%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM721^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:18:40 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 169 ( 36 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 292 ( 20 ~; 14 |; 0 &; 252 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 71 ( 35 ^; 36 !; 0 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
x: nat ).
thf(func_def_1,type,
y: nat ).
thf(func_def_2,type,
z: nat ).
thf(func_def_3,type,
u: nat ).
thf(func_def_4,type,
some: ( nat > $o ) > $o ).
thf(func_def_5,type,
diffprop: nat > nat > nat > $o ).
thf(func_def_7,type,
ts: nat > nat > nat ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,axiom,
( some
@ ^ [X0: nat] : ( diffprop @ y @ x @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
thf(f2,axiom,
( some
@ ^ [X0: nat] : ( diffprop @ u @ z @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k) ).
thf(f3,axiom,
! [X2: nat,X0: nat,X1: nat,X3: nat] :
( ( some
@ ^ [X3: nat] : ( diffprop @ X0 @ X1 @ X3 ) )
=> ( ( some
@ ^ [X4: nat] : ( diffprop @ X2 @ X3 @ X4 ) )
=> ( some
@ ^ [X4: nat] : ( diffprop @ ( ts @ X0 @ X2 ) @ ( ts @ X1 @ X3 ) @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz34) ).
thf(f4,conjecture,
( some
@ ^ [X0: nat] : ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz34a) ).
thf(f5,negated_conjecture,
~ ( some
@ ^ [X0: nat] : ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( some
@ ^ [X4: nat] : ( diffprop @ X1 @ X2 @ X4 ) )
=> ( ( some
@ ^ [X5: nat] : ( diffprop @ X0 @ X3 @ X5 ) )
=> ( some
@ ^ [X6: nat] : ( diffprop @ ( ts @ X1 @ X0 ) @ ( ts @ X2 @ X3 ) @ X6 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
! [X1: nat,X2: nat,X3: nat,X0: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ X1 @ X2 @ Y0 ) )
= $true )
=> ( ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X3 @ Y0 ) ) )
=> ( ( some
@ ^ [Y0: nat] : ( diffprop @ ( ts @ X1 @ X0 ) @ ( ts @ X2 @ X3 ) @ Y0 ) )
= $true ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
~ ( some
@ ^ [X0: nat] : ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) @ X0 ) ),
inference(rectify,[],[f5]) ).
thf(f9,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) @ Y0 ) )
!= $true ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( some
@ ^ [X0: nat] : ( diffprop @ y @ x @ X0 ) ),
inference(rectify,[],[f1]) ).
thf(f11,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ y @ x @ Y0 ) )
= $true ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( some
@ ^ [X0: nat] : ( diffprop @ u @ z @ X0 ) ),
inference(rectify,[],[f2]) ).
thf(f13,plain,
( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ u @ z @ Y0 ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) @ Y0 ) )
!= $true ),
inference(flattening,[],[f9]) ).
thf(f15,plain,
! [X1: nat,X2: nat,X3: nat,X0: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ ( ts @ X1 @ X0 ) @ ( ts @ X2 @ X3 ) @ Y0 ) )
= $true )
| ( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X3 @ Y0 ) ) )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X1 @ X2 @ Y0 ) )
!= $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f16,plain,
! [X1: nat,X0: nat,X3: nat,X2: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ X1 @ X2 @ Y0 ) )
!= $true )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ ( ts @ X1 @ X0 ) @ ( ts @ X2 @ X3 ) @ Y0 ) )
= $true )
| ( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X3 @ Y0 ) ) ) ),
inference(flattening,[],[f15]) ).
thf(f17,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X3 @ Y0 ) ) )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ ( ts @ X0 @ X1 ) @ ( ts @ X3 @ X2 ) @ Y0 ) )
= $true )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X1 @ X2 @ Y0 ) )
!= $true ) ),
inference(rectify,[],[f16]) ).
thf(f18,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) @ Y0 ) )
!= $true ),
inference(cnf_transformation,[],[f14]) ).
thf(f19,plain,
( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ u @ z @ Y0 ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f20,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ y @ x @ Y0 ) )
= $true ),
inference(cnf_transformation,[],[f11]) ).
thf(f21,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ X1 @ X2 @ Y0 ) )
!= $true )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ ( ts @ X0 @ X1 ) @ ( ts @ X3 @ X2 ) @ Y0 ) )
= $true )
| ( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X3 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f24,plain,
( ( some @ ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f25,plain,
( ( some @ ( diffprop @ y @ x ) )
= $true ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f26,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( ( some @ ( diffprop @ X1 @ X2 ) )
!= $true )
| ( ( some @ ( diffprop @ X0 @ X3 ) )
!= $true )
| ( ( some @ ( diffprop @ ( ts @ X0 @ X1 ) @ ( ts @ X3 @ X2 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f27,plain,
( ( some @ ( diffprop @ u @ z ) )
= $true ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f29,plain,
! [X0: nat,X1: nat] :
( ( $true != $true )
| ( ( some @ ( diffprop @ X0 @ X1 ) )
!= $true )
| ( $true
= ( some @ ( diffprop @ ( ts @ X0 @ u ) @ ( ts @ X1 @ z ) ) ) ) ),
inference(constrained_superposition,[],[f26,f27]) ).
thf(f30,plain,
! [X0: nat,X1: nat] :
( ( ( some @ ( diffprop @ X0 @ X1 ) )
!= $true )
| ( $true
= ( some @ ( diffprop @ ( ts @ X0 @ u ) @ ( ts @ X1 @ z ) ) ) ) ),
inference(trivial_inequality_removal,[],[f29]) ).
thf(f32,plain,
( ( $true != $true )
| ( ( some @ ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) ) )
= $true ) ),
inference(constrained_superposition,[],[f30,f25]) ).
thf(f35,plain,
( ( some @ ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) ) )
= $true ),
inference(trivial_inequality_removal,[],[f32]) ).
thf(f36,plain,
$false,
inference(forward_subsumption_resolution,[],[f35,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM721^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n006.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 12:44:55 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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 % (662944)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (662949)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4102497057:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (662949) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-662944-662949"...
% 0.21/0.28 % (662949)...printing done.
% 0.21/0.28 % (662949)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 % (662949)------------------------------
% 0.21/0.28 % (662949)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (662949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (662949)CaDiCaL version: 2.1.3
% 0.21/0.28 % (662949)Termination reason: Refutation
% 0.21/0.28 % (662949)Time elapsed: 0.002 s
% 0.21/0.28 % (662949)Peak memory usage: 12 MB
% 0.21/0.28 % (662949)Instructions burned: 4 (million)
% 0.21/0.28 % (662944)Success in time 0.036 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------