%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET162+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 12:43:19 PM UTC 2026
% Result : Theorem 0.10s 0.46s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 12 unt; 0 def)
% Number of atoms : 91 ( 14 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 93 ( 36 ~; 37 |; 15 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 66 ( 63 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X0)
| member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f2,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f9,conjecture,
! [X0] : union(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_union_empty_set) ).
fof(f10,negated_conjecture,
~ ! [X0] : union(X0,empty_set) = X0,
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f12,plain,
? [X0] : union(X0,empty_set) != X0,
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f16,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f15]) ).
fof(f17,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,[],[f11]) ).
fof(f18,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,[],[f17]) ).
fof(f19,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))],[f18]) ).
fof(f23,plain,
sK2 != union(sK2,empty_set),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f12]) ).
fof(f24,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f26,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f27,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f2]) ).
fof(f30,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f16]) ).
fof(f33,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f34,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f40,plain,
sK2 != union(sK2,empty_set),
inference(cnf_transformation,[],[f23]) ).
fof(f53,plain,
! [X2,X0,X1] :
( ~ member(sK0(X0,union(X1,X2)),X1)
| subset(X0,union(X1,X2)) ),
inference(resolution,[],[f34,f26]) ).
fof(f64,plain,
! [X2,X0,X1] :
( member(sK0(union(X0,X1),X2),X1)
| member(sK0(union(X0,X1),X2),X0)
| subset(union(X0,X1),X2) ),
inference(resolution,[],[f24,f33]) ).
fof(f84,plain,
! [X0,X1] :
( subset(X0,union(X0,X1))
| subset(X0,union(X0,X1)) ),
inference(resolution,[],[f53,f33]) ).
fof(f89,plain,
! [X0,X1] : subset(X0,union(X0,X1)),
inference(duplicate_literal_removal,[],[f84]) ).
fof(f91,plain,
! [X0,X1] :
( ~ subset(union(X0,X1),X0)
| union(X0,X1) = X0 ),
inference(resolution,[],[f89,f30]) ).
fof(f107,plain,
! [X0,X1] :
( member(sK0(union(X0,empty_set),X1),X0)
| subset(union(X0,empty_set),X1) ),
inference(resolution,[],[f64,f27]) ).
fof(f175,plain,
! [X0] :
( subset(union(X0,empty_set),X0)
| subset(union(X0,empty_set),X0) ),
inference(resolution,[],[f107,f34]) ).
fof(f184,plain,
! [X0] : subset(union(X0,empty_set),X0),
inference(duplicate_literal_removal,[],[f175]) ).
fof(f211,plain,
! [X0] : union(X0,empty_set) = X0,
inference(resolution,[],[f184,f91]) ).
fof(f525,plain,
sK2 != sK2,
inference(superposition,[],[f40,f211]) ).
fof(f526,plain,
$false,
inference(trivial_inequality_removal,[],[f525]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET162+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 00:57:06 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.10/0.46 % (712467)Will run a generic schedule for satisfiability detection.
% 0.10/0.46 % (712474)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3519468723:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.46 % (712472)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3596634100_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.46 % (712475)dis+10_1_sil=32000:sp=arity:random_seed=3595031505:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.46 % (712476)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2913407663:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.46 % (712473)% WARNING: option uhcvi not known.
% 0.10/0.46 % (712477)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1663290870:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.46 % (712478)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2311784941:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.46 % TRYING [1]
% 0.10/0.46 % TRYING [2]
% 0.10/0.46 % TRYING [3]
% 0.10/0.46 % TRYING [4]
% 0.10/0.46 % (712473)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1228612256:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.46 % TRYING [5]
% 0.10/0.46 % (712475) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-712467-712475"...
% 0.10/0.46 % (712475)...printing done.
% 0.10/0.46 % (712475)Refutation found. Thanks to Tanya!
% 0.10/0.46 % SZS status Theorem for theBenchmark
% 0.10/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.46 % (712475)------------------------------
% 0.10/0.46 % (712475)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.46 % (712475)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.46 % (712475)CaDiCaL version: 2.1.3
% 0.10/0.46 % (712475)Termination reason: Refutation
% 0.10/0.46 % (712475)Time elapsed: 0.011 s
% 0.10/0.46 % (712475)Peak memory usage: 11 MB
% 0.10/0.46 % (712475)Instructions burned: 15 (million)
% 0.10/0.46 % (712467)Success in time 0.048 s
% 0.10/0.46 % Vampire exiting
%------------------------------------------------------------------------------