%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU527_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:49:27 PM UTC 2026
% Result : Theorem 3.57s 1.37s
% Output : Refutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 167 ( 45 equ)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 93 ( 23 ~; 23 |; 13 &)
% ( 2 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 107 ( 74 fml; 33 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 60 ( 56 !; 4 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
tff(f1,axiom,
( emptysetE
= ( ! [X0: $i] :
( in(X0,emptyset)
=> ! [X1: $o] : (X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
tff(f2,axiom,
( setadjoinE
= ( ! [X0: $i,X1: $i,X2: $i] :
( in(X2,setadjoin(X0,X1))
=> ! [X3: $o] :
( ( ( X2 = X0 )
=> (X3) )
=> ( ( in(X2,X1)
=> (X3) )
=> (X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).
tff(f3,conjecture,
( emptysetE
=> ( setadjoinE
=> ! [X0: $i,X1: $i] :
( in(X0,setadjoin(X1,emptyset))
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
tff(f4,negated_conjecture,
~ ( emptysetE
=> ( setadjoinE
=> ! [X0: $i,X1: $i] :
( in(X0,setadjoin(X1,emptyset))
=> ( X0 = X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
tff(f5,plain,
( emptysetE
= ( ! [X0: $i] :
( in(X0,emptyset)
=> ! [X1: $o] : (X1) ) ) ),
inference(rectify,[],[f1]) ).
tff(f6,plain,
( emptysetE
<=> ! [X0: $i] :
( in(X0,emptyset)
=> ! [X1: $o] : ( $true = (X1) ) ) ),
inference(fool_elimination,[],[f5]) ).
tff(f7,plain,
( setadjoinE
= ( ! [X0: $i,X1: $i,X2: $i] :
( in(X2,setadjoin(X0,X1))
=> ! [X3: $o] :
( ( ( X2 = X0 )
=> (X3) )
=> ( ( in(X2,X1)
=> (X3) )
=> (X3) ) ) ) ) ),
inference(rectify,[],[f2]) ).
tff(f8,plain,
( setadjoinE
<=> ! [X0: $i,X1: $i,X2: $i] :
( in(X2,setadjoin(X0,X1))
=> ! [X3: $o] :
( ( ( X0 = X2 )
=> ( $true = (X3) ) )
=> ( ( in(X2,X1)
=> ( $true = (X3) ) )
=> ( $true = (X3) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
tff(f9,plain,
( setadjoinE
=> ! [X0: $i,X1: $i,X2: $i] :
( in(X2,setadjoin(X0,X1))
=> ! [X3: $o] :
( ( ( X0 = X2 )
=> ( $true = (X3) ) )
=> ( ( in(X2,X1)
=> ( $true = (X3) ) )
=> ( $true = (X3) ) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
tff(f10,plain,
( emptysetE
=> ! [X0: $i] :
( in(X0,emptyset)
=> ! [X1: $o] : ( $true = (X1) ) ) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
tff(f11,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& in(X0,setadjoin(X1,emptyset)) )
& setadjoinE
& emptysetE ),
inference(ennf_transformation,[],[f4]) ).
tff(f12,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& in(X0,setadjoin(X1,emptyset)) )
& setadjoinE
& emptysetE ),
inference(flattening,[],[f11]) ).
tff(f13,plain,
( ! [X0: $i] :
( ! [X1: $o] : ( $true = (X1) )
| ~ in(X0,emptyset) )
| ~ emptysetE ),
inference(ennf_transformation,[],[f10]) ).
tff(f14,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $o] :
( ( $true = (X3) )
| ( ( $true != (X3) )
& in(X2,X1) )
| ( ( $true != (X3) )
& ( X0 = X2 ) ) )
| ~ in(X2,setadjoin(X0,X1)) )
| ~ setadjoinE ),
inference(ennf_transformation,[],[f9]) ).
tff(f15,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $o] :
( ( $true = (X3) )
| ( ( $true != (X3) )
& in(X2,X1) )
| ( ( $true != (X3) )
& ( X0 = X2 ) ) )
| ~ in(X2,setadjoin(X0,X1)) )
| ~ setadjoinE ),
inference(flattening,[],[f14]) ).
tff(f16,plain,
( ( sK0 != sK1 )
& in(sK0,setadjoin(sK1,emptyset))
& setadjoinE
& emptysetE ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f12]) ).
tff(f17,plain,
emptysetE,
inference(cnf_transformation,[],[f16]) ).
tff(f18,plain,
setadjoinE,
inference(cnf_transformation,[],[f16]) ).
tff(f19,plain,
in(sK0,setadjoin(sK1,emptyset)),
inference(cnf_transformation,[],[f16]) ).
