%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET008+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 12:42:32 PM UTC 2026
% Result : Theorem 0.15s 5.66s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 16 unt; 0 def)
% Number of atoms : 106 ( 17 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 111 ( 45 ~; 39 |; 21 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 89 ( 85 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X0)
& member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( member(X2,X0)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f5,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f6,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f10,conjecture,
! [X0,X1] : intersection(difference(X0,X1),X1) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_difference_empty_set) ).
fof(f11,negated_conjecture,
~ ! [X0,X1] : intersection(difference(X0,X1),X1) = empty_set,
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f13,plain,
? [X0,X1] : empty_set != intersection(difference(X0,X1),X1),
inference(ennf_transformation,[],[f11]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) )
& ( ( member(X2,X0)
& member(X2,X1) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) )
& ( ( member(X2,X0)
& member(X2,X1) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f19,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f21,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f21]) ).
fof(f26,plain,
empty_set != intersection(difference(sK2,sK3),sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f13]) ).
fof(f27,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f33,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f36,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f19]) ).
fof(f37,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f39,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f46,plain,
empty_set != intersection(difference(sK2,sK3),sK3),
inference(cnf_transformation,[],[f26]) ).
fof(f51,plain,
empty_set != intersection(sK3,difference(sK2,sK3)),
inference(superposition,[],[f46,f37]) ).
fof(f57,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[],[f39,f33]) ).
fof(f58,plain,
! [X2,X0,X1] :
( member(sK0(intersection(X0,X1),X2),X0)
| subset(intersection(X0,X1),X2) ),
inference(resolution,[],[f39,f28]) ).
fof(f59,plain,
! [X2,X0,X1] :
( member(sK0(intersection(X0,X1),X2),X1)
| subset(intersection(X0,X1),X2) ),
inference(resolution,[],[f39,f27]) ).
fof(f65,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(resolution,[],[f36,f57]) ).
fof(f83,plain,
! [X2,X3,X0,X1] :
( ~ member(sK0(intersection(difference(X0,X1),X2),X3),X1)
| subset(intersection(difference(X0,X1),X2),X3) ),
inference(resolution,[],[f58,f30]) ).
fof(f901,plain,
! [X2,X0,X1] :
( subset(intersection(difference(X0,X1),X1),X2)
| subset(intersection(difference(X0,X1),X1),X2) ),
inference(resolution,[],[f83,f59]) ).
fof(f915,plain,
! [X2,X0,X1] : subset(intersection(difference(X0,X1),X1),X2),
inference(duplicate_literal_removal,[],[f901]) ).
fof(f917,plain,
! [X2,X0,X1] : subset(intersection(X1,difference(X0,X1)),X2),
inference(forward_demodulation,[],[f915,f37]) ).
fof(f921,plain,
! [X0,X1] : empty_set = intersection(X0,difference(X1,X0)),
inference(resolution,[],[f917,f65]) ).
fof(f1479,plain,
empty_set != empty_set,
inference(superposition,[],[f51,f921]) ).
fof(f1480,plain,
$false,
inference(trivial_inequality_removal,[],[f1479]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET008+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/5.54 % Computer : n008.cluster.edu
% 0.11/5.54 % Model : x86_64 x86_64
% 0.11/5.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.54 % Memory : 8046.5625MB
% 0.11/5.54 % OS : Linux 6.8.0-71-generic
% 0.11/5.54 % CPULimit : 300
% 0.11/5.54 % WCLimit : 300
% 0.11/5.54 % DateTime : Mon Sep 28 00:03:45 UTC 2026
% 0.11/5.54 % CPUTime :
% 0.11/5.54 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/5.58 Running first-order model finding
% 0.11/5.58 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
% 0.15/5.66 % (1745179)Will run a generic schedule for satisfiability detection.
% 0.15/5.66 % (1745184)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2015186218_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/5.66 % TRYING [1]
% 0.15/5.66 % TRYING [2]
% 0.15/5.66 % TRYING [3]
% 0.15/5.66 % TRYING [4]
% 0.15/5.66 % (1745185)% WARNING: option uhcvi not known.
% 0.15/5.66 % TRYING [5]
% 0.15/5.66 % (1745185)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2754533102:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/5.66 % (1745186)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2137699835:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/5.66 % (1745187)dis+10_1_sil=32000:sp=arity:random_seed=66439218:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/5.66 % (1745188)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1860463146:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/5.66 % (1745189)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1611342740:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/5.66 % (1745190)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3967263285:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/5.66 % TRYING [6]
% 0.15/5.66 % (1745187) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1745179-1745187"...
% 0.15/5.66 % TRYING [7]
% 0.15/5.66 % (1745190) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1745179-1745190"...
% 0.15/5.66 % (1745187)...printing done.
% 0.15/5.66 % (1745190)...printing done.
% 0.15/5.66 % (1745187)Refutation found. Thanks to Tanya!
% 0.15/5.66 % SZS status Theorem for theBenchmark
% 0.15/5.66 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/5.66 % (1745187)------------------------------
% 0.15/5.66 % (1745187)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/5.66 % (1745187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/5.66 % (1745187)CaDiCaL version: 2.1.3
% 0.15/5.66 % (1745187)Termination reason: Refutation
% 0.15/5.66 % (1745187)Time elapsed: 0.030 s
% 0.15/5.66 % (1745187)Peak memory usage: 12 MB
% 0.15/5.66 % (1745187)Instructions burned: 45 (million)
% 0.15/5.66 % (1745179)Success in time 0.068 s
% 0.15/5.66 % Vampire exiting
%------------------------------------------------------------------------------