%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET935+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 12:45:02 PM UTC 2026
% Result : Theorem 0.17s 0.53s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 70 ( 18 unt; 3 def)
% Number of atoms : 224 ( 36 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 250 ( 96 ~; 103 |; 40 &)
% ( 9 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 98 ( 1 sgn 91 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f4,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f5,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
| in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f6,axiom,
! [X0,X1] :
( inclusion_comparable(X0,X1)
<=> ( subset(X0,X1)
| subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_xboole_0) ).
fof(f12,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f15,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f16,conjecture,
! [X0,X1] :
( set_union2(powerset(X0),powerset(X1)) = powerset(set_union2(X0,X1))
=> inclusion_comparable(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_zfmisc_1) ).
fof(f17,negated_conjecture,
~ ! [X0,X1] :
( set_union2(powerset(X0),powerset(X1)) = powerset(set_union2(X0,X1))
=> inclusion_comparable(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f19,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f12]) ).
fof(f25,plain,
? [X0,X1] :
( ~ inclusion_comparable(X0,X1)
& set_union2(powerset(X0),powerset(X1)) = powerset(set_union2(X0,X1)) ),
inference(ennf_transformation,[],[f17]) ).
fof(f26,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f27,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ( X1 = powerset(X0)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0) )
& ( subset(X2,X0)
| ~ in(X2,X1) ) )
| powerset(X0) != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f29,plain,
! [X0,X1] :
( ( X1 = powerset(X0)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(rectify,[],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( ( X1 = powerset(X0)
| ( ( ~ subset(sK0(X0,X1),X0)
| ~ in(sK0(X0,X1),X1) )
& ( subset(sK0(X0,X1),X0)
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) )
& ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) )
& ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ( ( ( ~ in(sK1(X0,X1,X2),X0)
& ~ in(sK1(X0,X1,X2),X1) )
| ~ in(sK1(X0,X1,X2),X2) )
& ( in(sK1(X0,X1,X2),X0)
| in(sK1(X0,X1,X2),X1)
| in(sK1(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( ( inclusion_comparable(X0,X1)
| ( ~ subset(X0,X1)
& ~ subset(X1,X0) ) )
& ( subset(X0,X1)
| subset(X1,X0)
| ~ inclusion_comparable(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f36,plain,
! [X0,X1] :
( ( inclusion_comparable(X0,X1)
| ( ~ subset(X0,X1)
& ~ subset(X1,X0) ) )
& ( subset(X0,X1)
| subset(X1,X0)
| ~ inclusion_comparable(X0,X1) ) ),
inference(flattening,[],[f35]) ).
fof(f39,plain,
( ~ inclusion_comparable(sK4,sK5)
& set_union2(powerset(sK4),powerset(sK5)) = powerset(set_union2(sK4,sK5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f25]) ).
fof(f41,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f44,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f27]) ).
fof(f45,plain,
! [X3,X0,X1] :
( subset(X3,X0)
| ~ in(X3,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f30]) ).
fof(f46,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ subset(X3,X0)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f30]) ).
fof(f49,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f34]) ).
fof(f56,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| inclusion_comparable(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f57,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| inclusion_comparable(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f63,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f19]) ).
fof(f66,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f15]) ).
fof(f67,plain,
set_union2(powerset(sK4),powerset(sK5)) = powerset(set_union2(sK4,sK5)),
inference(cnf_transformation,[],[f39]) ).
fof(f68,plain,
~ inclusion_comparable(sK4,sK5),
inference(cnf_transformation,[],[f39]) ).
fof(f71,plain,
! [X3,X0] :
( in(X3,powerset(X0))
| ~ subset(X3,X0) ),
inference(equality_resolution,[],[f46]) ).
fof(f72,plain,
! [X3,X0] :
( ~ in(X3,powerset(X0))
| subset(X3,X0) ),
inference(equality_resolution,[],[f45]) ).
fof(f75,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f49]) ).
fof(f82,plain,
! [X0,X1] : inclusion_comparable(X0,set_union2(X0,X1)),
inference(resolution,[],[f57,f66]) ).
fof(f106,plain,
! [X0,X1] : subset(X1,set_union2(X0,X1)),
inference(superposition,[],[f66,f41]) ).
fof(f139,plain,
! [X0,X1] :
( ~ subset(set_union2(X0,X1),X0)
| set_union2(X0,X1) = X0 ),
inference(resolution,[],[f44,f66]) ).
fof(f171,plain,
! [X0] :
( ~ in(X0,powerset(set_union2(sK4,sK5)))
| in(X0,powerset(sK5))
| in(X0,powerset(sK4)) ),
inference(superposition,[],[f75,f67]) ).
fof(f229,plain,
! [X0] :
( ~ subset(X0,set_union2(sK4,sK5))
| in(X0,powerset(sK4))
| in(X0,powerset(sK5)) ),
inference(resolution,[],[f171,f71]) ).
fof(f716,plain,
( in(set_union2(sK4,sK5),powerset(sK4))
| in(set_union2(sK4,sK5),powerset(sK5)) ),
inference(resolution,[],[f229,f63]) ).
fof(f725,definition,
( spl6_9
<=> in(set_union2(sK4,sK5),powerset(sK5)) ),
introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition]) ).
fof(f727,plain,
( in(set_union2(sK4,sK5),powerset(sK5))
| ~ spl6_9 ),
inference(avatar_component_clause,[],[f725]) ).
fof(f729,definition,
( spl6_10
<=> in(set_union2(sK4,sK5),powerset(sK4)) ),
introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition]) ).
