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 --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n027.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 : Tue Apr 30 13:11:38 EDT 2024
% Result : Theorem 0.21s 0.50s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 94 ( 54 unt; 0 def)
% Number of atoms : 181 ( 106 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 152 ( 65 ~; 46 |; 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 96 ( 85 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4511,plain,
$false,
inference(subsumption_resolution,[],[f4476,f1217]) ).
fof(f1217,plain,
one = addition(c(sK0),sK0),
inference(forward_demodulation,[],[f1095,f1099]) ).
fof(f1099,plain,
c(sK0) = sK2(sK0),
inference(subsumption_resolution,[],[f1094,f47]) ).
fof(f47,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/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f1094,plain,
( c(sK0) = sK2(sK0)
| ~ test(sK0) ),
inference(resolution,[],[f1053,f60]) ).
fof(f60,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/benchmark/theBenchmark.p',test_3) ).
fof(f1053,plain,
complement(sK0,sK2(sK0)),
inference(subsumption_resolution,[],[f1052,f110]) ).
fof(f110,plain,
one = addition(sK0,sK2(sK0)),
inference(resolution,[],[f86,f47]) ).
fof(f86,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,sK2(X0)) ),
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/benchmark/theBenchmark.p',test_1) ).
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/benchmark/theBenchmark.p',test_2) ).
fof(f1052,plain,
( one != addition(sK0,sK2(sK0))
| complement(sK0,sK2(sK0)) ),
inference(forward_demodulation,[],[f1051,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/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f1051,plain,
( one != addition(sK2(sK0),sK0)
| complement(sK0,sK2(sK0)) ),
inference(subsumption_resolution,[],[f986,f102]) ).
fof(f102,plain,
zero = multiplication(sK2(sK0),sK0),
inference(resolution,[],[f84,f47]) ).
fof(f84,plain,
! [X0] :
( ~ test(X0)
| zero = multiplication(sK2(X0),X0) ),
inference(resolution,[],[f64,f56]) ).
fof(f64,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X1,X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f986,plain,
( one != addition(sK2(sK0),sK0)
| complement(sK0,sK2(sK0))
| zero != multiplication(sK2(sK0),sK0) ),
inference(trivial_inequality_removal,[],[f963]) ).
fof(f963,plain,
( zero != zero
| one != addition(sK2(sK0),sK0)
| complement(sK0,sK2(sK0))
| zero != multiplication(sK2(sK0),sK0) ),
inference(superposition,[],[f66,f91]) ).
fof(f91,plain,
zero = multiplication(sK0,sK2(sK0)),
inference(resolution,[],[f82,f47]) ).
fof(f82,plain,
! [X0] :
( ~ test(X0)
| zero = multiplication(X0,sK2(X0)) ),
inference(resolution,[],[f63,f56]) ).
fof(f63,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f66,plain,
! [X0,X1] :
( zero != multiplication(X1,X0)
| addition(X0,X1) != one
| complement(X1,X0)
| zero != multiplication(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f1095,plain,
one = addition(sK2(sK0),sK0),
inference(resolution,[],[f1053,f65]) ).
fof(f4476,plain,
one != addition(c(sK0),sK0),
inference(superposition,[],[f2062,f4249]) ).
fof(f4249,plain,
! [X0] : addition(X0,multiplication(X0,sK1)) = X0,
inference(forward_demodulation,[],[f4163,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/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f4163,plain,
! [X0] : multiplication(X0,one) = addition(X0,multiplication(X0,sK1)),
inference(superposition,[],[f310,f855]) ).
fof(f855,plain,
one = addition(one,sK1),
inference(superposition,[],[f852,f58]) ).
fof(f852,plain,
one = addition(sK1,one),
inference(forward_demodulation,[],[f847,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/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f847,plain,
addition(one,one) = addition(sK1,one),
inference(superposition,[],[f142,f146]) ).
fof(f146,plain,
one = addition(one,sK2(sK1)),
inference(forward_demodulation,[],[f141,f111]) ).
fof(f111,plain,
one = addition(sK1,sK2(sK1)),
inference(resolution,[],[f86,f46]) ).
fof(f46,plain,
test(sK1),
inference(cnf_transformation,[],[f38]) ).
fof(f141,plain,
addition(sK1,sK2(sK1)) = addition(one,sK2(sK1)),
inference(superposition,[],[f119,f54]) ).
fof(f119,plain,
! [X0] : addition(one,X0) = addition(sK1,addition(sK2(sK1),X0)),
inference(superposition,[],[f67,f111]) ).
