%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU362+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 12:53:01 PM UTC 2026
% Result : Theorem 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 73 ( 24 unt; 2 def)
% Number of atoms : 196 ( 10 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 200 ( 77 ~; 66 |; 27 &)
% ( 7 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 3 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 87 ( 0 sgn 75 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( rel_str(X1)
=> ( subrelstr(X1,X0)
<=> ( subset(the_carrier(X1),the_carrier(X0))
& subset(the_InternalRel(X1),the_InternalRel(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_yellow_0) ).
fof(f6,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( related(X0,X1,X2)
<=> in(ordered_pair(X1,X2),the_InternalRel(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_orders_2) ).
fof(f15,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( subrelstr(X1,X0)
=> rel_str(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_yellow_0) ).
fof(f35,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f36,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f37,axiom,
! [X0,X1,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f38,axiom,
! [X0,X1,X2] :
~ ( in(X0,X1)
& element(X1,powerset(X2))
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f39,conjecture,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( subrelstr(X1,X0)
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ! [X3] :
( element(X3,the_carrier(X0))
=> ! [X4] :
( element(X4,the_carrier(X1))
=> ! [X5] :
( element(X5,the_carrier(X1))
=> ( ( X4 = X2
& X5 = X3
& related(X1,X4,X5) )
=> related(X0,X2,X3) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_yellow_0) ).
fof(f40,negated_conjecture,
~ ! [X0] :
( rel_str(X0)
=> ! [X1] :
( subrelstr(X1,X0)
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ! [X3] :
( element(X3,the_carrier(X0))
=> ! [X4] :
( element(X4,the_carrier(X1))
=> ! [X5] :
( element(X5,the_carrier(X1))
=> ( ( X4 = X2
& X5 = X3
& related(X1,X4,X5) )
=> related(X0,X2,X3) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( ( subrelstr(X1,X0)
<=> ( subset(the_carrier(X1),the_carrier(X0))
& subset(the_InternalRel(X1),the_InternalRel(X0)) ) )
| ~ rel_str(X1) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( related(X0,X1,X2)
<=> in(ordered_pair(X1,X2),the_InternalRel(X0)) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( rel_str(X1)
| ~ subrelstr(X1,X0) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f62,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f63,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(ennf_transformation,[],[f37]) ).
fof(f65,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| ~ empty(X2) ),
inference(ennf_transformation,[],[f38]) ).
fof(f67,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ related(X0,X2,X3)
& X4 = X2
& X5 = X3
& related(X1,X4,X5)
& element(X5,the_carrier(X1)) )
& element(X4,the_carrier(X1)) )
& element(X3,the_carrier(X0)) )
& element(X2,the_carrier(X0)) )
& subrelstr(X1,X0) )
& rel_str(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f68,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ related(X0,X2,X3)
& X4 = X2
& X5 = X3
& related(X1,X4,X5)
& element(X5,the_carrier(X1)) )
& element(X4,the_carrier(X1)) )
& element(X3,the_carrier(X0)) )
& element(X2,the_carrier(X0)) )
& subrelstr(X1,X0) )
& rel_str(X0) ),
inference(flattening,[],[f67]) ).
fof(f75,plain,
! [X0,X1] :
( ~ rel_str(X0)
| ~ rel_str(X1)
| subset(the_InternalRel(X1),the_InternalRel(X0))
| ~ subrelstr(X1,X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f78,plain,
! [X2,X0,X1] :
( related(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ in(ordered_pair(X1,X2),the_InternalRel(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f79,plain,
! [X2,X0,X1] :
( ~ related(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| in(ordered_pair(X1,X2),the_InternalRel(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f80,plain,
! [X0,X1] :
( ~ subrelstr(X1,X0)
| ~ rel_str(X0)
| rel_str(X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f104,plain,
! [X0,X1] :
( in(X0,X1)
| ~ element(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f105,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f107,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| element(X0,X2) ),
inference(cnf_transformation,[],[f65]) ).
fof(f108,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| ~ empty(X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f109,plain,
element(sK15,the_carrier(sK11)),
inference(cnf_transformation,[],[f68]) ).
fof(f110,plain,
related(sK11,sK14,sK15),
inference(cnf_transformation,[],[f68]) ).
