%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM642^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:18:21 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 9 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 9 ( 8 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 52 ( 4 ~; 0 |; 0 &; 48 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 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,
suc: nat > nat ).
thf(func_def_3,type,
pl: nat > nat > nat ).
thf(f1,axiom,
! [X0: nat,X1: nat] :
( ( pl @ ( suc @ X0 ) @ X1 )
= ( suc @ ( pl @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz4d) ).
thf(f2,conjecture,
( ( suc @ ( pl @ x @ y ) )
= ( pl @ ( suc @ x ) @ y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz4h) ).
thf(f3,negated_conjecture,
( ( suc @ ( pl @ x @ y ) )
!= ( pl @ ( suc @ x ) @ y ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
! [X0: nat,X1: nat] :
( ( pl @ ( suc @ X0 ) @ X1 )
= ( suc @ ( pl @ X0 @ X1 ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f5,plain,
( ( suc @ ( pl @ x @ y ) )
!= ( pl @ ( suc @ x ) @ y ) ),
inference(fool_elimination,[],[f3]) ).
thf(f6,plain,
( ( suc @ ( pl @ x @ y ) )
!= ( pl @ ( suc @ x ) @ y ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
! [X0: nat,X1: nat] :
( ( pl @ ( suc @ X0 ) @ X1 )
= ( suc @ ( pl @ X0 @ X1 ) ) ),
inference(cnf_transformation,[],[f4]) ).
thf(f8,plain,
( ( suc @ ( pl @ x @ y ) )
!= ( pl @ ( suc @ x ) @ y ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f9,plain,
$false,
inference(forward_subsumption_resolution,[],[f8,f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM642^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n004.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 12:24:07 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.21 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
% 0.08/0.25 % (1217933)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.25 % (1217940)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3662779354:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.08/0.25 % (1217940) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1217933-1217940"...
% 0.08/0.25 % (1217940)...printing done.
% 0.08/0.25 % (1217940)Refutation found. Thanks to Tanya!
% 0.08/0.25 % SZS status Theorem for theBenchmark
% 0.08/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.25 % (1217940)------------------------------
% 0.08/0.25 % (1217940)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.25 % (1217940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.25 % (1217940)CaDiCaL version: 2.1.3
% 0.08/0.25 % (1217940)Termination reason: Refutation
% 0.08/0.25 % (1217940)Time elapsed: 0.001 s
% 0.08/0.25 % (1217940)Peak memory usage: 11 MB
% 0.08/0.25 % (1217933)Success in time 0.028 s
% 0.08/0.25 % Vampire exiting
%------------------------------------------------------------------------------