%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU321+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 12:48:20 PM UTC 2026
% Result : Theorem 0.17s 1.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 56 ( 9 unt; 2 def)
% Number of atoms : 177 ( 8 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 198 ( 77 ~; 74 |; 29 &)
% ( 4 <=>; 12 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 35 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f191,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(f201,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f264,conjecture,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,subset_complement(the_carrier(X0),X1))
<=> ~ in(X2,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l40_tops_1) ).
fof(f265,negated_conjecture,
~ ! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,subset_complement(the_carrier(X0),X1))
<=> ~ in(X2,X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f264]) ).
fof(f475,axiom,
! [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/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
fof(f479,axiom,
! [X0,X1,X2] :
( element(X2,powerset(X0))
=> ~ ( in(X1,subset_complement(X0,X2))
& in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
fof(f746,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f201]) ).
fof(f747,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f746]) ).
fof(f812,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,subset_complement(the_carrier(X0),X1))
<~> ~ in(X2,X1) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& ~ empty_carrier(X0)
& one_sorted_str(X0) ),
inference(ennf_transformation,[],[f265]) ).
fof(f813,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,subset_complement(the_carrier(X0),X1))
<~> ~ in(X2,X1) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& ~ empty_carrier(X0)
& one_sorted_str(X0) ),
inference(flattening,[],[f812]) ).
fof(f1055,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0) )
| ~ element(X1,powerset(X0)) )
| empty_set = X0 ),
inference(ennf_transformation,[],[f475]) ).
fof(f1056,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0) )
| ~ element(X1,powerset(X0)) )
| empty_set = X0 ),
inference(flattening,[],[f1055]) ).
fof(f1063,plain,
! [X0,X1,X2] :
( ~ in(X1,subset_complement(X0,X2))
| ~ in(X1,X2)
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f479]) ).
fof(f1064,plain,
! [X0,X1,X2] :
( ~ in(X1,subset_complement(X0,X2))
| ~ in(X1,X2)
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f1063]) ).
fof(f1393,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,X1)
| ~ in(X2,subset_complement(the_carrier(X0),X1)) )
& ( ~ in(X2,X1)
| in(X2,subset_complement(the_carrier(X0),X1)) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& ~ empty_carrier(X0)
& one_sorted_str(X0) ),
inference(nnf_transformation,[],[f813]) ).
fof(f1394,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,X1)
| ~ in(X2,subset_complement(the_carrier(X0),X1)) )
& ( ~ in(X2,X1)
| in(X2,subset_complement(the_carrier(X0),X1)) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& ~ empty_carrier(X0)
& one_sorted_str(X0) ),
inference(flattening,[],[f1393]) ).
fof(f1395,plain,
( ( in(sK159,sK158)
| ~ in(sK159,subset_complement(the_carrier(sK157),sK158)) )
& ( ~ in(sK159,sK158)
| in(sK159,subset_complement(the_carrier(sK157),sK158)) )
& element(sK159,the_carrier(sK157))
& element(sK158,powerset(the_carrier(sK157)))
& ~ empty_carrier(sK157)
& one_sorted_str(sK157) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK157,sK158,sK159]),skolemize(X0,sK157),skolemize(X1,sK158),skolemize(X2,sK159)],[f1394]) ).
fof(f2170,plain,
empty(empty_set),
inference(cnf_transformation,[],[f191]) ).
fof(f2194,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f747]) ).
fof(f2327,plain,
one_sorted_str(sK157),
inference(cnf_transformation,[],[f1395]) ).
fof(f2328,plain,
~ empty_carrier(sK157),
inference(cnf_transformation,[],[f1395]) ).
fof(f2329,plain,
element(sK158,powerset(the_carrier(sK157))),
inference(cnf_transformation,[],[f1395]) ).
fof(f2330,plain,
element(sK159,the_carrier(sK157)),
inference(cnf_transformation,[],[f1395]) ).
fof(f2331,plain,
( ~ in(sK159,sK158)
| in(sK159,subset_complement(the_carrier(sK157),sK158)) ),
inference(cnf_transformation,[],[f1395]) ).
fof(f2332,plain,
( in(sK159,sK158)
| ~ in(sK159,subset_complement(the_carrier(sK157),sK158)) ),
inference(cnf_transformation,[],[f1395]) ).
fof(f3014,plain,
! [X2,X0,X1] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0)
| ~ element(X1,powerset(X0))
| empty_set = X0 ),
inference(cnf_transformation,[],[f1056]) ).
fof(f3034,plain,
! [X2,X0,X1] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(cnf_transformation,[],[f1064]) ).
fof(f3564,definition,
( spl395_55
<=> in(sK159,subset_complement(the_carrier(sK157),sK158)) ),
introduced(definition,[new_symbols(definition,[spl395_55])],[avatar_definition]) ).
