%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET788+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 12:41:56 PM UTC 2026
% Result : Theorem 0.17s 1.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 1
% Syntax : Number of formulae : 24 ( 4 unt; 0 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 128 ( 47 ~; 50 |; 16 &)
% ( 11 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 59 ( 51 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0,X1] :
( equalish(X0,X1)
<=> ! [X2] :
( a_member_of(X2,X0)
<=> a_member_of(X2,X1) ) )
=> ! [X0,X1] :
( equalish(X0,X1)
<=> equalish(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f2,negated_conjecture,
~ ( ! [X0,X1] :
( equalish(X0,X1)
<=> ! [X2] :
( a_member_of(X2,X0)
<=> a_member_of(X2,X1) ) )
=> ! [X0,X1] :
( equalish(X0,X1)
<=> equalish(X1,X0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ! [X0,X1] :
( equalish(X0,X1)
<=> ! [X2] :
( a_member_of(X2,X0)
<=> a_member_of(X2,X1) ) )
=> ! [X3,X4] :
( equalish(X3,X4)
<=> equalish(X4,X3) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ? [X3,X4] :
( equalish(X3,X4)
<~> equalish(X4,X3) )
& ! [X0,X1] :
( equalish(X0,X1)
<=> ! [X2] :
( a_member_of(X2,X0)
<=> a_member_of(X2,X1) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ? [X3,X4] :
( ( ~ equalish(X4,X3)
| ~ equalish(X3,X4) )
& ( equalish(X4,X3)
| equalish(X3,X4) ) )
& ! [X0,X1] :
( ( equalish(X0,X1)
| ? [X2] :
( ( ~ a_member_of(X2,X1)
| ~ a_member_of(X2,X0) )
& ( a_member_of(X2,X1)
| a_member_of(X2,X0) ) ) )
& ( ! [X2] :
( ( a_member_of(X2,X0)
| ~ a_member_of(X2,X1) )
& ( a_member_of(X2,X1)
| ~ a_member_of(X2,X0) ) )
| ~ equalish(X0,X1) ) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
( ? [X0,X1] :
( ( ~ equalish(X1,X0)
| ~ equalish(X0,X1) )
& ( equalish(X1,X0)
| equalish(X0,X1) ) )
& ! [X2,X3] :
( ( equalish(X2,X3)
| ? [X4] :
( ( ~ a_member_of(X4,X3)
| ~ a_member_of(X4,X2) )
& ( a_member_of(X4,X3)
| a_member_of(X4,X2) ) ) )
& ( ! [X5] :
( ( a_member_of(X5,X2)
| ~ a_member_of(X5,X3) )
& ( a_member_of(X5,X3)
| ~ a_member_of(X5,X2) ) )
| ~ equalish(X2,X3) ) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ( ~ equalish(sK1,sK0)
| ~ equalish(sK0,sK1) )
& ( equalish(sK1,sK0)
| equalish(sK0,sK1) )
& ! [X2,X3] :
( ( equalish(X2,X3)
| ( ( ~ a_member_of(sK2(X2,X3),X3)
| ~ a_member_of(sK2(X2,X3),X2) )
& ( a_member_of(sK2(X2,X3),X3)
| a_member_of(sK2(X2,X3),X2) ) ) )
& ( ! [X5] :
( ( a_member_of(X5,X2)
| ~ a_member_of(X5,X3) )
& ( a_member_of(X5,X3)
| ~ a_member_of(X5,X2) ) )
| ~ equalish(X2,X3) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X4,sK2(X2,X3))],[f6]) ).
