%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU321+1 : 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 : 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 12:48:20 PM UTC 2026
% Result : Theorem 2.59s 1.29s
% Output : Refutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 12 unt; 4 def)
% Number of atoms : 183 ( 7 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 206 ( 84 ~; 70 |; 32 &)
% ( 6 <=>; 12 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 37 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f33,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f34,axiom,
( empty(empty_set)
& v1_membered(empty_set)
& v2_membered(empty_set)
& v3_membered(empty_set)
& v4_membered(empty_set)
& v5_membered(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_membered) ).
fof(f40,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/sandbox/benchmark/theBenchmark.p',l40_tops_1) ).
fof(f41,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)],[f40]) ).
fof(f42,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/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).
fof(f43,axiom,
! [X0,X1,X2] :
( element(X2,powerset(X0))
=> ~ ( in(X1,subset_complement(X0,X2))
& in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
fof(f80,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f81,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f80]) ).
fof(f88,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,[],[f41]) ).
fof(f89,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,[],[f88]) ).
fof(f90,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,[],[f42]) ).
fof(f91,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,[],[f90]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ~ in(X1,subset_complement(X0,X2))
| ~ in(X1,X2)
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f43]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ~ in(X1,subset_complement(X0,X2))
| ~ in(X1,X2)
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f92]) ).
fof(f99,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,[],[f89]) ).
fof(f100,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,[],[f99]) ).
fof(f101,plain,
( ( in(sK7,sK6)
| ~ in(sK7,subset_complement(the_carrier(sK5),sK6)) )
& ( ~ in(sK7,sK6)
| in(sK7,subset_complement(the_carrier(sK5),sK6)) )
& element(sK7,the_carrier(sK5))
& element(sK6,powerset(the_carrier(sK5)))
& ~ empty_carrier(sK5)
& one_sorted_str(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7)],[f100]) ).
fof(f145,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f151,plain,
empty(empty_set),
inference(cnf_transformation,[],[f34]) ).
fof(f157,plain,
one_sorted_str(sK5),
inference(cnf_transformation,[],[f101]) ).
fof(f158,plain,
~ empty_carrier(sK5),
inference(cnf_transformation,[],[f101]) ).
fof(f159,plain,
element(sK6,powerset(the_carrier(sK5))),
inference(cnf_transformation,[],[f101]) ).
fof(f160,plain,
element(sK7,the_carrier(sK5)),
inference(cnf_transformation,[],[f101]) ).
fof(f161,plain,
( ~ in(sK7,sK6)
| in(sK7,subset_complement(the_carrier(sK5),sK6)) ),
inference(cnf_transformation,[],[f101]) ).
fof(f162,plain,
( in(sK7,sK6)
| ~ in(sK7,subset_complement(the_carrier(sK5),sK6)) ),
inference(cnf_transformation,[],[f101]) ).
fof(f163,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X0))
| in(X2,X1)
| ~ element(X2,X0)
| in(X2,subset_complement(X0,X1))
| empty_set = X0 ),
inference(cnf_transformation,[],[f91]) ).
fof(f164,plain,
! [X2,X0,X1] :
( ~ in(X1,subset_complement(X0,X2))
| ~ in(X1,X2)
| ~ element(X2,powerset(X0)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f166,definition,
( spl8_1
<=> in(sK7,subset_complement(the_carrier(sK5),sK6)) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
fof(f168,plain,
( in(sK7,subset_complement(the_carrier(sK5),sK6))
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f170,definition,
( spl8_2
<=> in(sK7,sK6) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
fof(f171,plain,
( in(sK7,sK6)
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f173,plain,
( spl8_1
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f161,f170,f166]) ).
fof(f174,plain,
( ~ spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f162,f170,f166]) ).
fof(f195,plain,
! [X0] :
( in(X0,sK6)
| ~ element(X0,the_carrier(sK5))
| in(X0,subset_complement(the_carrier(sK5),sK6))
| empty_set = the_carrier(sK5) ),
inference(resolution,[],[f163,f159]) ).
