%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET877+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 0.18s 1.60s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 8 unt; 0 def)
% Number of atoms : 62 ( 41 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 65 ( 25 ~; 24 |; 11 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 35 ( 31 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_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(f5,axiom,
! [X0,X1] :
( set_intersection2(X0,singleton(X1)) = singleton(X1)
=> in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l30_zfmisc_1) ).
fof(f8,conjecture,
! [X0,X1] :
( set_intersection2(singleton(X0),singleton(X1)) = singleton(X0)
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1] :
( set_intersection2(singleton(X0),singleton(X1)) = singleton(X0)
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f11,plain,
? [X0,X1] :
( X0 != X1
& set_intersection2(singleton(X0),singleton(X1)) = singleton(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f12,plain,
! [X0,X1] :
( in(X1,X0)
| singleton(X1) != set_intersection2(X0,singleton(X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f14,plain,
( sK0 != sK1
& singleton(sK0) = set_intersection2(singleton(sK0),singleton(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f11]) ).
fof(f15,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(f16,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,[],[f15]) ).
fof(f17,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))],[f16]) ).
fof(f18,plain,
singleton(sK0) = set_intersection2(singleton(sK0),singleton(sK1)),
inference(cnf_transformation,[],[f14]) ).
fof(f19,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f14]) ).
fof(f21,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f22,plain,
! [X0,X1] :
( singleton(X1) != set_intersection2(X0,singleton(X1))
| in(X1,X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f23,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f17]) ).
fof(f30,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f23]) ).
fof(f33,plain,
singleton(sK0) = set_intersection2(singleton(sK1),singleton(sK0)),
inference(superposition,[],[f21,f18]) ).
fof(f39,plain,
( singleton(sK0) != singleton(sK0)
| in(sK0,singleton(sK1)) ),
inference(superposition,[],[f22,f33]) ).
fof(f44,plain,
in(sK0,singleton(sK1)),
inference(trivial_inequality_removal,[],[f39]) ).
fof(f45,plain,
sK0 = sK1,
inference(resolution,[],[f44,f30]) ).
fof(f47,plain,
$false,
inference(forward_subsumption_resolution,[],[f45,f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET877+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.60 % Computer : n005.cluster.edu
% 0.11/0.60 % Model : x86_64 x86_64
% 0.11/0.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.60 % Memory : 8046.5625MB
% 0.11/0.60 % OS : Linux 6.8.0-71-generic
% 0.11/0.60 % CPULimit : 300
% 0.11/0.60 % WCLimit : 300
% 0.11/0.60 % DateTime : Mon Sep 28 03:05:33 UTC 2026
% 0.11/0.60 % CPUTime :
% 0.11/0.60 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.64 Running first-order theorem proving
% 0.16/0.64 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
% 0.18/1.60 % (394386)Detected formulas, will run a generic FOF schedule.
% 0.18/1.60 % (394395)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=352144468:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.18/1.60 % (394395)First to succeed.
% 0.18/1.60 % (394395)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-394386"
% 0.18/1.60 % (394393)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=3043520335:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.18/1.60 % (394391)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=1056058288:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.18/1.60 % (394396)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3943874202:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.18/1.60 % (394397)dis-21_1_sil=8000:lcm=predicate:random_seed=2007858265: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)
% 0.18/1.60 % (394392)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=1160493758:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.18/1.60 % (394394)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1140053257:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.18/1.60 % (394394)Refutation not found, incomplete strategy
% 0.18/1.60 % (394394)------------------------------
% 0.18/1.60 % (394394)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.60 % (394394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.60 % (394394)CaDiCaL version: 2.1.3
% 0.18/1.60 % (394394)Termination reason: Refutation not found, incomplete strategy
% 0.18/1.60 % (394394)Time elapsed: 0.002 s
% 0.18/1.60 % (394394)Peak memory usage: 88 MB
% 0.18/1.60 % (394396)Also succeeded, but the first one will report.
% 0.18/1.60 % (394397)Instruction limit reached!
% 0.18/1.60 % (394397)------------------------------
% 0.18/1.60 % (394397)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.60 % (394397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.60 % (394397)CaDiCaL version: 2.1.3
% 0.18/1.60 % (394397)Termination reason: Instruction limit
% 0.18/1.60 % (394397)Termination phase: Saturation
% 0.18/1.60 % (394397)Time elapsed: 0.059 s
% 0.18/1.60 % (394397)Peak memory usage: 88 MB
% 0.18/1.60 % (394397)Instructions burned: 129 (million)
% 0.18/1.60 % (394395)Refutation found. Thanks to Tanya!
% 0.18/1.60 % SZS status Theorem for theBenchmark
% 0.18/1.60 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.60 % (394395)------------------------------
% 0.18/1.60 % (394395)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.60 % (394395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.60 % (394395)CaDiCaL version: 2.1.3
% 0.18/1.60 % (394395)Termination reason: Refutation
% 0.18/1.60 % (394395)Time elapsed: 0.002 s
% 0.18/1.60 % (394395)Peak memory usage: 88 MB
% 0.18/1.60 % (394395)Instructions burned: 2 (million)
% 0.18/1.60 % (394395)------------------------------
% 0.18/1.60 % (394395)------------------------------
% 0.18/1.60 % (394386)Success in time 0.317 s
% 0.18/1.60 % Vampire exiting
%------------------------------------------------------------------------------