%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM419^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 08:18:19 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 26 ( 25 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 166 ( 15 ~; 3 |; 0 &; 148 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 87 ( 87 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 1 con; 0-4 aty)
% Number of variables : 81 ( 71 ^; 8 !; 2 ?; 81 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
zero: ( $i > $i ) > $i > $i ).
thf(func_def_1,type,
one: ( $i > $i ) > $i > $i ).
thf(func_def_2,type,
two: ( $i > $i ) > $i > $i ).
thf(func_def_3,type,
three: ( $i > $i ) > $i > $i ).
thf(func_def_4,type,
four: ( $i > $i ) > $i > $i ).
thf(func_def_5,type,
five: ( $i > $i ) > $i > $i ).
thf(func_def_6,type,
six: ( $i > $i ) > $i > $i ).
thf(func_def_7,type,
seven: ( $i > $i ) > $i > $i ).
thf(func_def_8,type,
eight: ( $i > $i ) > $i > $i ).
thf(func_def_9,type,
nine: ( $i > $i ) > $i > $i ).
thf(func_def_10,type,
ten: ( $i > $i ) > $i > $i ).
thf(func_def_11,type,
succ: ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(func_def_12,type,
plus: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(func_def_13,type,
mult: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(func_def_15,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_18,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
sK0: ( ( $i > $i ) > $i > $i ) > $i > $i ).
thf(func_def_21,type,
sK1: ( ( $i > $i ) > $i > $i ) > $i ).
thf(f4,axiom,
( ( ^ [X0: $i > $i,X1: $i] : ( X0 @ ( X0 @ ( X0 @ X1 ) ) ) )
= three ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM006^0.ax',three_ax) ).
thf(f5,axiom,
( ( ^ [X0: $i > $i,X1: $i] : ( X0 @ ( X0 @ ( X0 @ ( X0 @ X1 ) ) ) ) )
= four ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM006^0.ax',four_ax) ).
thf(f13,axiom,
( plus
= ( ^ [X0: ( $i > $i ) > $i > $i,X1: ( $i > $i ) > $i > $i,X2: $i > $i,X3: $i] : ( X0 @ X2 @ ( X1 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM006^0.ax',plus_ax) ).
thf(f15,conjecture,
? [X0: ( $i > $i ) > $i > $i] :
( ( plus @ X0 @ three )
= four ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f16,negated_conjecture,
~ ? [X0: ( $i > $i ) > $i > $i] :
( ( plus @ X0 @ three )
= four ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f19,plain,
( four
= ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f21,plain,
( three
= ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f24,plain,
( plus
= ( ^ [Y0: ( $i > $i ) > $i > $i,Y1: ( $i > $i ) > $i > $i,Y2: $i > $i,Y3: $i] : ( Y0 @ Y2 @ ( Y1 @ Y2 @ Y3 ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f31,plain,
! [X0: ( $i > $i ) > $i > $i] :
( four
!= ( plus @ X0 @ three ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f32,plain,
( plus
= ( ^ [Y0: ( $i > $i ) > $i > $i,Y1: ( $i > $i ) > $i > $i,Y2: $i > $i,Y3: $i] : ( Y0 @ Y2 @ ( Y1 @ Y2 @ Y3 ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f36,plain,
! [X0: ( $i > $i ) > $i > $i] :
( four
!= ( plus @ X0 @ three ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f41,plain,
( three
= ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f43,plain,
( four
= ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f47,plain,
! [X0: ( $i > $i ) > $i > $i] :
( ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) )
!= ( ^ [Y0: ( $i > $i ) > $i > $i,Y1: ( $i > $i ) > $i > $i,Y2: $i > $i,Y3: $i] : ( Y0 @ Y2 @ ( Y1 @ Y2 @ Y3 ) )
@ X0
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f36,f43,f32,f41]) ).
thf(f48,plain,
! [X0: ( $i > $i ) > $i > $i] :
( ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) )
!= ( ^ [Y0: $i > $i,Y1: $i] : ( X0 @ Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f47]) ).
