TSTP Solution File: KLE010+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---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 : n026.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 : Fri Sep 1 17:09:02 EDT 2023
% Result : Theorem 0.23s 0.68s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 75 ( 47 unt; 0 def)
% Number of atoms : 144 ( 73 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 113 ( 44 ~; 26 |; 28 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 97 (; 86 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f27377,plain,
$false,
inference(subsumption_resolution,[],[f27376,f227]) ).
fof(f227,plain,
one = addition(sK0,c(sK0)),
inference(superposition,[],[f185,f59]) ).
fof(f59,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/sandbox/tmp/tmp.ac8iraEuO6/Vampire---4.8_13843',additive_commutativity) ).
fof(f185,plain,
one = addition(c(sK0),sK0),
inference(unit_resulting_resolution,[],[f175,f68]) ).
fof(f68,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,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,[],[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(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/sandbox/tmp/tmp.ac8iraEuO6/Vampire---4.8_13843',test_2) ).
fof(f175,plain,
complement(sK0,c(sK0)),
inference(forward_demodulation,[],[f171,f54]) ).
fof(f54,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/tmp/tmp.ac8iraEuO6/Vampire---4.8_13843',multiplicative_left_identity) ).
fof(f171,plain,
complement(sK0,multiplication(one,c(sK0))),
inference(unit_resulting_resolution,[],[f48,f54,f60]) ).
fof(f60,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
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/sandbox/tmp/tmp.ac8iraEuO6/Vampire---4.8_13843',test_3) ).
fof(f48,plain,
test(sK0),
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/sandbox/tmp/tmp.ac8iraEuO6/Vampire---4.8_13843',goals) ).
fof(f27376,plain,
one != addition(sK0,c(sK0)),
inference(forward_demodulation,[],[f27375,f21238]) ).
fof(f21238,plain,
! [X2] : addition(X2,multiplication(X2,sK1)) = X2,
inference(superposition,[],[f20754,f59]) ).
fof(f20754,plain,
! [X0] : addition(multiplication(X0,sK1),X0) = X0,
inference(unit_resulting_resolution,[],[f20734,f64]) ).
fof(f64,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/tmp/tmp.ac8iraEuO6/Vampire---4.8_13843',order) ).
fof(f20734,plain,
! [X126] : leq(multiplication(X126,sK1),X126),
inference(forward_demodulation,[],[f20670,f53]) ).
fof(f53,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/tmp/tmp.ac8iraEuO6/Vampire---4.8_13843',multiplicative_right_identity) ).
fof(f20670,plain,
! [X126] : leq(multiplication(X126,sK1),multiplication(X126,one)),
inference(superposition,[],[f3271,f706]) ).
fof(f706,plain,
one = addition(sK1,one),
inference(superposition,[],[f642,f136]) ).
fof(f136,plain,
one = addition(sK1,sK2(sK1)),
inference(unit_resulting_resolution,[],[f74,f68]) ).
fof(f74,plain,
complement(sK2(sK1),sK1),
inference(unit_resulting_resolution,[],[f47,f57]) ).
fof(f57,plain,
! [X0] :
( ~ test(X0)
| complement(sK2(X0),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/sandbox/tmp/tmp.ac8iraEuO6/Vampire---4.8_13843',test_1) ).
fof(f47,plain,
test(sK1),
inference(cnf_transformation,[],[f38]) ).
fof(f642,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f70,f55]) ).
fof(f55,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/tmp/tmp.ac8iraEuO6/Vampire---4.8_13843',additive_idempotence) ).
fof(f70,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/sandbox/tmp/tmp.ac8iraEuO6/Vampire---4.8_13843',additive_associativity) ).
fof(f3271,plain,
! [X21,X22,X23] : leq(multiplication(X21,X22),multiplication(X21,addition(X22,X23))),
inference(superposition,[],[f681,f72]) ).
fof(f72,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/sandbox/tmp/tmp.ac8iraEuO6/Vampire---4.8_13843',right_distributivity) ).