fof(f731,plain,
( in(set_union2(sK4,sK5),powerset(sK4))
| ~ spl6_10 ),
inference(avatar_component_clause,[],[f729]) ).
fof(f732,plain,
( spl6_9
| spl6_10 ),
inference(avatar_split_clause,[],[f716,f729,f725]) ).
fof(f767,definition,
( spl6_16
<=> subset(sK5,sK4) ),
introduced(definition,[new_symbols(definition,[spl6_16])],[avatar_definition]) ).
fof(f768,plain,
( subset(sK5,sK4)
| ~ spl6_16 ),
inference(avatar_component_clause,[],[f767]) ).
fof(f778,plain,
( subset(set_union2(sK4,sK5),sK5)
| ~ spl6_9 ),
inference(resolution,[],[f727,f72]) ).
fof(f793,plain,
( ~ subset(sK5,set_union2(sK4,sK5))
| sK5 = set_union2(sK4,sK5)
| ~ spl6_9 ),
inference(resolution,[],[f778,f44]) ).
fof(f796,plain,
( sK5 = set_union2(sK4,sK5)
| ~ spl6_9 ),
inference(forward_subsumption_resolution,[],[f793,f106]) ).
fof(f879,plain,
( inclusion_comparable(sK4,sK5)
| ~ spl6_9 ),
inference(superposition,[],[f82,f796]) ).
fof(f904,plain,
( $false
| ~ spl6_9 ),
inference(forward_subsumption_resolution,[],[f879,f68]) ).
fof(f905,plain,
~ spl6_9,
inference(avatar_contradiction_clause,[],[f904]) ).
fof(f934,plain,
( subset(set_union2(sK4,sK5),sK4)
| ~ spl6_10 ),
inference(resolution,[],[f731,f72]) ).
fof(f944,plain,
( sK4 = set_union2(sK4,sK5)
| ~ spl6_10 ),
inference(resolution,[],[f934,f139]) ).
fof(f1026,plain,
( subset(sK5,sK4)
| ~ spl6_10 ),
inference(superposition,[],[f106,f944]) ).
fof(f1048,plain,
( spl6_16
| ~ spl6_10 ),
inference(avatar_split_clause,[],[f1026,f729,f767]) ).
fof(f1058,plain,
( inclusion_comparable(sK4,sK5)
| ~ spl6_16 ),
inference(resolution,[],[f768,f56]) ).
fof(f1059,plain,
( $false
| ~ spl6_16 ),
inference(forward_subsumption_resolution,[],[f1058,f68]) ).
fof(f1060,plain,
~ spl6_16,
inference(avatar_contradiction_clause,[],[f1059]) ).
cnf(s6,plain,
( spl6_9
| spl6_10 ),
inference(sat_conversion,[],[f732]) ).
cnf(s12,plain,
~ spl6_9,
inference(sat_conversion,[],[f905]) ).
cnf(s16,plain,
( ~ spl6_10
| spl6_16 ),
inference(sat_conversion,[],[f1048]) ).
cnf(s20,plain,
~ spl6_16,
inference(sat_conversion,[],[f1060]) ).
cnf(s21,plain,
~ spl6_10,
inference(rat,[],[s16,s20]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s6,s21,s12]) ).
fof(f1061,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET935+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 % Computer : n010.cluster.edu
% 0.11/0.41 % Model : x86_64 x86_64
% 0.11/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.41 % Memory : 8046.5625MB
% 0.11/0.41 % OS : Linux 6.8.0-71-generic
% 0.11/0.41 % CPULimit : 300
% 0.11/0.41 % WCLimit : 300
% 0.11/0.41 % DateTime : Mon Sep 28 03:15:56 UTC 2026
% 0.11/0.42 % CPUTime :
% 0.11/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.45 Running first-order model finding
% 0.11/0.45 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
% 0.17/0.53 % (1528649)Will run a generic schedule for satisfiability detection.
% 0.17/0.53 % (1528654)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1736308409_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.53 % TRYING [1]
% 0.17/0.53 % TRYING [2]
% 0.17/0.53 % TRYING [3]
% 0.17/0.53 % TRYING [4]
% 0.17/0.53 % (1528655)% WARNING: option uhcvi not known.
% 0.17/0.53 % TRYING [5]
% 0.17/0.53 % (1528656)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3909932522:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.53 % (1528657)dis+10_1_sil=32000:sp=arity:random_seed=1666891340:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.53 % (1528655)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1217027797:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.53 % (1528658)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1289441155:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.53 % (1528659)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2735576250:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.53 % (1528660)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=190937940:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.53 % TRYING [6]
% 0.17/0.53 % (1528657) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1528649-1528657"...
% 0.17/0.53 % (1528657)...printing done.
% 0.17/0.53 % (1528657)Refutation found. Thanks to Tanya!
% 0.17/0.53 % SZS status Theorem for theBenchmark
% 0.17/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.53 % (1528657)------------------------------
% 0.17/0.53 % (1528657)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.53 % (1528657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.53 % (1528657)CaDiCaL version: 2.1.3
% 0.17/0.53 % (1528657)Termination reason: Refutation
% 0.17/0.53 % (1528657)Time elapsed: 0.035 s
% 0.17/0.53 % (1528657)Peak memory usage: 12 MB
% 0.17/0.53 % (1528657)Instructions burned: 55 (million)
% 0.17/0.53 % (1528649)Success in time 0.068 s
% 0.17/0.53 % Vampire exiting
%------------------------------------------------------------------------------