%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU308+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 : n026.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 12:48:16 PM UTC 2026
% Result : Theorem 0.23s 1.71s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 12 unt; 3 def)
% Number of atoms : 84 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 76 ( 35 ~; 26 |; 5 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 30 ( 0 sgn 28 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f40,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X0))
& element(X2,powerset(X0)) )
=> subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(f42,axiom,
! [X0] :
( one_sorted_str(X0)
=> element(cast_as_carrier_subset(X0),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
fof(f51,axiom,
! [X0] :
( one_sorted_str(X0)
=> cast_as_carrier_subset(X0) = the_carrier(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pre_topc) ).
fof(f52,conjecture,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_complement(the_carrier(X0),X1) = subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_pre_topc) ).
fof(f53,negated_conjecture,
~ ! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_complement(the_carrier(X0),X1) = subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) ) ),
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f54,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(f56,plain,
? [X0] :
( ? [X1] :
( subset_complement(the_carrier(X0),X1) != subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)
& element(X1,powerset(the_carrier(X0))) )
& one_sorted_str(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f57,plain,
! [X0,X1] :
( subset_complement(X0,X1) = set_difference(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f54]) ).
fof(f62,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f40]) ).
fof(f63,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0] :
( cast_as_carrier_subset(X0) = the_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f65,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f66,plain,
( subset_complement(the_carrier(sK0),sK1) != subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),sK1)
& element(sK1,powerset(the_carrier(sK0)))
& one_sorted_str(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f56]) ).
fof(f69,plain,
one_sorted_str(sK0),
inference(cnf_transformation,[],[f66]) ).
fof(f70,plain,
element(sK1,powerset(the_carrier(sK0))),
inference(cnf_transformation,[],[f66]) ).
fof(f71,plain,
subset_complement(the_carrier(sK0),sK1) != subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),sK1),
inference(cnf_transformation,[],[f66]) ).
fof(f72,plain,
! [X0,X1] :
( set_difference(X0,X1) = subset_complement(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f76,plain,
! [X2,X0,X1] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f77,plain,
! [X0] :
( cast_as_carrier_subset(X0) = the_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f78,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f81,definition,
~ sP4(subset_complement(the_carrier(sK0),sK1)),
introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction]) ).
fof(f82,plain,
sP4(subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),sK1)),
inference(inequality_splitting,[],[f71,f81]) ).
fof(f83,plain,
( ~ sP4(set_difference(the_carrier(sK0),sK1))
| ~ element(sK1,powerset(the_carrier(sK0))) ),
inference(superposition,[],[f81,f72]) ).
fof(f84,plain,
~ sP4(set_difference(the_carrier(sK0),sK1)),
inference(forward_subsumption_resolution,[],[f83,f70]) ).
fof(f86,plain,
( sP4(set_difference(cast_as_carrier_subset(sK0),sK1))
| ~ element(cast_as_carrier_subset(sK0),powerset(the_carrier(sK0)))
| ~ element(sK1,powerset(the_carrier(sK0))) ),
inference(superposition,[],[f82,f76]) ).
fof(f87,plain,
( sP4(set_difference(cast_as_carrier_subset(sK0),sK1))
| ~ element(cast_as_carrier_subset(sK0),powerset(the_carrier(sK0))) ),
inference(forward_subsumption_resolution,[],[f86,f70]) ).
fof(f90,definition,
( spl5_1
<=> element(cast_as_carrier_subset(sK0),powerset(the_carrier(sK0))) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f92,plain,
( ~ element(cast_as_carrier_subset(sK0),powerset(the_carrier(sK0)))
| spl5_1 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f94,definition,
( spl5_2
<=> sP4(set_difference(cast_as_carrier_subset(sK0),sK1)) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f96,plain,
( sP4(set_difference(cast_as_carrier_subset(sK0),sK1))
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,plain,
( ~ spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f87,f94,f90]) ).
