%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET903+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 : n013.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 12:42:16 PM UTC 2026
% Result : Theorem 3.40s 1.24s
% Output : Refutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 23 ( 7 unt; 0 def)
% Number of atoms : 65 ( 64 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 75 ( 33 ~; 21 |; 21 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 29 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0,X1,X2] :
~ ( singleton(X0) = set_union2(X1,X2)
& ~ ( X1 = singleton(X0)
& X2 = singleton(X0) )
& ~ ( X1 = empty_set
& X2 = singleton(X0) )
& ~ ( X1 = singleton(X0)
& X2 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_zfmisc_1) ).
fof(f9,conjecture,
! [X0,X1,X2] :
~ ( singleton(X0) = set_union2(X1,X2)
& X1 != X2
& X1 != empty_set
& X2 != empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( singleton(X0) = set_union2(X1,X2)
& X1 != X2
& X1 != empty_set
& X2 != empty_set ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f12,plain,
? [X0,X1,X2] :
( singleton(X0) = set_union2(X1,X2)
& X1 != X2
& X1 != empty_set
& X2 != empty_set ),
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
! [X0,X1,X2] :
( singleton(X0) != set_union2(X1,X2)
| ( X1 = singleton(X0)
& X2 = singleton(X0) )
| ( X1 = empty_set
& X2 = singleton(X0) )
| ( X1 = singleton(X0)
& X2 = empty_set ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f16,plain,
( singleton(sK0) = set_union2(sK1,sK2)
& sK1 != sK2
& empty_set != sK1
& empty_set != sK2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f12]) ).
fof(f19,plain,
empty_set != sK2,
inference(cnf_transformation,[],[f16]) ).
fof(f20,plain,
empty_set != sK1,
inference(cnf_transformation,[],[f16]) ).
fof(f21,plain,
sK1 != sK2,
inference(cnf_transformation,[],[f16]) ).
fof(f22,plain,
singleton(sK0) = set_union2(sK1,sK2),
inference(cnf_transformation,[],[f16]) ).
fof(f26,plain,
! [X2,X0,X1] :
( singleton(X0) != set_union2(X1,X2)
| singleton(X0) = X2
| singleton(X0) = X2
| empty_set = X2 ),
inference(cnf_transformation,[],[f13]) ).
fof(f33,plain,
! [X2,X0,X1] :
( singleton(X0) != set_union2(X1,X2)
| singleton(X0) = X1
| empty_set = X1
| singleton(X0) = X1 ),
inference(cnf_transformation,[],[f13]) ).
fof(f38,plain,
! [X2,X0,X1] :
( singleton(X0) != set_union2(X1,X2)
| singleton(X0) = X2
| empty_set = X2 ),
inference(duplicate_literal_removal,[],[f26]) ).
fof(f41,plain,
! [X2,X0,X1] :
( singleton(X0) != set_union2(X1,X2)
| singleton(X0) = X1
| empty_set = X1 ),
inference(duplicate_literal_removal,[],[f33]) ).
fof(f50,plain,
! [X0] :
( singleton(X0) != singleton(sK0)
| singleton(X0) = sK2
| empty_set = sK2 ),
inference(superposition,[],[f38,f22]) ).
fof(f54,plain,
! [X0] :
( singleton(X0) != singleton(sK0)
| singleton(X0) = sK2 ),
inference(forward_subsumption_resolution,[],[f50,f19]) ).
fof(f55,plain,
sK2 = singleton(sK0),
inference(equality_resolution,[],[f54]) ).
fof(f59,plain,
! [X0] :
( singleton(X0) != singleton(sK0)
| singleton(X0) = sK1
| empty_set = sK1 ),
inference(superposition,[],[f41,f22]) ).
fof(f63,plain,
! [X0] :
( singleton(X0) != singleton(sK0)
| singleton(X0) = sK1 ),
inference(forward_subsumption_resolution,[],[f59,f20]) ).
fof(f64,plain,
! [X0] :
( singleton(X0) != sK2
| singleton(X0) = sK1 ),
inference(forward_demodulation,[],[f63,f55]) ).
fof(f70,plain,
( sK2 != sK2
| sK1 = sK2 ),
inference(superposition,[],[f64,f55]) ).
fof(f71,plain,
sK1 = sK2,
inference(trivial_inequality_removal,[],[f70]) ).
fof(f72,plain,
$false,
inference(forward_subsumption_resolution,[],[f71,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET903+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n013.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 03:07:06 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.40/1.24 % (768757)Detected formulas, will run a generic FOF schedule.
% 3.40/1.24 % (768762)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=2793532623:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.40/1.24 % (768768)dis-21_1_sil=8000:lcm=predicate:random_seed=484745936: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)
% 3.40/1.24 % (768767)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4142563664:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.40/1.24 % (768763)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=1460880073:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.40/1.24 % (768764)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=894676547:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.40/1.24 % (768765)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=37438162:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.40/1.24 % (768766)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3530972028:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.40/1.24 % (768768)Refutation not found, incomplete strategy
% 3.40/1.24 % (768768)------------------------------
% 3.40/1.24 % (768768)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.24 % (768768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.24 % (768768)CaDiCaL version: 2.1.3
% 3.40/1.24 % (768768)Termination reason: Refutation not found, incomplete strategy
% 3.40/1.24 % (768768)Time elapsed: 0.002 s
% 3.40/1.24 % (768768)Peak memory usage: 88 MB
% 3.40/1.24 % (768768)Instructions burned: 1 (million)
% 3.40/1.24 % (768766)First to succeed.
% 3.40/1.24 % (768767)Also succeeded, but the first one will report.
% 3.40/1.24 % (768766)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-768757"
% 3.40/1.24 % (768765)Also succeeded, but the first one will report.
% 3.40/1.24 % (768768)------------------------------
% 3.40/1.24 % (768768)------------------------------
% 3.40/1.24 % (768766)Refutation found. Thanks to Tanya!
% 3.40/1.24 % SZS status Theorem for theBenchmark
% 3.40/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 3.40/1.24 % (768766)------------------------------
% 3.40/1.24 % (768766)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.24 % (768766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.24 % (768766)CaDiCaL version: 2.1.3
% 3.40/1.24 % (768766)Termination reason: Refutation
% 3.40/1.24 % (768766)Time elapsed: 0.003 s
% 3.40/1.24 % (768766)Peak memory usage: 88 MB
% 3.40/1.24 % (768766)Instructions burned: 2 (million)
% 3.40/1.24 % (768766)------------------------------
% 3.40/1.24 % (768766)------------------------------
% 3.40/1.24 % (768757)Success in time 0.43 s
% 3.40/1.24 % Vampire exiting
%------------------------------------------------------------------------------