%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU502_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 12:49:20 PM UTC 2026
% Result : Theorem 3.39s 1.37s
% Output : Refutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 14 unt; 0 typ; 4 def)
% Number of atoms : 102 ( 8 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 60 ( 26 ~; 16 |; 2 &)
% ( 5 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 46 ( 33 fml; 13 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 25 ( 0 sgn 24 !; 1 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
tff(pred_def_3,type,
sQ1_eqProxy: ( $o * $o ) > $o ).
tff(f1,axiom,
( emptysetE
= ( ! [X0: $i] :
( in(X0,emptyset)
=> ! [X1: $o] : (X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
tff(f2,conjecture,
( emptysetE
=> ! [X0: $i] :
( in(X0,emptyset)
=> $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
tff(f3,negated_conjecture,
~ ( emptysetE
=> ! [X0: $i] :
( in(X0,emptyset)
=> $false ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f4,plain,
( emptysetE
= ( ! [X0: $i] :
( in(X0,emptyset)
=> ! [X1: $o] : (X1) ) ) ),
inference(rectify,[],[f1]) ).
tff(f5,plain,
( emptysetE
<=> ! [X0: $i] :
( in(X0,emptyset)
=> ! [X1: $o] : ( $true = (X1) ) ) ),
inference(fool_elimination,[],[f4]) ).
tff(f6,plain,
~ ( emptysetE
=> ! [X0: $i] : ~ in(X0,emptyset) ),
inference(true_and_false_elimination,[],[f3]) ).
tff(f7,plain,
~ ( emptysetE
=> ! [X0: $i] : ~ in(X0,emptyset) ),
inference(flattening,[],[f6]) ).
tff(f8,plain,
( emptysetE
=> ! [X0: $i] :
( in(X0,emptyset)
=> ! [X1: $o] : ( $true = (X1) ) ) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
tff(f9,plain,
( ! [X0: $i] :
( ! [X1: $o] : ( $true = (X1) )
| ~ in(X0,emptyset) )
| ~ emptysetE ),
inference(ennf_transformation,[],[f8]) ).
tff(f10,plain,
( ? [X0: $i] : in(X0,emptyset)
& emptysetE ),
inference(ennf_transformation,[],[f7]) ).
tff(f11,plain,
( in(sK0,emptyset)
& emptysetE ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f10]) ).
tff(f12,plain,
! [X0: $i,X1: $o] :
( ( $true = (X1) )
| ~ in(X0,emptyset)
| ~ emptysetE ),
inference(cnf_transformation,[],[f9]) ).
tff(f13,plain,
emptysetE,
inference(cnf_transformation,[],[f11]) ).
tff(f14,plain,
in(sK0,emptyset),
inference(cnf_transformation,[],[f11]) ).
tff(f15,plain,
$true != $false,
introduced(definition,[],[fool_distinctness_axiom]) ).
tff(f17,definition,
! [X0: $o,X1: $o] :
( sQ1_eqProxy((X0),(X1))
<=> ( (X0) = (X1) ) ),
introduced(definition,[new_symbols(definition,[sQ1_eqProxy])],[equality_proxy_definition]) ).
tff(f19,plain,
~ sQ1_eqProxy($true,$false),
inference(equality_proxy_replacement,[],[f15,f17]) ).
tff(f20,plain,
! [X0: $i,X1: $o] :
( sQ1_eqProxy($true,(X1))
| ~ in(X0,emptyset)
| ~ emptysetE ),
inference(equality_proxy_replacement,[],[f12,f17]) ).
tff(f24,definition,
( spl2_1
<=> emptysetE ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f25,plain,
( ~ emptysetE
| spl2_1 ),
inference(avatar_component_clause,[],[f24]) ).
tff(f27,definition,
( spl2_2
<=> ! [X0: $i] : ~ in(X0,emptyset) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f28,plain,
( ! [X0: $i] : ~ in(X0,emptyset)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f27]) ).
