%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU141+2 : 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 : n011.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 12:52:04 PM UTC 2026
% Result : Theorem 0.10s 5.49s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 64 ( 8 unt; 2 def)
% Number of atoms : 212 ( 43 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 246 ( 98 ~; 94 |; 44 &)
% ( 9 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 89 ( 0 sgn 79 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f10,axiom,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& ~ in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f11,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f23,axiom,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(f39,axiom,
! [X0,X1] : subset(set_difference(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(f43,axiom,
! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] :
~ ( in(X2,X0)
& in(X2,X1) ) )
& ~ ( ? [X2] :
( in(X2,X0)
& in(X2,X1) )
& disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f47,axiom,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_intersection2(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(f55,conjecture,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f56,negated_conjecture,
~ ! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f63,plain,
! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] :
~ ( in(X2,X0)
& in(X2,X1) ) )
& ~ ( ? [X3] :
( in(X3,X0)
& in(X3,X1) )
& disjoint(X0,X1) ) ),
inference(rectify,[],[f43]) ).
fof(f83,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| ? [X2] :
( in(X2,X0)
& in(X2,X1) ) )
& ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X3,X1) )
| ~ disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f63]) ).
fof(f92,plain,
? [X0,X1] :
( disjoint(X0,X1)
<~> set_difference(X0,X1) = X0 ),
inference(ennf_transformation,[],[f56]) ).
fof(f96,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f97,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f96]) ).
fof(f112,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(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_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(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_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f112]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(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_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f113]) ).
fof(f115,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ( ( ~ in(sK4(X0,X1,X2),X0)
| in(sK4(X0,X1,X2),X1)
| ~ in(sK4(X0,X1,X2),X2) )
& ( ( in(sK4(X0,X1,X2),X0)
& ~ in(sK4(X0,X1,X2),X1) )
| in(sK4(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( ( in(X4,X0)
& ~ in(X4,X1) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f114]) ).
fof(f116,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
& ( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f117,plain,
! [X0,X1] :
( ( set_difference(X0,X1) = empty_set
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f123,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| ( in(sK8(X0,X1),X0)
& in(sK8(X0,X1),X1) ) )
& ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X3,X1) )
| ~ disjoint(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X2,sK8(X0,X1))],[f83]) ).
fof(f125,plain,
? [X0,X1] :
( ( set_difference(X0,X1) != X0
| ~ disjoint(X0,X1) )
& ( set_difference(X0,X1) = X0
| disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f92]) ).
fof(f126,plain,
( ( sK10 != set_difference(sK10,sK11)
| ~ disjoint(sK10,sK11) )
& ( sK10 = set_difference(sK10,sK11)
| disjoint(sK10,sK11) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X0,sK10),skolemize(X1,sK11)],[f125]) ).
fof(f133,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f97]) ).
fof(f151,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f115]) ).
fof(f157,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f166,plain,
! [X0,X1] :
( empty_set != set_difference(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f184,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f39]) ).
fof(f190,plain,
! [X0,X1] :
( in(sK8(X0,X1),X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f123]) ).
fof(f191,plain,
! [X0,X1] :
( in(sK8(X0,X1),X0)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f123]) ).
fof(f195,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
inference(cnf_transformation,[],[f47]) ).
fof(f204,plain,
( sK10 = set_difference(sK10,sK11)
| disjoint(sK10,sK11) ),
inference(cnf_transformation,[],[f126]) ).
fof(f205,plain,
( sK10 != set_difference(sK10,sK11)
| ~ disjoint(sK10,sK11) ),
inference(cnf_transformation,[],[f126]) ).
fof(f216,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| empty_set = set_difference(X0,set_difference(X0,X1)) ),
inference(definition_unfolding,[],[f157,f195]) ).
fof(f236,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f151]) ).
fof(f238,definition,
( spl12_1
<=> disjoint(sK10,sK11) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f239,plain,
( ~ disjoint(sK10,sK11)
| spl12_1 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f240,plain,
( disjoint(sK10,sK11)
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f242,definition,
( spl12_2
<=> sK10 = set_difference(sK10,sK11) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f243,plain,
( sK10 != set_difference(sK10,sK11)
| spl12_2 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f244,plain,
( sK10 = set_difference(sK10,sK11)
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f245,plain,
( spl12_1
| spl12_2 ),
inference(avatar_split_clause,[],[f204,f242,f238]) ).
fof(f246,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(avatar_split_clause,[],[f205,f242,f238]) ).
fof(f385,plain,
( ! [X0] :
( ~ in(X0,sK11)
| ~ in(X0,sK10) )
| ~ spl12_2 ),
inference(superposition,[],[f236,f244]) ).
fof(f392,plain,
( ! [X0] :
( ~ in(sK8(X0,sK11),sK10)
| disjoint(X0,sK11) )
| ~ spl12_2 ),
inference(resolution,[],[f385,f190]) ).
