%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET588+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:41:14 PM UTC 2026
% Result : Theorem 0.16s 1.14s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 8 unt; 0 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 76 ( 30 ~; 27 |; 13 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 53 ( 48 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f4,conjecture,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(difference(X0,X2),difference(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_difference_subset1) ).
fof(f5,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,X1)
=> subset(difference(X0,X2),difference(X1,X2)) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f7,plain,
? [X0,X1,X2] :
( ~ subset(difference(X0,X2),difference(X1,X2))
& subset(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f8,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,[],[f1]) ).
fof(f9,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,[],[f8]) ).
fof(f10,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,[],[f6]) ).
fof(f11,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,[],[f10]) ).
fof(f12,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))],[f11]) ).
fof(f13,plain,
( ~ subset(difference(sK1,sK3),difference(sK2,sK3))
& subset(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f7]) ).
fof(f14,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f15,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f9]) ).
fof(f16,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,difference(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f17,plain,
! [X3,X0,X1] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f18,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f19,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f21,plain,
subset(sK1,sK2),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
~ subset(difference(sK1,sK3),difference(sK2,sK3)),
inference(cnf_transformation,[],[f13]) ).
fof(f23,plain,
member(sK0(difference(sK1,sK3),difference(sK2,sK3)),difference(sK1,sK3)),
inference(resolution,[],[f18,f22]) ).
fof(f24,plain,
member(sK0(difference(sK1,sK3),difference(sK2,sK3)),sK1),
inference(resolution,[],[f23,f15]) ).
fof(f25,plain,
~ member(sK0(difference(sK1,sK3),difference(sK2,sK3)),sK3),
inference(resolution,[],[f23,f14]) ).
fof(f27,plain,
! [X0] :
( ~ subset(sK1,X0)
| member(sK0(difference(sK1,sK3),difference(sK2,sK3)),X0) ),
inference(resolution,[],[f17,f24]) ).
fof(f30,plain,
member(sK0(difference(sK1,sK3),difference(sK2,sK3)),sK2),
inference(resolution,[],[f27,f21]) ).
fof(f35,plain,
! [X0] :
( member(sK0(difference(sK1,sK3),difference(sK2,sK3)),difference(sK2,X0))
| member(sK0(difference(sK1,sK3),difference(sK2,sK3)),X0) ),
inference(resolution,[],[f30,f16]) ).
fof(f115,plain,
( member(sK0(difference(sK1,sK3),difference(sK2,sK3)),sK3)
| subset(difference(sK1,sK3),difference(sK2,sK3)) ),
inference(resolution,[],[f35,f19]) ).
fof(f120,plain,
subset(difference(sK1,sK3),difference(sK2,sK3)),
inference(forward_subsumption_resolution,[],[f115,f25]) ).
fof(f121,plain,
$false,
inference(forward_subsumption_resolution,[],[f120,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET588+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 02:16:39 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.16/1.14 % (365295)Detected formulas, will run a generic FOF schedule.
% 0.16/1.14 % (365305)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2844640673:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.16/1.14 % (365305)First to succeed.
% 0.16/1.14 % (365304)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2384470375:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.16/1.14 % (365300)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=1191792148:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.16/1.14 % (365306)dis-21_1_sil=8000:lcm=predicate:random_seed=2582995585: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)
% 0.16/1.14 % (365302)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=2139620488:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.16/1.14 % (365303)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3672982598:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.16/1.14 % (365301)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=4067724712:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.16/1.14 % (365305)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-365295"
% 0.16/1.14 % (365303)Refutation not found, incomplete strategy
% 0.16/1.14 % (365303)------------------------------
% 0.16/1.14 % (365303)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.14 % (365303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.14 % (365303)CaDiCaL version: 2.1.3
% 0.16/1.14 % (365303)Termination reason: Refutation not found, incomplete strategy
% 0.16/1.14 % (365303)Time elapsed: 0.001 s
% 0.16/1.14 % (365303)Peak memory usage: 88 MB
% 0.16/1.14 % (365306)Also succeeded, but the first one will report.
% 0.16/1.14 % (365304)Also succeeded, but the first one will report.
% 0.16/1.14 % (365305)Refutation found. Thanks to Tanya!
% 0.16/1.14 % SZS status Theorem for theBenchmark
% 0.16/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.14 % (365305)------------------------------
% 0.16/1.14 % (365305)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.14 % (365305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.14 % (365305)CaDiCaL version: 2.1.3
% 0.16/1.14 % (365305)Termination reason: Refutation
% 0.16/1.14 % (365305)Time elapsed: 0.003 s
% 0.16/1.14 % (365305)Peak memory usage: 88 MB
% 0.16/1.14 % (365305)Instructions burned: 5 (million)
% 0.16/1.14 % (365305)------------------------------
% 0.16/1.14 % (365305)------------------------------
% 0.16/1.14 % (365295)Success in time 0.318 s
% 0.16/1.14 % Vampire exiting
%------------------------------------------------------------------------------