%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM635^1 : 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 : 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 08:18:19 AM UTC 2026
% Result : Theorem 0.09s 0.28s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 22 ( 21 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 40 ( 12 ~; 4 |; 0 &; 22 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 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 : 11 ( 0 ^; 11 !; 0 ?; 11 :)
% 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_4,type,
inv_suc_0: nat > nat ).
thf(f1,axiom,
x != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).
thf(f2,axiom,
! [X0: nat,X1: nat] :
( ( ( suc @ X0 )
= ( suc @ X1 ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
thf(f3,conjecture,
( ( suc @ x )
!= ( suc @ y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz1) ).
thf(f4,negated_conjecture,
~ ( ( ( suc @ x )
!= ( suc @ y ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X1: nat,X0: nat] :
( ( ( suc @ X0 )
= ( suc @ X1 ) )
=> ( X0 = X1 ) ),
inference(fool_elimination,[],[f2]) ).
thf(f6,plain,
~ ( ( ( suc @ x )
!= ( suc @ y ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f7,plain,
x != y,
inference(fool_elimination,[],[f1]) ).
thf(f8,plain,
( ( suc @ x )
= ( suc @ y ) ),
inference(flattening,[],[f6]) ).
thf(f9,plain,
! [X1: nat,X0: nat] :
( ( X0 = X1 )
| ( ( suc @ X0 )
!= ( suc @ X1 ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f10,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( ( suc @ X0 )
!= ( suc @ X1 ) ) ),
inference(rectify,[],[f9]) ).
thf(f11,plain,
( ( suc @ x )
= ( suc @ y ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
! [X0: nat,X1: nat] :
( ( ( suc @ X0 )
!= ( suc @ X1 ) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f13,plain,
x != y,
inference(cnf_transformation,[],[f7]) ).
thf(f15,plain,
! [X0: nat] :
( ( ( suc @ X0 )
!= ( suc @ y ) )
| ( x = X0 ) ),
inference(constrained_superposition,[],[f12,f11]) ).
thf(f18,plain,
x = y,
inference(equality_resolution,[],[f15]) ).
thf(f19,plain,
$false,
inference(forward_subsumption_resolution,[],[f18,f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM635^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n004.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 12:10:36 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.09/0.28 % (1211964)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.28 % (1211971)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=877477738:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.09/0.28 % (1211971) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1211964-1211971"...
% 0.09/0.28 % (1211971)...printing done.
% 0.09/0.28 % (1211971)Refutation found. Thanks to Tanya!
% 0.09/0.28 % SZS status Theorem for theBenchmark
% 0.09/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.28 % (1211971)------------------------------
% 0.09/0.28 % (1211971)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.28 % (1211971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.28 % (1211971)CaDiCaL version: 2.1.3
% 0.09/0.28 % (1211971)Termination reason: Refutation
% 0.09/0.28 % (1211971)Time elapsed: 0.001 s
% 0.09/0.28 % (1211971)Peak memory usage: 12 MB
% 0.09/0.28 % (1211971)Instructions burned: 1 (million)
% 0.09/0.28 % (1211964)Success in time 0.03 s
% 0.09/0.28 % Vampire exiting
%------------------------------------------------------------------------------