%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU171+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 : n013.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 2.99s 1.17s
% Output : Refutation 2.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 12 unt; 1 def)
% Number of atoms : 164 ( 23 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 191 ( 72 ~; 62 |; 38 &)
% ( 7 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 60 ( 0 sgn 51 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
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(f18,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,X1) = set_difference(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
fof(f95,conjecture,
! [X0] :
( X0 != empty_set
=> ! [X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,X0)
=> ( ~ in(X2,X1)
=> in(X2,subset_complement(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).
fof(f96,negated_conjecture,
~ ! [X0] :
( X0 != empty_set
=> ! [X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,X0)
=> ( ~ in(X2,X1)
=> in(X2,subset_complement(X0,X1)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f101,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f126,plain,
! [X0,X1] :
( ( ( element(X1,X0)
<=> in(X1,X0) )
| empty(X0) )
& ( ( element(X1,X0)
<=> empty(X1) )
| ~ empty(X0) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f128,plain,
! [X0,X1] :
( subset_complement(X0,X1) = set_difference(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f166,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ in(X2,subset_complement(X0,X1))
& ~ in(X2,X1)
& element(X2,X0) )
& element(X1,powerset(X0)) )
& X0 != empty_set ),
inference(ennf_transformation,[],[f96]) ).
fof(f167,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ in(X2,subset_complement(X0,X1))
& ~ in(X2,X1)
& element(X2,X0) )
& element(X1,powerset(X0)) )
& X0 != empty_set ),
inference(flattening,[],[f166]) ).
fof(f171,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f101]) ).
fof(f193,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,[],[f126]) ).
fof(f215,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(f216,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,[],[f215]) ).
fof(f217,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,[],[f216]) ).
fof(f218,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))],[f217]) ).
fof(f245,plain,
( ~ in(sK27,subset_complement(sK25,sK26))
& ~ in(sK27,sK26)
& element(sK27,sK25)
& element(sK26,powerset(sK25))
& empty_set != sK25 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25,sK26,sK27]),skolemize(X0,sK25),skolemize(X1,sK26),skolemize(X2,sK27)],[f167]) ).
fof(f269,plain,
! [X0,X1] :
( empty(X0)
| ~ element(X1,X0)
| in(X1,X0) ),
inference(cnf_transformation,[],[f193]) ).
fof(f308,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f218]) ).
fof(f312,plain,
! [X0,X1] :
( set_difference(X0,X1) = subset_complement(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f128]) ).
fof(f404,plain,
empty_set != sK25,
inference(cnf_transformation,[],[f245]) ).
fof(f405,plain,
element(sK26,powerset(sK25)),
inference(cnf_transformation,[],[f245]) ).
fof(f406,plain,
element(sK27,sK25),
inference(cnf_transformation,[],[f245]) ).
fof(f407,plain,
~ in(sK27,sK26),
inference(cnf_transformation,[],[f245]) ).
fof(f408,plain,
~ in(sK27,subset_complement(sK25,sK26)),
inference(cnf_transformation,[],[f245]) ).
fof(f414,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f171]) ).
fof(f457,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,X1))
| ~ in(X4,X0)
| in(X4,X1) ),
inference(equality_resolution,[],[f308]) ).
fof(f1084,definition,
( spl30_4
<=> empty(sK25) ),
introduced(definition,[new_symbols(definition,[spl30_4])],[avatar_definition]) ).
fof(f1085,plain,
( empty(sK25)
| ~ spl30_4 ),
inference(avatar_component_clause,[],[f1084]) ).
fof(f1086,plain,
( ~ empty(sK25)
| spl30_4 ),
inference(avatar_component_clause,[],[f1084]) ).
fof(f1105,plain,
( ! [X0] :
( ~ element(X0,sK25)
| in(X0,sK25) )
| spl30_4 ),
inference(resolution,[],[f1086,f269]) ).
fof(f1151,plain,
( in(sK27,sK25)
| spl30_4 ),
inference(resolution,[],[f1105,f406]) ).
fof(f1171,plain,
( ~ in(sK27,set_difference(sK25,sK26))
| ~ element(sK26,powerset(sK25)) ),
inference(superposition,[],[f408,f312]) ).
fof(f1174,plain,
~ in(sK27,set_difference(sK25,sK26)),
inference(forward_subsumption_resolution,[],[f1171,f405]) ).
fof(f1282,plain,
( ~ in(sK27,sK25)
| in(sK27,sK26) ),
inference(resolution,[],[f457,f1174]) ).
