%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA098^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:45:54 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 69 ( 21 equ; 0 cnn)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 400 ( 7 ~; 0 |; 0 &; 393 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 52 ( 52 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 1 con; 0-6 aty)
% Number of variables : 81 ( 12 ^; 63 !; 6 ?; 81 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/realax/real': $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/ITSET':
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 > X1 ) > ( X0 > $o ) > X1 > X1 ) ).
thf(func_def_1,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_3,type,
'const/iterate/support':
!>[X0: $tType,X1: $tType] : ( ( X0 > X0 > X0 ) > ( X1 > X0 ) > ( X1 > $o ) > X1 > $o ) ).
thf(func_def_4,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_5,type,
'const/iterate/neutral':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_6,type,
'const/iterate/iterate':
!>[X0: $tType,X1: $tType] : ( ( X1 > X1 > X1 ) > ( X0 > $o ) > ( X0 > X1 ) > X1 ) ).
thf(func_def_7,type,
'const/class/COND':
!>[X0: $tType] : ( $o > X0 > X0 > X0 ) ).
thf(func_def_9,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_12,type,
sK1: sK0 > $o ).
thf(func_def_13,type,
sK2: sK0 > 'type/realax/real' ).
thf(func_def_16,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X1: $tType,X0: $tType,X3: X0 > X1,X5: X1 > X1 > X1,X4: X0 > $o] :
( ( 'const/iterate/iterate' @ X0 @ X1 @ X5 @ X4 @ X3 )
= ( 'const/class/COND' @ X1 @ ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X5 @ X3 @ X4 ) )
@ ( 'const/sets/ITSET' @ X0 @ X1
@ ^ [X6: X0,X7: X1] : ( X5 @ ( X3 @ X6 ) @ X7 )
@ ( 'const/iterate/support' @ X1 @ X0 @ X5 @ X3 @ X4 )
@ ( 'const/iterate/neutral' @ X1 @ X5 ) )
@ ( 'const/iterate/neutral' @ X1 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/iterate_') ).
thf(f2,axiom,
! [X0: $tType] :
( 'const/iterate/sum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/sum_') ).
thf(f3,axiom,
! [X1: $tType,X0: $tType,X3: X1 > X0,X2: X0 > X0 > X0,X4: X1 > $o] :
( ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ X4 ) )
= ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUPPORT_SUPPORT_') ).
thf(f4,conjecture,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o] :
( ( 'const/iterate/sum' @ X0 @ ( 'const/iterate/support' @ 'type/realax/real' @ X0 @ 'const/realax/real_add' @ X1 @ X2 ) @ X1 )
= ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_SUPPORT_') ).
thf(f5,negated_conjecture,
~ ! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o] :
( ( 'const/iterate/sum' @ X0 @ ( 'const/iterate/support' @ 'type/realax/real' @ X0 @ 'const/realax/real_add' @ X1 @ X2 ) @ X1 )
= ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
! [X0: $tType,X1: $tType,X2: X1 > X0,X3: X0 > X0 > X0,X4: X1 > $o] :
( ( 'const/iterate/iterate' @ X1 @ X0 @ X3 @ X4 @ X2 )
= ( 'const/class/COND' @ X0 @ ( 'const/sets/FINITE' @ X1 @ ( 'const/iterate/support' @ X0 @ X1 @ X3 @ X2 @ X4 ) )
@ ( 'const/sets/ITSET' @ X1 @ X0
@ ^ [X5: X1,X6: X0] : ( X3 @ ( X2 @ X5 ) @ X6 )
@ ( 'const/iterate/support' @ X0 @ X1 @ X3 @ X2 @ X4 )
@ ( 'const/iterate/neutral' @ X0 @ X3 ) )
@ ( 'const/iterate/neutral' @ X0 @ X3 ) ) ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
! [X0: $tType,X1: $tType,X3: X0 > X0 > X0,X4: X1 > $o,X2: X1 > X0] :
( ( 'const/class/COND' @ X0 @ ( 'const/sets/FINITE' @ X1 @ ( 'const/iterate/support' @ X0 @ X1 @ X3 @ X2 @ X4 ) )
@ ( 'const/sets/ITSET' @ X1 @ X0
@ ^ [Y0: X1,Y1: X0] : ( X3 @ ( X2 @ Y0 ) @ Y1 )
@ ( 'const/iterate/support' @ X0 @ X1 @ X3 @ X2 @ X4 )
@ ( 'const/iterate/neutral' @ X0 @ X3 ) )
@ ( 'const/iterate/neutral' @ X0 @ X3 ) )
= ( 'const/iterate/iterate' @ X1 @ X0 @ X3 @ X4 @ X2 ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X0: $tType,X2: X0 > $o,X1: X0 > 'type/realax/real'] :
( ( 'const/iterate/sum' @ X0 @ ( 'const/iterate/support' @ 'type/realax/real' @ X0 @ 'const/realax/real_add' @ X1 @ X2 ) @ X1 )
!= ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f9,plain,
! [X0: $tType,X1: $tType,X2: X0 > X1,X3: X1 > X1 > X1,X4: X0 > $o] :
( ( 'const/iterate/support' @ X1 @ X0 @ X3 @ X2 @ X4 )
= ( 'const/iterate/support' @ X1 @ X0 @ X3 @ X2 @ ( 'const/iterate/support' @ X1 @ X0 @ X3 @ X2 @ X4 ) ) ),
inference(rectify,[],[f3]) ).
