%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU170+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 12:52:14 PM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 75 ( 9 unt; 4 def)
% Number of atoms : 187 ( 7 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 191 ( 79 ~; 78 |; 15 &)
% ( 10 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 73 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f3,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(f4,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(f14,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( in(X2,X1)
=> in(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_subset_1) ).
fof(f22,axiom,
! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] :
~ ( in(X2,X0)
& in(X2,X1) ) )
& ~ ( ? [X2] :
( in(X2,X0)
& in(X2,X1) )
& disjoint(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f23,conjecture,
! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,powerset(X0))
=> ( disjoint(X1,X2)
<=> subset(X1,subset_complement(X0,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_subset_1) ).
fof(f24,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,powerset(X0))
=> ( disjoint(X1,X2)
<=> subset(X1,subset_complement(X0,X2)) ) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f30,plain,
! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] :
~ ( in(X2,X0)
& in(X2,X1) ) )
& ~ ( ? [X3] :
( in(X3,X0)
& in(X3,X1) )
& disjoint(X0,X1) ) ),
inference(rectify,[],[f22]) ).
fof(f32,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f33,plain,
! [X0,X1] :
( subset_complement(X0,X1) = set_difference(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f36,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
| ~ in(X2,X1) )
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f14]) ).
fof(f39,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| ? [X2] :
( in(X2,X0)
& in(X2,X1) ) )
& ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X3,X1) )
| ~ disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f40,plain,
? [X0,X1] :
( ? [X2] :
( ( disjoint(X1,X2)
<~> subset(X1,subset_complement(X0,X2)) )
& element(X2,powerset(X0)) )
& element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f24]) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f46,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f47,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f51,plain,
! [X2,X3,X0,X1] :
( ~ in(X3,X1)
| ~ in(X3,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f3]) ).
fof(f53,plain,
! [X2,X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f3]) ).
fof(f54,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| set_difference(X0,X1) = subset_complement(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f60,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X0))
| ~ in(X2,X1)
| in(X2,X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f70,plain,
! [X0,X1] :
( disjoint(X0,X1)
| in(sK7(X0,X1),X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f71,plain,
! [X0,X1] :
( disjoint(X0,X1)
| in(sK7(X0,X1),X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f72,plain,
! [X3,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X3,X1)
| ~ in(X3,X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f73,plain,
( subset(sK9,subset_complement(sK8,sK10))
| disjoint(sK9,sK10) ),
inference(cnf_transformation,[],[f40]) ).
fof(f74,plain,
( ~ subset(sK9,subset_complement(sK8,sK10))
| ~ disjoint(sK9,sK10) ),
inference(cnf_transformation,[],[f40]) ).
fof(f75,plain,
element(sK10,powerset(sK8)),
inference(cnf_transformation,[],[f40]) ).
fof(f76,plain,
element(sK9,powerset(sK8)),
inference(cnf_transformation,[],[f40]) ).
fof(f81,plain,
! [X3,X0,X1] :
( in(X3,set_difference(X0,X1))
| ~ in(X3,X0)
| in(X3,X1) ),
inference(equality_resolution,[],[f53]) ).
fof(f83,plain,
! [X3,X0,X1] :
( ~ in(X3,set_difference(X0,X1))
| ~ in(X3,X1) ),
inference(equality_resolution,[],[f51]) ).
fof(f85,definition,
( spl11_1
<=> disjoint(sK9,sK10) ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
fof(f86,plain,
( ~ disjoint(sK9,sK10)
| spl11_1 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f87,plain,
( disjoint(sK9,sK10)
| ~ spl11_1 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f89,definition,
( spl11_2
<=> subset(sK9,subset_complement(sK8,sK10)) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
fof(f90,plain,
( ~ subset(sK9,subset_complement(sK8,sK10))
| spl11_2 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f91,plain,
( subset(sK9,subset_complement(sK8,sK10))
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f92,plain,
( spl11_1
| spl11_2 ),
inference(avatar_split_clause,[],[f73,f89,f85]) ).
fof(f93,plain,
( ~ spl11_1
| ~ spl11_2 ),
inference(avatar_split_clause,[],[f74,f89,f85]) ).
fof(f117,plain,
( in(sK7(sK9,sK10),sK10)
| spl11_1 ),
inference(resolution,[],[f70,f86]) ).
fof(f121,plain,
( in(sK7(sK9,sK10),sK9)
| spl11_1 ),
inference(resolution,[],[f71,f86]) ).
fof(f129,plain,
( ! [X0] :
( in(X0,subset_complement(sK8,sK10))
| ~ in(X0,sK9) )
| ~ spl11_2 ),
inference(resolution,[],[f45,f91]) ).
fof(f141,plain,
! [X0] :
( in(X0,sK8)
| ~ in(X0,sK9) ),
inference(resolution,[],[f60,f76]) ).
fof(f160,plain,
subset_complement(sK8,sK10) = set_difference(sK8,sK10),
inference(resolution,[],[f54,f75]) ).
fof(f271,plain,
( ! [X0] :
( in(X0,set_difference(sK8,sK10))
| ~ in(X0,sK9) )
| ~ spl11_2 ),
inference(superposition,[],[f129,f160]) ).
fof(f489,plain,
( ! [X0] :
( ~ in(X0,sK10)
| ~ in(X0,sK9) )
| ~ spl11_2 ),
inference(resolution,[],[f271,f83]) ).
fof(f518,plain,
( ~ in(sK7(sK9,sK10),sK9)
| spl11_1
| ~ spl11_2 ),
inference(resolution,[],[f489,f117]) ).
fof(f524,plain,
( $false
| spl11_1
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f518,f121]) ).
