TSTP Solution File: KLE026+2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE026+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 : n004.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 07:17:04 EDT 2024
% Result : Theorem 1.22s 0.52s
% Output : Refutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 48 ( 25 unt; 0 def)
% Number of atoms : 111 ( 47 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 89 ( 26 ~; 18 |; 31 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 85 ( 71 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11994,plain,
$false,
inference(subsumption_resolution,[],[f11990,f51]) ).
fof(f51,plain,
~ leq(multiplication(sK1,sK0),multiplication(sK0,sK2)),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
( ~ leq(multiplication(sK1,sK0),multiplication(sK0,sK2))
& multiplication(sK1,sK0) = multiplication(multiplication(sK1,sK0),sK2)
& test(sK2)
& test(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f31,f39]) ).
fof(f39,plain,
( ? [X0,X1,X2] :
( ~ leq(multiplication(X1,X0),multiplication(X0,X2))
& multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
& test(X2)
& test(X1) )
=> ( ~ leq(multiplication(sK1,sK0),multiplication(sK0,sK2))
& multiplication(sK1,sK0) = multiplication(multiplication(sK1,sK0),sK2)
& test(sK2)
& test(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
? [X0,X1,X2] :
( ~ leq(multiplication(X1,X0),multiplication(X0,X2))
& multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
& test(X2)
& test(X1) ),
inference(flattening,[],[f30]) ).
fof(f30,plain,
? [X0,X1,X2] :
( ~ leq(multiplication(X1,X0),multiplication(X0,X2))
& multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
& test(X2)
& test(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
=> leq(multiplication(X1,X0),multiplication(X0,X2)) ) ),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ! [X3,X4,X5] :
( ( test(X5)
& test(X4) )
=> ( multiplication(X4,X3) = multiplication(multiplication(X4,X3),X5)
=> leq(multiplication(X4,X3),multiplication(X3,X5)) ) ),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
! [X3,X4,X5] :
( ( test(X5)
& test(X4) )
=> ( multiplication(X4,X3) = multiplication(multiplication(X4,X3),X5)
=> leq(multiplication(X4,X3),multiplication(X3,X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f11990,plain,
leq(multiplication(sK1,sK0),multiplication(sK0,sK2)),
inference(superposition,[],[f11972,f1307]) ).
fof(f1307,plain,
multiplication(sK1,sK0) = multiplication(sK1,multiplication(sK0,sK2)),
inference(superposition,[],[f72,f50]) ).
fof(f50,plain,
multiplication(sK1,sK0) = multiplication(multiplication(sK1,sK0),sK2),
inference(cnf_transformation,[],[f40]) ).
fof(f72,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f11972,plain,
! [X0] : leq(multiplication(sK1,X0),X0),
inference(forward_demodulation,[],[f11923,f56]) ).
fof(f56,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f11923,plain,
! [X0] : leq(multiplication(sK1,X0),multiplication(one,X0)),
inference(superposition,[],[f5244,f634]) ).
fof(f634,plain,
one = addition(sK1,one),
inference(superposition,[],[f539,f196]) ).
fof(f196,plain,
one = addition(sK1,sK3(sK1)),
inference(unit_resulting_resolution,[],[f76,f68]) ).
fof(f68,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,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,[],[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(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(f76,plain,
complement(sK3(sK1),sK1),
inference(unit_resulting_resolution,[],[f48,f59]) ).
fof(f59,plain,
! [X0] :
( ~ test(X0)
| complement(sK3(X0),X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( complement(sK3(X0),X0)
| ~ test(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f42,f43]) ).
fof(f43,plain,
! [X0] :
( ? [X2] : complement(X2,X0)
=> complement(sK3(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f42,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( ? [X2] : complement(X2,X0)
| ~ test(X0) ) ),
inference(rectify,[],[f41]) ).
fof(f41,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(f48,plain,
test(sK1),
inference(cnf_transformation,[],[f40]) ).
fof(f539,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f71,f57]) ).
fof(f57,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f71,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(f5244,plain,
! [X2,X0,X1] : leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)),
inference(superposition,[],[f610,f74]) ).
fof(f74,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/benchmark/theBenchmark.p',left_distributivity) ).
fof(f610,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(unit_resulting_resolution,[],[f539,f70]) ).
fof(f70,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( addition(X0,X1) = X1
=> leq(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE026+2 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n004.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 21:22:53 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (3864)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (3867)WARNING: value z3 for option sas not known
% 0.15/0.37 % (3866)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37 % (3868)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37 % (3865)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37 % (3867)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)
% 0.15/0.37 % (3869)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)
% 0.15/0.37 % (3870)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)
% 0.15/0.37 % (3871)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 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [3]
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.21/0.39 TRYING [4]
% 0.21/0.40 TRYING [3]
% 0.21/0.42 TRYING [5]
% 0.21/0.44 TRYING [4]
% 0.21/0.46 TRYING [1]
% 0.21/0.46 TRYING [2]
% 0.21/0.46 TRYING [3]
% 0.21/0.48 TRYING [4]
% 0.21/0.50 TRYING [6]
% 1.22/0.52 % (3871)First to succeed.
% 1.22/0.52 % (3867)Also succeeded, but the first one will report.
% 1.22/0.52 % (3871)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3864"
% 1.22/0.52 % (3871)Refutation found. Thanks to Tanya!
% 1.22/0.52 % SZS status Theorem for theBenchmark
% 1.22/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 1.22/0.52 % (3871)------------------------------
% 1.22/0.52 % (3871)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.22/0.52 % (3871)Termination reason: Refutation
% 1.22/0.52
% 1.22/0.52 % (3871)Memory used [KB]: 2709
% 1.22/0.52 % (3871)Time elapsed: 0.148 s
% 1.22/0.52 % (3871)Instructions burned: 318 (million)
% 1.22/0.52 % (3864)Success in time 0.153 s
%------------------------------------------------------------------------------