TSTP Solution File: KLE131+1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : KLE131+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 05:36:56 EDT 2023
% Result : Theorem 0.22s 0.44s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 54 ( 48 unt; 0 def)
% Number of atoms : 62 ( 61 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 16 ( 8 ~; 0 |; 4 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 16 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 50 (; 48 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f565,plain,
$false,
inference(subsumption_resolution,[],[f557,f92]) ).
fof(f92,plain,
zero != sF1,
inference(definition_folding,[],[f54,f91]) ).
fof(f91,plain,
divergence(sK0) = sF1,
introduced(function_definition,[]) ).
fof(f54,plain,
zero != divergence(sK0),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
( zero != divergence(sK0)
& ! [X1] : forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1)))) = addition(domain(X1),forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1))))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f49,f51]) ).
fof(f51,plain,
( ? [X0] :
( zero != divergence(X0)
& ! [X1] : forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))) = addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) )
=> ( zero != divergence(sK0)
& ! [X1] : forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1)))) = addition(domain(X1),forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1))))) ) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
? [X0] :
( zero != divergence(X0)
& ! [X1] : forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))) = addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,plain,
~ ! [X0] :
( ! [X1] : forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))) = addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))))
=> zero = divergence(X0) ),
inference(rectify,[],[f30]) ).
fof(f30,negated_conjecture,
~ ! [X3] :
( ! [X4] : forward_diamond(star(X3),domain_difference(domain(X4),forward_diamond(X3,domain(X4)))) = addition(domain(X4),forward_diamond(star(X3),domain_difference(domain(X4),forward_diamond(X3,domain(X4)))))
=> zero = divergence(X3) ),
inference(negated_conjecture,[],[f29]) ).
fof(f29,conjecture,
! [X3] :
( ! [X4] : forward_diamond(star(X3),domain_difference(domain(X4),forward_diamond(X3,domain(X4)))) = addition(domain(X4),forward_diamond(star(X3),domain_difference(domain(X4),forward_diamond(X3,domain(X4)))))
=> zero = divergence(X3) ),
file('/export/starexec/sandbox/tmp/tmp.RRhHfmWL8E/Vampire---4.8_5787',goals) ).
fof(f557,plain,
zero = sF1,
inference(superposition,[],[f553,f57]) ).
fof(f57,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/tmp/tmp.RRhHfmWL8E/Vampire---4.8_5787',additive_identity) ).
fof(f553,plain,
zero = addition(sF1,zero),
inference(forward_demodulation,[],[f552,f98]) ).
fof(f98,plain,
zero = antidomain(one),
inference(superposition,[],[f62,f58]) ).
fof(f58,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/tmp/tmp.RRhHfmWL8E/Vampire---4.8_5787',multiplicative_right_identity) ).
fof(f62,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X3] : zero = multiplication(antidomain(X3),X3),
file('/export/starexec/sandbox/tmp/tmp.RRhHfmWL8E/Vampire---4.8_5787',domain1) ).
fof(f552,plain,
antidomain(one) = addition(sF1,antidomain(one)),
inference(forward_demodulation,[],[f551,f129]) ).
fof(f129,plain,
one = antidomain(zero),
inference(superposition,[],[f114,f57]) ).
fof(f114,plain,
one = addition(antidomain(zero),zero),
inference(superposition,[],[f68,f98]) ).
fof(f68,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X3] : one = addition(antidomain(antidomain(X3)),antidomain(X3)),
file('/export/starexec/sandbox/tmp/tmp.RRhHfmWL8E/Vampire---4.8_5787',domain3) ).
fof(f551,plain,
antidomain(antidomain(zero)) = addition(sF1,antidomain(antidomain(zero))),
inference(forward_demodulation,[],[f550,f55]) ).
fof(f55,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] : zero = multiplication(X0,zero),
file('/export/starexec/sandbox/tmp/tmp.RRhHfmWL8E/Vampire---4.8_5787',right_annihilation) ).
fof(f550,plain,
antidomain(antidomain(multiplication(sF2,zero))) = addition(sF1,antidomain(antidomain(multiplication(sF2,zero)))),
inference(forward_demodulation,[],[f549,f98]) ).
fof(f549,plain,
antidomain(antidomain(multiplication(sF2,antidomain(one)))) = addition(sF1,antidomain(antidomain(multiplication(sF2,antidomain(one))))),
inference(forward_demodulation,[],[f548,f129]) ).
fof(f548,plain,
antidomain(antidomain(multiplication(sF2,antidomain(antidomain(zero))))) = addition(sF1,antidomain(antidomain(multiplication(sF2,antidomain(antidomain(zero)))))),
inference(forward_demodulation,[],[f547,f62]) ).
fof(f547,plain,
antidomain(antidomain(multiplication(sF2,antidomain(antidomain(multiplication(antidomain(antidomain(sF1)),antidomain(sF1))))))) = addition(sF1,antidomain(antidomain(multiplication(sF2,antidomain(antidomain(multiplication(antidomain(antidomain(sF1)),antidomain(sF1)))))))),
inference(forward_demodulation,[],[f532,f186]) ).