fof(f525,plain,
( spl11_1
| ~ spl11_2 ),
inference(avatar_contradiction_clause,[],[f524]) ).
fof(f526,plain,
( ~ subset(sK9,set_difference(sK8,sK10))
| spl11_2 ),
inference(forward_demodulation,[],[f90,f160]) ).
fof(f527,plain,
( ! [X0] :
( ~ in(X0,sK10)
| ~ in(X0,sK9) )
| ~ spl11_1 ),
inference(resolution,[],[f87,f72]) ).
fof(f528,plain,
( ~ in(sK0(sK9,set_difference(sK8,sK10)),set_difference(sK8,sK10))
| spl11_2 ),
inference(resolution,[],[f526,f47]) ).
fof(f529,plain,
( in(sK0(sK9,set_difference(sK8,sK10)),sK9)
| spl11_2 ),
inference(resolution,[],[f526,f46]) ).
fof(f548,plain,
( ~ in(sK0(sK9,set_difference(sK8,sK10)),sK8)
| in(sK0(sK9,set_difference(sK8,sK10)),sK10)
| spl11_2 ),
inference(resolution,[],[f528,f81]) ).
fof(f552,definition,
( spl11_5
<=> in(sK0(sK9,set_difference(sK8,sK10)),sK10) ),
introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition]) ).
fof(f554,plain,
( in(sK0(sK9,set_difference(sK8,sK10)),sK10)
| ~ spl11_5 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f556,definition,
( spl11_6
<=> in(sK0(sK9,set_difference(sK8,sK10)),sK8) ),
introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition]) ).
fof(f558,plain,
( ~ in(sK0(sK9,set_difference(sK8,sK10)),sK8)
| spl11_6 ),
inference(avatar_component_clause,[],[f556]) ).
fof(f559,plain,
( spl11_5
| ~ spl11_6
| spl11_2 ),
inference(avatar_split_clause,[],[f548,f89,f556,f552]) ).
fof(f562,plain,
( ~ in(sK0(sK9,set_difference(sK8,sK10)),sK9)
| spl11_6 ),
inference(resolution,[],[f558,f141]) ).
fof(f567,plain,
( $false
| spl11_2
| spl11_6 ),
inference(forward_subsumption_resolution,[],[f562,f529]) ).
fof(f568,plain,
( spl11_2
| spl11_6 ),
inference(avatar_contradiction_clause,[],[f567]) ).
fof(f578,plain,
( ~ in(sK0(sK9,set_difference(sK8,sK10)),sK9)
| ~ spl11_1
| ~ spl11_5 ),
inference(resolution,[],[f554,f527]) ).
fof(f588,plain,
( $false
| ~ spl11_1
| spl11_2
| ~ spl11_5 ),
inference(forward_subsumption_resolution,[],[f578,f529]) ).
fof(f589,plain,
( ~ spl11_1
| spl11_2
| ~ spl11_5 ),
inference(avatar_contradiction_clause,[],[f588]) ).
cnf(s1,plain,
( spl11_1
| spl11_2 ),
inference(sat_conversion,[],[f92]) ).
cnf(s2,plain,
( ~ spl11_1
| ~ spl11_2 ),
inference(sat_conversion,[],[f93]) ).
cnf(s5,plain,
( spl11_1
| ~ spl11_2 ),
inference(sat_conversion,[],[f525]) ).
cnf(s6,plain,
( spl11_2
| spl11_5
| ~ spl11_6 ),
inference(sat_conversion,[],[f559]) ).
cnf(s8,plain,
( spl11_2
| spl11_6 ),
inference(sat_conversion,[],[f568]) ).
cnf(s9,plain,
( ~ spl11_1
| spl11_2
| ~ spl11_5 ),
inference(sat_conversion,[],[f589]) ).
cnf(s10,plain,
spl11_1,
inference(rat,[],[s1,s5]) ).
cnf(s11,plain,
~ spl11_2,
inference(rat,[],[s2,s10]) ).
cnf(s12,plain,
~ spl11_5,
inference(rat,[],[s9,s10,s11]) ).
cnf(s13,plain,
spl11_6,
inference(rat,[],[s8,s11]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s6,s13,s12,s11]) ).
fof(f590,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU170+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.35 % Computer : n001.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 28 03:58:17 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 Running first-order model finding
% 0.10/0.39 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.45 % (1325)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (1335)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=612380007:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.45 % (1331)% WARNING: option uhcvi not known.
% 0.10/0.45 % (1330)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2694217695_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.45 % (1336)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1220759267:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.45 % (1331)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1044055258:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.45 % (1333)dis+10_1_sil=32000:sp=arity:random_seed=3596936123:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.45 % (1332)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1967508031:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.45 % (1334)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1368956578:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.45 % TRYING [1]
% 0.10/0.45 % TRYING [2]
% 0.10/0.45 % TRYING [3]
% 0.10/0.45 % TRYING [4]
% 0.10/0.45 % TRYING [5]
% 0.10/0.45 % (1334) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1325-1334"...
% 0.10/0.45 % (1334)...printing done.
% 0.10/0.45 % (1334)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (1334)------------------------------
% 0.10/0.45 % (1334)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (1334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (1334)CaDiCaL version: 2.1.3
% 0.10/0.45 % (1334)Termination reason: Refutation
% 0.10/0.45 % (1334)Time elapsed: 0.020 s
% 0.10/0.45 % (1334)Peak memory usage: 13 MB
% 0.10/0.45 % (1334)Instructions burned: 29 (million)
% 0.10/0.45 % (1325)Success in time 0.053 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------