fof(f425,plain,
( disjoint(sK10,sK11)
| disjoint(sK10,sK11)
| ~ spl12_2 ),
inference(resolution,[],[f392,f191]) ).
fof(f426,plain,
( disjoint(sK10,sK11)
| ~ spl12_2 ),
inference(duplicate_literal_removal,[],[f425]) ).
fof(f427,plain,
( $false
| spl12_1
| ~ spl12_2 ),
inference(forward_subsumption_resolution,[],[f426,f239]) ).
fof(f428,plain,
( spl12_1
| ~ spl12_2 ),
inference(avatar_contradiction_clause,[],[f427]) ).
fof(f545,plain,
( empty_set = set_difference(sK10,set_difference(sK10,sK11))
| ~ spl12_1 ),
inference(resolution,[],[f216,f240]) ).
fof(f553,plain,
( empty_set != empty_set
| subset(sK10,set_difference(sK10,sK11))
| ~ spl12_1 ),
inference(superposition,[],[f166,f545]) ).
fof(f562,plain,
( subset(sK10,set_difference(sK10,sK11))
| ~ spl12_1 ),
inference(trivial_inequality_removal,[],[f553]) ).
fof(f573,plain,
( ~ subset(set_difference(sK10,sK11),sK10)
| sK10 = set_difference(sK10,sK11)
| ~ spl12_1 ),
inference(resolution,[],[f562,f133]) ).
fof(f583,plain,
( sK10 = set_difference(sK10,sK11)
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f573,f184]) ).
fof(f586,plain,
( $false
| ~ spl12_1
| spl12_2 ),
inference(forward_subsumption_resolution,[],[f583,f243]) ).
fof(f587,plain,
( ~ spl12_1
| spl12_2 ),
inference(avatar_contradiction_clause,[],[f586]) ).
cnf(s1,plain,
( spl12_1
| spl12_2 ),
inference(sat_conversion,[],[f245]) ).
cnf(s2,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(sat_conversion,[],[f246]) ).
cnf(s5,plain,
( spl12_1
| ~ spl12_2 ),
inference(sat_conversion,[],[f428]) ).
cnf(s7,plain,
( ~ spl12_1
| spl12_2 ),
inference(sat_conversion,[],[f587]) ).
cnf(s8,plain,
spl12_1,
inference(rat,[],[s1,s5]) ).
cnf(s9,plain,
spl12_2,
inference(rat,[],[s7,s8]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s2,s9,s8]) ).
fof(f588,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU141+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/5.40 % Computer : n011.cluster.edu
% 0.10/5.40 % Model : x86_64 x86_64
% 0.10/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.40 % Memory : 8046.5625MB
% 0.10/5.40 % OS : Linux 6.8.0-71-generic
% 0.10/5.40 % CPULimit : 300
% 0.10/5.40 % WCLimit : 300
% 0.10/5.40 % DateTime : Mon Sep 28 03:42:37 UTC 2026
% 0.10/5.40 % CPUTime :
% 0.10/5.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/5.43 Running first-order model finding
% 0.10/5.43 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
% 0.10/5.49 % (2996208)Will run a generic schedule for satisfiability detection.
% 0.10/5.49 % (2996213)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1780901697_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/5.49 % TRYING [1]
% 0.10/5.49 % TRYING [2]
% 0.10/5.49 % (2996214)% WARNING: option uhcvi not known.
% 0.10/5.49 % TRYING [3]
% 0.10/5.49 % (2996214)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=991892872:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/5.49 % (2996215)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=267333840:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/5.49 % (2996216)dis+10_1_sil=32000:sp=arity:random_seed=2939878879:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/5.49 % (2996217)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2931973357:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/5.49 % (2996218)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1710160574:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/5.49 % (2996219)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1389664460:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/5.49 % TRYING [4]
% 0.10/5.49 % (2996216) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2996208-2996216"...
% 0.10/5.49 % (2996216)...printing done.
% 0.10/5.49 % (2996216)Refutation found. Thanks to Tanya!
% 0.10/5.49 % SZS status Theorem for theBenchmark
% 0.10/5.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/5.49 % (2996216)------------------------------
% 0.10/5.49 % (2996216)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/5.49 % (2996216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/5.49 % (2996216)CaDiCaL version: 2.1.3
% 0.10/5.49 % (2996216)Termination reason: Refutation
% 0.10/5.49 % (2996216)Time elapsed: 0.011 s
% 0.10/5.49 % (2996216)Peak memory usage: 12 MB
% 0.10/5.49 % (2996216)Instructions burned: 14 (million)
% 0.10/5.49 % (2996208)Success in time 0.047 s
% 0.10/5.49 % Vampire exiting
%------------------------------------------------------------------------------