.42 thf(func_def_12, type, ph5: !>[X0: $tType]:(X0)).
% 1.66/1.42 thf(func_def_13, type, sK6: !>[X0: $tType]:('type/realax/real' > 'type/realax/real' > (X0 > 'type/realax/real') > (X0 > 'type/realax/real') > X0)).
% 1.66/1.42 thf(func_def_14, type, sK7: 'type/realax/real' > (sK0 > 'type/realax/real') > sK0).
% 1.66/1.42 thf(f28,plain,(
% 1.66/1.42 $false),
% 1.66/1.42 inference(subsumption_resolution,[status(thm)],[f25,f13])).
% 1.66/1.42 thf(f13,plain,(
% 1.66/1.42 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_mul' @ X0 @ X1) = ('const/realax/real_mul' @ X1 @ X0))) )),
% 1.66/1.42 inference(cnf_transformation,[status(thm)],[f2])).
% 1.66/1.42 thf(f2,axiom,(
% 1.66/1.42 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_mul' @ X0 @ X1) = ('const/realax/real_mul' @ X1 @ X0))),
% 1.66/1.42 file('/export/starexec/sandbox/tmp/tmp.ar4cLvm9z5/DTF2THF_29524.p','thm/realax/REAL_MUL_SYM_')).
% 1.66/1.42 thf(f25,plain,(
% 1.66/1.42 (('const/realax/real_mul' @ sK2 @ (sK1 @ (sK7 @ sK2 @ sK1))) != ('const/realax/real_mul' @ (sK1 @ (sK7 @ sK2 @ sK1)) @ sK2))),
% 1.66/1.42 inference(trivial_inequality_removal,[status(thm)],[f24])).
% 1.66/1.42 thf(f24,plain,(
% 1.66/1.42 (('const/realax/real_mul' @ sK2 @ (sK1 @ (sK7 @ sK2 @ sK1))) != ('const/realax/real_mul' @ (sK1 @ (sK7 @ sK2 @ sK1)) @ sK2)) | (sK3 != sK3)),
% 1.66/1.42 inference(equality_resolution,[status(thm)],[f20])).
% 1.66/1.42 thf(f20,plain,(
% 1.66/1.42 ( ! [X2 : sK0 > 'type/realax/real',X0 : sK0 > $o,X1 : 'type/realax/real'] : ((('const/realax/real_mul' @ X1 @ ('const/iterate/sum' @ sK0 @ X0 @ X2)) != ('const/realax/real_mul' @ sK2 @ ('const/iterate/sum' @ sK0 @ sK3 @ sK1))) | (sK3 != X0) | (('const/realax/real_mul' @ (sK1 @ (sK7 @ X1 @ X2)) @ sK2) != ('const/realax/real_mul' @ X1 @ (X2 @ (sK7 @ X1 @ X2))))) )),
% 1.66/1.42 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.66/1.42 thf(f19,plain,(
% 1.66/1.42 ( ! [X2 : sK0 > 'type/realax/real',X0 : sK0 > $o,X1 : 'type/realax/real'] : ((((^[Y0 : sK0]: ('const/realax/real_mul' @ (sK1 @ Y0) @ sK2)) @ (sK7 @ X1 @ X2)) != ((^[Y0 : sK0]: ('const/realax/real_mul' @ X1 @ (X2 @ Y0))) @ (sK7 @ X1 @ X2))) | (('const/realax/real_mul' @ X1 @ ('const/iterate/sum' @ sK0 @ X0 @ X2)) != ('const/realax/real_mul' @ sK2 @ ('const/iterate/sum' @ sK0 @ sK3 @ sK1))) | (sK3 != X0)) )),
% 1.66/1.42 inference(negative_extensionality,[status(thm)],[f16])).
% 1.66/1.42 thf(f16,plain,(
% 1.66/1.42 ( ! [X2 : sK0 > 'type/realax/real',X0 : sK0 > $o,X1 : 'type/realax/real'] : (((^[Y0 : sK0]: ('const/realax/real_mul' @ X1 @ (X2 @ Y0))) != (^[Y0 : sK0]: ('const/realax/real_mul' @ (sK1 @ Y0) @ sK2))) | (('const/realax/real_mul' @ X1 @ ('const/iterate/sum' @ sK0 @ X0 @ X2)) != ('const/realax/real_mul' @ sK2 @ ('const/iterate/sum' @ sK0 @ sK3 @ sK1))) | (sK3 != X0)) )),
% 1.66/1.42 inference(constrained_superposition,[status(thm)],[f14,f12])).
% 1.66/1.42 thf(f12,plain,(
% 1.66/1.42 ( ! [X0 : $tType,X2 : 'type/realax/real',X3 : X0 > $o,X1 : X0 > 'type/realax/real'] : ((('const/realax/real_mul' @ X2 @ ('const/iterate/sum' @ X0 @ X3 @ X1)) = ('const/iterate/sum' @ X0 @ X3 @ (^[Y0 : X0]: ('const/realax/real_mul' @ X2 @ (X1 @ Y0)))))) )),
% 1.66/1.42 inference(cnf_transformation,[status(thm)],[f7])).
% 1.66/1.42 thf(f7,plain,(
% 1.66/1.42 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : 'type/realax/real',X3 : X0 > $o] : (('const/realax/real_mul' @ X2 @ ('const/iterate/sum' @ X0 @ X3 @ X1)) = ('const/iterate/sum' @ X0 @ X3 @ (^[Y0 : X0]: ('const/realax/real_mul' @ X2 @ (X1 @ Y0)))))),
% 1.66/1.42 inference(fool_elimination,[status(thm)],[f1])).
