%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET908+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:42:17 PM UTC 2026
% Result : Theorem 3.49s 1.46s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 9 unt; 0 def)
% Number of atoms : 130 ( 46 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 166 ( 64 ~; 65 |; 32 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 71 ( 62 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f4,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f5,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
| in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f12,conjecture,
! [X0,X1] : set_union2(singleton(X0),X1) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_zfmisc_1) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] : set_union2(singleton(X0),X1) != empty_set,
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f15,plain,
? [X0,X1] : empty_set = set_union2(singleton(X0),X1),
inference(ennf_transformation,[],[f13]) ).
fof(f19,plain,
empty_set = set_union2(singleton(sK0),sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f15]) ).
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)
| ( ( sK2(X0,X1) != X0
| ~ in(sK2(X0,X1),X1) )
& ( sK2(X0,X1) = X0
| in(sK2(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f21]) ).
fof(f23,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f24,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f23]) ).
fof(f25,plain,
! [X0] :
( ( X0 = empty_set
| in(sK3(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) )
& ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) )
& ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ( ( ( ~ in(sK4(X0,X1,X2),X0)
& ~ in(sK4(X0,X1,X2),X1) )
| ~ in(sK4(X0,X1,X2),X2) )
& ( in(sK4(X0,X1,X2),X0)
| in(sK4(X0,X1,X2),X1)
| in(sK4(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f28]) ).
fof(f32,plain,
empty_set = set_union2(singleton(sK0),sK1),
inference(cnf_transformation,[],[f19]) ).
fof(f36,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f40,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f25]) ).
fof(f44,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f29]) ).
fof(f53,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f36]) ).
fof(f54,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f53]) ).
fof(f56,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f40]) ).
fof(f57,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f44]) ).
fof(f85,plain,
! [X0] :
( in(X0,empty_set)
| ~ in(X0,singleton(sK0)) ),
inference(superposition,[],[f57,f32]) ).
fof(f91,plain,
! [X0] : ~ in(X0,singleton(sK0)),
inference(forward_subsumption_resolution,[],[f85,f56]) ).
fof(f104,plain,
$false,
inference(resolution,[],[f91,f54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET908+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 03:11:54 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 3.49/1.46 % (3431050)Detected formulas, will run a generic FOF schedule.
% 3.49/1.46 % (3431061)dis-21_1_sil=8000:lcm=predicate:random_seed=565380271: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)
% 3.49/1.46 % (3431055)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=1614249057:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.49/1.46 % (3431061)Instruction limit reached!
% 3.49/1.46 % (3431061)------------------------------
% 3.49/1.46 % (3431061)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.46 % (3431061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.46 % (3431061)CaDiCaL version: 2.1.3
% 3.49/1.46 % (3431061)Termination reason: Instruction limit
% 3.49/1.46 % (3431061)Termination phase: Saturation
% 3.49/1.46 % (3431061)Time elapsed: 0.041 s
% 3.49/1.46 % (3431061)Peak memory usage: 89 MB
% 3.49/1.46 % (3431061)Instructions burned: 130 (million)
% 3.49/1.46 % (3431060)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1212238302:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.49/1.46 % (3431059)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2529766608:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.49/1.46 % (3431058)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3541782841:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.49/1.46 % (3431056)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=1303918149:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.49/1.46 % (3431057)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=2967706564:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.49/1.46 % (3431058)Refutation not found, incomplete strategy
% 3.49/1.46 % (3431058)------------------------------
% 3.49/1.46 % (3431058)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.46 % (3431058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.46 % (3431058)CaDiCaL version: 2.1.3
% 3.49/1.46 % (3431058)Termination reason: Refutation not found, incomplete strategy
% 3.49/1.46 % (3431058)Time elapsed: 0.001 s
% 3.49/1.46 % (3431058)Peak memory usage: 88 MB
% 3.49/1.46 % (3431059)First to succeed.
% 3.49/1.46 % (3431060)Also succeeded, but the first one will report.
% 3.49/1.46 % (3431059)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3431050"
% 3.49/1.46 % (3431069)lrs+10_1_sil=8000:sp=occurrence:random_seed=1060591837:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.49/1.46 % (3431069)Also succeeded, but the first one will report.
% 3.49/1.46 % (3431058)------------------------------
% 3.49/1.46 % (3431058)------------------------------
% 3.49/1.46 % (3431059)Refutation found. Thanks to Tanya!
% 3.49/1.46 % SZS status Theorem for theBenchmark
% 3.49/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/1.46 % (3431059)------------------------------
% 3.49/1.46 % (3431059)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.46 % (3431059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.46 % (3431059)CaDiCaL version: 2.1.3
% 3.49/1.46 % (3431059)Termination reason: Refutation
% 3.49/1.46 % (3431059)Time elapsed: 0.003 s
% 3.49/1.46 % (3431059)Peak memory usage: 88 MB
% 3.49/1.46 % (3431059)Instructions burned: 3 (million)
% 3.49/1.46 % (3431059)------------------------------
% 3.49/1.46 % (3431059)------------------------------
% 3.49/1.46 % (3431050)Success in time 0.407 s
% 3.49/1.46 % Vampire exiting
%------------------------------------------------------------------------------