%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM635^2 : 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 : n010.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 0.28s 0.40s
% Output : Refutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 25 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 50 ( 15 ~; 3 |; 3 &; 24 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 19 ( 0 ^; 15 !; 4 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
succ: $i > $i ).
thf(func_def_7,type,
sK2: ( $i > $o ) > $i ).
thf(func_def_8,type,
vNOT: $o > $o ).
thf(f2,axiom,
! [X1: $i,X0: $i] :
( ( ( succ @ X0 )
= ( succ @ X1 ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_injective) ).
thf(f4,conjecture,
! [X1: $i,X0: $i] :
( ( X0 != X1 )
=> ( ( succ @ X0 )
!= ( succ @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz1) ).
thf(f5,negated_conjecture,
~ ! [X1: $i,X0: $i] :
( ( X0 != X1 )
=> ( ( succ @ X0 )
!= ( succ @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f8,plain,
~ ! [X0: $i,X1: $i] :
( ( X0 != X1 )
=> ( ( succ @ X0 )
!= ( succ @ X1 ) ) ),
inference(rectify,[],[f5]) ).
thf(f9,plain,
! [X0: $i,X1: $i] :
( ( ( succ @ X0 )
= ( succ @ X1 ) )
=> ( X0 = X1 ) ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( succ @ X0 )
!= ( succ @ X1 ) ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f13,plain,
? [X1: $i,X0: $i] :
( ( X0 != X1 )
& ( ( succ @ X0 )
= ( succ @ X1 ) ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f14,plain,
? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( succ @ X0 )
= ( succ @ X1 ) ) ),
inference(rectify,[],[f13]) ).
thf(f15,plain,
( ( sK1 != sK0 )
& ( ( succ @ sK0 )
= ( succ @ sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f14]) ).
thf(f18,plain,
( ( succ @ sK0 )
= ( succ @ sK1 ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f19,plain,
sK1 != sK0,
inference(cnf_transformation,[],[f15]) ).
thf(f20,plain,
! [X0: $i,X1: $i] :
( ( ( succ @ X0 )
!= ( succ @ X1 ) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f26,plain,
! [X0: $i] :
( ( ( succ @ X0 )
!= ( succ @ sK0 ) )
| ( sK1 = X0 ) ),
inference(superposition,[],[f20,f18]) ).
thf(f29,plain,
sK1 = sK0,
inference(equality_resolution,[],[f26]) ).
thf(f30,plain,
$false,
inference(forward_subsumption_resolution,[],[f29,f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM635^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.27 % Computer : n010.cluster.edu
% 0.11/0.27 % Model : x86_64 x86_64
% 0.11/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.27 % Memory : 8046.5625MB
% 0.11/0.27 % OS : Linux 6.8.0-71-generic
% 0.11/0.27 % CPULimit : 300
% 0.11/0.27 % WCLimit : 300
% 0.11/0.27 % DateTime : Tue Sep 29 11:59:48 UTC 2026
% 0.11/0.27 % CPUTime :
% 0.11/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.28/0.33 Running higher-order theorem proving
% 0.28/0.34 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
% 0.28/0.40 % (2765358)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.28/0.40 % (2765367)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3932020464:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.28/0.40 % (2765367) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2765358-2765367"...
% 0.28/0.40 % (2765367)...printing done.
% 0.28/0.40 % (2765367)Refutation found. Thanks to Tanya!
% 0.28/0.40 % SZS status Theorem for theBenchmark
% 0.28/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.28/0.40 % (2765367)------------------------------
% 0.28/0.40 % (2765367)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.40 % (2765367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.40 % (2765367)CaDiCaL version: 2.1.3
% 0.28/0.40 % (2765367)Termination reason: Refutation
% 0.28/0.40 % (2765367)Time elapsed: 0.002 s
% 0.28/0.40 % (2765367)Peak memory usage: 12 MB
% 0.28/0.40 % (2765367)Instructions burned: 1 (million)
% 0.28/0.40 % (2765358)Success in time 0.037 s
% 0.28/0.40 % Vampire exiting
%------------------------------------------------------------------------------