thf(f10,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > 'type/realax/real'] :
( ( 'const/iterate/sum' @ X0 @ X1 @ X2 )
!= ( 'const/iterate/sum' @ X0 @ ( 'const/iterate/support' @ 'type/realax/real' @ X0 @ 'const/realax/real_add' @ X2 @ X1 ) @ X2 ) ),
inference(rectify,[],[f8]) ).
thf(f11,plain,
( ( 'const/iterate/sum' @ sK0 @ sK1 @ sK2 )
!= ( 'const/iterate/sum' @ sK0 @ ( 'const/iterate/support' @ 'type/realax/real' @ sK0 @ 'const/realax/real_add' @ sK2 @ sK1 ) @ sK2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f10]) ).
thf(f12,plain,
! [X0: $tType,X1: $tType,X2: X0 > X0 > X0,X3: X1 > $o,X4: X1 > X0] :
( ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X3 @ X4 )
= ( 'const/class/COND' @ X0 @ ( 'const/sets/FINITE' @ X1 @ ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X4 @ X3 ) )
@ ( 'const/sets/ITSET' @ X1 @ X0
@ ^ [Y0: X1,Y1: X0] : ( X2 @ ( X4 @ Y0 ) @ Y1 )
@ ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X4 @ X3 )
@ ( 'const/iterate/neutral' @ X0 @ X2 ) )
@ ( 'const/iterate/neutral' @ X0 @ X2 ) ) ),
inference(rectify,[],[f7]) ).
thf(f13,plain,
! [X1: $tType,X0: $tType,X2: X0 > X1,X3: X1 > X1 > X1,X4: X0 > $o] :
( ( 'const/iterate/support' @ X1 @ X0 @ X3 @ X2 @ X4 )
= ( 'const/iterate/support' @ X1 @ X0 @ X3 @ X2 @ ( 'const/iterate/support' @ X1 @ X0 @ X3 @ X2 @ X4 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f14,plain,
( ( 'const/iterate/sum' @ sK0 @ sK1 @ sK2 )
!= ( 'const/iterate/sum' @ sK0 @ ( 'const/iterate/support' @ 'type/realax/real' @ sK0 @ 'const/realax/real_add' @ sK2 @ sK1 ) @ sK2 ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f15,plain,
! [X1: $tType,X0: $tType,X2: X0 > X0 > X0,X3: X1 > $o,X4: X1 > X0] :
( ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X3 @ X4 )
= ( 'const/class/COND' @ X0 @ ( 'const/sets/FINITE' @ X1 @ ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X4 @ X3 ) )
@ ( 'const/sets/ITSET' @ X1 @ X0
@ ^ [Y0: X1,Y1: X0] : ( X2 @ ( X4 @ Y0 ) @ Y1 )
@ ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X4 @ X3 )
@ ( 'const/iterate/neutral' @ X0 @ X2 ) )
@ ( 'const/iterate/neutral' @ X0 @ X2 ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f16,plain,
! [X0: $tType] :
( 'const/iterate/sum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
inference(cnf_transformation,[],[f2]) ).
thf(f19,plain,
( ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ sK2 )
!= ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/iterate/support' @ 'type/realax/real' @ sK0 @ 'const/realax/real_add' @ sK2 @ sK1 ) @ sK2 ) ),
inference(definition_unfolding,[],[f14,f16,f16]) ).
thf(f20,plain,
! [X1: $tType,X0: $tType,X2: X0 > X0 > X0,X3: X1 > $o,X4: X1 > X0] :
( ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X3 @ X4 )
= ( 'const/class/COND' @ X0 @ ( 'const/sets/FINITE' @ X1 @ ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X4 @ X3 ) )
@ ( 'const/sets/ITSET' @ X1 @ X0
@ ^ [Y0: X1] : ( X2 @ ( X4 @ Y0 ) )
@ ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X4 @ X3 )
@ ( 'const/iterate/neutral' @ X0 @ X2 ) )
@ ( 'const/iterate/neutral' @ X0 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f30,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X3: X0 > X1,X4: X0 > $o] :
( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X3 @ X4 ) @ X3 )
= ( 'const/class/COND' @ X1 @ ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X3 @ X4 ) )
@ ( 'const/sets/ITSET' @ X0 @ X1
@ ^ [Y0: X0] : ( X2 @ ( X3 @ Y0 ) )
@ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X3 @ X4 )
@ ( 'const/iterate/neutral' @ X1 @ X2 ) )
@ ( 'const/iterate/neutral' @ X1 @ X2 ) ) ),
inference(constrained_superposition,[],[f20,f13]) ).
thf(f31,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X3: X0 > X1,X4: X0 > $o] :
( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X3 @ X4 ) @ X3 )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 ) ),
inference(forward_demodulation,[],[f30,f20]) ).
thf(f33,plain,
( ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ sK2 )
!= ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ sK2 ) ),
inference(constrained_superposition,[],[f19,f31]) ).
thf(f34,plain,
$false,
inference(trivial_inequality_removal,[],[f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA098^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n005.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 17:41:01 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.28 % (1982768)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (1982786)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=558322091:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28 % (1982786) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1982768-1982786"...
% 0.20/0.28 % (1982786)...printing done.
% 0.20/0.28 % (1982786)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (1982786)------------------------------
% 0.20/0.28 % (1982786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1982786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1982786)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1982786)Termination reason: Refutation
% 0.20/0.28 % (1982786)Time elapsed: 0.003 s
% 0.20/0.28 % (1982786)Peak memory usage: 12 MB
% 0.20/0.28 % (1982786)Instructions burned: 8 (million)
% 0.20/0.28 % (1982768)Success in time 0.04 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------