fof(f1291,plain,
( in(sK27,sK26)
| spl30_4 ),
inference(forward_subsumption_resolution,[],[f1282,f1151]) ).
fof(f1292,plain,
( $false
| spl30_4 ),
inference(forward_subsumption_resolution,[],[f1291,f407]) ).
fof(f1293,plain,
spl30_4,
inference(avatar_contradiction_clause,[],[f1292]) ).
fof(f1298,plain,
( empty_set = sK25
| ~ spl30_4 ),
inference(resolution,[],[f1085,f414]) ).
fof(f1299,plain,
( $false
| ~ spl30_4 ),
inference(forward_subsumption_resolution,[],[f1298,f404]) ).
fof(f1300,plain,
~ spl30_4,
inference(avatar_contradiction_clause,[],[f1299]) ).
cnf(s4,plain,
spl30_4,
inference(sat_conversion,[],[f1293]) ).
cnf(s5,plain,
~ spl30_4,
inference(sat_conversion,[],[f1300]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s4,s5]) ).
fof(f1301,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU171+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n013.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 03:52:07 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 2.99/1.17 % (785873)Detected formulas, will run a generic FOF schedule.
% 2.99/1.17 % (785883)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2844546383:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.99/1.17 % (785882)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3450347343:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.99/1.17 % (785880)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=1630279891:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.99/1.17 % (785878)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=1975389599:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.99/1.17 % (785884)dis-21_1_sil=8000:lcm=predicate:random_seed=2458078821: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)
% 2.99/1.17 % (785881)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1086493444:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.99/1.17 % (785879)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=901209357:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.99/1.17 % (785883)First to succeed.
% 2.99/1.17 % (785883)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-785873"
% 2.99/1.17 % (785881)Instruction limit reached!
% 2.99/1.17 % (785881)------------------------------
% 2.99/1.17 % (785881)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.17 % (785881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.17 % (785881)CaDiCaL version: 2.1.3
% 2.99/1.17 % (785881)Termination reason: Instruction limit
% 2.99/1.17 % (785881)Termination phase: Saturation
% 2.99/1.17 % (785881)Time elapsed: 0.071 s
% 2.99/1.17 % (785881)Peak memory usage: 89 MB
% 2.99/1.17 % (785881)Instructions burned: 110 (million)
% 2.99/1.17 % (785882)Instruction limit reached!
% 2.99/1.17 % (785882)------------------------------
% 2.99/1.17 % (785882)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.17 % (785882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.17 % (785882)CaDiCaL version: 2.1.3
% 2.99/1.17 % (785882)Termination reason: Instruction limit
% 2.99/1.17 % (785882)Termination phase: Saturation
% 2.99/1.17 % (785882)Time elapsed: 0.075 s
% 2.99/1.17 % (785882)Peak memory usage: 89 MB
% 2.99/1.17 % (785882)Instructions burned: 119 (million)
% 2.99/1.17 % (785884)Instruction limit reached!
% 2.99/1.17 % (785884)------------------------------
% 2.99/1.17 % (785884)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.17 % (785884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.17 % (785884)CaDiCaL version: 2.1.3
% 2.99/1.17 % (785884)Termination reason: Instruction limit
% 2.99/1.17 % (785884)Termination phase: Saturation
% 2.99/1.17 % (785884)Time elapsed: 0.076 s
% 2.99/1.17 % (785884)Peak memory usage: 89 MB
% 2.99/1.17 % (785884)Instructions burned: 129 (million)
% 2.99/1.17 % (785894)lrs+1011_1_sil=32000:sp=occurrence:random_seed=371373849:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.99/1.17 % (785893)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3621853474:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.99/1.17 % (785892)lrs+10_1_sil=8000:sp=occurrence:random_seed=2016472440:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.99/1.17 % (785883)Refutation found. Thanks to Tanya!
% 2.99/1.17 % SZS status Theorem for theBenchmark
% 2.99/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 2.99/1.17 % (785883)------------------------------
% 2.99/1.17 % (785883)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.17 % (785883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.17 % (785883)CaDiCaL version: 2.1.3
% 2.99/1.17 % (785883)Termination reason: Refutation
% 2.99/1.17 % (785883)Time elapsed: 0.028 s
% 2.99/1.17 % (785883)Peak memory usage: 90 MB
% 2.99/1.17 % (785883)Instructions burned: 37 (million)
% 2.99/1.17 % (785883)------------------------------
% 2.99/1.17 % (785883)------------------------------
% 2.99/1.17 % (785873)Success in time 0.367 s
% 2.99/1.17 % Vampire exiting
%------------------------------------------------------------------------------