%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET577+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:41:11 PM UTC 2026
% Result : Theorem 2.68s 1.36s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 40 ( 7 unt; 0 def)
% Number of atoms : 146 ( 32 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 170 ( 64 ~; 75 |; 23 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 80 ( 69 !; 11 ?)
% 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(f3,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f7,conjecture,
! [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( member(X3,X1)
| member(X3,X2) ) )
=> X0 = union(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th18) ).
fof(f8,negated_conjecture,
~ ! [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( member(X3,X1)
| member(X3,X2) ) )
=> X0 = union(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
? [X0,X1,X2] :
( union(X1,X2) != X0
& ! [X3] :
( member(X3,X0)
<=> ( member(X3,X1)
| member(X3,X2) ) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f10,plain,
? [X0,X1,X2] :
( union(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,[],[f9]) ).
fof(f11,plain,
? [X0,X1,X2] :
( union(X1,X2) != X0
& ! [X3] :
( ( member(X3,X0)
| ( ~ member(X3,X1)
& ~ member(X3,X2) ) )
& ( member(X3,X1)
| member(X3,X2)
| ~ member(X3,X0) ) ) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
( sK0 != union(sK1,sK2)
& ! [X3] :
( ( member(X3,sK0)
| ( ~ member(X3,sK1)
& ~ member(X3,sK2) ) )
& ( member(X3,sK1)
| member(X3,sK2)
| ~ member(X3,sK0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X2] :
( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f14,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(rectify,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( X0 = X1
| ( ( ~ member(sK3(X0,X1),X1)
| ~ member(sK3(X0,X1),X0) )
& ( member(sK3(X0,X1),X1)
| member(sK3(X0,X1),X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f14]) ).
fof(f16,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(f17,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,[],[f16]) ).
fof(f18,plain,
! [X3] :
( member(X3,sK2)
| member(X3,sK1)
| ~ member(X3,sK0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f19,plain,
! [X3] :
( member(X3,sK0)
| ~ member(X3,sK2) ),
inference(cnf_transformation,[],[f12]) ).
fof(f20,plain,
! [X3] :
( member(X3,sK0)
| ~ member(X3,sK1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f21,plain,
sK0 != union(sK1,sK2),
inference(cnf_transformation,[],[f12]) ).
fof(f24,plain,
! [X0,X1] :
( member(sK3(X0,X1),X1)
| X0 = X1
| member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f25,plain,
! [X0,X1] :
( ~ member(sK3(X0,X1),X1)
| X0 = X1
| ~ member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f27,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f28,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f29,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f40,plain,
! [X2,X0,X1] :
( member(sK3(X0,union(X1,X2)),X2)
| member(sK3(X0,union(X1,X2)),X0)
| union(X1,X2) = X0
| member(sK3(X0,union(X1,X2)),X1) ),
inference(resolution,[],[f24,f27]) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ member(sK3(X0,union(X1,X2)),X1)
| ~ member(sK3(X0,union(X1,X2)),X0)
| union(X1,X2) = X0 ),
inference(resolution,[],[f25,f29]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ member(sK3(X0,union(X1,X2)),X2)
| ~ member(sK3(X0,union(X1,X2)),X0)
| union(X1,X2) = X0 ),
inference(resolution,[],[f25,f28]) ).
fof(f57,plain,
! [X0,X1] :
( member(sK3(X0,union(sK2,X1)),sK1)
| union(sK2,X1) = X0
| ~ member(sK3(X0,union(sK2,X1)),X0)
| ~ member(sK3(X0,union(sK2,X1)),sK0) ),
inference(resolution,[],[f45,f18]) ).
fof(f121,plain,
! [X0] :
( union(sK2,sK1) = X0
| ~ member(sK3(X0,union(sK2,sK1)),X0)
| ~ member(sK3(X0,union(sK2,sK1)),sK0)
| ~ member(sK3(X0,union(sK2,sK1)),X0)
| union(sK2,sK1) = X0 ),
inference(resolution,[],[f57,f46]) ).
fof(f126,plain,
! [X0] :
( union(sK2,sK1) = X0
| ~ member(sK3(X0,union(sK2,sK1)),X0)
| ~ member(sK3(X0,union(sK2,sK1)),sK0) ),
inference(duplicate_literal_removal,[],[f121]) ).
