%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO901_11 : TPTP v9.3.1. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 : Tue Sep 29 02:32:52 PM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 24 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 124 ( 0 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 151 ( 51 ~; 51 |; 26 &)
% ( 7 <=>; 15 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 49 ( 39 !; 10 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'$ki_world': $tType ).
tff(func_def_0,type,
'$ki_local_world': '$ki_world' ).
tff(func_def_1,type,
sK0: '$ki_world' ).
tff(func_def_2,type,
sK1: '$ki_world' ).
tff(func_def_3,type,
sK2: '$ki_world' ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
p: '$ki_world' > $o ).
tff(pred_def_3,type,
q: '$ki_world' > $o ).
tff(pred_def_4,type,
sP3: '$ki_world' > $o ).
tff(pred_def_6,type,
sP5: '$ki_world' > $o ).
tff(f1,axiom,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_universal) ).
tff(f2,conjecture,
( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( p(X0)
<=> q(X0) ) )
=> ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( ! [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
=> p(X1) )
<=> ! [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
=> q(X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f3,negated_conjecture,
~ ( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( p(X0)
<=> q(X0) ) )
=> ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( ! [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
=> p(X1) )
<=> ! [X1: '$ki_world'] :
( '$ki_accessible'(X0,X1)
=> q(X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f4,plain,
~ ( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( p(X0)
<=> q(X0) ) )
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ( ! [X2: '$ki_world'] :
( '$ki_accessible'(X1,X2)
=> p(X2) )
<=> ! [X3: '$ki_world'] :
( '$ki_accessible'(X1,X3)
=> q(X3) ) ) ) ),
inference(rectify,[],[f3]) ).
tff(f5,plain,
( ? [X1: '$ki_world'] :
( ( ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(X1,X2) )
<~> ! [X3: '$ki_world'] :
( q(X3)
| ~ '$ki_accessible'(X1,X3) ) )
& '$ki_accessible'('$ki_local_world',X1) )
& ! [X0: '$ki_world'] :
( ( p(X0)
<=> q(X0) )
| ~ '$ki_accessible'('$ki_local_world',X0) ) ),
inference(ennf_transformation,[],[f4]) ).
tff(f6,plain,
( ? [X1: '$ki_world'] :
( ( ? [X3: '$ki_world'] :
( ~ q(X3)
& '$ki_accessible'(X1,X3) )
| ? [X2: '$ki_world'] :
( ~ p(X2)
& '$ki_accessible'(X1,X2) ) )
& ( ! [X3: '$ki_world'] :
( q(X3)
| ~ '$ki_accessible'(X1,X3) )
| ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(X1,X2) ) )
& '$ki_accessible'('$ki_local_world',X1) )
& ! [X0: '$ki_world'] :
( ( ( p(X0)
| ~ q(X0) )
& ( q(X0)
| ~ p(X0) ) )
| ~ '$ki_accessible'('$ki_local_world',X0) ) ),
inference(nnf_transformation,[],[f5]) ).
tff(f7,plain,
( ? [X1: '$ki_world'] :
( ( ? [X3: '$ki_world'] :
( ~ q(X3)
& '$ki_accessible'(X1,X3) )
| ? [X2: '$ki_world'] :
( ~ p(X2)
& '$ki_accessible'(X1,X2) ) )
& ( ! [X3: '$ki_world'] :
( q(X3)
| ~ '$ki_accessible'(X1,X3) )
| ! [X2: '$ki_world'] :
( p(X2)
| ~ '$ki_accessible'(X1,X2) ) )
& '$ki_accessible'('$ki_local_world',X1) )
& ! [X0: '$ki_world'] :
( ( ( p(X0)
| ~ q(X0) )
& ( q(X0)
| ~ p(X0) ) )
| ~ '$ki_accessible'('$ki_local_world',X0) ) ),
inference(flattening,[],[f6]) ).
tff(f8,plain,
( ? [X0: '$ki_world'] :
( ( ? [X1: '$ki_world'] :
( ~ q(X1)
& '$ki_accessible'(X0,X1) )
| ? [X2: '$ki_world'] :
( ~ p(X2)
& '$ki_accessible'(X0,X2) ) )
& ( ! [X3: '$ki_world'] :
( q(X3)
| ~ '$ki_accessible'(X0,X3) )
| ! [X4: '$ki_world'] :
( p(X4)
| ~ '$ki_accessible'(X0,X4) ) )
& '$ki_accessible'('$ki_local_world',X0) )
& ! [X5: '$ki_world'] :
( ( ( p(X5)
| ~ q(X5) )
& ( q(X5)
| ~ p(X5) ) )
| ~ '$ki_accessible'('$ki_local_world',X5) ) ),
inference(rectify,[],[f7]) ).
