%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW469^1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:40:17 AM UTC 2026
% Result : Theorem 0.22s 0.27s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 30 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 32 ( 18 ~; 8 |; 3 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 22 ( 22 fml; 0 var)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 3 usr; 5 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 27 ( 16 !; 11 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
state: $tType ).
tff(func_def_0,type,
induct_false: $o ).
tff(func_def_1,type,
induct_true: $o ).
tff(func_def_2,type,
hoare_1821564147gleton: $o ).
tff(func_def_5,type,
sK0: state ).
tff(func_def_6,type,
sK1: state ).
tff(func_def_7,type,
sK2: state ).
tff(f1,axiom,
( hoare_1821564147gleton
<=> ? [X0: state,X1: state] : ( X0 != X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_state__not__singleton__def) ).
tff(f5,axiom,
hoare_1821564147gleton,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f6,conjecture,
! [X0: state] :
~ ! [X1: state] : ( X1 = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(f7,negated_conjecture,
~ ! [X0: state] :
~ ! [X1: state] : ( X1 = X0 ),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f8,plain,
( hoare_1821564147gleton
<=> ? [X0: state,X1: state] : ( X0 != X1 ) ),
inference(rectify,[],[f1]) ).
tff(f9,plain,
( ( hoare_1821564147gleton = $true )
<=> ? [X0: state,X1: state] : ( X0 != X1 ) ),
inference(fool_elimination,[],[f8]) ).
tff(f16,plain,
hoare_1821564147gleton,
inference(rectify,[],[f5]) ).
tff(f17,plain,
hoare_1821564147gleton = $true,
inference(fool_elimination,[],[f16]) ).
tff(f19,plain,
? [X0: state] :
! [X1: state] : ( X1 = X0 ),
inference(ennf_transformation,[],[f7]) ).
tff(f20,plain,
( ( ( hoare_1821564147gleton = $true )
| ! [X0: state,X1: state] : ( X0 = X1 ) )
& ( ? [X0: state,X1: state] : ( X0 != X1 )
| ( hoare_1821564147gleton != $true ) ) ),
inference(nnf_transformation,[],[f9]) ).
tff(f21,plain,
( ( ( hoare_1821564147gleton = $true )
| ! [X0: state,X1: state] : ( X0 = X1 ) )
& ( ? [X2: state,X3: state] : ( X2 != X3 )
| ( hoare_1821564147gleton != $true ) ) ),
inference(rectify,[],[f20]) ).
tff(f22,plain,
( ( ( hoare_1821564147gleton = $true )
| ! [X0: state,X1: state] : ( X0 = X1 ) )
& ( ( sK0 != sK1 )
| ( hoare_1821564147gleton != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0),skolemize(X3,sK1)],[f21]) ).
tff(f23,plain,
! [X1: state] : ( sK2 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f19]) ).
tff(f24,plain,
( ( sK0 != sK1 )
| ( hoare_1821564147gleton != $true ) ),
inference(cnf_transformation,[],[f22]) ).
tff(f29,plain,
hoare_1821564147gleton = $true,
inference(cnf_transformation,[],[f17]) ).
tff(f30,plain,
! [X1: state] : ( sK2 = X1 ),
inference(cnf_transformation,[],[f23]) ).
tff(f34,plain,
( ( sK0 != sK1 )
| ( $true != $true ) ),
inference(definition_unfolding,[],[f24,f29]) ).
tff(f36,plain,
sK0 != sK1,
inference(trivial_inequality_removal,[],[f34]) ).
tff(f37,plain,
! [X0: state,X1: state] : ( X0 = X1 ),
inference(superposition,[],[f30,f30]) ).
tff(f41,plain,
! [X0: state] : ( sK0 != X0 ),
inference(superposition,[],[f36,f37]) ).
tff(f42,plain,
$false,
inference(forward_subsumption_resolution,[],[f41,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW469^1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n026.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 16:07:27 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.22/0.27 % (789062)Detected formulas, will run a generic FOF schedule.
% 0.22/0.27 % (789067)lrs+1011_1_sp=occurrence:random_seed=54624345:st=6:sd=4:ss=included_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.27 % (789067) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-789062-789067"...
% 0.22/0.27 % (789067)...printing done.
% 0.22/0.27 % (789067)Refutation found. Thanks to Tanya!
% 0.22/0.27 % SZS status Theorem for theBenchmark
% 0.22/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.27 % (789067)------------------------------
% 0.22/0.27 % (789067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.27 % (789067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.27 % (789067)CaDiCaL version: 2.1.3
% 0.22/0.27 % (789067)Termination reason: Refutation
% 0.22/0.27 % (789067)Time elapsed: 0.001 s
% 0.22/0.27 % (789067)Peak memory usage: 12 MB
% 0.22/0.27 % (789067)Instructions burned: 1 (million)
% 0.22/0.27 % (789062)Success in time 0.023 s
% 0.22/0.27 % Vampire exiting
%------------------------------------------------------------------------------