%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO891_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 : n020.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 02:32:50 PM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 103 ( 0 equ)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 110 ( 35 ~; 26 |; 36 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 8 ( 8 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; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 61 ( 37 !; 24 ?; 61 :)
% 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' > $i ).
tff(func_def_3,type,
sK2: '$ki_world' ).
tff(func_def_4,type,
sK3: ( $i * '$ki_world' ) > $i ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
qmltpeq: ( '$ki_world' * $i * $i ) > $o ).
tff(pred_def_3,type,
p: ( '$ki_world' * $i ) > $o ).
tff(pred_def_4,type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff(f3,axiom,
! [X0: '$ki_world',X1: '$ki_world',X2: $i] :
( ( '$ki_exists_in_world_$i'(X0,X2)
& '$ki_accessible'(X0,X1) )
=> '$ki_exists_in_world_$i'(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_cumul') ).
tff(f9,conjecture,
( ! [X0: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ? [X2: $i] :
( '$ki_exists_in_world_$i'(X1,X2)
& qmltpeq(X1,X0,X2) ) ) )
=> ( ? [X0: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
& ? [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
& p(X1,X0) ) )
=> ? [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
& ? [X0: $i] :
( '$ki_exists_in_world_$i'(X1,X0)
& p(X1,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(f10,negated_conjecture,
~ ( ! [X0: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ? [X2: $i] :
( '$ki_exists_in_world_$i'(X1,X2)
& qmltpeq(X1,X0,X2) ) ) )
=> ( ? [X0: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
& ? [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
& p(X1,X0) ) )
=> ? [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
& ? [X0: $i] :
( '$ki_exists_in_world_$i'(X1,X0)
& p(X1,X0) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
tff(f11,plain,
~ ( ! [X0: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X0)
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ? [X2: $i] :
( '$ki_exists_in_world_$i'(X1,X2)
& qmltpeq(X1,X0,X2) ) ) )
=> ( ? [X3: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X3)
& ? [X4: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X4)
& p(X4,X3) ) )
=> ? [X5: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X5)
& ? [X6: $i] :
( '$ki_exists_in_world_$i'(X5,X6)
& p(X5,X6) ) ) ) ),
inference(rectify,[],[f10]) ).
tff(f14,plain,
! [X0: '$ki_world',X1: '$ki_world',X2: $i] :
( '$ki_exists_in_world_$i'(X1,X2)
| ~ '$ki_exists_in_world_$i'(X0,X2)
| ~ '$ki_accessible'(X0,X1) ),
inference(ennf_transformation,[],[f3]) ).
tff(f15,plain,
! [X0: '$ki_world',X1: '$ki_world',X2: $i] :
( '$ki_exists_in_world_$i'(X1,X2)
| ~ '$ki_exists_in_world_$i'(X0,X2)
| ~ '$ki_accessible'(X0,X1) ),
inference(flattening,[],[f14]) ).
tff(f23,plain,
( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X5)
| ! [X6: $i] :
( ~ '$ki_exists_in_world_$i'(X5,X6)
| ~ p(X5,X6) ) )
& ? [X3: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X3)
& ? [X4: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X4)
& p(X4,X3) ) )
& ! [X0: $i] :
( ! [X1: '$ki_world'] :
( ? [X2: $i] :
( '$ki_exists_in_world_$i'(X1,X2)
& qmltpeq(X1,X0,X2) )
| ~ '$ki_accessible'('$ki_local_world',X1) )
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X0) ) ),
inference(ennf_transformation,[],[f11]) ).
tff(f24,plain,
( ! [X5: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X5)
| ! [X6: $i] :
( ~ '$ki_exists_in_world_$i'(X5,X6)
| ~ p(X5,X6) ) )
& ? [X3: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X3)
& ? [X4: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X4)
& p(X4,X3) ) )
& ! [X0: $i] :
( ! [X1: '$ki_world'] :
( ? [X2: $i] :
( '$ki_exists_in_world_$i'(X1,X2)
& qmltpeq(X1,X0,X2) )
| ~ '$ki_accessible'('$ki_local_world',X1) )
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X0) ) ),
inference(flattening,[],[f23]) ).