tff(f9,plain,
( ( ( ~ q(sK1)
& '$ki_accessible'(sK0,sK1) )
| ( ~ p(sK2)
& '$ki_accessible'(sK0,sK2) ) )
& ( ! [X3: '$ki_world'] :
( q(X3)
| ~ '$ki_accessible'(sK0,X3) )
| ! [X4: '$ki_world'] :
( p(X4)
| ~ '$ki_accessible'(sK0,X4) ) )
& '$ki_accessible'('$ki_local_world',sK0)
& ! [X5: '$ki_world'] :
( ( ( p(X5)
| ~ q(X5) )
& ( q(X5)
| ~ p(X5) ) )
| ~ '$ki_accessible'('$ki_local_world',X5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f8]) ).
tff(f10,plain,
! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
inference(cnf_transformation,[],[f1]) ).
tff(f11,plain,
! [X5: '$ki_world'] :
( q(X5)
| ~ p(X5)
| ~ '$ki_accessible'('$ki_local_world',X5) ),
inference(cnf_transformation,[],[f9]) ).
tff(f12,plain,
! [X5: '$ki_world'] :
( p(X5)
| ~ q(X5)
| ~ '$ki_accessible'('$ki_local_world',X5) ),
inference(cnf_transformation,[],[f9]) ).
tff(f13,plain,
'$ki_accessible'('$ki_local_world',sK0),
inference(cnf_transformation,[],[f9]) ).
tff(f14,plain,
! [X3: '$ki_world',X4: '$ki_world'] :
( q(X3)
| ~ '$ki_accessible'(sK0,X3)
| p(X4)
| ~ '$ki_accessible'(sK0,X4) ),
inference(cnf_transformation,[],[f9]) ).
tff(f15,plain,
( '$ki_accessible'(sK0,sK1)
| '$ki_accessible'(sK0,sK2) ),
inference(cnf_transformation,[],[f9]) ).
tff(f16,plain,
( '$ki_accessible'(sK0,sK1)
| ~ p(sK2) ),
inference(cnf_transformation,[],[f9]) ).
tff(f17,plain,
( ~ q(sK1)
| '$ki_accessible'(sK0,sK2) ),
inference(cnf_transformation,[],[f9]) ).
tff(f18,plain,
( ~ q(sK1)
| ~ p(sK2) ),
inference(cnf_transformation,[],[f9]) ).
tff(f19,plain,
( q(sK1)
| ~ p(sK2) ),
inference(consistent_polarity_flipping,[],[f18]) ).
tff(f20,plain,
( q(sK1)
| '$ki_accessible'(sK0,sK2) ),
inference(consistent_polarity_flipping,[],[f17]) ).
tff(f21,plain,
! [X3: '$ki_world',X4: '$ki_world'] :
( ~ q(X3)
| ~ '$ki_accessible'(sK0,X3)
| p(X4)
| ~ '$ki_accessible'(sK0,X4) ),
inference(consistent_polarity_flipping,[],[f14]) ).
tff(f22,plain,
! [X5: '$ki_world'] :
( p(X5)
| q(X5)
| ~ '$ki_accessible'('$ki_local_world',X5) ),
inference(consistent_polarity_flipping,[],[f12]) ).
tff(f23,plain,
! [X5: '$ki_world'] :
( ~ q(X5)
| ~ p(X5)
| ~ '$ki_accessible'('$ki_local_world',X5) ),
inference(consistent_polarity_flipping,[],[f11]) ).
tff(f46,plain,
$false,
inference(finite_model_not_found_(exhaustively_excluded_all_possible_domain_size_assignments),[],[f10,f19,f20,f16,f15,f21,f13,f22,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO901_11 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n016.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 : Mon Sep 28 18:45:34 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.25 % (3865222)Will run a generic schedule for satisfiability detection.
% 0.09/0.25 % (3865227)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=605588363_3000 on theBenchmark for (3000ds/0Mi)
% 0.09/0.25 % Detected minimum model sizes of [1]
% 0.09/0.25 % Detected maximum model sizes of [4]
% 0.09/0.25 % TRYING [1]
% 0.09/0.25 % TRYING [2]
% 0.09/0.25 % TRYING [3]
% 0.09/0.25 % TRYING [4]
% 0.09/0.25 % (3865227) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3865222-3865227"...
% 0.09/0.25 % (3865227)...printing done.
% 0.09/0.25 % (3865227)Refutation found. Thanks to Tanya!
% 0.09/0.25 % SZS status Theorem for theBenchmark
% 0.09/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.25 % (3865227)------------------------------
% 0.09/0.25 % (3865227)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (3865227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (3865227)CaDiCaL version: 2.1.3
% 0.09/0.25 % (3865227)Termination reason: Refutation
% 0.09/0.25 % (3865227)Time elapsed: 0.001 s
% 0.09/0.25 % (3865227)Peak memory usage: 11 MB
% 0.09/0.25 % (3865227)Instructions burned: 3 (million)
% 0.09/0.25 % (3865222)Success in time 0.014 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------