%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM648^1 : 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 : 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 08:18:23 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 18 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 36 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 80 ( 11 ~; 5 |; 6 &; 50 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 26 ( 0 ^; 22 !; 4 ?; 26 :)
% 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,
pl: nat > nat > nat ).
thf(func_def_4,type,
sK0: nat ).
thf(func_def_5,type,
sK1: nat ).
thf(f1,axiom,
! [X1: nat,X2: nat,X0: nat] :
( ( ( pl @ X0 @ X1 )
= ( pl @ X0 @ X2 ) )
=> ( X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz8a) ).
thf(f2,conjecture,
! [X1: nat,X0: nat] :
( ( x
= ( pl @ y @ X0 ) )
=> ( ( x
= ( pl @ y @ X1 ) )
=> ( X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz8b) ).
thf(f3,negated_conjecture,
~ ! [X1: nat,X0: nat] :
( ( x
= ( pl @ y @ X0 ) )
=> ( ( x
= ( pl @ y @ X1 ) )
=> ( X0 = X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
! [X1: nat,X2: nat,X0: nat] :
( ( ( pl @ X2 @ X0 )
= ( pl @ X2 @ X1 ) )
=> ( X0 = X1 ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
~ ! [X1: nat,X0: nat] :
( ( x
= ( pl @ y @ X1 ) )
=> ( ( x
= ( pl @ y @ X0 ) )
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f6,plain,
! [X1: nat,X2: nat,X0: nat] :
( ( X0 = X1 )
| ( ( pl @ X2 @ X0 )
!= ( pl @ X2 @ X1 ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f7,plain,
? [X1: nat,X0: nat] :
( ( X0 != X1 )
& ( x
= ( pl @ y @ X0 ) )
& ( x
= ( pl @ y @ X1 ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f8,plain,
? [X0: nat,X1: nat] :
( ( x
= ( pl @ y @ X1 ) )
& ( x
= ( pl @ y @ X0 ) )
& ( X0 != X1 ) ),
inference(flattening,[],[f7]) ).
thf(f9,plain,
( ( x
= ( pl @ y @ sK1 ) )
& ( x
= ( pl @ y @ sK0 ) )
& ( sK1 != sK0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f8]) ).
thf(f10,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( X0 = X2 )
| ( ( pl @ X1 @ X2 )
!= ( pl @ X1 @ X0 ) ) ),
inference(rectify,[],[f6]) ).
thf(f11,plain,
sK1 != sK0,
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
( x
= ( pl @ y @ sK0 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
( x
= ( pl @ y @ sK1 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f14,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( pl @ X1 @ X2 )
!= ( pl @ X1 @ X0 ) )
| ( X0 = X2 ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f15,plain,
! [X0: nat] :
( ( x
!= ( pl @ y @ X0 ) )
| ( sK0 = X0 ) ),
inference(constrained_superposition,[],[f14,f12]) ).
thf(f20,plain,
( ( x != x )
| ( sK1 = sK0 ) ),
inference(constrained_superposition,[],[f15,f13]) ).
thf(f21,plain,
sK1 = sK0,
inference(trivial_inequality_removal,[],[f20]) ).
thf(f22,plain,
$false,
inference(forward_subsumption_resolution,[],[f21,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM648^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n017.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 12:26:37 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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
% 0.21/0.29 % (271738)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (271754)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3210800075:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (271754) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-271738-271754"...
% 0.21/0.29 % (271754)...printing done.
% 0.21/0.29 % (271754)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (271754)------------------------------
% 0.21/0.29 % (271754)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (271754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (271754)CaDiCaL version: 2.1.3
% 0.21/0.29 % (271754)Termination reason: Refutation
% 0.21/0.29 % (271754)Time elapsed: 0.001 s
% 0.21/0.29 % (271754)Peak memory usage: 12 MB
% 0.21/0.29 % (271754)Instructions burned: 1 (million)
% 0.21/0.29 % (271738)Success in time 0.036 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------