%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM415^1 : 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 : n017.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 08:18:18 AM UTC 2026
% Result : Theorem 0.34s 0.42s
% Output : Refutation 0.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 27 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 208 ( 5 ~; 0 |; 0 &; 203 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 101 ( 101 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 1 con; 0-4 aty)
% Number of variables : 92 ( 92 ^; 0 !; 0 ?; 92 :)
% 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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_19,type,
db3:
!>[X0: $tType] : X0 ).
thf(f2,axiom,
( ( ^ [X0: $i > $i,X1: $i] : ( X0 @ X1 ) )
= one ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM006^0.ax',one_ax) ).
thf(f3,axiom,
( ( ^ [X0: $i > $i,X1: $i] : ( X0 @ ( X0 @ X1 ) ) )
= two ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM006^0.ax',two_ax) ).
thf(f4,axiom,
( three
= ( ^ [X0: $i > $i,X1: $i] : ( X0 @ ( X0 @ ( X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM006^0.ax',three_ax) ).
thf(f6,axiom,
( five
= ( ^ [X0: $i > $i,X1: $i] : ( X0 @ ( X0 @ ( X0 @ ( X0 @ ( X0 @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM006^0.ax',five_ax) ).
thf(f8,axiom,
( seven
= ( ^ [X0: $i > $i,X1: $i] : ( X0 @ ( X0 @ ( X0 @ ( X0 @ ( X0 @ ( X0 @ ( X0 @ X1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM006^0.ax',seven_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(f14,axiom,
( ( ^ [X0: ( $i > $i ) > $i > $i,X1: ( $i > $i ) > $i > $i,X2: $i > $i,X3: $i] : ( X0 @ ( X1 @ X2 ) @ X3 ) )
= mult ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM006^0.ax',mult_ax) ).
thf(f15,conjecture,
( ( mult @ two @ ( plus @ three @ seven ) )
= ( mult @ ( mult @ two @ five ) @ ( plus @ one @ one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f16,negated_conjecture,
( ( mult @ two @ ( plus @ three @ seven ) )
!= ( mult @ ( mult @ two @ five ) @ ( plus @ one @ one ) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f20,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(f22,plain,
( seven
= ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f24,plain,
( two
= ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f25,plain,
( mult
= ( ^ [Y0: ( $i > $i ) > $i > $i,Y1: ( $i > $i ) > $i > $i,Y2: $i > $i,Y3: $i] : ( Y0 @ ( Y1 @ Y2 ) @ Y3 ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f26,plain,
( three
= ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f27,plain,
( five
= ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f29,plain,
( one
= ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f31,plain,
( ( mult @ two @ ( plus @ three @ seven ) )
!= ( mult @ ( mult @ two @ five ) @ ( plus @ one @ one ) ) ),
inference(flattening,[],[f16]) ).
thf(f32,plain,
( five
= ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f33,plain,
( one
= ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f34,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,[],[f20]) ).
thf(f36,plain,
( three
= ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f39,plain,
( ( mult @ two @ ( plus @ three @ seven ) )
!= ( mult @ ( mult @ two @ five ) @ ( plus @ one @ one ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f41,plain,
( seven
= ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f44,plain,
( two
= ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f46,plain,
( mult
= ( ^ [Y0: ( $i > $i ) > $i > $i,Y1: ( $i > $i ) > $i > $i,Y2: $i > $i,Y3: $i] : ( Y0 @ ( Y1 @ Y2 ) @ Y3 ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f47,plain,
( ( ^ [Y0: ( $i > $i ) > $i > $i,Y1: ( $i > $i ) > $i > $i,Y2: $i > $i,Y3: $i] : ( Y0 @ ( Y1 @ Y2 ) @ Y3 )
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $i ) > $i > $i,Y1: ( $i > $i ) > $i > $i,Y2: $i > $i,Y3: $i] : ( Y0 @ Y2 @ ( Y1 @ Y2 @ Y3 ) )
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) )
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) ) ) ) )
!= ( ^ [Y0: ( $i > $i ) > $i > $i,Y1: ( $i > $i ) > $i > $i,Y2: $i > $i,Y3: $i] : ( Y0 @ ( Y1 @ Y2 ) @ Y3 )
@ ( ^ [Y0: ( $i > $i ) > $i > $i,Y1: ( $i > $i ) > $i > $i,Y2: $i > $i,Y3: $i] : ( Y0 @ ( Y1 @ Y2 ) @ Y3 )
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ Y1 ) )
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( 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 ) )
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ Y1 )
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f39,f46,f44,f34,f36,f41,f46,f46,f44,f32,f34,f33,f33]) ).
thf(f48,plain,
( ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f47]) ).
thf(f49,plain,
$false,
inference(trivial_inequality_removal,[],[f48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM415^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.30 % Computer : n017.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8046.5625MB
% 0.12/0.30 % OS : Linux 6.8.0-71-generic
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue Sep 29 11:49:25 UTC 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.29/0.35 Running higher-order theorem proving
% 0.29/0.37 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
% 0.34/0.42 % (242824)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.34/0.42 % (242830)lrs+10_16_si=on:nwc=1.5:random_seed=358669709:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.34/0.42 % (242830) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-242824-242830"...
% 0.34/0.42 % (242830)...printing done.
% 0.34/0.42 % (242830)Refutation found. Thanks to Tanya!
% 0.34/0.42 % SZS status Theorem for theBenchmark
% 0.34/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.34/0.42 % (242830)------------------------------
% 0.34/0.42 % (242830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.42 % (242830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.42 % (242830)CaDiCaL version: 2.1.3
% 0.34/0.42 % (242830)Termination reason: Refutation
% 0.34/0.42 % (242830)Time elapsed: 0.003 s
% 0.34/0.42 % (242830)Peak memory usage: 12 MB
% 0.34/0.42 % (242830)Instructions burned: 7 (million)
% 0.34/0.42 % (242824)Success in time 0.036 s
% 0.34/0.42 % Vampire exiting
%------------------------------------------------------------------------------