fof(f98,plain,
( ~ one_sorted_str(sK0)
| spl5_1 ),
inference(resolution,[],[f92,f78]) ).
fof(f101,plain,
( $false
| spl5_1 ),
inference(forward_subsumption_resolution,[],[f98,f69]) ).
fof(f102,plain,
spl5_1,
inference(avatar_contradiction_clause,[],[f101]) ).
fof(f103,plain,
( sP4(set_difference(the_carrier(sK0),sK1))
| ~ one_sorted_str(sK0)
| ~ spl5_2 ),
inference(superposition,[],[f96,f77]) ).
fof(f104,plain,
( ~ one_sorted_str(sK0)
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f103,f84]) ).
fof(f105,plain,
( $false
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f104,f69]) ).
fof(f106,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f105]) ).
cnf(s1,plain,
( ~ spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f97]) ).
cnf(s2,plain,
spl5_1,
inference(sat_conversion,[],[f102]) ).
cnf(s3,plain,
~ spl5_2,
inference(sat_conversion,[],[f106]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f107,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU308+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.41 % Computer : n026.cluster.edu
% 0.17/0.41 % Model : x86_64 x86_64
% 0.17/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.41 % Memory : 8046.5625MB
% 0.17/0.41 % OS : Linux 6.8.0-71-generic
% 0.17/0.41 % CPULimit : 300
% 0.17/0.41 % WCLimit : 300
% 0.17/0.41 % DateTime : Mon Sep 28 04:40:56 UTC 2026
% 0.17/0.41 % CPUTime :
% 0.17/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.46 Running first-order theorem proving
% 0.17/0.46 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
% 0.23/1.71 % (3463540)Detected formulas, will run a generic FOF schedule.
% 0.23/1.71 % (3463548)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2049638177:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.23/1.71 % (3463548)First to succeed.
% 0.23/1.71 % (3463548)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3463540"
% 0.23/1.71 % (3463551)dis-21_1_sil=8000:lcm=predicate:random_seed=459238271: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)
% 0.23/1.71 % (3463549)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2797447742:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.23/1.71 % (3463546)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=434726509:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.23/1.71 % (3463545)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=2444802762:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.23/1.71 % (3463547)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=2526582252:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.23/1.71 % (3463549)Also succeeded, but the first one will report.
% 0.23/1.71 % (3463550)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3274814405:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.23/1.71 % (3463550)Also succeeded, but the first one will report.
% 0.23/1.71 % (3463551)Instruction limit reached!
% 0.23/1.71 % (3463551)------------------------------
% 0.23/1.71 % (3463551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.23/1.71 % (3463551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/1.71 % (3463551)CaDiCaL version: 2.1.3
% 0.23/1.71 % (3463551)Termination reason: Instruction limit
% 0.23/1.71 % (3463551)Termination phase: Saturation
% 0.23/1.71 % (3463551)Time elapsed: 0.125 s
% 0.23/1.71 % (3463551)Peak memory usage: 89 MB
% 0.23/1.71 % (3463551)Instructions burned: 129 (million)
% 0.23/1.71 % (3463548)Refutation found. Thanks to Tanya!
% 0.23/1.71 % SZS status Theorem for theBenchmark
% 0.23/1.71 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/1.71 % (3463548)------------------------------
% 0.23/1.71 % (3463548)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.23/1.71 % (3463548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/1.71 % (3463548)CaDiCaL version: 2.1.3
% 0.23/1.71 % (3463548)Termination reason: Refutation
% 0.23/1.71 % (3463548)Time elapsed: 0.004 s
% 0.23/1.71 % (3463548)Peak memory usage: 89 MB
% 0.23/1.71 % (3463548)Instructions burned: 2 (million)
% 0.23/1.71 % (3463548)------------------------------
% 0.23/1.71 % (3463548)------------------------------
% 0.23/1.71 % (3463540)Success in time 0.41 s
% 0.23/1.71 % Vampire exiting
%------------------------------------------------------------------------------