fof(f111,plain,
sK13 = sK15,
inference(cnf_transformation,[],[f68]) ).
fof(f112,plain,
sK12 = sK14,
inference(cnf_transformation,[],[f68]) ).
fof(f113,plain,
~ related(sK10,sK12,sK13),
inference(cnf_transformation,[],[f68]) ).
fof(f114,plain,
element(sK14,the_carrier(sK11)),
inference(cnf_transformation,[],[f68]) ).
fof(f115,plain,
element(sK13,the_carrier(sK10)),
inference(cnf_transformation,[],[f68]) ).
fof(f116,plain,
element(sK12,the_carrier(sK10)),
inference(cnf_transformation,[],[f68]) ).
fof(f117,plain,
subrelstr(sK11,sK10),
inference(cnf_transformation,[],[f68]) ).
fof(f118,plain,
rel_str(sK10),
inference(cnf_transformation,[],[f68]) ).
fof(f122,plain,
element(sK14,the_carrier(sK10)),
inference(definition_unfolding,[],[f116,f112]) ).
fof(f123,plain,
element(sK15,the_carrier(sK10)),
inference(definition_unfolding,[],[f115,f111]) ).
fof(f124,plain,
~ related(sK10,sK14,sK15),
inference(definition_unfolding,[],[f113,f112,f111]) ).
fof(f125,plain,
! [X0,X1] :
( subset(the_InternalRel(X1),the_InternalRel(X0))
| ~ rel_str(X0)
| ~ subrelstr(X1,X0) ),
inference(forward_subsumption_resolution,[],[f75,f80]) ).
fof(f130,plain,
( ~ rel_str(sK10)
| rel_str(sK11) ),
inference(resolution,[],[f80,f117]) ).
fof(f133,plain,
rel_str(sK11),
inference(forward_subsumption_resolution,[],[f130,f118]) ).
fof(f161,plain,
! [X0,X1] :
( ~ subrelstr(X1,X0)
| ~ rel_str(X0)
| element(the_InternalRel(X1),powerset(the_InternalRel(X0))) ),
inference(resolution,[],[f125,f105]) ).
fof(f165,plain,
( ~ element(sK14,the_carrier(sK10))
| ~ element(sK15,the_carrier(sK10))
| ~ in(ordered_pair(sK14,sK15),the_InternalRel(sK10))
| ~ rel_str(sK10) ),
inference(resolution,[],[f78,f124]) ).
fof(f166,plain,
( ~ element(sK15,the_carrier(sK10))
| ~ in(ordered_pair(sK14,sK15),the_InternalRel(sK10))
| ~ rel_str(sK10) ),
inference(forward_subsumption_resolution,[],[f165,f122]) ).
fof(f167,plain,
( ~ in(ordered_pair(sK14,sK15),the_InternalRel(sK10))
| ~ rel_str(sK10) ),
inference(forward_subsumption_resolution,[],[f166,f123]) ).
fof(f168,plain,
~ in(ordered_pair(sK14,sK15),the_InternalRel(sK10)),
inference(forward_subsumption_resolution,[],[f167,f118]) ).
fof(f169,plain,
( ~ element(ordered_pair(sK14,sK15),the_InternalRel(sK10))
| empty(the_InternalRel(sK10)) ),
inference(resolution,[],[f168,f104]) ).
fof(f171,definition,
( spl16_1
<=> empty(the_InternalRel(sK10)) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
fof(f173,plain,
( empty(the_InternalRel(sK10))
| ~ spl16_1 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f175,definition,
( spl16_2
<=> element(ordered_pair(sK14,sK15),the_InternalRel(sK10)) ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
fof(f177,plain,
( ~ element(ordered_pair(sK14,sK15),the_InternalRel(sK10))
| spl16_2 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f178,plain,
( spl16_1
| ~ spl16_2 ),
inference(avatar_split_clause,[],[f169,f175,f171]) ).
fof(f179,plain,
( ~ element(sK14,the_carrier(sK11))
| ~ element(sK15,the_carrier(sK11))
| in(ordered_pair(sK14,sK15),the_InternalRel(sK11))
| ~ rel_str(sK11) ),
inference(resolution,[],[f79,f110]) ).
