%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET881+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 : n003.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 12:42:14 PM UTC 2026
% Result : Theorem 2.56s 1.32s
% Output : Refutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 11 unt; 0 def)
% Number of atoms : 86 ( 59 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 106 ( 42 ~; 40 |; 21 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 48 ( 43 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f3,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(f5,axiom,
! [X0,X1] :
( set_difference(singleton(X0),X1) = empty_set
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).
fof(f8,conjecture,
! [X0,X1] : set_difference(singleton(X0),unordered_pair(X0,X1)) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1] : set_difference(singleton(X0),unordered_pair(X0,X1)) = empty_set,
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,plain,
? [X0,X1] : empty_set != set_difference(singleton(X0),unordered_pair(X0,X1)),
inference(ennf_transformation,[],[f9]) ).
fof(f12,plain,
empty_set != set_difference(singleton(sK0),unordered_pair(sK0,sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f10]) ).
fof(f13,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,[],[f3]) ).
fof(f14,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,[],[f13]) ).
fof(f15,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,[],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ( ( ( sK2(X0,X1,X2) != X0
& sK2(X0,X1,X2) != X1 )
| ~ in(sK2(X0,X1,X2),X2) )
& ( sK2(X0,X1,X2) = X0
| sK2(X0,X1,X2) = X1
| in(sK2(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,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( set_difference(singleton(X0),X1) = empty_set
| ~ in(X0,X1) )
& ( in(X0,X1)
| empty_set != set_difference(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f20,plain,
empty_set != set_difference(singleton(sK0),unordered_pair(sK0,sK1)),
inference(cnf_transformation,[],[f12]) ).
fof(f22,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X1 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f30,plain,
! [X0,X1] :
( empty_set = set_difference(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f36,plain,
! [X2,X0,X4] :
( in(X4,X2)
| unordered_pair(X0,X4) != X2 ),
inference(equality_resolution,[],[f22]) ).
fof(f37,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f36]) ).
fof(f42,plain,
empty_set != set_difference(singleton(sK0),unordered_pair(sK1,sK0)),
inference(superposition,[],[f20,f27]) ).
fof(f51,plain,
( empty_set != empty_set
| ~ in(sK0,unordered_pair(sK1,sK0)) ),
inference(superposition,[],[f42,f30]) ).
fof(f53,plain,
~ in(sK0,unordered_pair(sK1,sK0)),
inference(trivial_inequality_removal,[],[f51]) ).
fof(f55,plain,
$false,
inference(forward_subsumption_resolution,[],[f53,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET881+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n003.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 03:07:57 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.56/1.32 % (1144675)Detected formulas, will run a generic FOF schedule.
% 2.56/1.32 % (1144684)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=630687912:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.56/1.32 % (1144684)First to succeed.
% 2.56/1.32 % (1144684)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1144675"
% 2.56/1.32 % (1144686)dis-21_1_sil=8000:lcm=predicate:random_seed=3298672909: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)
% 2.56/1.32 % (1144686)Also succeeded, but the first one will report.
% 2.56/1.32 % (1144683)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=506540857:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.56/1.32 % (1144681)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=4104874563:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.56/1.32 % (1144680)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=404290655:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.56/1.32 % (1144682)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=1960672422:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.56/1.32 % (1144683)Also succeeded, but the first one will report.
% 2.56/1.32 % (1144685)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=536244595:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.56/1.32 % (1144685)Also succeeded, but the first one will report.
% 2.56/1.32 % (1144684)Refutation found. Thanks to Tanya!
% 2.56/1.32 % SZS status Theorem for theBenchmark
% 2.56/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.56/1.33 % (1144684)------------------------------
% 2.56/1.33 % (1144684)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.33 % (1144684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.33 % (1144684)CaDiCaL version: 2.1.3
% 2.56/1.33 % (1144684)Termination reason: Refutation
% 2.56/1.33 % (1144684)Time elapsed: 0.001 s
% 2.56/1.33 % (1144684)Peak memory usage: 89 MB
% 2.56/1.33 % (1144684)Instructions burned: 2 (million)
% 2.56/1.33 % (1144684)------------------------------
% 2.56/1.33 % (1144684)------------------------------
% 2.56/1.33 % (1144675)Success in time 0.272 s
% 2.56/1.33 % Vampire exiting
%------------------------------------------------------------------------------