%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET009+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 4 unt; 0 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 56 ( 21 ~; 27 |; 2 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 68 ( 65 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( member(X2,X0)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f4,conjecture,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(difference(X2,X1),difference(X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_subset_difference) ).
fof(f5,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,X1)
=> subset(difference(X2,X1),difference(X2,X0)) ),
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(X2,X1),difference(X2,X0))
& subset(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f8,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f1]) ).
fof(f9,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f1]) ).
fof(f10,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f1]) ).
fof(f11,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
fof(f12,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
fof(f13,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
fof(f15,plain,
subset(sK1,sK2),
inference(cnf_transformation,[],[f7]) ).
fof(f16,plain,
~ subset(difference(sK3,sK2),difference(sK3,sK1)),
inference(cnf_transformation,[],[f7]) ).
fof(f17,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0)
| ~ member(X2,X1) ),
inference(consistent_polarity_flipping,[],[f10]) ).
fof(f18,plain,
! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| ~ member(X2,X0) ),
inference(consistent_polarity_flipping,[],[f9]) ).
fof(f19,plain,
! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| member(X2,X1) ),
inference(consistent_polarity_flipping,[],[f8]) ).
fof(f20,plain,
! [X0,X1] :
( member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(consistent_polarity_flipping,[],[f13]) ).
fof(f21,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(consistent_polarity_flipping,[],[f12]) ).
fof(f22,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X2,X1)
| member(X2,X0) ),
inference(consistent_polarity_flipping,[],[f11]) ).
fof(f24,plain,
! [X2,X0,X1] :
( member(sK0(difference(X0,X1),X2),X1)
| subset(difference(X0,X1),X2) ),
inference(resolution,[],[f21,f19]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ~ member(sK0(difference(X0,X1),X2),X0)
| subset(difference(X0,X1),X2) ),
inference(resolution,[],[f21,f18]) ).
fof(f27,plain,
! [X0] :
( ~ member(X0,sK2)
| member(X0,sK1) ),
inference(resolution,[],[f22,f15]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ member(sK0(X0,difference(X1,X2)),X2)
| member(sK0(X0,difference(X1,X2)),X1)
| subset(X0,difference(X1,X2)) ),
inference(resolution,[],[f17,f20]) ).
fof(f34,plain,
! [X0,X1] :
( member(sK0(difference(X0,sK2),X1),sK1)
| subset(difference(X0,sK2),X1) ),
inference(resolution,[],[f24,f27]) ).
fof(f50,plain,
! [X0,X1] :
( subset(difference(X0,sK2),difference(X1,sK1))
| member(sK0(difference(X0,sK2),difference(X1,sK1)),X1)
| subset(difference(X0,sK2),difference(X1,sK1)) ),
inference(resolution,[],[f34,f31]) ).
fof(f51,plain,
! [X0,X1] :
( member(sK0(difference(X0,sK2),difference(X1,sK1)),X1)
| subset(difference(X0,sK2),difference(X1,sK1)) ),
inference(duplicate_literal_removal,[],[f50]) ).
fof(f157,plain,
! [X0] :
( subset(difference(X0,sK2),difference(X0,sK1))
| subset(difference(X0,sK2),difference(X0,sK1)) ),
inference(resolution,[],[f51,f25]) ).
fof(f168,plain,
! [X0] : subset(difference(X0,sK2),difference(X0,sK1)),
inference(duplicate_literal_removal,[],[f157]) ).
fof(f169,plain,
$false,
inference(backward_subsumption_resolution,[],[f16,f168]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET009+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 00:05:38 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.45 % (4031390)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (4031396)% WARNING: option uhcvi not known.
% 0.10/0.45 % (4031396)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1449000514:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.45 % (4031396) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4031390-4031396"...
% 0.10/0.45 % (4031396)...printing done.
% 0.10/0.45 % (4031396)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 % (4031396)------------------------------
% 0.10/0.45 % (4031396)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (4031396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (4031396)CaDiCaL version: 2.1.3
% 0.10/0.45 % (4031396)Termination reason: Refutation
% 0.10/0.45 % (4031396)Time elapsed: 0.003 s
% 0.10/0.45 % (4031396)Peak memory usage: 11 MB
% 0.10/0.45 % (4031396)Instructions burned: 5 (million)
% 0.10/0.45 % (4031390)Success in time 0.037 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------