TSTP Solution File: KLE010+3 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : KLE010+3 : 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 : n032.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 05:36:17 EDT 2023
% Result : Theorem 0.15s 0.42s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 24
% Syntax : Number of formulae : 89 ( 61 unt; 0 def)
% Number of atoms : 156 ( 90 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 102 ( 35 ~; 26 |; 27 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 15 con; 0-2 aty)
% Number of variables : 87 (; 76 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4442,plain,
$false,
inference(subsumption_resolution,[],[f4441,f83]) ).
fof(f83,plain,
one != sF13,
inference(definition_folding,[],[f48,f82,f81,f73,f78,f80,f79,f78,f77,f76,f75,f74,f73,f72]) ).
fof(f72,plain,
multiplication(sK1,sK0) = sF3,
introduced(function_definition,[]) ).
fof(f74,plain,
multiplication(sF4,sK0) = sF5,
introduced(function_definition,[]) ).
fof(f75,plain,
addition(sF3,sF5) = sF6,
introduced(function_definition,[]) ).
fof(f76,plain,
multiplication(sK0,sK1) = sF7,
introduced(function_definition,[]) ).
fof(f77,plain,
addition(sF6,sF7) = sF8,
introduced(function_definition,[]) ).
fof(f79,plain,
multiplication(sF9,sK1) = sF10,
introduced(function_definition,[]) ).
fof(f80,plain,
addition(sF8,sF10) = sF11,
introduced(function_definition,[]) ).
fof(f78,plain,
c(sK0) = sF9,
introduced(function_definition,[]) ).
fof(f73,plain,
c(sK1) = sF4,
introduced(function_definition,[]) ).
fof(f81,plain,
multiplication(sF9,sF4) = sF12,
introduced(function_definition,[]) ).
fof(f82,plain,
addition(sF11,sF12) = sF13,
introduced(function_definition,[]) ).
fof(f48,plain,
one != addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
( one != addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))
& test(sK0)
& test(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f30,f37]) ).
fof(f37,plain,
( ? [X0,X1] :
( one != addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))
& test(X0)
& test(X1) )
=> ( one != addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))
& test(sK0)
& test(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
? [X0,X1] :
( one != addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))
& test(X0)
& test(X1) ),
inference(flattening,[],[f29]) ).
fof(f29,plain,
? [X0,X1] :
( one != addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))
& test(X0)
& test(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> one = addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ! [X3,X4] :
( ( test(X3)
& test(X4) )
=> one = addition(addition(addition(addition(multiplication(X4,X3),multiplication(c(X4),X3)),multiplication(X3,X4)),multiplication(c(X3),X4)),multiplication(c(X3),c(X4))) ),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
! [X3,X4] :
( ( test(X3)
& test(X4) )
=> one = addition(addition(addition(addition(multiplication(X4,X3),multiplication(c(X4),X3)),multiplication(X3,X4)),multiplication(c(X3),X4)),multiplication(c(X3),c(X4))) ),
file('/export/starexec/sandbox2/tmp/tmp.65gTqaqk5t/Vampire---4.8_25529',goals) ).
fof(f4441,plain,
one = sF13,
inference(forward_demodulation,[],[f4440,f105]) ).
fof(f105,plain,
one = addition(sF9,sK0),
inference(resolution,[],[f65,f87]) ).
fof(f87,plain,
complement(sK0,sF9),
inference(subsumption_resolution,[],[f85,f47]) ).
fof(f47,plain,
test(sK0),
inference(cnf_transformation,[],[f38]) ).
fof(f85,plain,
( complement(sK0,sF9)
| ~ test(sK0) ),
inference(superposition,[],[f71,f78]) ).
fof(f71,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X3,X4] :
( test(X3)
=> ( c(X3) = X4
<=> complement(X3,X4) ) ),
file('/export/starexec/sandbox2/tmp/tmp.65gTqaqk5t/Vampire---4.8_25529',test_3) ).