tff(f26,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ! [X1: $i] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ p(X0,X1) ) )
& ? [X2: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',X2)
& ? [X3: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X3)
& p(X3,X2) ) )
& ! [X4: $i] :
( ! [X5: '$ki_world'] :
( ? [X6: $i] :
( '$ki_exists_in_world_$i'(X5,X6)
& qmltpeq(X5,X4,X6) )
| ~ '$ki_accessible'('$ki_local_world',X5) )
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X4) ) ),
inference(rectify,[],[f24]) ).
tff(f27,plain,
( ! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| ! [X1: $i] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ p(X0,X1) ) )
& '$ki_exists_in_world_$i'('$ki_local_world',sK1)
& '$ki_accessible'('$ki_local_world',sK2)
& p(sK2,sK1)
& ! [X4: $i] :
( ! [X5: '$ki_world'] :
( ( '$ki_exists_in_world_$i'(X5,sK3(X4,X5))
& qmltpeq(X5,X4,sK3(X4,X5)) )
| ~ '$ki_accessible'('$ki_local_world',X5) )
| ~ '$ki_exists_in_world_$i'('$ki_local_world',X4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1),skolemize(X3,sK2),skolemize(X6,sK3(X4,X5))],[f26]) ).
tff(f30,plain,
! [X2: $i,X0: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_exists_in_world_$i'(X0,X2)
| '$ki_exists_in_world_$i'(X1,X2)
| ~ '$ki_accessible'(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
tff(f38,plain,
p(sK2,sK1),
inference(cnf_transformation,[],[f27]) ).
tff(f39,plain,
'$ki_accessible'('$ki_local_world',sK2),
inference(cnf_transformation,[],[f27]) ).
tff(f40,plain,
'$ki_exists_in_world_$i'('$ki_local_world',sK1),
inference(cnf_transformation,[],[f27]) ).
tff(f41,plain,
! [X0: '$ki_world',X1: $i] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ '$ki_accessible'('$ki_local_world',X0)
| ~ p(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
tff(f134,plain,
! [X0: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X0)
| '$ki_exists_in_world_$i'(X0,sK1) ),
inference(resolution,[],[f30,f40]) ).
tff(f141,plain,
'$ki_exists_in_world_$i'(sK2,sK1),
inference(resolution,[],[f134,f39]) ).
tff(f155,plain,
( ~ '$ki_accessible'('$ki_local_world',sK2)
| ~ p(sK2,sK1) ),
inference(resolution,[],[f141,f41]) ).
tff(f156,plain,
~ p(sK2,sK1),
inference(forward_subsumption_resolution,[],[f155,f39]) ).
tff(f157,plain,
$false,
inference(forward_subsumption_resolution,[],[f156,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO891_16 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 % Computer : n020.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Mon Sep 28 18:41:04 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 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
% 0.20/0.27 % (406208)Will run a generic schedule for satisfiability detection.
% 0.20/0.27 % (406219)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2717996320:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.27 % (406219) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-406208-406219"...
% 0.20/0.27 % (406219)...printing done.
% 0.20/0.27 % (406218)% WARNING: option uhcvi not known.
% 0.20/0.27 % (406219)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (406219)------------------------------
% 0.20/0.27 % (406219)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (406219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (406219)CaDiCaL version: 2.1.3
% 0.20/0.27 % (406219)Termination reason: Refutation
% 0.20/0.27 % (406219)Time elapsed: 0.002 s
% 0.20/0.27 % (406219)Peak memory usage: 11 MB
% 0.20/0.27 % (406219)Instructions burned: 3 (million)
% 0.20/0.27 % (406208)Success in time 0.029 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------