%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET579+3 : TPTP v9.3.1. Released v2.2.0.
% 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 12:43:59 PM UTC 2026
% Result : Theorem 0.20s 0.48s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 43 ( 5 unt; 0 def)
% Number of atoms : 141 ( 14 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 155 ( 57 ~; 59 |; 29 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 87 ( 76 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( member(X2,X0)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(f2,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f5,conjecture,
! [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( member(X3,X1)
& ~ member(X3,X2) ) )
=> X0 = difference(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th20) ).
fof(f6,negated_conjecture,
~ ! [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( member(X3,X1)
& ~ member(X3,X2) ) )
=> X0 = difference(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f8,plain,
? [X0,X1,X2] :
( difference(X1,X2) != X0
& ! [X3] :
( member(X3,X0)
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f9,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f10,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f12,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f14,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f14]) ).
fof(f16,plain,
? [X0,X1,X2] :
( difference(X1,X2) != X0
& ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1)
| member(X3,X2) )
& ( ( member(X3,X1)
& ~ member(X3,X2) )
| ~ member(X3,X0) ) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f17,plain,
? [X0,X1,X2] :
( difference(X1,X2) != X0
& ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1)
| member(X3,X2) )
& ( ( member(X3,X1)
& ~ member(X3,X2) )
| ~ member(X3,X0) ) ) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
( sK1 != difference(sK2,sK3)
& ! [X3] :
( ( member(X3,sK1)
| ~ member(X3,sK2)
| member(X3,sK3) )
& ( ( member(X3,sK2)
& ~ member(X3,sK3) )
| ~ member(X3,sK1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f17]) ).
fof(f19,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f20,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f10]) ).
fof(f21,plain,
! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f24,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f12]) ).
fof(f26,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f27,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X3] :
( ~ member(X3,sK3)
| ~ member(X3,sK1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f30,plain,
! [X3] :
( ~ member(X3,sK1)
| member(X3,sK2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
! [X3] :
( ~ member(X3,sK2)
| member(X3,sK1)
| member(X3,sK3) ),
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
sK1 != difference(sK2,sK3),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
! [X2,X0,X1] :
( member(sK0(difference(X0,X1),X2),X0)
| subset(difference(X0,X1),X2) ),
inference(resolution,[],[f26,f20]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ member(sK0(difference(X0,X1),X2),X1)
| subset(difference(X0,X1),X2) ),
inference(resolution,[],[f26,f19]) ).
fof(f37,plain,
! [X0] :
( member(sK0(sK1,X0),sK2)
| subset(sK1,X0) ),
inference(resolution,[],[f26,f30]) ).
fof(f60,plain,
! [X2,X0,X1] :
( ~ member(sK0(X0,difference(X1,X2)),X1)
| member(sK0(X0,difference(X1,X2)),X2)
| subset(X0,difference(X1,X2)) ),
inference(resolution,[],[f21,f27]) ).
fof(f77,plain,
! [X0,X1] :
( member(sK0(difference(sK2,X0),X1),sK3)
| member(sK0(difference(sK2,X0),X1),sK1)
| subset(difference(sK2,X0),X1) ),
inference(resolution,[],[f35,f31]) ).
fof(f96,plain,
! [X0] :
( member(sK0(sK1,difference(sK2,X0)),X0)
| subset(sK1,difference(sK2,X0))
| subset(sK1,difference(sK2,X0)) ),
inference(resolution,[],[f60,f37]) ).
fof(f100,plain,
! [X0] :
( member(sK0(sK1,difference(sK2,X0)),X0)
| subset(sK1,difference(sK2,X0)) ),
inference(duplicate_literal_removal,[],[f96]) ).
fof(f124,plain,
( subset(sK1,difference(sK2,sK3))
| ~ member(sK0(sK1,difference(sK2,sK3)),sK1) ),
inference(resolution,[],[f100,f29]) ).
fof(f126,plain,
subset(sK1,difference(sK2,sK3)),
inference(forward_subsumption_resolution,[],[f124,f26]) ).
fof(f137,plain,
( ~ subset(difference(sK2,sK3),sK1)
| sK1 = difference(sK2,sK3) ),
inference(resolution,[],[f126,f24]) ).
fof(f138,plain,
~ subset(difference(sK2,sK3),sK1),
inference(forward_subsumption_resolution,[],[f137,f32]) ).
fof(f139,plain,
! [X0] :
( member(sK0(difference(sK2,sK3),X0),sK1)
| subset(difference(sK2,sK3),X0)
| subset(difference(sK2,sK3),X0) ),
inference(resolution,[],[f77,f36]) ).
fof(f145,plain,
! [X0] :
( member(sK0(difference(sK2,sK3),X0),sK1)
| subset(difference(sK2,sK3),X0) ),
inference(duplicate_literal_removal,[],[f139]) ).
fof(f349,plain,
( subset(difference(sK2,sK3),sK1)
| subset(difference(sK2,sK3),sK1) ),
inference(resolution,[],[f145,f27]) ).
fof(f355,plain,
subset(difference(sK2,sK3),sK1),
inference(duplicate_literal_removal,[],[f349]) ).
fof(f356,plain,
$false,
inference(forward_subsumption_resolution,[],[f355,f138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET579+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n004.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 02:12:37 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 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
% 0.20/0.48 % (4079108)Will run a generic schedule for satisfiability detection.
% 0.20/0.48 % (4079117)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2210632057:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.48 % (4079114)% WARNING: option uhcvi not known.
% 0.20/0.48 % (4079114)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=163146242:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.48 % (4079115)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=19516572:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.48 % (4079113)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1965822588_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.48 % (4079116)dis+10_1_sil=32000:sp=arity:random_seed=2105232834:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.48 % (4079118)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3375178455:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.48 % (4079119)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=286206040:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.48 % TRYING [1]
% 0.20/0.48 % TRYING [2]
% 0.20/0.48 % TRYING [3]
% 0.20/0.48 % TRYING [4]
% 0.20/0.48 % (4079116) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4079108-4079116"...
% 0.20/0.48 % (4079116)...printing done.
% 0.20/0.48 % (4079116)Refutation found. Thanks to Tanya!
% 0.20/0.48 % SZS status Theorem for theBenchmark
% 0.20/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.49 % (4079116)------------------------------
% 0.20/0.49 % (4079116)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.49 % (4079116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.49 % (4079116)CaDiCaL version: 2.1.3
% 0.20/0.49 % (4079116)Termination reason: Refutation
% 0.20/0.49 % (4079116)Time elapsed: 0.008 s
% 0.20/0.49 % (4079116)Peak memory usage: 11 MB
% 0.20/0.49 % (4079116)Instructions burned: 10 (million)
% 0.20/0.49 % (4079108)Success in time 0.049 s
% 0.20/0.49 % Vampire exiting
%------------------------------------------------------------------------------