%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU173+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:47:34 PM UTC 2026
% Result : Theorem 2.45s 1.32s
% Output : Refutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 70 ( 14 unt; 4 def)
% Number of atoms : 237 ( 27 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 273 ( 106 ~; 109 |; 38 &)
% ( 13 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 113 ( 0 sgn 105 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f10,axiom,
! [X0,X1] :
( ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) )
& ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f17,axiom,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& ~ in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f34,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f35,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f49,axiom,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(f55,conjecture,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
=> element(X0,powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l71_subset_1) ).
fof(f56,negated_conjecture,
~ ! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
=> element(X0,powerset(X1)) ),
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f103,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f128,plain,
! [X0,X1] :
( ( ( element(X1,X0)
<=> in(X1,X0) )
| empty(X0) )
& ( ( element(X1,X0)
<=> empty(X1) )
| ~ empty(X0) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f144,plain,
? [X0,X1] :
( ~ element(X0,powerset(X1))
& ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f56]) ).
fof(f176,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f103]) ).
fof(f195,plain,
! [X0,X1] :
( ( X1 = powerset(X0)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0) )
& ( subset(X2,X0)
| ~ in(X2,X1) ) )
| powerset(X0) != X1 ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f196,plain,
! [X0,X1] :
( ( X1 = powerset(X0)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(rectify,[],[f195]) ).
fof(f197,plain,
! [X0,X1] :
( ( X1 = powerset(X0)
| ( ( ~ subset(sK2(X0,X1),X0)
| ~ in(sK2(X0,X1),X1) )
& ( subset(sK2(X0,X1),X0)
| in(sK2(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f196]) ).
fof(f198,plain,
! [X0,X1] :
( ( ( ( element(X1,X0)
| ~ in(X1,X0) )
& ( in(X1,X0)
| ~ element(X1,X0) ) )
| empty(X0) )
& ( ( ( element(X1,X0)
| ~ empty(X1) )
& ( empty(X1)
| ~ element(X1,X0) ) )
| ~ empty(X0) ) ),
inference(nnf_transformation,[],[f128]) ).
fof(f220,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f221,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f220]) ).
fof(f222,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( ( in(X4,X0)
& ~ in(X4,X1) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f221]) ).
fof(f223,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ( ( ~ in(sK15(X0,X1,X2),X0)
| in(sK15(X0,X1,X2),X1)
| ~ in(sK15(X0,X1,X2),X2) )
& ( ( in(sK15(X0,X1,X2),X0)
& ~ in(sK15(X0,X1,X2),X1) )
| in(sK15(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( ( in(X4,X0)
& ~ in(X4,X1) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X3,sK15(X0,X1,X2))],[f222]) ).
fof(f225,plain,
! [X0] : element(sK16(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X1,sK16(X0))],[f34]) ).
fof(f227,plain,
! [X0,X1] :
( ( set_difference(X0,X1) = empty_set
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f49]) ).
fof(f232,plain,
( ~ element(sK17,powerset(sK18))
& ! [X2] :
( in(X2,sK18)
| ~ in(X2,sK17) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18]),skolemize(X0,sK17),skolemize(X1,sK18)],[f144]) ).
fof(f269,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ subset(X3,X0)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f197]) ).
fof(f274,plain,
! [X0,X1] :
( ~ element(X1,X0)
| in(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f275,plain,
! [X0,X1] :
( element(X1,X0)
| ~ in(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f311,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f223]) ).
fof(f312,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f223]) ).
fof(f323,plain,
! [X0] : element(sK16(X0),X0),
inference(cnf_transformation,[],[f225]) ).
fof(f324,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f35]) ).
fof(f339,plain,
! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) ),
inference(cnf_transformation,[],[f227]) ).
fof(f350,plain,
! [X2] :
( in(X2,sK18)
| ~ in(X2,sK17) ),
inference(cnf_transformation,[],[f232]) ).
