%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET185+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 : n012.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 12:43:23 PM UTC 2026
% Result : Theorem 0.07s 0.38s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 9 unt; 0 def)
% Number of atoms : 107 ( 15 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 104 ( 36 ~; 44 |; 17 &)
% ( 4 <=>; 3 =>; 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 : 72 ( 68 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X0)
| member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f4,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f7,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> union(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_subset_union) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> union(X0,X1) = X1 ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f10,plain,
? [X0,X1] :
( union(X0,X1) != X1
& subset(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f11,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(f12,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,[],[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,[],[f9]) ).
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] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f17,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f16]) ).
fof(f21,plain,
( sK3 != union(sK2,sK3)
& subset(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f10]) ).
fof(f22,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f23,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f25,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f15]) ).
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(f30,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f17]) ).
fof(f31,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f37,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f21]) ).
fof(f38,plain,
sK3 != union(sK2,sK3),
inference(cnf_transformation,[],[f21]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ member(sK0(X0,union(X1,X2)),X2)
| subset(X0,union(X1,X2)) ),
inference(resolution,[],[f27,f23]) ).
fof(f51,plain,
! [X0] :
( ~ member(X0,sK2)
| member(X0,sK3) ),
inference(resolution,[],[f25,f37]) ).
fof(f67,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,[],[f22,f26]) ).
fof(f109,plain,
! [X0,X1] :
( subset(X0,union(X1,X0))
| subset(X0,union(X1,X0)) ),
inference(resolution,[],[f49,f26]) ).
fof(f116,plain,
! [X0,X1] : subset(X0,union(X1,X0)),
inference(duplicate_literal_removal,[],[f109]) ).
fof(f125,plain,
! [X0,X1] :
( member(sK0(union(X0,sK2),X1),sK3)
| member(sK0(union(X0,sK2),X1),X0)
| subset(union(X0,sK2),X1) ),
inference(resolution,[],[f67,f51]) ).
fof(f240,plain,
! [X0] :
( member(sK0(union(X0,sK2),X0),sK3)
| subset(union(X0,sK2),X0)
| subset(union(X0,sK2),X0) ),
inference(resolution,[],[f125,f27]) ).
fof(f251,plain,
! [X0] :
( member(sK0(union(X0,sK2),X0),sK3)
| subset(union(X0,sK2),X0) ),
inference(duplicate_literal_removal,[],[f240]) ).
fof(f1216,plain,
( subset(union(sK3,sK2),sK3)
| subset(union(sK3,sK2),sK3) ),
inference(resolution,[],[f251,f27]) ).
fof(f1231,plain,
subset(union(sK3,sK2),sK3),
inference(duplicate_literal_removal,[],[f1216]) ).
fof(f1238,plain,
subset(union(sK2,sK3),sK3),
inference(forward_demodulation,[],[f1231,f31]) ).
fof(f1239,plain,
( ~ subset(sK3,union(sK2,sK3))
| sK3 = union(sK2,sK3) ),
inference(resolution,[],[f1238,f30]) ).
fof(f1241,plain,
sK3 = union(sK2,sK3),
inference(forward_subsumption_resolution,[],[f1239,f116]) ).
fof(f1242,plain,
$false,
inference(forward_subsumption_resolution,[],[f1241,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET185+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Mon Sep 28 01:02:34 UTC 2026
% 0.05/0.31 % CPUTime :
% 0.05/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.33 Running first-order model finding
% 0.07/0.33 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
% 0.07/0.38 % (2917686)Will run a generic schedule for satisfiability detection.
% 0.07/0.38 % (2917692)% WARNING: option uhcvi not known.
% 0.07/0.38 % (2917693)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2302908144:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.38 % (2917691)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1131782718_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.38 % (2917694)dis+10_1_sil=32000:sp=arity:random_seed=806024408:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.38 % (2917692)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2917550562:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.38 % (2917695)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3986648529:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.38 % (2917696)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4283747822:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.38 % (2917697)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2732965671:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.38 % TRYING [1]
% 0.07/0.38 % TRYING [2]
% 0.07/0.38 % TRYING [3]
% 0.07/0.38 % TRYING [4]
% 0.07/0.38 % TRYING [5]
% 0.07/0.38 % TRYING [6]
% 0.07/0.38 % TRYING [7]
% 0.07/0.38 % (2917694) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2917686-2917694"...
% 0.07/0.38 % (2917694)...printing done.
% 0.07/0.38 % (2917694)Refutation found. Thanks to Tanya!
% 0.07/0.38 % SZS status Theorem for theBenchmark
% 0.07/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.38 % (2917694)------------------------------
% 0.07/0.38 % (2917694)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.38 % (2917694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.38 % (2917694)CaDiCaL version: 2.1.3
% 0.07/0.38 % (2917694)Termination reason: Refutation
% 0.07/0.38 % (2917694)Time elapsed: 0.020 s
% 0.07/0.38 % (2917694)Peak memory usage: 12 MB
% 0.07/0.38 % (2917694)Instructions burned: 61 (million)
% 0.07/0.38 % (2917686)Success in time 0.045 s
% 0.07/0.38 % Vampire exiting
%------------------------------------------------------------------------------