fof(f3565,plain,
( ~ in(sK159,subset_complement(the_carrier(sK157),sK158))
| spl395_55 ),
inference(avatar_component_clause,[],[f3564]) ).
fof(f3566,plain,
( in(sK159,subset_complement(the_carrier(sK157),sK158))
| ~ spl395_55 ),
inference(avatar_component_clause,[],[f3564]) ).
fof(f3568,definition,
( spl395_56
<=> in(sK159,sK158) ),
introduced(definition,[new_symbols(definition,[spl395_56])],[avatar_definition]) ).
fof(f3569,plain,
( in(sK159,sK158)
| ~ spl395_56 ),
inference(avatar_component_clause,[],[f3568]) ).
fof(f3570,plain,
( ~ in(sK159,sK158)
| spl395_56 ),
inference(avatar_component_clause,[],[f3568]) ).
fof(f3571,plain,
( spl395_55
| ~ spl395_56 ),
inference(avatar_split_clause,[],[f2331,f3568,f3564]) ).
fof(f3572,plain,
( ~ spl395_55
| spl395_56 ),
inference(avatar_split_clause,[],[f2332,f3568,f3564]) ).
fof(f3639,plain,
( in(sK159,sK158)
| ~ element(sK159,the_carrier(sK157))
| ~ element(sK158,powerset(the_carrier(sK157)))
| empty_set = the_carrier(sK157)
| spl395_55 ),
inference(resolution,[],[f3014,f3565]) ).
fof(f3644,plain,
( ~ element(sK159,the_carrier(sK157))
| ~ element(sK158,powerset(the_carrier(sK157)))
| empty_set = the_carrier(sK157)
| spl395_55
| spl395_56 ),
inference(forward_subsumption_resolution,[],[f3639,f3570]) ).
fof(f3645,plain,
( ~ element(sK158,powerset(the_carrier(sK157)))
| empty_set = the_carrier(sK157)
| spl395_55
| spl395_56 ),
inference(forward_subsumption_resolution,[],[f3644,f2330]) ).
fof(f3646,plain,
( empty_set = the_carrier(sK157)
| spl395_55
| spl395_56 ),
inference(forward_subsumption_resolution,[],[f3645,f2329]) ).
fof(f3663,plain,
( ~ empty(empty_set)
| empty_carrier(sK157)
| ~ one_sorted_str(sK157)
| spl395_55
| spl395_56 ),
inference(superposition,[],[f2194,f3646]) ).
fof(f3699,plain,
( empty_carrier(sK157)
| ~ one_sorted_str(sK157)
| spl395_55
| spl395_56 ),
inference(forward_subsumption_resolution,[],[f3663,f2170]) ).
fof(f3755,plain,
( ~ one_sorted_str(sK157)
| spl395_55
| spl395_56 ),
inference(forward_subsumption_resolution,[],[f3699,f2328]) ).
fof(f3775,plain,
( $false
| spl395_55
| spl395_56 ),
inference(forward_subsumption_resolution,[],[f3755,f2327]) ).
fof(f3776,plain,
( spl395_55
| spl395_56 ),
inference(avatar_contradiction_clause,[],[f3775]) ).
fof(f3777,plain,
( ! [X0] :
( ~ in(sK159,subset_complement(X0,sK158))
| ~ element(sK158,powerset(X0)) )
| ~ spl395_56 ),
inference(resolution,[],[f3569,f3034]) ).
fof(f3858,plain,
( ~ element(sK158,powerset(the_carrier(sK157)))
| ~ spl395_55
| ~ spl395_56 ),
inference(resolution,[],[f3777,f3566]) ).
fof(f3863,plain,
( $false
| ~ spl395_55
| ~ spl395_56 ),
inference(forward_subsumption_resolution,[],[f3858,f2329]) ).
fof(f3864,plain,
( ~ spl395_55
| ~ spl395_56 ),
inference(avatar_contradiction_clause,[],[f3863]) ).
cnf(s46,plain,
( spl395_55
| ~ spl395_56 ),
inference(sat_conversion,[],[f3571]) ).
cnf(s47,plain,
( ~ spl395_55
| spl395_56 ),
inference(sat_conversion,[],[f3572]) ).
cnf(s62,plain,
( spl395_55
| spl395_56 ),
inference(sat_conversion,[],[f3776]) ).
cnf(s63,plain,
( ~ spl395_55
| ~ spl395_56 ),
inference(sat_conversion,[],[f3864]) ).
cnf(s64,plain,
spl395_55,
inference(rat,[],[s46,s62]) ).
cnf(s65,plain,
~ spl395_56,
inference(rat,[],[s63,s64]) ).
cnf(s66,plain,
$false,
inference(rat,[],[s47,s65,s64]) ).
fof(f3865,plain,
$false,
inference(avatar_sat_refutation,[],[s66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU321+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n017.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 04:36:36 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.57/1.31 % (3207787)Detected formulas, will run a generic FOF schedule.