fof(f351,plain,
~ element(sK17,powerset(sK18)),
inference(cnf_transformation,[],[f232]) ).
fof(f418,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f176]) ).
fof(f497,plain,
! [X3,X0] :
( ~ subset(X3,X0)
| in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f269]) ).
fof(f519,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f312]) ).
fof(f520,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f311]) ).
fof(f525,definition,
! [X0,X1] :
( sQ29_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ29_eqProxy])],[equality_proxy_definition]) ).
fof(f567,plain,
! [X0,X1] :
( ~ sQ29_eqProxy(empty_set,set_difference(X0,X1))
| subset(X0,X1) ),
inference(equality_proxy_replacement,[],[f339,f525]) ).
fof(f592,plain,
! [X0] :
( sQ29_eqProxy(empty_set,X0)
| ~ empty(X0) ),
inference(equality_proxy_replacement,[],[f418,f525]) ).
fof(f666,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ empty(set_difference(X0,X1)) ),
inference(resolution,[],[f567,f592]) ).
fof(f674,definition,
( spl30_2
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ empty(set_difference(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl30_2])],[avatar_definition]) ).
fof(f675,plain,
( ! [X0,X1] :
( ~ empty(set_difference(X0,X1))
| subset(X0,X1) )
| ~ spl30_2 ),
inference(avatar_component_clause,[],[f674]) ).
fof(f677,plain,
spl30_2,
inference(avatar_split_clause,[],[f666,f674]) ).
fof(f690,plain,
! [X0] :
( empty(X0)
| in(sK16(X0),X0) ),
inference(resolution,[],[f274,f323]) ).
fof(f701,plain,
( ! [X0,X1] :
( subset(X0,X1)
| in(sK16(set_difference(X0,X1)),set_difference(X0,X1)) )
| ~ spl30_2 ),
inference(resolution,[],[f690,f675]) ).
fof(f707,plain,
( ! [X0,X1] :
( in(sK16(set_difference(X0,X1)),set_difference(X0,X1))
| in(X0,powerset(X1)) )
| ~ spl30_2 ),
inference(resolution,[],[f701,f497]) ).
fof(f714,plain,
( ~ in(sK17,powerset(sK18))
| empty(powerset(sK18)) ),
inference(resolution,[],[f275,f351]) ).
fof(f719,definition,
( spl30_3
<=> empty(powerset(sK18)) ),
introduced(definition,[new_symbols(definition,[spl30_3])],[avatar_definition]) ).
fof(f720,plain,
( empty(powerset(sK18))
| ~ spl30_3 ),
inference(avatar_component_clause,[],[f719]) ).
fof(f722,definition,
( spl30_4
<=> in(sK17,powerset(sK18)) ),
introduced(definition,[new_symbols(definition,[spl30_4])],[avatar_definition]) ).
fof(f723,plain,
( ~ in(sK17,powerset(sK18))
| spl30_4 ),
inference(avatar_component_clause,[],[f722]) ).
fof(f724,plain,
( spl30_3
| ~ spl30_4 ),
inference(avatar_split_clause,[],[f714,f722,f719]) ).
fof(f750,plain,
( ! [X0,X1] :
( in(sK16(set_difference(X0,X1)),X0)
| in(X0,powerset(X1)) )
| ~ spl30_2 ),
inference(resolution,[],[f519,f707]) ).
fof(f812,plain,
( ! [X0,X1] :
( ~ in(sK16(set_difference(X0,X1)),X1)
| in(X0,powerset(X1)) )
| ~ spl30_2 ),
inference(resolution,[],[f520,f707]) ).
fof(f821,plain,
( ! [X0] :
( ~ in(sK16(set_difference(X0,sK18)),sK17)
| in(X0,powerset(sK18)) )
| ~ spl30_2 ),
inference(resolution,[],[f812,f350]) ).
fof(f824,plain,
( in(sK17,powerset(sK18))
| in(sK17,powerset(sK18))
| ~ spl30_2 ),
inference(resolution,[],[f821,f750]) ).
