%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET874+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 : n016.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 2.77s 21.61s
% Output : Refutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 10 unt; 1 def)
% Number of atoms : 87 ( 55 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 106 ( 42 ~; 40 |; 20 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 50 ( 45 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X0
| X3 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f8,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).
fof(f11,conjecture,
! [X0,X1] : set_union2(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] : set_union2(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(X0,X1),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f17,plain,
! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f18,plain,
? [X0,X1] : unordered_pair(X0,X1) != set_union2(singleton(X0),unordered_pair(X0,X1)),
inference(ennf_transformation,[],[f12]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( X3 = X0
| X3 = X1
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( X3 = X0
| X3 = X1
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ( ( ( sK0(X0,X1,X2) != X0
& sK0(X0,X1,X2) != X1 )
| ~ in(sK0(X0,X1,X2),X2) )
& ( sK0(X0,X1,X2) = X0
| sK0(X0,X1,X2) = X1
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f21]) ).
fof(f25,plain,
unordered_pair(sK3,sK4) != set_union2(singleton(sK3),unordered_pair(sK3,sK4)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f18]) ).
fof(f31,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f38,plain,
! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f41,plain,
unordered_pair(sK3,sK4) != set_union2(singleton(sK3),unordered_pair(sK3,sK4)),
inference(cnf_transformation,[],[f25]) ).
fof(f42,plain,
! [X2,X1,X4] :
( in(X4,X2)
| unordered_pair(X4,X1) != X2 ),
inference(equality_resolution,[],[f31]) ).
fof(f43,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f42]) ).
fof(f47,definition,
! [X0,X1] :
( sQ5_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ5_eqProxy])],[equality_proxy_definition]) ).
fof(f55,plain,
! [X0,X1] :
( sQ5_eqProxy(set_union2(singleton(X0),X1),X1)
| ~ in(X0,X1) ),
inference(equality_proxy_replacement,[],[f38,f47]) ).
fof(f56,plain,
~ sQ5_eqProxy(unordered_pair(sK3,sK4),set_union2(singleton(sK3),unordered_pair(sK3,sK4))),
inference(equality_proxy_replacement,[],[f41,f47]) ).
fof(f58,plain,
! [X0,X1] :
( sQ5_eqProxy(X1,X0)
| ~ sQ5_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f47]) ).
fof(f60,plain,
~ sQ5_eqProxy(set_union2(singleton(sK3),unordered_pair(sK3,sK4)),unordered_pair(sK3,sK4)),
inference(resolution,[],[f58,f56]) ).
fof(f62,plain,
~ in(sK3,unordered_pair(sK3,sK4)),
inference(resolution,[],[f55,f60]) ).
fof(f63,plain,
$false,
inference(resolution,[],[f62,f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET874+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 % Computer : n016.cluster.edu
% 0.13/0.42 % Model : x86_64 x86_64
% 0.13/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.42 % Memory : 8046.5625MB
% 0.13/0.42 % OS : Linux 6.8.0-71-generic
% 0.11/20.66 % CPULimit : 300
% 0.11/20.66 % WCLimit : 300
% 0.11/20.66 % DateTime : Mon Sep 28 03:06:21 UTC 2026
% 0.11/20.67 % CPUTime :
% 0.11/20.67 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.35/20.70 Running first-order theorem proving
% 0.35/20.70 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
% 2.77/21.61 % (1827159)Detected formulas, will run a generic FOF schedule.
% 2.77/21.61 % (1827170)dis-21_1_sil=8000:lcm=predicate:random_seed=3482812054: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)
% 2.77/21.61 % (1827170)First to succeed.
% 2.77/21.61 % (1827170)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1827159"
% 2.77/21.61 % (1827168)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3836003415:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.77/21.61 % (1827169)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=513981582:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.77/21.61 % (1827164)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=113607098:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.77/21.61 % (1827167)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4258224541:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.77/21.61 % (1827165)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=2283485747:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.77/21.61 % (1827166)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=2294094548:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.77/21.61 % (1827167)Also succeeded, but the first one will report.
% 2.77/21.61 % (1827168)Also succeeded, but the first one will report.
% 2.77/21.61 % (1827169)Also succeeded, but the first one will report.
% 2.77/21.61 % (1827170)Refutation found. Thanks to Tanya!
% 2.77/21.61 % SZS status Theorem for theBenchmark
% 2.77/21.61 % SZS output start Proof for theBenchmark
% See solution above
% 2.77/21.61 % (1827170)------------------------------
% 2.77/21.61 % (1827170)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/21.61 % (1827170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/21.61 % (1827170)CaDiCaL version: 2.1.3
% 2.77/21.61 % (1827170)Termination reason: Refutation
% 2.77/21.61 % (1827170)Time elapsed: 0.001 s
% 2.77/21.61 % (1827170)Peak memory usage: 88 MB
% 2.77/21.61 % (1827170)Instructions burned: 1 (million)
% 2.77/21.61 % (1827170)------------------------------
% 2.77/21.61 % (1827170)------------------------------
% 2.77/21.61 % (1827159)Success in time 0.271 s
% 2.77/21.61 % Vampire exiting
%------------------------------------------------------------------------------