fof(f65,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1] :
( ( complement(X1,X0)
| addition(X0,X1) != one
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1) )
& ( ( addition(X0,X1) = one
& zero = multiplication(X1,X0)
& zero = multiplication(X0,X1) )
| ~ complement(X1,X0) ) ),
inference(flattening,[],[f44]) ).
fof(f44,plain,
! [X0,X1] :
( ( complement(X1,X0)
| addition(X0,X1) != one
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1) )
& ( ( addition(X0,X1) = one
& zero = multiplication(X1,X0)
& zero = multiplication(X0,X1) )
| ~ complement(X1,X0) ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& zero = multiplication(X1,X0)
& zero = multiplication(X0,X1) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X3,X4] :
( complement(X4,X3)
<=> ( one = addition(X3,X4)
& zero = multiplication(X4,X3)
& zero = multiplication(X3,X4) ) ),
file('/export/starexec/sandbox2/tmp/tmp.65gTqaqk5t/Vampire---4.8_25529',test_2) ).
fof(f4440,plain,
sF13 = addition(sF9,sK0),
inference(backward_demodulation,[],[f3558,f4433]) ).
fof(f4433,plain,
sK0 = sF8,
inference(forward_demodulation,[],[f4423,f1792]) ).
fof(f1792,plain,
sK0 = addition(sK0,sF7),
inference(forward_demodulation,[],[f1791,f52]) ).
fof(f52,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/tmp/tmp.65gTqaqk5t/Vampire---4.8_25529',multiplicative_right_identity) ).
fof(f1791,plain,
multiplication(sK0,one) = addition(sK0,sF7),
inference(forward_demodulation,[],[f1715,f659]) ).
fof(f659,plain,
one = addition(one,sK1),
inference(superposition,[],[f614,f58]) ).
fof(f58,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/tmp/tmp.65gTqaqk5t/Vampire---4.8_25529',additive_commutativity) ).
fof(f614,plain,
one = addition(sK1,one),
inference(superposition,[],[f124,f560]) ).
fof(f560,plain,
one = addition(sK1,sK2(sK1)),
inference(resolution,[],[f107,f46]) ).
fof(f46,plain,
test(sK1),
inference(cnf_transformation,[],[f38]) ).
fof(f107,plain,
! [X1] :
( ~ test(X1)
| one = addition(X1,sK2(X1)) ),
inference(resolution,[],[f65,f56]) ).
fof(f56,plain,
! [X0] :
( complement(sK2(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( complement(sK2(X0),X0)
| ~ test(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f40,f41]) ).
fof(f41,plain,
! [X0] :
( ? [X2] : complement(X2,X0)
=> complement(sK2(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( ? [X2] : complement(X2,X0)
| ~ test(X0) ) ),
inference(rectify,[],[f39]) ).
fof(f39,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X3] :
( test(X3)
<=> ? [X4] : complement(X4,X3) ),
file('/export/starexec/sandbox2/tmp/tmp.65gTqaqk5t/Vampire---4.8_25529',test_1) ).
fof(f124,plain,
! [X2,X3] : addition(X2,X3) = addition(X2,addition(X2,X3)),
inference(superposition,[],[f67,f54]) ).
fof(f54,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/tmp/tmp.65gTqaqk5t/Vampire---4.8_25529',additive_idempotence) ).
fof(f67,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X2,X1,X0] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
file('/export/starexec/sandbox2/tmp/tmp.65gTqaqk5t/Vampire---4.8_25529',additive_associativity) ).
fof(f1715,plain,
multiplication(sK0,addition(one,sK1)) = addition(sK0,sF7),
inference(superposition,[],[f192,f76]) ).
fof(f192,plain,
! [X2,X3] : multiplication(X2,addition(one,X3)) = addition(X2,multiplication(X2,X3)),
inference(superposition,[],[f69,f52]) ).
fof(f69,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox2/tmp/tmp.65gTqaqk5t/Vampire---4.8_25529',right_distributivity) ).
fof(f4423,plain,
sF8 = addition(sK0,sF7),
inference(backward_demodulation,[],[f77,f4414]) ).
fof(f4414,plain,
sK0 = sF6,
inference(backward_demodulation,[],[f75,f4391]) ).