fof(f827,plain,
( in(sK17,powerset(sK18))
| ~ spl30_2 ),
inference(duplicate_literal_removal,[],[f824]) ).
fof(f835,plain,
( $false
| ~ spl30_2
| spl30_4 ),
inference(resolution,[],[f827,f723]) ).
fof(f836,plain,
( ~ spl30_2
| spl30_4 ),
inference(avatar_contradiction_clause,[],[f835]) ).
fof(f837,plain,
( $false
| ~ spl30_3 ),
inference(resolution,[],[f720,f324]) ).
fof(f841,plain,
~ spl30_3,
inference(avatar_contradiction_clause,[],[f837]) ).
cnf(s2,plain,
spl30_2,
inference(sat_conversion,[],[f677]) ).
cnf(s3,plain,
( spl30_3
| ~ spl30_4 ),
inference(sat_conversion,[],[f724]) ).
cnf(s4,plain,
( ~ spl30_2
| spl30_4 ),
inference(sat_conversion,[],[f836]) ).
cnf(s5,plain,
~ spl30_3,
inference(sat_conversion,[],[f841]) ).
cnf(s6,plain,
~ spl30_4,
inference(rat,[],[s3,s5]) ).
cnf(s7,plain,
~ spl30_2,
inference(rat,[],[s4,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s2,s7]) ).
fof(f842,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU173+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n020.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 03:54:04 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.45/1.32 % (4009303)Detected formulas, will run a generic FOF schedule.
% 2.45/1.32 % (4009308)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=2396396502:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.45/1.32 % (4009310)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=547552351:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.45/1.32 % (4009314)dis-21_1_sil=8000:lcm=predicate:random_seed=1170046279: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)
% 2.45/1.32 % (4009312)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3569257414:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.45/1.32 % (4009309)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=2151960694:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.45/1.32 % (4009311)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2313882699:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.45/1.32 % (4009313)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1210684830:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.45/1.32 % (4009314)First to succeed.
% 2.45/1.32 % (4009314)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4009303"
% 2.45/1.32 % (4009312)Also succeeded, but the first one will report.
% 2.45/1.32 % (4009313)Also succeeded, but the first one will report.
% 2.45/1.32 % (4009311)Instruction limit reached!
% 2.45/1.32 % (4009311)------------------------------
% 2.45/1.32 % (4009311)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.45/1.32 % (4009311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.45/1.32 % (4009311)CaDiCaL version: 2.1.3
% 2.45/1.32 % (4009311)Termination reason: Instruction limit
% 2.45/1.32 % (4009311)Termination phase: Saturation
% 2.45/1.32 % (4009311)Time elapsed: 0.072 s
% 2.45/1.32 % (4009311)Peak memory usage: 89 MB
% 2.45/1.32 % (4009311)Instructions burned: 109 (million)
% 2.45/1.32 % (4009322)lrs+10_1_sil=8000:sp=occurrence:random_seed=839195321:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.45/1.32 % (4009314)Refutation found. Thanks to Tanya!
% 2.45/1.32 % SZS status Theorem for theBenchmark
% 2.45/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.77/1.51 % (4009314)------------------------------
% 3.77/1.51 % (4009314)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.51 % (4009314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.51 % (4009314)CaDiCaL version: 2.1.3
% 3.77/1.51 % (4009314)Termination reason: Refutation
% 3.77/1.51 % (4009314)Time elapsed: 0.011 s
% 3.77/1.51 % (4009314)Peak memory usage: 89 MB
% 3.77/1.51 % (4009314)Instructions burned: 16 (million)
% 3.77/1.51 % (4009314)------------------------------
% 3.77/1.51 % (4009314)------------------------------
% 3.77/1.51 % (4009303)Success in time 0.448 s
% 3.77/1.51 % Vampire exiting
%------------------------------------------------------------------------------