fof(f197,definition,
( spl8_3
<=> empty_set = the_carrier(sK5) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
fof(f199,plain,
( empty_set = the_carrier(sK5)
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f201,definition,
( spl8_4
<=> ! [X0] :
( in(X0,sK6)
| in(X0,subset_complement(the_carrier(sK5),sK6))
| ~ element(X0,the_carrier(sK5)) ) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
fof(f202,plain,
( ! [X0] :
( ~ element(X0,the_carrier(sK5))
| in(X0,subset_complement(the_carrier(sK5),sK6))
| in(X0,sK6) )
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f203,plain,
( spl8_3
| spl8_4 ),
inference(avatar_split_clause,[],[f195,f201,f197]) ).
fof(f208,plain,
( ~ empty(empty_set)
| empty_carrier(sK5)
| ~ one_sorted_str(sK5)
| ~ spl8_3 ),
inference(superposition,[],[f145,f199]) ).
fof(f209,plain,
( empty_carrier(sK5)
| ~ one_sorted_str(sK5)
| ~ spl8_3 ),
inference(forward_subsumption_resolution,[],[f208,f151]) ).
fof(f211,plain,
( ~ one_sorted_str(sK5)
| ~ spl8_3 ),
inference(forward_subsumption_resolution,[],[f209,f158]) ).
fof(f213,plain,
( $false
| ~ spl8_3 ),
inference(forward_subsumption_resolution,[],[f211,f157]) ).
fof(f214,plain,
~ spl8_3,
inference(avatar_contradiction_clause,[],[f213]) ).
fof(f216,plain,
( in(sK7,subset_complement(the_carrier(sK5),sK6))
| in(sK7,sK6)
| ~ spl8_4 ),
inference(resolution,[],[f202,f160]) ).
fof(f229,plain,
( spl8_2
| spl8_1
| ~ spl8_4 ),
inference(avatar_split_clause,[],[f216,f201,f166,f170]) ).
fof(f234,plain,
( ~ in(sK7,sK6)
| ~ element(sK6,powerset(the_carrier(sK5)))
| ~ spl8_1 ),
inference(resolution,[],[f168,f164]) ).
fof(f239,plain,
( ~ element(sK6,powerset(the_carrier(sK5)))
| ~ spl8_1
| ~ spl8_2 ),
inference(forward_subsumption_resolution,[],[f234,f171]) ).
fof(f240,plain,
( $false
| ~ spl8_1
| ~ spl8_2 ),
inference(forward_subsumption_resolution,[],[f239,f159]) ).
fof(f241,plain,
( ~ spl8_1
| ~ spl8_2 ),
inference(avatar_contradiction_clause,[],[f240]) ).
cnf(s1,plain,
( spl8_1
| ~ spl8_2 ),
inference(sat_conversion,[],[f173]) ).
cnf(s2,plain,
( ~ spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f174]) ).
cnf(s3,plain,
( spl8_3
| spl8_4 ),
inference(sat_conversion,[],[f203]) ).
cnf(s4,plain,
~ spl8_3,
inference(sat_conversion,[],[f214]) ).
cnf(s7,plain,
( spl8_1
| spl8_2
| ~ spl8_4 ),
inference(sat_conversion,[],[f229]) ).
cnf(s8,plain,
( ~ spl8_1
| ~ spl8_2 ),
inference(sat_conversion,[],[f241]) ).
cnf(s9,plain,
spl8_4,
inference(rat,[],[s3,s4]) ).
cnf(s10,plain,
spl8_1,
inference(rat,[],[s1,s7,s9]) ).
cnf(s11,plain,
~ spl8_2,
inference(rat,[],[s8,s10]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s2,s11,s10]) ).
fof(f242,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU321+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n008.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Mon Sep 28 04:42:09 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 2.59/1.29 % (1881160)Detected formulas, will run a generic FOF schedule.
% 2.59/1.29 % (1881171)dis-21_1_sil=8000:lcm=predicate:random_seed=2430641218: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)
% 2.59/1.29 % (1881171)Instruction limit reached!
