%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET635+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 12:44:16 PM UTC 2026
% Result : Theorem 0.16s 0.47s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 26 unt; 0 def)
% Number of atoms : 34 ( 27 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 3 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 51 ( 48 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_empty_set) ).
fof(f3,axiom,
! [X0] : union(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_empty_set) ).
fof(f4,axiom,
! [X0,X1,X2] : difference(X0,intersection(X1,X2)) = union(difference(X0,X1),difference(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_and_intersection_and_union) ).
fof(f5,axiom,
! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_and_intersection) ).
fof(f9,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f11,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f13,axiom,
! [X0] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
fof(f16,conjecture,
! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),intersection(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th117) ).
fof(f17,negated_conjecture,
~ ! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),intersection(X0,X2)),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f19,plain,
? [X0,X1,X2] : intersection(X0,difference(X1,X2)) != difference(intersection(X0,X1),intersection(X0,X2)),
inference(ennf_transformation,[],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( ( difference(X0,X1) = empty_set
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| difference(X0,X1) != empty_set ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f33,plain,
intersection(sK2,difference(sK3,sK4)) != difference(intersection(sK2,sK3),intersection(sK2,sK4)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f19]) ).
fof(f36,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| difference(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f20]) ).
fof(f37,plain,
! [X0] : union(X0,empty_set) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f38,plain,
! [X2,X0,X1] : difference(X0,intersection(X1,X2)) = union(difference(X0,X1),difference(X0,X2)),
inference(cnf_transformation,[],[f4]) ).
fof(f39,plain,
! [X2,X0,X1] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f49,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f51,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f55,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f13]) ).
fof(f60,plain,
intersection(sK2,difference(sK3,sK4)) != difference(intersection(sK2,sK3),intersection(sK2,sK4)),
inference(cnf_transformation,[],[f33]) ).
fof(f65,plain,
! [X0] : union(empty_set,X0) = X0,
inference(superposition,[],[f37,f49]) ).
fof(f74,plain,
! [X0] : empty_set = difference(X0,X0),
inference(resolution,[],[f36,f55]) ).
fof(f81,plain,
! [X0,X1] : union(difference(X0,X0),X1) = X1,
inference(superposition,[],[f65,f74]) ).
fof(f197,plain,
! [X2,X0,X1] : difference(intersection(X0,X1),X2) = intersection(X1,difference(X0,X2)),
inference(superposition,[],[f39,f51]) ).
fof(f271,plain,
! [X0,X1] : difference(X0,X1) = difference(X0,intersection(X0,X1)),
inference(superposition,[],[f81,f38]) ).
fof(f921,plain,
intersection(sK2,difference(sK3,sK4)) != intersection(sK3,difference(sK2,intersection(sK2,sK4))),
inference(superposition,[],[f60,f197]) ).
fof(f922,plain,
! [X2,X0,X1] : intersection(X0,difference(X1,X2)) = intersection(X1,difference(X0,X2)),
inference(superposition,[],[f39,f197]) ).
fof(f963,plain,
intersection(sK2,difference(sK3,sK4)) != intersection(sK3,difference(sK2,sK4)),
inference(forward_demodulation,[],[f921,f271]) ).
fof(f980,plain,
$false,
inference(forward_subsumption_resolution,[],[f963,f922]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET635+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n008.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 28 02:24:24 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 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
% 0.16/0.47 % (1809269)Will run a generic schedule for satisfiability detection.
% 0.16/0.47 % (1809274)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2002411221_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.47 % TRYING [1]
% 0.16/0.47 % TRYING [2]
% 0.16/0.47 % TRYING [3]
% 0.16/0.47 % (1809275)% WARNING: option uhcvi not known.
% 0.16/0.47 % TRYING [4]
% 0.16/0.47 % (1809275)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2310894514:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.47 % (1809276)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3021715714:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.47 % (1809277)dis+10_1_sil=32000:sp=arity:random_seed=4145723512:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.47 % (1809279)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1424086771:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.47 % (1809278)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2116206568:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.47 % (1809280)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2023171153:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.47 % TRYING [5]
% 0.16/0.47 % (1809279) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1809269-1809279"...
% 0.16/0.47 % (1809279)...printing done.
% 0.16/0.47 % (1809279)Refutation found. Thanks to Tanya!
% 0.16/0.47 % SZS status Theorem for theBenchmark
% 0.16/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (1809279)------------------------------
% 0.16/0.47 % (1809279)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (1809279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (1809279)CaDiCaL version: 2.1.3
% 0.16/0.47 % (1809279)Termination reason: Refutation
% 0.16/0.47 % (1809279)Time elapsed: 0.018 s
% 0.16/0.47 % (1809279)Peak memory usage: 11 MB
% 0.16/0.47 % (1809279)Instructions burned: 26 (million)
% 0.16/0.47 % (1809269)Success in time 0.063 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------