fof(f8,plain,
! [X2,X3,X5] :
( a_member_of(X5,X3)
| ~ a_member_of(X5,X2)
| ~ equalish(X2,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X2,X3,X5] :
( a_member_of(X5,X2)
| ~ a_member_of(X5,X3)
| ~ equalish(X2,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
! [X2,X3] :
( a_member_of(sK2(X2,X3),X3)
| equalish(X2,X3)
| a_member_of(sK2(X2,X3),X2) ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X2,X3] :
( ~ a_member_of(sK2(X2,X3),X3)
| equalish(X2,X3)
| ~ a_member_of(sK2(X2,X3),X2) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
( equalish(sK1,sK0)
| equalish(sK0,sK1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
( ~ equalish(sK1,sK0)
| ~ equalish(sK0,sK1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f16,plain,
! [X2,X0,X1] :
( ~ a_member_of(sK2(X0,X1),X2)
| ~ a_member_of(sK2(X0,X1),X0)
| equalish(X0,X1)
| ~ equalish(X1,X2) ),
inference(resolution,[],[f11,f9]) ).
fof(f28,plain,
! [X0,X1] :
( ~ a_member_of(sK2(X0,X1),X0)
| equalish(X0,X1)
| ~ equalish(X1,X0) ),
inference(factoring,[],[f16]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ a_member_of(sK2(X0,X1),X2)
| ~ equalish(X1,X0)
| equalish(X0,X1)
| ~ equalish(X2,X0) ),
inference(resolution,[],[f28,f8]) ).
fof(f48,plain,
! [X0,X1] :
( ~ equalish(X0,X1)
| equalish(X1,X0)
| ~ equalish(X0,X1)
| equalish(X1,X0)
| a_member_of(sK2(X1,X0),X1) ),
inference(resolution,[],[f37,f10]) ).
fof(f51,plain,
! [X0,X1] :
( ~ equalish(X0,X1)
| equalish(X1,X0)
| a_member_of(sK2(X1,X0),X1) ),
inference(duplicate_literal_removal,[],[f48]) ).
fof(f52,plain,
! [X0,X1] :
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(forward_subsumption_resolution,[],[f51,f28]) ).
fof(f58,plain,
( ~ equalish(sK0,sK1)
| ~ equalish(sK0,sK1) ),
inference(resolution,[],[f52,f13]) ).
fof(f59,plain,
~ equalish(sK0,sK1),
inference(duplicate_literal_removal,[],[f58]) ).
fof(f65,plain,
~ equalish(sK1,sK0),
inference(resolution,[],[f59,f52]) ).
fof(f66,plain,
equalish(sK0,sK1),
inference(resolution,[],[f65,f12]) ).
fof(f68,plain,
$false,
inference(forward_subsumption_resolution,[],[f66,f59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET788+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n020.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 02:50:19 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 0.17/1.50 % (3984414)Detected formulas, will run a generic FOF schedule.
% 0.17/1.50 % (3984419)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=2502271384:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.17/1.50 % (3984424)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3360160750:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.17/1.50 % (3984422)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=457461641:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.17/1.50 % (3984421)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=1855820719:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.17/1.50 % (3984420)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=1588535030:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.17/1.50 % (3984425)dis-21_1_sil=8000:lcm=predicate:random_seed=3931722087: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)
% 0.17/1.50 % (3984423)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1653235445:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.17/1.50 % (3984423)First to succeed.
% 0.17/1.50 % (3984425)Also succeeded, but the first one will report.
% 0.17/1.50 % (3984422)Also succeeded, but the first one will report.
% 0.17/1.50 % (3984424)Also succeeded, but the first one will report.
% 0.17/1.50 % (3984423)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3984414"
% 0.17/1.50 % (3984423)Refutation found. Thanks to Tanya!
% 0.17/1.50 % SZS status Theorem for theBenchmark
% 0.17/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.50 % (3984423)------------------------------
% 0.17/1.50 % (3984423)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (3984423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (3984423)CaDiCaL version: 2.1.3
% 0.17/1.50 % (3984423)Termination reason: Refutation
% 0.17/1.50 % (3984423)Time elapsed: 0.003 s
% 0.17/1.50 % (3984423)Peak memory usage: 88 MB
% 0.17/1.50 % (3984423)Instructions burned: 2 (million)
% 0.17/1.50 % (3984423)------------------------------
% 0.17/1.50 % (3984423)------------------------------
% 0.17/1.50 % (3984414)Success in time 0.434 s
% 0.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------