% 2.59/1.29 % (1881171)------------------------------
% 2.59/1.29 % (1881171)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.29 % (1881171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.29 % (1881171)CaDiCaL version: 2.1.3
% 2.59/1.29 % (1881171)Termination reason: Instruction limit
% 2.59/1.29 % (1881171)Termination phase: Saturation
% 2.59/1.29 % (1881171)Time elapsed: 0.037 s
% 2.59/1.29 % (1881171)Peak memory usage: 89 MB
% 2.59/1.29 % (1881171)Instructions burned: 131 (million)
% 2.59/1.29 % (1881166)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=2667904432:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.59/1.29 % (1881169)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2482774644:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.59/1.29 % (1881168)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3060014472:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.59/1.29 % (1881165)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=4271785626:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.59/1.29 % (1881167)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=4210635379:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.59/1.29 % (1881170)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=733139909:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.59/1.29 % (1881168)Refutation not found, incomplete strategy
% 2.59/1.29 % (1881168)------------------------------
% 2.59/1.29 % (1881168)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.29 % (1881168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.29 % (1881168)CaDiCaL version: 2.1.3
% 2.59/1.29 % (1881168)Termination reason: Refutation not found, incomplete strategy
% 2.59/1.29 % (1881168)Time elapsed: 0.002 s
% 2.59/1.29 % (1881168)Peak memory usage: 88 MB
% 2.59/1.29 % (1881168)Instructions burned: 1 (million)
% 2.59/1.29 % (1881170)First to succeed.
% 2.59/1.29 % (1881170)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1881160"
% 2.59/1.29 % (1881169)Instruction limit reached!
% 2.59/1.29 % (1881169)------------------------------
% 2.59/1.29 % (1881169)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.29 % (1881169)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.29 % (1881169)CaDiCaL version: 2.1.3
% 2.59/1.29 % (1881169)Termination reason: Instruction limit
% 2.59/1.29 % (1881169)Termination phase: Saturation
% 2.59/1.29 % (1881169)Time elapsed: 0.070 s
% 2.59/1.29 % (1881169)Peak memory usage: 88 MB
% 2.59/1.29 % (1881169)Instructions burned: 120 (million)
% 2.59/1.29 % (1881179)lrs+10_1_sil=8000:sp=occurrence:random_seed=209868721:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.59/1.29 % (1881179)Also succeeded, but the first one will report.
% 2.59/1.29 % (1881168)------------------------------
% 2.59/1.29 % (1881168)------------------------------
% 2.59/1.29 % (1881180)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3035859451:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.59/1.29 % (1881180)Refutation not found, incomplete strategy
% 2.59/1.29 % (1881180)------------------------------
% 2.59/1.29 % (1881180)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.29 % (1881180)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.29 % (1881180)CaDiCaL version: 2.1.3
% 2.59/1.29 % (1881180)Termination reason: Refutation not found, incomplete strategy
% 2.59/1.29 % (1881180)Time elapsed: 0.008 s
% 2.59/1.29 % (1881180)Peak memory usage: 89 MB
% 2.59/1.29 % (1881180)Instructions burned: 10 (million)
% 2.59/1.29 % (1881170)Refutation found. Thanks to Tanya!
% 2.59/1.29 % SZS status Theorem for theBenchmark
% 2.59/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.65/1.45 % (1881170)------------------------------
% 3.65/1.45 % (1881170)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.45 % (1881170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.45 % (1881170)CaDiCaL version: 2.1.3
% 3.65/1.45 % (1881170)Termination reason: Refutation
% 3.65/1.45 % (1881170)Time elapsed: 0.006 s
% 3.65/1.45 % (1881170)Peak memory usage: 90 MB
% 3.65/1.45 % (1881170)Instructions burned: 6 (million)
% 3.65/1.45 % (1881170)------------------------------
% 3.65/1.45 % (1881170)------------------------------
% 3.65/1.45 % (1881160)Success in time 0.434 s
% 3.65/1.45 % Vampire exiting
%------------------------------------------------------------------------------