%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO889_16 : TPTP v9.3.1. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 02:32:49 PM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 24 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 126 ( 0 equ)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 133 ( 43 ~; 44 |; 34 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 12 ( 12 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 65 ( 41 !; 24 ?; 65 :)
% 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' > $i ).
tff(func_def_2,type,
sK1: '$ki_world' ).
tff(func_def_4,type,
sK3: ( '$ki_world' * $i ) > '$ki_world' ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
a: ( '$ki_world' * $i ) > $o ).
tff(pred_def_3,type,
b: ( '$ki_world' * $i ) > $o ).
tff(pred_def_4,type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff(f5,conjecture,
( ( ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> a(X2,X1) ) ) )
& ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ? [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
& b(X2,X1) ) ) ) )
=> ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& ? [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
& a(X2,X1)
& b(X2,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(f6,negated_conjecture,
~ ( ( ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> a(X2,X1) ) ) )
& ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ! [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
=> ? [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
& b(X2,X1) ) ) ) )
=> ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& ? [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
& a(X2,X1)
& b(X2,X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
tff(f7,plain,
~ ( ( ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& ! [X2: '$ki_world'] :
( '$ki_accessible'(X0,X2)
=> a(X2,X1) ) ) )
& ! [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
=> ! [X4: $i] :
( '$ki_exists_in_world_$i'(X3,X4)
=> ? [X5: '$ki_world'] :
( '$ki_accessible'(X3,X5)
& b(X5,X4) ) ) ) )
=> ? [X6: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X6)
& ? [X7: $i] :
( '$ki_exists_in_world_$i'(X6,X7)
& ? [X8: '$ki_world'] :
( '$ki_accessible'(X6,X8)
& a(X8,X7)
& b(X8,X7) ) ) ) ),
inference(rectify,[],[f6]) ).
tff(f12,plain,
( ! [X6: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X6)
| ! [X7: $i] :
( ~ '$ki_exists_in_world_$i'(X6,X7)
| ! [X8: '$ki_world'] :
( ~ '$ki_accessible'(X6,X8)
| ~ a(X8,X7)
| ~ b(X8,X7) ) ) )
& ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& ! [X2: '$ki_world'] :
( a(X2,X1)
| ~ '$ki_accessible'(X0,X2) ) ) )
& ! [X3: '$ki_world'] :
( ! [X4: $i] :
( ? [X5: '$ki_world'] :
( '$ki_accessible'(X3,X5)
& b(X5,X4) )
| ~ '$ki_exists_in_world_$i'(X3,X4) )
| ~ '$ki_accessible'('$ki_local_world',X3) ) ),
inference(ennf_transformation,[],[f7]) ).
tff(f13,plain,
( ! [X6: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X6)
| ! [X7: $i] :
( ~ '$ki_exists_in_world_$i'(X6,X7)
| ! [X8: '$ki_world'] :
( ~ '$ki_accessible'(X6,X8)
| ~ a(X8,X7)
| ~ b(X8,X7) ) ) )
& ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& ! [X2: '$ki_world'] :
( a(X2,X1)
| ~ '$ki_accessible'(X0,X2) ) ) )
& ! [X3: '$ki_world'] :
( ! [X4: $i] :
( ? [X5: '$ki_world'] :
( '$ki_accessible'(X3,X5)
& b(X5,X4) )
| ~ '$ki_exists_in_world_$i'(X3,X4) )
| ~ '$ki_accessible'('$ki_local_world',X3) ) ),
inference(flattening,[],[f12]) ).
tff(f18,plain,
! [X8: '$ki_world',X6: '$ki_world',X7: $i] :
( ~ b(X8,X7)
| ~ a(X8,X7)
| ~ '$ki_accessible'(X6,X8)
| ~ '$ki_exists_in_world_$i'(X6,X7)
| ~ '$ki_accessible'('$ki_local_world',X6) ),
inference(cnf_transformation,[],[f13]) ).
tff(f19,plain,
! [X2: '$ki_world'] :
( ~ '$ki_accessible'(sK1,X2)
| a(X2,sK2) ),
inference(cnf_transformation,[],[f13]) ).
tff(f20,plain,
! [X3: '$ki_world',X4: $i] :
( ~ '$ki_accessible'('$ki_local_world',X3)
| ~ '$ki_exists_in_world_$i'(X3,X4)
| b(sK3(X3,X4),X4) ),
inference(cnf_transformation,[],[f13]) ).
tff(f21,plain,
! [X3: '$ki_world',X4: $i] :
( ~ '$ki_accessible'('$ki_local_world',X3)
| ~ '$ki_exists_in_world_$i'(X3,X4)
| '$ki_accessible'(X3,sK3(X3,X4)) ),
inference(cnf_transformation,[],[f13]) ).