fof(f186,plain,
sF1 = antidomain(antidomain(multiplication(sK0,antidomain(antidomain(sF1))))),
inference(superposition,[],[f89,f91]) ).
fof(f89,plain,
! [X0] : divergence(X0) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(divergence(X0)))))),
inference(definition_unfolding,[],[f66,f86]) ).
fof(f86,plain,
! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(definition_unfolding,[],[f74,f65,f65]) ).
fof(f65,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X3] : antidomain(antidomain(X3)) = domain(X3),
file('/export/starexec/sandbox/tmp/tmp.RRhHfmWL8E/Vampire---4.8_5787',domain4) ).
fof(f74,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(rectify,[],[f23]) ).
fof(f23,axiom,
! [X3,X4] : forward_diamond(X3,X4) = domain(multiplication(X3,domain(X4))),
file('/export/starexec/sandbox/tmp/tmp.RRhHfmWL8E/Vampire---4.8_5787',forward_diamond) ).
fof(f66,plain,
! [X0] : divergence(X0) = forward_diamond(X0,divergence(X0)),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0] : divergence(X0) = forward_diamond(X0,divergence(X0)),
inference(rectify,[],[f27]) ).
fof(f27,axiom,
! [X3] : divergence(X3) = forward_diamond(X3,divergence(X3)),
file('/export/starexec/sandbox/tmp/tmp.RRhHfmWL8E/Vampire---4.8_5787',divergence1) ).
fof(f532,plain,
antidomain(antidomain(multiplication(sF2,antidomain(antidomain(multiplication(antidomain(antidomain(sF1)),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(sF1)))))))))))) = addition(sF1,antidomain(antidomain(multiplication(sF2,antidomain(antidomain(multiplication(antidomain(antidomain(sF1)),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(sF1))))))))))))),
inference(superposition,[],[f94,f186]) ).
fof(f94,plain,
! [X1] : antidomain(antidomain(multiplication(sF2,antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(X1)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X1)))))))))))))) = addition(antidomain(antidomain(X1)),antidomain(antidomain(multiplication(sF2,antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(X1)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X1))))))))))))))),
inference(definition_folding,[],[f88,f93,f93]) ).
fof(f93,plain,
star(sK0) = sF2,
introduced(function_definition,[]) ).
fof(f88,plain,
! [X1] : antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(X1)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X1)))))))))))))) = addition(antidomain(antidomain(X1)),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(X1)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X1))))))))))))))),
inference(definition_unfolding,[],[f53,f86,f85,f65,f86,f65,f65,f86,f85,f65,f86,f65]) ).
fof(f85,plain,
! [X0,X1] : domain_difference(X0,X1) = multiplication(antidomain(antidomain(X0)),antidomain(X1)),
inference(definition_unfolding,[],[f73,f65]) ).
fof(f73,plain,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X3,X4] : domain_difference(X3,X4) = multiplication(domain(X3),antidomain(X4)),
file('/export/starexec/sandbox/tmp/tmp.RRhHfmWL8E/Vampire---4.8_5787',domain_difference) ).
fof(f53,plain,
! [X1] : forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1)))) = addition(domain(X1),forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1))))),
inference(cnf_transformation,[],[f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : KLE131+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.36 % Computer : n020.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 29 11:24:43 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.14/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.RRhHfmWL8E/Vampire---4.8_5787
% 0.14/0.36 % (5894)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42 % (5896)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.22/0.42 % (5898)lrs-3_8_anc=none:bce=on:cond=on:drc=off:flr=on:fsd=off:fsr=off:fde=unused:gsp=on:gs=on:gsaa=full_model:lcm=predicate:lma=on:nm=16:sos=all:sp=weighted_frequency:tgt=ground:urr=ec_only:stl=188_482 on Vampire---4 for (482ds/0Mi)
% 0.22/0.42 % (5899)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_424 on Vampire---4 for (424ds/0Mi)
% 0.22/0.42 % (5897)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.22/0.42 % (5901)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_386 on Vampire---4 for (386ds/0Mi)
% 0.22/0.42 % (5900)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.22/0.43 % (5895)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_730 on Vampire---4 for (730ds/0Mi)
% 0.22/0.44 % (5900)First to succeed.
% 0.22/0.44 % (5900)Refutation found. Thanks to Tanya!
% 0.22/0.44 % SZS status Theorem for Vampire---4
% 0.22/0.44 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.45 % (5900)------------------------------
% 0.22/0.45 % (5900)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.45 % (5900)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.45 % (5900)Termination reason: Refutation
% 0.22/0.45
% 0.22/0.45 % (5900)Memory used [KB]: 5884
% 0.22/0.45 % (5900)Time elapsed: 0.019 s
% 0.22/0.45 % (5900)------------------------------
% 0.22/0.45 % (5900)------------------------------
% 0.22/0.45 % (5894)Success in time 0.079 s
% 0.22/0.45 % Vampire---4.8 exiting
%------------------------------------------------------------------------------