tff(f30,definition,
( spl2_3
<=> ! [X1: $o] : sQ1_eqProxy($true,(X1)) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
tff(f31,plain,
( ! [X1: $o] : sQ1_eqProxy($true,(X1))
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f30]) ).
tff(f32,plain,
( ~ spl2_1
| spl2_2
| spl2_3 ),
inference(avatar_split_clause,[],[f20,f30,f27,f24]) ).
tff(f33,plain,
( $false
| spl2_1 ),
inference(resolution,[],[f25,f13]) ).
tff(f34,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f33]) ).
tff(f35,plain,
( $false
| ~ spl2_3 ),
inference(resolution,[],[f19,f31]) ).
tff(f36,plain,
~ spl2_3,
inference(avatar_contradiction_clause,[],[f35]) ).
tff(f37,plain,
( $false
| ~ spl2_2 ),
inference(resolution,[],[f28,f14]) ).
tff(f38,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f37]) ).
cnf(s1,plain,
( ~ spl2_1
| spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f32]) ).
cnf(s2,plain,
spl2_1,
inference(sat_conversion,[],[f34]) ).
cnf(s3,plain,
~ spl2_3,
inference(sat_conversion,[],[f36]) ).
cnf(s4,plain,
~ spl2_2,
inference(sat_conversion,[],[f38]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s3,s4,s2]) ).
tff(f39,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU502_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n002.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 05:43:37 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 3.39/1.37 % (65071)Detected formulas, will run a generic FOF schedule.
% 3.39/1.37 % (65077)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=2163479519:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.39/1.37 % (65078)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=3884116480:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.39/1.37 % (65080)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2365021308:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.39/1.37 % (65079)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1111760440:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.39/1.37 % (65082)dis-21_1_sil=8000:lcm=predicate:random_seed=2911686701: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)
% 3.39/1.37 % (65076)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=2118498940:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.39/1.37 % (65080)Refutation not found, incomplete strategy
% 3.39/1.37 % (65080)------------------------------
% 3.39/1.37 % (65080)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.37 % (65080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.37 % (65080)CaDiCaL version: 2.1.3
% 3.39/1.37 % (65080)Termination reason: Refutation not found, incomplete strategy
% 3.39/1.37 % (65080)Time elapsed: 0.001 s
% 3.39/1.37 % (65079)Refutation not found, incomplete strategy
% 3.39/1.37 % (65079)------------------------------
% 3.39/1.37 % (65079)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.37 % (65080)Peak memory usage: 87 MB
% 3.39/1.37 % (65079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.37 % (65079)CaDiCaL version: 2.1.3
% 3.39/1.37 % (65079)Termination reason: Refutation not found, incomplete strategy
% 3.39/1.37 % (65079)Time elapsed: 0.001 s
% 3.39/1.37 % (65079)Peak memory usage: 87 MB
% 3.39/1.37 % (65082)First to succeed.
% 3.39/1.37 % (65082)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-65071"
% 3.39/1.37 % (65081)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2261499615:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.39/1.37 % (65081)Also succeeded, but the first one will report.
% 3.39/1.37 % (65079)------------------------------
% 3.39/1.37 % (65079)------------------------------
% 3.39/1.37 % (65080)------------------------------
% 3.39/1.37 % (65080)------------------------------
% 3.39/1.37 % (65082)Refutation found. Thanks to Tanya!
% 3.39/1.37 % SZS status Theorem for theBenchmark
% 3.39/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 3.39/1.37 % (65082)------------------------------
% 3.39/1.37 % (65082)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.37 % (65082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.37 % (65082)CaDiCaL version: 2.1.3
% 3.39/1.37 % (65082)Termination reason: Refutation
% 3.39/1.37 % (65082)Time elapsed: 0.002 s
% 3.39/1.37 % (65082)Peak memory usage: 89 MB
% 3.39/1.37 % (65082)Instructions burned: 1 (million)
% 3.39/1.37 % (65082)------------------------------
% 3.39/1.37 % (65082)------------------------------
% 3.39/1.37 % (65071)Success in time 0.413 s
% 3.39/1.37 % Vampire exiting
%------------------------------------------------------------------------------