tff(f22,plain,
'$ki_exists_in_world_$i'(sK1,sK2),
inference(cnf_transformation,[],[f13]) ).
tff(f23,plain,
'$ki_accessible'('$ki_local_world',sK1),
inference(cnf_transformation,[],[f13]) ).
tff(f27,plain,
~ '$ki_accessible'('$ki_local_world',sK1),
inference(consistent_polarity_flipping,[],[f23]) ).
tff(f28,plain,
! [X3: '$ki_world',X4: $i] :
( ~ '$ki_accessible'(X3,sK3(X3,X4))
| ~ '$ki_exists_in_world_$i'(X3,X4)
| '$ki_accessible'('$ki_local_world',X3) ),
inference(consistent_polarity_flipping,[],[f21]) ).
tff(f29,plain,
! [X3: '$ki_world',X4: $i] :
( b(sK3(X3,X4),X4)
| ~ '$ki_exists_in_world_$i'(X3,X4)
| '$ki_accessible'('$ki_local_world',X3) ),
inference(consistent_polarity_flipping,[],[f20]) ).
tff(f30,plain,
! [X2: '$ki_world'] :
( a(X2,sK2)
| '$ki_accessible'(sK1,X2) ),
inference(consistent_polarity_flipping,[],[f19]) ).
tff(f31,plain,
! [X8: '$ki_world',X6: '$ki_world',X7: $i] :
( ~ '$ki_exists_in_world_$i'(X6,X7)
| ~ a(X8,X7)
| '$ki_accessible'(X6,X8)
| ~ b(X8,X7)
| '$ki_accessible'('$ki_local_world',X6) ),
inference(consistent_polarity_flipping,[],[f18]) ).
tff(f32,plain,
! [X0: '$ki_world'] :
( ~ a(X0,sK2)
| '$ki_accessible'(sK1,X0)
| ~ b(X0,sK2)
| '$ki_accessible'('$ki_local_world',sK1) ),
inference(resolution,[],[f31,f22]) ).
tff(f33,plain,
! [X0: '$ki_world'] :
( '$ki_accessible'(sK1,X0)
| ~ b(X0,sK2)
| '$ki_accessible'('$ki_local_world',sK1) ),
inference(forward_subsumption_resolution,[],[f32,f30]) ).
tff(f34,plain,
! [X0: '$ki_world'] :
( ~ b(X0,sK2)
| '$ki_accessible'(sK1,X0) ),
inference(forward_subsumption_resolution,[],[f33,f27]) ).
tff(f35,plain,
! [X0: '$ki_world'] :
( '$ki_accessible'(sK1,sK3(X0,sK2))
| ~ '$ki_exists_in_world_$i'(X0,sK2)
| '$ki_accessible'('$ki_local_world',X0) ),
inference(resolution,[],[f34,f29]) ).
tff(f37,plain,
( ~ '$ki_exists_in_world_$i'(sK1,sK2)
| '$ki_accessible'('$ki_local_world',sK1)
| ~ '$ki_exists_in_world_$i'(sK1,sK2)
| '$ki_accessible'('$ki_local_world',sK1) ),
inference(resolution,[],[f35,f28]) ).
tff(f38,plain,
( ~ '$ki_exists_in_world_$i'(sK1,sK2)
| '$ki_accessible'('$ki_local_world',sK1) ),
inference(duplicate_literal_removal,[],[f37]) ).
tff(f39,plain,
'$ki_accessible'('$ki_local_world',sK1),
inference(forward_subsumption_resolution,[],[f38,f22]) ).
tff(f40,plain,
$false,
inference(forward_subsumption_resolution,[],[f39,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO889_16 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n003.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 18:41:42 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.25 % (1850149)Will run a generic schedule for satisfiability detection.
% 0.09/0.25 % (1850155)% WARNING: option uhcvi not known.
% 0.09/0.25 % (1850155)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2086301999:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.25 % (1850155) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1850149-1850155"...
% 0.09/0.25 % (1850155)...printing done.
% 0.09/0.25 % (1850155)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 % (1850155)------------------------------
% 0.09/0.25 % (1850155)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (1850155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (1850155)CaDiCaL version: 2.1.3
% 0.09/0.25 % (1850155)Termination reason: Refutation
% 0.09/0.25 % (1850155)Time elapsed: 0.001 s
% 0.09/0.25 % (1850155)Peak memory usage: 11 MB
% 0.09/0.25 % (1850155)Instructions burned: 1 (million)
% 0.09/0.25 % (1850149)Success in time 0.035 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------