% 1.66/1.42 thf(f1,axiom,(
% 1.66/1.42 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : 'type/realax/real',X3 : X0 > $o] : (('const/realax/real_mul' @ X2 @ ('const/iterate/sum' @ X0 @ X3 @ X1)) = ('const/iterate/sum' @ X0 @ X3 @ (^[X4 : X0] : ('const/realax/real_mul' @ X2 @ (X1 @ X4)))))),
% 1.66/1.42 file('/export/starexec/sandbox/tmp/tmp.ar4cLvm9z5/DTF2THF_29524.p','thm/iterate/SUM_LMUL_')).
% 1.66/1.42 thf(f14,plain,(
% 1.66/1.42 (('const/iterate/sum' @ sK0 @ sK3 @ (^[Y0 : sK0]: ('const/realax/real_mul' @ (sK1 @ Y0) @ sK2))) != ('const/realax/real_mul' @ sK2 @ ('const/iterate/sum' @ sK0 @ sK3 @ sK1)))),
% 1.66/1.42 inference(backward_demodulation,[status(thm)],[f11,f13])).
% 1.66/1.42 thf(f11,plain,(
% 1.66/1.42 (('const/iterate/sum' @ sK0 @ sK3 @ (^[Y0 : sK0]: ('const/realax/real_mul' @ (sK1 @ Y0) @ sK2))) != ('const/realax/real_mul' @ ('const/iterate/sum' @ sK0 @ sK3 @ sK1) @ sK2))),
% 1.66/1.42 inference(cnf_transformation,[status(thm)],[f10])).
% 1.66/1.42 thf(f10,plain,(
% 1.66/1.42 (('const/iterate/sum' @ sK0 @ sK3 @ (^[Y0 : sK0]: ('const/realax/real_mul' @ (sK1 @ Y0) @ sK2))) != ('const/realax/real_mul' @ ('const/iterate/sum' @ sK0 @ sK3 @ sK1) @ sK2))),
% 1.66/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f9])).
% 1.66/1.42 thf(f9,plain,(
% 1.66/1.42 ? [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : 'type/realax/real',X3 : X0 > $o] : (('const/realax/real_mul' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ X2) != ('const/iterate/sum' @ X0 @ X3 @ (^[Y0 : X0]: ('const/realax/real_mul' @ (X1 @ Y0) @ X2)))) => (('const/iterate/sum' @ sK0 @ sK3 @ (^[Y0 : sK0]: ('const/realax/real_mul' @ (sK1 @ Y0) @ sK2))) != ('const/realax/real_mul' @ ('const/iterate/sum' @ sK0 @ sK3 @ sK1) @ sK2))),
% 1.66/1.42 introduced(definition,[],[choice_axiom])).
% 1.66/1.42 thf(f8,plain,(
% 1.66/1.42 ? [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : 'type/realax/real',X3 : X0 > $o] : (('const/realax/real_mul' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ X2) != ('const/iterate/sum' @ X0 @ X3 @ (^[Y0 : X0]: ('const/realax/real_mul' @ (X1 @ Y0) @ X2))))),
% 1.66/1.42 inference(ennf_transformation,[status(thm)],[f6])).
% 1.66/1.42 thf(f6,plain,(
% 1.66/1.42 ~! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : 'type/realax/real',X3 : X0 > $o] : (('const/realax/real_mul' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ X2) = ('const/iterate/sum' @ X0 @ X3 @ (^[Y0 : X0]: ('const/realax/real_mul' @ (X1 @ Y0) @ X2))))),
% 1.66/1.42 inference(fool_elimination,[status(thm)],[f4])).
% 1.66/1.42 thf(f4,negated_conjecture,(
% 1.66/1.42 ~! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : 'type/realax/real',X3 : X0 > $o] : (('const/realax/real_mul' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ X2) = ('const/iterate/sum' @ X0 @ X3 @ (^[X4 : X0] : ('const/realax/real_mul' @ (X1 @ X4) @ X2))))),
% 1.66/1.42 inference(negated_conjecture,[status(cth)],[f3])).
% 1.66/1.42 thf(f3,conjecture,(
% 1.66/1.42 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : 'type/realax/real',X3 : X0 > $o] : (('const/realax/real_mul' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ X2) = ('const/iterate/sum' @ X0 @ X3 @ (^[X4 : X0] : ('const/realax/real_mul' @ (X1 @ X4) @ X2))))),
% 1.66/1.42 file('/export/starexec/sandbox/tmp/tmp.ar4cLvm9z5/DTF2THF_29524.p','thm/iterate/SUM_RMUL_')).
% 1.66/1.42 % SZS output end Proof for DTF2THF_29524
% 1.66/1.42 % (29628)------------------------------
% 1.66/1.42 % (29628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.42 % (29628)Termination reason: Refutation
% 1.66/1.42
% 1.66/1.42 % (29628)Memory used [KB]: 5628
% 1.66/1.42 % (29628)Time elapsed: 0.008 s
% 1.66/1.42 % (29628)Instructions burned: 12 (million)
% 1.66/1.42 % (29628)------------------------------
% 1.66/1.42 % (29628)------------------------------
% 1.66/1.42 % (29621)Success in time 0.022 s
%------------------------------------------------------------------------------