TSTP Solution File: KLE009+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE009+2 : 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 : n013.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 : Sun May 5 07:16:48 EDT 2024
% Result : Theorem 0.22s 0.44s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 73 ( 33 unt; 0 def)
% Number of atoms : 160 ( 85 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 148 ( 61 ~; 46 |; 27 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 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 : 80 ( 69 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2057,plain,
$false,
inference(subsumption_resolution,[],[f2056,f1311]) ).
fof(f1311,plain,
one = addition(sK0,c(sK0)),
inference(superposition,[],[f110,f1276]) ).
fof(f1276,plain,
c(sK0) = sK2(sK0),
inference(subsumption_resolution,[],[f1271,f47]) ).
fof(f47,plain,
test(sK0),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
( one != addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(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(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))
& test(X0)
& test(X1) )
=> ( one != addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(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(multiplication(X0,X1),multiplication(X0,c(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(multiplication(X0,X1),multiplication(X0,c(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(multiplication(X0,X1),multiplication(X0,c(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(multiplication(X3,X4),multiplication(X3,c(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(multiplication(X3,X4),multiplication(X3,c(X4))),multiplication(c(X3),X4)),multiplication(c(X3),c(X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f1271,plain,
( c(sK0) = sK2(sK0)
| ~ test(sK0) ),
inference(resolution,[],[f1230,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/sandbox/benchmark/theBenchmark.p',test_3) ).
fof(f1230,plain,
complement(sK0,sK2(sK0)),
inference(subsumption_resolution,[],[f1229,f110]) ).
fof(f1229,plain,
( one != addition(sK0,sK2(sK0))
| complement(sK0,sK2(sK0)) ),
inference(forward_demodulation,[],[f1228,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/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f1228,plain,
( one != addition(sK2(sK0),sK0)
| complement(sK0,sK2(sK0)) ),
inference(subsumption_resolution,[],[f1163,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(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/sandbox/benchmark/theBenchmark.p',test_1) ).
fof(f64,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X1,X0) ),
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/sandbox/benchmark/theBenchmark.p',test_2) ).
fof(f1163,plain,
( one != addition(sK2(sK0),sK0)
| complement(sK0,sK2(sK0))
| zero != multiplication(sK2(sK0),sK0) ),
inference(trivial_inequality_removal,[],[f1140]) ).
fof(f1140,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(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(f65,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f45]) ).
fof(f2056,plain,
one != addition(sK0,c(sK0)),
inference(forward_demodulation,[],[f2055,f52]) ).
fof(f52,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f2055,plain,
one != addition(multiplication(sK0,one),c(sK0)),
inference(forward_demodulation,[],[f2054,f52]) ).
fof(f2054,plain,
one != addition(multiplication(sK0,one),multiplication(c(sK0),one)),
inference(forward_demodulation,[],[f2053,f1356]) ).
fof(f1356,plain,
one = addition(sK1,c(sK1)),
inference(superposition,[],[f111,f1289]) ).
fof(f1289,plain,
c(sK1) = sK2(sK1),
inference(subsumption_resolution,[],[f1284,f46]) ).
fof(f46,plain,
test(sK1),
inference(cnf_transformation,[],[f38]) ).
fof(f1284,plain,
( c(sK1) = sK2(sK1)
| ~ test(sK1) ),
inference(resolution,[],[f1262,f60]) ).
fof(f1262,plain,
complement(sK1,sK2(sK1)),
inference(subsumption_resolution,[],[f1261,f111]) ).
fof(f1261,plain,
( one != addition(sK1,sK2(sK1))
| complement(sK1,sK2(sK1)) ),
inference(forward_demodulation,[],[f1260,f58]) ).
fof(f1260,plain,
( one != addition(sK2(sK1),sK1)
| complement(sK1,sK2(sK1)) ),
inference(subsumption_resolution,[],[f1159,f103]) ).
fof(f103,plain,
zero = multiplication(sK2(sK1),sK1),
inference(resolution,[],[f84,f46]) ).
fof(f1159,plain,
( one != addition(sK2(sK1),sK1)
| complement(sK1,sK2(sK1))
| zero != multiplication(sK2(sK1),sK1) ),
inference(trivial_inequality_removal,[],[f1150]) ).
fof(f1150,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(f111,plain,
one = addition(sK1,sK2(sK1)),
inference(resolution,[],[f86,f46]) ).
fof(f2053,plain,
one != addition(multiplication(sK0,addition(sK1,c(sK1))),multiplication(c(sK0),addition(sK1,c(sK1)))),
inference(forward_demodulation,[],[f1988,f69]) ).
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/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
fof(f1988,plain,
one != addition(multiplication(sK0,addition(sK1,c(sK1))),addition(multiplication(c(sK0),sK1),multiplication(c(sK0),c(sK1)))),
inference(superposition,[],[f938,f114]) ).
fof(f114,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(superposition,[],[f67,f58]) ).
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/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
fof(f938,plain,
one != addition(addition(multiplication(c(sK0),sK1),multiplication(sK0,addition(sK1,c(sK1)))),multiplication(c(sK0),c(sK1))),
inference(forward_demodulation,[],[f937,f69]) ).
fof(f937,plain,
one != addition(addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1)))),multiplication(c(sK0),c(sK1))),
inference(forward_demodulation,[],[f48,f58]) ).
fof(f48,plain,
one != addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),
inference(cnf_transformation,[],[f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : KLE009+2 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n013.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 21:23:23 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (997)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (1000)WARNING: value z3 for option sas not known
% 0.15/0.38 % (1001)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (999)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (1003)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)
% 0.15/0.38 % (1002)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)
% 0.15/0.38 % (1000)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)
% 0.15/0.38 % (1004)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)
% 0.15/0.38 % (998)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.39 TRYING [3]
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.40 TRYING [4]
% 0.15/0.40 TRYING [1]
% 0.15/0.40 TRYING [2]
% 0.15/0.40 TRYING [3]
% 0.15/0.41 TRYING [3]
% 0.22/0.42 TRYING [4]
% 0.22/0.43 TRYING [5]
% 0.22/0.43 % (1000)First to succeed.
% 0.22/0.44 % (1000)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-997"
% 0.22/0.44 % (1000)Refutation found. Thanks to Tanya!
% 0.22/0.44 % SZS status Theorem for theBenchmark
% 0.22/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.44 % (1000)------------------------------
% 0.22/0.44 % (1000)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.44 % (1000)Termination reason: Refutation
% 0.22/0.44
% 0.22/0.44 % (1000)Memory used [KB]: 1665
% 0.22/0.44 % (1000)Time elapsed: 0.056 s
% 0.22/0.44 % (1000)Instructions burned: 101 (million)
% 0.22/0.44 % (997)Success in time 0.073 s
%------------------------------------------------------------------------------