thf(f49,plain,
! [X0: ( $i > $i ) > $i > $i] :
( ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) )
@ ( sK0 @ X0 ) )
!= ( ^ [Y0: $i > $i,Y1: $i] : ( X0 @ Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) )
@ ( sK0 @ X0 ) ) ),
inference(negative_extensionality,[],[f48]) ).
thf(f50,plain,
! [X0: ( $i > $i ) > $i > $i] :
( ( ^ [Y0: $i] : ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 @ ( sK0 @ X0 @ ( sK0 @ X0 @ Y0 ) ) ) ) )
!= ( ^ [Y0: $i] : ( sK0 @ X0 @ ( sK0 @ X0 @ ( sK0 @ X0 @ ( sK0 @ X0 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f49]) ).
thf(f51,plain,
! [X0: ( $i > $i ) > $i > $i] :
( ( ^ [Y0: $i] : ( sK0 @ X0 @ ( sK0 @ X0 @ ( sK0 @ X0 @ ( sK0 @ X0 @ Y0 ) ) ) )
@ ( sK1 @ X0 ) )
!= ( ^ [Y0: $i] : ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 @ ( sK0 @ X0 @ ( sK0 @ X0 @ Y0 ) ) ) )
@ ( sK1 @ X0 ) ) ),
inference(negative_extensionality,[],[f50]) ).
thf(f52,plain,
! [X0: ( $i > $i ) > $i > $i] :
( ( sK0 @ X0 @ ( sK0 @ X0 @ ( sK0 @ X0 @ ( sK0 @ X0 @ ( sK1 @ X0 ) ) ) ) )
!= ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 @ ( sK0 @ X0 @ ( sK0 @ X0 @ ( sK1 @ X0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f51]) ).
thf(f54,plain,
( ( ( ^ [Y0: $i > $i,Y1: $i] :
( Y0
@ ( ^ [Y2: $i > $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) )
!= ( ^ [Y0: $i > $i] : Y0 ) )
| ( ( ^ [Y0: $i > $i,Y1: $i] :
( Y0
@ ( ^ [Y2: $i > $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) )
!= ( ^ [Y0: $i > $i] : Y0 ) )
| ( ( ^ [Y0: $i > $i,Y1: $i] :
( Y0
@ ( ^ [Y2: $i > $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) )
!= ( ^ [Y0: $i > $i] : Y0 ) )
| ( ( ^ [Y0: $i > $i,Y1: $i] :
( Y0
@ ( ^ [Y2: $i > $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) )
!= ( ^ [Y0: $i > $i] : Y0 ) ) ),
inference(equality_resolution,[],[f52]) ).
thf(f64,plain,
( ( ^ [Y0: $i > $i,Y1: $i] :
( Y0
@ ( ^ [Y2: $i > $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) )
!= ( ^ [Y0: $i > $i] : Y0 ) ),
inference(duplicate_literal_removal,[],[f54]) ).
thf(f65,plain,
( ( ^ [Y0: $i > $i] : Y0 )
!= ( ^ [Y0: $i > $i] : Y0 ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
$false,
inference(trivial_inequality_removal,[],[f65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM419^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n011.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 12:02:16 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.28 % (4187509)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (4187515)lrs+10_16_si=on:nwc=1.5:random_seed=2631822089:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.28 % (4187515) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4187509-4187515"...
% 0.21/0.28 % (4187515)...printing done.
% 0.21/0.28 % (4187515)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (4187515)------------------------------
% 0.21/0.28 % (4187515)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (4187515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (4187515)CaDiCaL version: 2.1.3
% 0.21/0.28 % (4187515)Termination reason: Refutation
% 0.21/0.28 % (4187515)Time elapsed: 0.003 s
% 0.21/0.28 % (4187515)Peak memory usage: 12 MB
% 0.21/0.28 % (4187515)Instructions burned: 9 (million)
% 0.21/0.28 % (4187509)Success in time 0.039 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------