% 2.57/1.31 % (3207796)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1707978796:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.57/1.31 % (3207797)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2120981194:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.57/1.31 % (3207796)Instruction limit reached!
% 2.57/1.31 % (3207796)------------------------------
% 2.57/1.31 % (3207796)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.31 % (3207796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.31 % (3207796)CaDiCaL version: 2.1.3
% 2.57/1.31 % (3207796)Termination reason: Instruction limit
% 2.57/1.31 % (3207796)Termination phase: Saturation
% 2.57/1.31 % (3207796)Time elapsed: 0.044 s
% 2.57/1.31 % (3207796)Peak memory usage: 90 MB
% 2.57/1.31 % (3207796)Instructions burned: 120 (million)
% 2.57/1.31 % (3207795)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3122222314:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.57/1.31 % (3207792)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=969721201:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.57/1.31 % (3207793)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=4071303000:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.57/1.31 % (3207798)dis-21_1_sil=8000:lcm=predicate:random_seed=358479918: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)
% 2.57/1.31 % (3207794)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=2966268332:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.57/1.31 % (3207797)First to succeed.
% 2.57/1.31 % (3207797)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3207787"
% 2.57/1.31 % (3207795)Instruction limit reached!
% 2.57/1.31 % (3207795)------------------------------
% 2.57/1.31 % (3207795)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.31 % (3207795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.31 % (3207795)CaDiCaL version: 2.1.3
% 2.57/1.31 % (3207795)Termination reason: Instruction limit
% 2.57/1.31 % (3207795)Termination phase: Saturation
% 2.57/1.31 % (3207795)Time elapsed: 0.062 s
% 2.57/1.31 % (3207795)Peak memory usage: 91 MB
% 2.57/1.31 % (3207795)Instructions burned: 109 (million)
% 2.57/1.31 % (3207798)Instruction limit reached!
% 2.57/1.31 % (3207798)------------------------------
% 2.57/1.31 % (3207798)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.31 % (3207798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.31 % (3207798)CaDiCaL version: 2.1.3
% 2.57/1.31 % (3207798)Termination reason: Instruction limit
% 2.57/1.31 % (3207798)Termination phase: Saturation
% 2.57/1.31 % (3207798)Time elapsed: 0.066 s
% 2.57/1.31 % (3207798)Peak memory usage: 90 MB
% 2.57/1.31 % (3207798)Instructions burned: 129 (million)
% 2.57/1.31 % (3207806)lrs+10_1_sil=8000:sp=occurrence:random_seed=3911354909:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.57/1.31 % (3207807)lrs+10_1_sil=32000:urr=on:br=off:random_seed=228998107:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.57/1.31 % (3207806)Instruction limit reached!
% 2.57/1.31 % (3207806)------------------------------
% 2.57/1.31 % (3207806)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.31 % (3207806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.31 % (3207806)CaDiCaL version: 2.1.3
% 2.57/1.31 % (3207806)Termination reason: Instruction limit
% 2.57/1.31 % (3207806)Termination phase: Saturation
% 2.57/1.31 % (3207806)Time elapsed: 0.105 s
% 2.57/1.31 % (3207806)Peak memory usage: 95 MB
% 2.57/1.31 % (3207806)Instructions burned: 287 (million)
% 2.57/1.31 % (3207808)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3341764276:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.57/1.31 % (3207811)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3430475253:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 0.17/1.50 % (3207807)Instruction limit reached!
% 0.17/1.50 % (3207807)------------------------------
% 0.17/1.50 % (3207807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (3207807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (3207807)CaDiCaL version: 2.1.3
% 0.17/1.50 % (3207807)Termination reason: Instruction limit
% 0.17/1.50 % (3207807)Termination phase: Saturation
% 0.17/1.50 % (3207807)Time elapsed: 0.094 s
% 0.17/1.50 % (3207807)Peak memory usage: 91 MB
% 0.17/1.50 % (3207807)Instructions burned: 157 (million)
% 0.17/1.50 % (3207797)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
% 0.17/1.51 % (3207797)------------------------------
% 0.17/1.51 % (3207797)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.51 % (3207797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.51 % (3207797)CaDiCaL version: 2.1.3
% 0.17/1.51 % (3207797)Termination reason: Refutation
% 0.17/1.51 % (3207797)Time elapsed: 0.049 s
% 0.17/1.51 % (3207797)Peak memory usage: 92 MB
% 0.17/1.51 % (3207797)Instructions burned: 79 (million)
% 0.17/1.51 % (3207797)------------------------------
% 0.17/1.51 % (3207797)------------------------------
% 0.17/1.51 % (3207787)Success in time 0.46 s
% 0.17/1.51 % Vampire exiting
%------------------------------------------------------------------------------