fof(f128,plain,
! [X0] :
( union(sK1,sK2) = X0
| ~ member(sK3(X0,union(sK2,sK1)),X0)
| ~ member(sK3(X0,union(sK2,sK1)),sK0) ),
inference(forward_demodulation,[],[f126,f26]) ).
fof(f129,plain,
! [X0] :
( ~ member(sK3(X0,union(sK1,sK2)),X0)
| union(sK1,sK2) = X0
| ~ member(sK3(X0,union(sK2,sK1)),sK0) ),
inference(forward_demodulation,[],[f128,f26]) ).
fof(f130,plain,
! [X0] :
( ~ member(sK3(X0,union(sK1,sK2)),sK0)
| ~ member(sK3(X0,union(sK1,sK2)),X0)
| union(sK1,sK2) = X0 ),
inference(forward_demodulation,[],[f129,f26]) ).
fof(f373,plain,
( ~ member(sK3(sK0,union(sK1,sK2)),sK0)
| sK0 = union(sK1,sK2) ),
inference(factoring,[],[f130]) ).
fof(f374,plain,
~ member(sK3(sK0,union(sK1,sK2)),sK0),
inference(forward_subsumption_resolution,[],[f373,f21]) ).
fof(f376,plain,
~ member(sK3(sK0,union(sK1,sK2)),sK2),
inference(resolution,[],[f374,f19]) ).
fof(f430,plain,
( member(sK3(sK0,union(sK1,sK2)),sK0)
| sK0 = union(sK1,sK2)
| member(sK3(sK0,union(sK1,sK2)),sK1) ),
inference(resolution,[],[f376,f40]) ).
fof(f432,plain,
( member(sK3(sK0,union(sK1,sK2)),sK0)
| sK0 = union(sK1,sK2) ),
inference(forward_subsumption_resolution,[],[f430,f20]) ).
fof(f433,plain,
sK0 = union(sK1,sK2),
inference(forward_subsumption_resolution,[],[f432,f374]) ).
fof(f434,plain,
$false,
inference(forward_subsumption_resolution,[],[f433,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET577+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n001.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 02:18:17 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.68/1.36 % (4150457)Detected formulas, will run a generic FOF schedule.
% 2.68/1.36 % (4150467)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3431717694:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.68/1.36 % (4150467)First to succeed.
% 2.68/1.36 % (4150467)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4150457"
% 2.68/1.36 % (4150464)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3946561618:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.68/1.36 % (4150463)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=4291021959:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.68/1.36 % (4150465)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1463892331:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.68/1.36 % (4150466)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1567995751:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.68/1.36 % (4150466)Refutation not found, incomplete strategy
% 2.68/1.36 % (4150466)------------------------------
% 2.68/1.36 % (4150466)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.36 % (4150466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.36 % (4150466)CaDiCaL version: 2.1.3
% 2.68/1.36 % (4150466)Termination reason: Refutation not found, incomplete strategy
% 2.68/1.36 % (4150466)Time elapsed: 0.002 s
% 2.68/1.36 % (4150466)Peak memory usage: 88 MB
% 2.68/1.36 % (4150466)Instructions burned: 1 (million)
% 2.68/1.36 % (4150469)dis-21_1_sil=8000:lcm=predicate:random_seed=4051029704:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.68/1.36 % (4150468)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3517215393:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.68/1.36 % (4150469)Also succeeded, but the first one will report.
% 2.68/1.36 % (4150468)Also succeeded, but the first one will report.
% 2.68/1.36 % (4150467)Refutation found. Thanks to Tanya!
% 2.68/1.36 % SZS status Theorem for theBenchmark
% 2.68/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.36 % (4150467)------------------------------
% 2.68/1.36 % (4150467)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.36 % (4150467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.36 % (4150467)CaDiCaL version: 2.1.3
% 2.68/1.36 % (4150467)Termination reason: Refutation
% 2.68/1.36 % (4150467)Time elapsed: 0.007 s
% 2.68/1.36 % (4150467)Peak memory usage: 88 MB
% 2.68/1.36 % (4150467)Instructions burned: 18 (million)
% 2.68/1.36 % (4150467)------------------------------
% 2.68/1.36 % (4150467)------------------------------
% 2.68/1.36 % (4150457)Success in time 0.294 s
% 2.68/1.36 % Vampire exiting
%------------------------------------------------------------------------------