%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET873+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:42:13 PM UTC 2026
% Result : Theorem 3.33s 1.35s
% Output : Refutation 3.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 9 unt; 0 def)
% Number of atoms : 67 ( 39 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 69 ( 27 ~; 26 |; 11 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 39 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f3,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f7,axiom,
! [X0,X1] :
( subset(set_union2(singleton(X0),X1),X1)
=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l21_zfmisc_1) ).
fof(f10,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f11,conjecture,
! [X0,X1] :
( set_union2(singleton(X0),singleton(X1)) = singleton(X0)
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] :
( set_union2(singleton(X0),singleton(X1)) = singleton(X0)
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f14,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f10]) ).
fof(f18,plain,
! [X0,X1] :
( in(X0,X1)
| ~ subset(set_union2(singleton(X0),X1),X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f19,plain,
? [X0,X1] :
( X0 != X1
& set_union2(singleton(X0),singleton(X1)) = singleton(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f20,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X2 = X0
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f21,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f21]) ).
fof(f25,plain,
( sK3 != sK4
& singleton(sK3) = set_union2(singleton(sK3),singleton(sK4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f19]) ).
fof(f27,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f28,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f35,plain,
! [X0,X1] :
( in(X0,X1)
| ~ subset(set_union2(singleton(X0),X1),X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f38,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f14]) ).
fof(f39,plain,
singleton(sK3) = set_union2(singleton(sK3),singleton(sK4)),
inference(cnf_transformation,[],[f25]) ).
fof(f40,plain,
sK3 != sK4,
inference(cnf_transformation,[],[f25]) ).
fof(f43,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f28]) ).
fof(f60,plain,
! [X0,X1] :
( ~ subset(set_union2(singleton(X0),singleton(X1)),singleton(X1))
| X0 = X1 ),
inference(resolution,[],[f35,f43]) ).
fof(f85,plain,
! [X0,X1] :
( ~ subset(set_union2(singleton(X0),singleton(X1)),singleton(X0))
| X0 = X1 ),
inference(superposition,[],[f60,f27]) ).
fof(f109,plain,
( ~ subset(singleton(sK3),singleton(sK3))
| sK3 = sK4 ),
inference(superposition,[],[f85,f39]) ).
fof(f112,plain,
sK3 = sK4,
inference(forward_subsumption_resolution,[],[f109,f38]) ).
fof(f113,plain,
$false,
inference(forward_subsumption_resolution,[],[f112,f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET873+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n005.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 03:05:04 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.33/1.35 % (393582)Detected formulas, will run a generic FOF schedule.
% 3.33/1.35 % (393591)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=665018362:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.33/1.35 % (393591)Refutation not found, incomplete strategy
% 3.33/1.35 % (393591)------------------------------
% 3.33/1.35 % (393591)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.33/1.35 % (393591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/1.35 % (393591)CaDiCaL version: 2.1.3
% 3.33/1.35 % (393591)Termination reason: Refutation not found, incomplete strategy
% 3.33/1.35 % (393591)Time elapsed: 0.001 s
% 3.33/1.35 % (393591)Peak memory usage: 88 MB
% 3.33/1.35 % (393591)Instructions burned: 1 (million)
% 3.33/1.35 % (393592)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=789684836:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.33/1.35 % (393589)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=565250227:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.33/1.35 % (393592)First to succeed.
% 3.33/1.35 % (393592)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-393582"
% 3.33/1.35 % (393587)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=1201587452:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.33/1.35 % (393588)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=3256265259:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.33/1.35 % (393590)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3229228093:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.33/1.35 % (393590)Refutation not found, incomplete strategy
% 3.33/1.35 % (393590)------------------------------
% 3.33/1.35 % (393590)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.33/1.35 % (393590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/1.35 % (393590)CaDiCaL version: 2.1.3
% 3.33/1.35 % (393590)Termination reason: Refutation not found, incomplete strategy
% 3.33/1.35 % (393590)Time elapsed: 0.001 s
% 3.33/1.35 % (393590)Peak memory usage: 88 MB
% 3.33/1.35 % (393593)dis-21_1_sil=8000:lcm=predicate:random_seed=1687437164: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)
% 3.33/1.35 % (393593)Instruction limit reached!
% 3.33/1.35 % (393593)------------------------------
% 3.33/1.35 % (393593)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.33/1.35 % (393593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/1.35 % (393593)CaDiCaL version: 2.1.3
% 3.33/1.35 % (393593)Termination reason: Instruction limit
% 3.33/1.35 % (393593)Termination phase: Saturation
% 3.33/1.35 % (393593)Time elapsed: 0.057 s
% 3.33/1.35 % (393593)Peak memory usage: 88 MB
% 3.33/1.35 % (393593)Instructions burned: 131 (million)
% 3.33/1.35 % (393591)------------------------------
% 3.33/1.35 % (393591)------------------------------
% 3.33/1.35 % (393602)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1790639827:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.33/1.35 % (393601)lrs+10_1_sil=8000:sp=occurrence:random_seed=3525070337:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.33/1.35 % (393601)Also succeeded, but the first one will report.
% 3.33/1.35 % (393590)------------------------------
% 3.33/1.35 % (393590)------------------------------
% 3.33/1.35 % (393592)Refutation found. Thanks to Tanya!
% 3.33/1.35 % SZS status Theorem for theBenchmark
% 3.33/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.33/1.35 % (393592)------------------------------
% 3.33/1.35 % (393592)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.33/1.35 % (393592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/1.35 % (393592)CaDiCaL version: 2.1.3
% 3.33/1.35 % (393592)Termination reason: Refutation
% 3.33/1.35 % (393592)Time elapsed: 0.004 s
% 3.33/1.35 % (393592)Peak memory usage: 89 MB
% 3.33/1.35 % (393592)Instructions burned: 4 (million)
% 3.33/1.35 % (393592)------------------------------
% 3.33/1.35 % (393592)------------------------------
% 3.33/1.35 % (393582)Success in time 0.397 s
% 3.33/1.35 % Vampire exiting
%------------------------------------------------------------------------------