fof(f681,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(unit_resulting_resolution,[],[f642,f65]) ).
fof(f65,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f27375,plain,
one != addition(addition(sK0,multiplication(sK0,sK1)),c(sK0)),
inference(forward_demodulation,[],[f27374,f54]) ).
fof(f27374,plain,
one != addition(addition(multiplication(one,sK0),multiplication(sK0,sK1)),c(sK0)),
inference(forward_demodulation,[],[f27373,f59]) ).
fof(f27373,plain,
one != addition(addition(multiplication(sK0,sK1),multiplication(one,sK0)),c(sK0)),
inference(forward_demodulation,[],[f27372,f239]) ).
fof(f239,plain,
one = addition(sK1,c(sK1)),
inference(superposition,[],[f206,f59]) ).
fof(f206,plain,
one = addition(c(sK1),sK1),
inference(unit_resulting_resolution,[],[f176,f68]) ).
fof(f176,plain,
complement(sK1,c(sK1)),
inference(forward_demodulation,[],[f170,f54]) ).
fof(f170,plain,
complement(sK1,multiplication(one,c(sK1))),
inference(unit_resulting_resolution,[],[f47,f54,f60]) ).
fof(f27372,plain,
one != addition(addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)),c(sK0)),
inference(forward_demodulation,[],[f27371,f73]) ).
fof(f73,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/sandbox/tmp/tmp.ac8iraEuO6/Vampire---4.8_13843',left_distributivity) ).
fof(f27371,plain,
one != addition(addition(multiplication(sK0,sK1),addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0))),c(sK0)),
inference(forward_demodulation,[],[f27370,f59]) ).
fof(f27370,plain,
one != addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),c(sK0)),
inference(forward_demodulation,[],[f27369,f53]) ).
fof(f27369,plain,
one != addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),one)),
inference(forward_demodulation,[],[f27368,f239]) ).
fof(f27368,plain,
one != addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),addition(sK1,c(sK1)))),
inference(forward_demodulation,[],[f27271,f72]) ).
fof(f27271,plain,
one != addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),addition(multiplication(c(sK0),sK1),multiplication(c(sK0),c(sK1)))),
inference(superposition,[],[f49,f70]) ).
fof(f49,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]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : KLE010+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.37 % Computer : n026.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Wed Aug 30 18:05:51 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.23/0.43 % (14197)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.44 % (14218)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.23/0.44 % (14219)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.23/0.44 % (14221)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.23/0.44 % (14220)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.23/0.44 % (14222)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.23/0.44 % (14223)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.23/0.44 % (14224)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.23/0.44 TRYING [1]
% 0.23/0.44 TRYING [2]
% 0.23/0.44 TRYING [3]
% 0.23/0.44 TRYING [1]
% 0.23/0.45 TRYING [2]
% 0.23/0.45 TRYING [4]
% 0.23/0.46 TRYING [3]
% 0.23/0.49 TRYING [5]
% 0.23/0.50 TRYING [4]
% 0.23/0.58 TRYING [6]
% 0.23/0.62 TRYING [5]
% 0.23/0.68 % (14224)First to succeed.
% 0.23/0.68 % (14224)Refutation found. Thanks to Tanya!
% 0.23/0.68 % SZS status Theorem for Vampire---4
% 0.23/0.68 % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.68 % (14224)------------------------------
% 0.23/0.68 % (14224)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.68 % (14224)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.68 % (14224)Termination reason: Refutation
% 0.23/0.68
% 0.23/0.68 % (14224)Memory used [KB]: 6396
% 0.23/0.68 % (14224)Time elapsed: 0.242 s
% 0.23/0.68 % (14224)------------------------------
% 0.23/0.68 % (14224)------------------------------
% 0.23/0.68 % (14197)Success in time 0.285 s
% 0.23/0.68 % Vampire---4.8 exiting
%------------------------------------------------------------------------------