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/benchmark/theBenchmark.p',additive_associativity) ).
fof(f142,plain,
! [X0] : addition(one,X0) = addition(sK1,addition(X0,sK2(sK1))),
inference(superposition,[],[f119,f58]) ).
fof(f310,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
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/benchmark/theBenchmark.p',right_distributivity) ).
fof(f2062,plain,
one != addition(c(sK0),addition(sK0,multiplication(sK0,sK1))),
inference(superposition,[],[f2024,f58]) ).
fof(f2024,plain,
one != addition(addition(sK0,multiplication(sK0,sK1)),c(sK0)),
inference(forward_demodulation,[],[f2023,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/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f2023,plain,
one != addition(addition(multiplication(one,sK0),multiplication(sK0,sK1)),c(sK0)),
inference(forward_demodulation,[],[f2022,f58]) ).
fof(f2022,plain,
one != addition(addition(multiplication(sK0,sK1),multiplication(one,sK0)),c(sK0)),
inference(forward_demodulation,[],[f2021,f52]) ).
fof(f2021,plain,
one != addition(addition(multiplication(sK0,sK1),multiplication(one,sK0)),multiplication(c(sK0),one)),
inference(forward_demodulation,[],[f2020,f1173]) ).
fof(f1173,plain,
one = addition(sK1,c(sK1)),
inference(superposition,[],[f111,f1112]) ).
fof(f1112,plain,
c(sK1) = sK2(sK1),
inference(subsumption_resolution,[],[f1107,f46]) ).
fof(f1107,plain,
( c(sK1) = sK2(sK1)
| ~ test(sK1) ),
inference(resolution,[],[f1085,f60]) ).
fof(f1085,plain,
complement(sK1,sK2(sK1)),
inference(subsumption_resolution,[],[f1084,f111]) ).
fof(f1084,plain,
( one != addition(sK1,sK2(sK1))
| complement(sK1,sK2(sK1)) ),
inference(forward_demodulation,[],[f1083,f58]) ).
fof(f1083,plain,
( one != addition(sK2(sK1),sK1)
| complement(sK1,sK2(sK1)) ),
inference(subsumption_resolution,[],[f982,f103]) ).
fof(f103,plain,
zero = multiplication(sK2(sK1),sK1),
inference(resolution,[],[f84,f46]) ).
fof(f982,plain,
( one != addition(sK2(sK1),sK1)
| complement(sK1,sK2(sK1))
| zero != multiplication(sK2(sK1),sK1) ),
inference(trivial_inequality_removal,[],[f973]) ).
fof(f973,plain,
( zero != zero
| one != addition(sK2(sK1),sK1)
| complement(sK1,sK2(sK1))
| zero != multiplication(sK2(sK1),sK1) ),
inference(superposition,[],[f66,f92]) ).
fof(f92,plain,
zero = multiplication(sK1,sK2(sK1)),
inference(resolution,[],[f82,f46]) ).
fof(f2020,plain,
one != addition(addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)),multiplication(c(sK0),addition(sK1,c(sK1)))),
inference(forward_demodulation,[],[f1967,f69]) ).
fof(f1967,plain,
one != addition(addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)),addition(multiplication(c(sK0),sK1),multiplication(c(sK0),c(sK1)))),
inference(superposition,[],[f1170,f114]) ).
fof(f114,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(superposition,[],[f67,f58]) ).
fof(f1170,plain,
one != addition(addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0))),multiplication(c(sK0),c(sK1))),
inference(forward_demodulation,[],[f1169,f70]) ).
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/benchmark/theBenchmark.p',left_distributivity) ).
fof(f1169,plain,
one != addition(addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)))),multiplication(c(sK0),c(sK1))),
inference(forward_demodulation,[],[f1168,f58]) ).
fof(f1168,plain,
one != addition(addition(multiplication(c(sK0),sK1),addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1))),multiplication(c(sK0),c(sK1))),
inference(forward_demodulation,[],[f48,f58]) ).
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]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : KLE010+3 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n027.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 Apr 30 05:32:02 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (19711)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (19714)WARNING: value z3 for option sas not known
% 0.14/0.38 % (19715)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (19712)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (19713)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (19716)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 theBenchmark for (531ds/0Mi)
% 0.14/0.38 % (19717)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 theBenchmark for (522ds/0Mi)
% 0.14/0.38 % (19714)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 theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (19718)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 theBenchmark for (497ds/0Mi)
% 0.14/0.38 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.14/0.39 TRYING [3]
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.14/0.40 TRYING [4]
% 0.14/0.41 TRYING [3]
% 0.21/0.43 TRYING [5]
% 0.21/0.45 TRYING [4]
% 0.21/0.50 % (19714)First to succeed.
% 0.21/0.50 % (19714)Refutation found. Thanks to Tanya!
% 0.21/0.50 % SZS status Theorem for theBenchmark
% 0.21/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.50 % (19714)------------------------------
% 0.21/0.50 % (19714)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.50 % (19714)Termination reason: Refutation
% 0.21/0.50
% 0.21/0.50 % (19714)Memory used [KB]: 2397
% 0.21/0.50 % (19714)Time elapsed: 0.116 s
% 0.21/0.50 % (19714)Instructions burned: 245 (million)
% 0.21/0.50 % (19714)------------------------------
% 0.21/0.50 % (19714)------------------------------
% 0.21/0.50 % (19711)Success in time 0.12 s
%------------------------------------------------------------------------------