tff(f20,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f16]) ).
tff(f21,plain,
! [X0: $i,X1: $o] :
( ( $true = (X1) )
| ~ in(X0,emptyset)
| ~ emptysetE ),
inference(cnf_transformation,[],[f13]) ).
tff(f22,plain,
! [X2: $i,X3: $o,X0: $i,X1: $i] :
( ( $true = (X3) )
| in(X2,X1)
| ( X0 = X2 )
| ~ in(X2,setadjoin(X0,X1))
| ~ setadjoinE ),
inference(cnf_transformation,[],[f15]) ).
tff(f26,plain,
$true != $false,
introduced(definition,[],[fool_distinctness_axiom]) ).
tff(f34,plain,
! [X0: $i,X1: $o] :
( ~ in(X0,emptyset)
| ( $true = (X1) ) ),
inference(forward_subsumption_resolution,[],[f21,f17]) ).
tff(f35,plain,
! [X2: $i,X3: $o,X0: $i,X1: $i] :
( ~ in(X2,setadjoin(X0,X1))
| in(X2,X1)
| ( X0 = X2 )
| ( $true = (X3) ) ),
inference(forward_subsumption_resolution,[],[f22,f18]) ).
tff(f36,plain,
! [X0: $o] :
( in(sK0,emptyset)
| ( sK0 = sK1 )
| ( $true = (X0) ) ),
inference(resolution,[],[f35,f19]) ).
tff(f37,plain,
! [X0: $o] :
( ( sK0 = sK1 )
| ( $true = (X0) ) ),
inference(forward_subsumption_resolution,[],[f36,f34]) ).
tff(f38,plain,
! [X0: $o] : ( $true = (X0) ),
inference(forward_subsumption_resolution,[],[f37,f20]) ).
tff(f39,plain,
! [X0: $o,X1: $o] : ( (X0) = (X1) ),
inference(superposition,[],[f38,f38]) ).
tff(f59,plain,
! [X0: $o] : ( $false != (X0) ),
inference(superposition,[],[f26,f39]) ).
tff(f61,plain,
$false,
inference(forward_subsumption_resolution,[],[f59,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU527_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 05:42:54 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 3.57/1.37 % (1955615)Detected formulas, will run a generic FOF schedule.
% 3.57/1.37 % (1955621)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=757359928:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.57/1.37 % (1955620)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=1495991320:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.57/1.37 % (1955622)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=89788065:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.57/1.37 % (1955623)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=528335486:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.57/1.37 % (1955623)Refutation not found, incomplete strategy
% 3.57/1.37 % (1955623)------------------------------
% 3.57/1.37 % (1955623)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.37 % (1955623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.37 % (1955623)CaDiCaL version: 2.1.3
% 3.57/1.37 % (1955623)Termination reason: Refutation not found, incomplete strategy
% 3.57/1.37 % (1955623)Time elapsed: 0.002 s
% 3.57/1.37 % (1955623)Peak memory usage: 88 MB
% 3.57/1.37 % (1955623)Instructions burned: 1 (million)
% 3.57/1.37 % (1955626)dis-21_1_sil=8000:lcm=predicate:random_seed=896064786: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)
% 3.57/1.37 % (1955624)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3867823223:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.57/1.37 % (1955625)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=171100713:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.57/1.37 % (1955624)First to succeed.
% 3.57/1.37 % (1955626)Also succeeded, but the first one will report.
% 3.57/1.37 % (1955624)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1955615"
% 3.57/1.37 % (1955625)Also succeeded, but the first one will report.
% 3.57/1.37 % (1955623)------------------------------
% 3.57/1.37 % (1955623)------------------------------
% 3.57/1.37 % (1955624)Refutation found. Thanks to Tanya!
% 3.57/1.37 % SZS status Theorem for theBenchmark
% 3.57/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 3.57/1.37 % (1955624)------------------------------
% 3.57/1.37 % (1955624)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.37 % (1955624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.37 % (1955624)CaDiCaL version: 2.1.3
% 3.57/1.37 % (1955624)Termination reason: Refutation
% 3.57/1.37 % (1955624)Time elapsed: 0.003 s
% 3.57/1.37 % (1955624)Peak memory usage: 88 MB
% 3.57/1.37 % (1955624)Instructions burned: 2 (million)
% 3.57/1.37 % (1955624)------------------------------
% 3.57/1.37 % (1955624)------------------------------
% 3.57/1.37 % (1955615)Success in time 0.44 s
% 3.57/1.37 % Vampire exiting
%------------------------------------------------------------------------------