fof(f4391,plain,
sK0 = addition(sF3,sF5),
inference(forward_demodulation,[],[f4390,f53]) ).
fof(f53,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/tmp/tmp.65gTqaqk5t/Vampire---4.8_25529',multiplicative_left_identity) ).
fof(f4390,plain,
addition(sF3,sF5) = multiplication(one,sK0),
inference(forward_demodulation,[],[f4370,f113]) ).
fof(f113,plain,
one = addition(sK1,sF4),
inference(superposition,[],[f106,f58]) ).
fof(f106,plain,
one = addition(sF4,sK1),
inference(resolution,[],[f65,f86]) ).
fof(f86,plain,
complement(sK1,sF4),
inference(subsumption_resolution,[],[f84,f46]) ).
fof(f84,plain,
( complement(sK1,sF4)
| ~ test(sK1) ),
inference(superposition,[],[f71,f73]) ).
fof(f4370,plain,
addition(sF3,sF5) = multiplication(addition(sK1,sF4),sK0),
inference(superposition,[],[f307,f74]) ).
fof(f307,plain,
! [X20] : multiplication(addition(sK1,X20),sK0) = addition(sF3,multiplication(X20,sK0)),
inference(superposition,[],[f70,f72]) ).
fof(f70,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/tmp/tmp.65gTqaqk5t/Vampire---4.8_25529',left_distributivity) ).
fof(f3558,plain,
sF13 = addition(sF9,sF8),
inference(forward_demodulation,[],[f3557,f82]) ).
fof(f3557,plain,
addition(sF11,sF12) = addition(sF9,sF8),
inference(forward_demodulation,[],[f3550,f58]) ).
fof(f3550,plain,
addition(sF11,sF12) = addition(sF8,sF9),
inference(superposition,[],[f134,f3538]) ).
fof(f3538,plain,
sF9 = addition(sF10,sF12),
inference(forward_demodulation,[],[f3537,f52]) ).
fof(f3537,plain,
multiplication(sF9,one) = addition(sF10,sF12),
inference(forward_demodulation,[],[f3519,f113]) ).
fof(f3519,plain,
multiplication(sF9,addition(sK1,sF4)) = addition(sF10,sF12),
inference(superposition,[],[f205,f81]) ).
fof(f205,plain,
! [X22] : multiplication(sF9,addition(sK1,X22)) = addition(sF10,multiplication(sF9,X22)),
inference(superposition,[],[f69,f79]) ).
fof(f134,plain,
! [X21] : addition(sF8,addition(sF10,X21)) = addition(sF11,X21),
inference(superposition,[],[f67,f80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : KLE010+3 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.11 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Aug 29 12:35:31 EDT 2023
% 0.11/0.30 % CPUTime :
% 0.11/0.30 This is a FOF_THM_RFO_SEQ problem
% 0.11/0.31 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.65gTqaqk5t/Vampire---4.8_25529
% 0.11/0.31 % (25715)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.35 % (25722)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)
% 0.15/0.35 % (25720)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)
% 0.15/0.35 % (25717)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)
% 0.15/0.35 % (25721)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.15/0.35 % (25716)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)
% 0.15/0.36 % (25719)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)
% 0.15/0.36 % (25718)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)
% 0.15/0.42 % (25721)First to succeed.
% 0.15/0.42 % (25721)Refutation found. Thanks to Tanya!
% 0.15/0.42 % SZS status Theorem for Vampire---4
% 0.15/0.42 % SZS output start Proof for Vampire---4
% See solution above
% 0.15/0.42 % (25721)------------------------------
% 0.15/0.42 % (25721)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.15/0.42 % (25721)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.15/0.42 % (25721)Termination reason: Refutation
% 0.15/0.42
% 0.15/0.42 % (25721)Memory used [KB]: 7547
% 0.15/0.42 % (25721)Time elapsed: 0.066 s
% 0.15/0.42 % (25721)------------------------------
% 0.15/0.42 % (25721)------------------------------
% 0.15/0.42 % (25715)Success in time 0.112 s
% 0.15/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------