fof(f182,plain,
( ~ element(sK15,the_carrier(sK11))
| in(ordered_pair(sK14,sK15),the_InternalRel(sK11))
| ~ rel_str(sK11) ),
inference(forward_subsumption_resolution,[],[f179,f114]) ).
fof(f183,plain,
( in(ordered_pair(sK14,sK15),the_InternalRel(sK11))
| ~ rel_str(sK11) ),
inference(forward_subsumption_resolution,[],[f182,f109]) ).
fof(f184,plain,
in(ordered_pair(sK14,sK15),the_InternalRel(sK11)),
inference(forward_subsumption_resolution,[],[f183,f133]) ).
fof(f188,plain,
! [X0] :
( element(ordered_pair(sK14,sK15),X0)
| ~ element(the_InternalRel(sK11),powerset(X0)) ),
inference(resolution,[],[f184,f107]) ).
fof(f189,plain,
! [X0] :
( ~ element(the_InternalRel(sK11),powerset(X0))
| ~ empty(X0) ),
inference(resolution,[],[f184,f108]) ).
fof(f217,plain,
( ~ rel_str(sK10)
| element(the_InternalRel(sK11),powerset(the_InternalRel(sK10))) ),
inference(resolution,[],[f161,f117]) ).
fof(f220,plain,
element(the_InternalRel(sK11),powerset(the_InternalRel(sK10))),
inference(forward_subsumption_resolution,[],[f217,f118]) ).
fof(f326,plain,
~ empty(the_InternalRel(sK10)),
inference(resolution,[],[f189,f220]) ).
fof(f358,plain,
( ~ element(the_InternalRel(sK11),powerset(the_InternalRel(sK10)))
| spl16_2 ),
inference(resolution,[],[f188,f177]) ).
fof(f376,plain,
( $false
| spl16_2 ),
inference(forward_subsumption_resolution,[],[f358,f220]) ).
fof(f377,plain,
spl16_2,
inference(avatar_contradiction_clause,[],[f376]) ).
fof(f378,plain,
( $false
| ~ spl16_1 ),
inference(forward_subsumption_resolution,[],[f326,f173]) ).
fof(f379,plain,
~ spl16_1,
inference(avatar_contradiction_clause,[],[f378]) ).
cnf(s1,plain,
( spl16_1
| ~ spl16_2 ),
inference(sat_conversion,[],[f178]) ).
cnf(s9,plain,
spl16_2,
inference(sat_conversion,[],[f377]) ).
cnf(s10,plain,
~ spl16_1,
inference(sat_conversion,[],[f379]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s9,s10]) ).
fof(f380,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU362+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n004.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 04:54:37 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.18/0.48 % (4160615)Will run a generic schedule for satisfiability detection.
% 0.18/0.48 % (4160620)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2477738750_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.48 % TRYING [1]
% 0.18/0.48 % TRYING [2]
% 0.18/0.48 % TRYING [3]
% 0.18/0.48 % (4160621)% WARNING: option uhcvi not known.
% 0.18/0.48 % (4160621)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3054930983:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.48 % (4160625)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3223133597:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.48 % (4160623)dis+10_1_sil=32000:sp=arity:random_seed=481911260:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.48 % (4160622)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=491573811:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.48 % (4160624)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3658882356:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.48 % (4160626)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1794506659:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.48 % (4160624) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4160615-4160624"...
% 0.18/0.48 % (4160624)...printing done.
% 0.18/0.48 % (4160624)Refutation found. Thanks to Tanya!
% 0.18/0.48 % SZS status Theorem for theBenchmark
% 0.18/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.48 % (4160624)------------------------------
% 0.18/0.48 % (4160624)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.48 % (4160624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.48 % (4160624)CaDiCaL version: 2.1.3
% 0.18/0.48 % (4160624)Termination reason: Refutation
% 0.18/0.48 % (4160624)Time elapsed: 0.010 s
% 0.18/0.48 % (4160624)Peak memory usage: 12 MB
% 0.18/0.48 % (4160624)Instructions burned: 14 (million)
% 0.18/0.48 % (4160615)Success in time 0.051 s
% 0.18/0.48 % Vampire exiting
%------------------------------------------------------------------------------