TSTP Solution File: KLE148+2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE148+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 : n017.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 13:12:03 EDT 2024
% Result : Theorem 0.21s 0.51s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 51 ( 36 unt; 0 def)
% Number of atoms : 77 ( 43 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 49 ( 23 ~; 13 |; 8 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 74 ( 70 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4277,plain,
$false,
inference(resolution,[],[f4258,f65]) ).
fof(f65,plain,
! [X0] : leq(X0,X0),
inference(trivial_inequality_removal,[],[f60]) ).
fof(f60,plain,
! [X0] :
( X0 != X0
| leq(X0,X0) ),
inference(superposition,[],[f43,f36]) ).
fof(f36,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',idempotence) ).
fof(f43,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f4258,plain,
~ leq(sK0,sK0),
inference(duplicate_literal_removal,[],[f4257]) ).
fof(f4257,plain,
( ~ leq(sK0,sK0)
| ~ leq(sK0,sK0) ),
inference(forward_demodulation,[],[f4256,f4255]) ).
fof(f4255,plain,
sK0 = multiplication(sK0,strong_iteration(sK1)),
inference(forward_demodulation,[],[f4227,f34]) ).
fof(f34,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(f4227,plain,
multiplication(sK0,strong_iteration(sK1)) = multiplication(sK0,one),
inference(superposition,[],[f1175,f39]) ).
fof(f39,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_unfold1) ).
fof(f1175,plain,
! [X0,X1] : multiplication(sK0,addition(multiplication(sK1,X0),X1)) = multiplication(sK0,X1),
inference(forward_demodulation,[],[f1165,f51]) ).
fof(f51,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f41,f33]) ).
fof(f33,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
fof(f41,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(f1165,plain,
! [X0,X1] : multiplication(sK0,addition(multiplication(sK1,X0),X1)) = addition(zero,multiplication(sK0,X1)),
inference(superposition,[],[f46,f1155]) ).
fof(f1155,plain,
! [X0] : zero = multiplication(sK0,multiplication(sK1,X0)),
inference(forward_demodulation,[],[f1146,f32]) ).
fof(f32,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] : zero = multiplication(zero,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
fof(f1146,plain,
! [X0] : multiplication(zero,X0) = multiplication(sK0,multiplication(sK1,X0)),
inference(superposition,[],[f45,f1140]) ).
fof(f1140,plain,
zero = multiplication(sK0,sK1),
inference(resolution,[],[f1126,f30]) ).
fof(f30,plain,
( ~ leq(sK0,multiplication(sK0,strong_iteration(sK1)))
| zero = multiplication(sK0,sK1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
( ~ leq(sK0,multiplication(sK0,strong_iteration(sK1)))
| ( ~ leq(multiplication(sK0,strong_iteration(sK1)),sK0)
& zero = multiplication(sK0,sK1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f23,f27]) ).
fof(f27,plain,
( ? [X0,X1] :
( ~ leq(X0,multiplication(X0,strong_iteration(X1)))
| ( ~ leq(multiplication(X0,strong_iteration(X1)),X0)
& zero = multiplication(X0,X1) ) )
=> ( ~ leq(sK0,multiplication(sK0,strong_iteration(sK1)))
| ( ~ leq(multiplication(sK0,strong_iteration(sK1)),sK0)
& zero = multiplication(sK0,sK1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
? [X0,X1] :
( ~ leq(X0,multiplication(X0,strong_iteration(X1)))
| ( ~ leq(multiplication(X0,strong_iteration(X1)),X0)
& zero = multiplication(X0,X1) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
~ ! [X0,X1] :
( leq(X0,multiplication(X0,strong_iteration(X1)))
& ( zero = multiplication(X0,X1)
=> leq(multiplication(X0,strong_iteration(X1)),X0) ) ),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ! [X3,X4] :
( leq(X3,multiplication(X3,strong_iteration(X4)))
& ( zero = multiplication(X3,X4)
=> leq(multiplication(X3,strong_iteration(X4)),X3) ) ),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
! [X3,X4] :
( leq(X3,multiplication(X3,strong_iteration(X4)))
& ( zero = multiplication(X3,X4)
=> leq(multiplication(X3,strong_iteration(X4)),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f1126,plain,
! [X0,X1] : leq(X1,multiplication(X1,strong_iteration(X0))),
inference(forward_demodulation,[],[f1112,f34]) ).
fof(f1112,plain,
! [X0,X1] : leq(multiplication(X1,one),multiplication(X1,strong_iteration(X0))),
inference(superposition,[],[f345,f103]) ).
fof(f103,plain,
! [X0] : strong_iteration(X0) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(superposition,[],[f39,f41]) ).
fof(f345,plain,
! [X2,X0,X1] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(superposition,[],[f196,f46]) ).
fof(f196,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(trivial_inequality_removal,[],[f194]) ).
fof(f194,plain,
! [X0,X1] :
( addition(X0,X1) != addition(X0,X1)
| leq(X0,addition(X0,X1)) ),
inference(superposition,[],[f43,f151]) ).
fof(f151,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f44,f36]) ).
fof(f44,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f22]) ).
fof(f22,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(f45,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(f46,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',distributivity1) ).
fof(f4256,plain,
( ~ leq(sK0,sK0)
| ~ leq(sK0,multiplication(sK0,strong_iteration(sK1))) ),
inference(backward_demodulation,[],[f31,f4255]) ).
fof(f31,plain,
( ~ leq(multiplication(sK0,strong_iteration(sK1)),sK0)
| ~ leq(sK0,multiplication(sK0,strong_iteration(sK1))) ),
inference(cnf_transformation,[],[f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : KLE148+2 : TPTP v8.1.2. Released v4.0.0.
% 0.04/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n017.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 : Tue Apr 30 04:35:19 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (11193)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.38 % (11196)WARNING: value z3 for option sas not known
% 0.21/0.38 % (11194)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38 % (11195)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38 % (11197)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38 % (11196)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)
% 0.21/0.38 % (11199)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)
% 0.21/0.38 % (11200)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)
% 0.21/0.38 % (11198)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)
% 0.21/0.38 TRYING [1]
% 0.21/0.38 TRYING [2]
% 0.21/0.39 TRYING [3]
% 0.21/0.39 TRYING [1]
% 0.21/0.39 TRYING [2]
% 0.21/0.40 TRYING [4]
% 0.21/0.41 TRYING [3]
% 0.21/0.44 TRYING [5]
% 0.21/0.45 TRYING [4]
% 0.21/0.51 % (11199)First to succeed.
% 0.21/0.51 % (11199)Refutation found. Thanks to Tanya!
% 0.21/0.51 % SZS status Theorem for theBenchmark
% 0.21/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.51 % (11199)------------------------------
% 0.21/0.51 % (11199)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.51 % (11199)Termination reason: Refutation
% 0.21/0.51
% 0.21/0.51 % (11199)Memory used [KB]: 2398
% 0.21/0.51 % (11199)Time elapsed: 0.131 s
% 0.21/0.51 % (11199)Instructions burned: 202 (million)
% 0.21/0.51 % (11199)------------------------------
% 0.21/0.51 % (11199)------------------------------
% 0.21/0.51 % (11193)Success in time 0.147 s
%------------------------------------------------------------------------------