TSTP Solution File: KLE144+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE144+1 : 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 : n012.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 13:12:02 EDT 2024
% Result : Theorem 2.23s 0.69s
% Output : Refutation 2.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 71 ( 60 unt; 0 def)
% Number of atoms : 84 ( 53 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 30 ( 17 ~; 9 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 122 ( 120 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f27394,plain,
$false,
inference(trivial_inequality_removal,[],[f27148]) ).
fof(f27148,plain,
strong_iteration(one) != strong_iteration(one),
inference(superposition,[],[f30,f27055]) ).
fof(f27055,plain,
! [X0] : strong_iteration(one) = strong_iteration(star(X0)),
inference(forward_demodulation,[],[f26758,f25381]) ).
fof(f25381,plain,
! [X0] : strong_iteration(one) = strong_iteration(strong_iteration(X0)),
inference(superposition,[],[f23982,f10990]) ).
fof(f10990,plain,
! [X0] : strong_iteration(one) = addition(strong_iteration(one),X0),
inference(superposition,[],[f10984,f40]) ).
fof(f40,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(f10984,plain,
! [X0] : strong_iteration(one) = addition(X0,strong_iteration(one)),
inference(unit_resulting_resolution,[],[f10983,f41]) ).
fof(f41,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = 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/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f10983,plain,
! [X0] : leq(X0,strong_iteration(one)),
inference(superposition,[],[f10971,f33]) ).
fof(f33,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(f10971,plain,
! [X0,X1] : leq(X0,multiplication(strong_iteration(one),X1)),
inference(subsumption_resolution,[],[f10938,f202]) ).
fof(f202,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(unit_resulting_resolution,[],[f177,f42]) ).
fof(f42,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f177,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f43,f35]) ).
fof(f35,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',idempotence) ).
fof(f43,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/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
fof(f10938,plain,
! [X0,X1] :
( ~ leq(X0,addition(X0,X1))
| leq(X0,multiplication(strong_iteration(one),X1)) ),
inference(superposition,[],[f47,f34]) ).
fof(f34,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(f47,plain,
! [X2,X0,X1] :
( ~ leq(X2,addition(multiplication(X0,X2),X1))
| leq(X2,multiplication(strong_iteration(X0),X1)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2] :
( leq(X2,multiplication(strong_iteration(X0),X1))
| ~ leq(X2,addition(multiplication(X0,X2),X1)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1,X2] :
( leq(X2,addition(multiplication(X0,X2),X1))
=> leq(X2,multiplication(strong_iteration(X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infty_coinduction) ).
fof(f23982,plain,
! [X0,X1] : strong_iteration(strong_iteration(X0)) = addition(X1,strong_iteration(strong_iteration(X0))),
inference(unit_resulting_resolution,[],[f23960,f41]) ).
fof(f23960,plain,
! [X0,X1] : leq(X1,strong_iteration(strong_iteration(X0))),
inference(superposition,[],[f23947,f213]) ).
fof(f213,plain,
! [X0] : strong_iteration(X0) = addition(one,strong_iteration(X0)),
inference(superposition,[],[f177,f97]) ).
fof(f97,plain,
! [X0] : strong_iteration(X0) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(superposition,[],[f36,f40]) ).
fof(f36,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/sandbox2/benchmark/theBenchmark.p',infty_unfold1) ).
fof(f23947,plain,
! [X0,X1] : leq(X1,strong_iteration(addition(one,X0))),
inference(superposition,[],[f23788,f33]) ).
fof(f23788,plain,
! [X2,X0,X1] : leq(X1,multiplication(strong_iteration(addition(one,X0)),X2)),
inference(subsumption_resolution,[],[f23787,f202]) ).
fof(f23787,plain,
! [X2,X0,X1] :
( ~ leq(X1,addition(X1,addition(multiplication(X0,X1),X2)))
| leq(X1,multiplication(strong_iteration(addition(one,X0)),X2)) ),
inference(forward_demodulation,[],[f23486,f43]) ).
fof(f23486,plain,
! [X2,X0,X1] :
( ~ leq(X1,addition(addition(X1,multiplication(X0,X1)),X2))
| leq(X1,multiplication(strong_iteration(addition(one,X0)),X2)) ),
inference(superposition,[],[f47,f7121]) ).
fof(f7121,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f46,f34]) ).
fof(f46,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',distributivity2) ).
fof(f26758,plain,
! [X0] : strong_iteration(star(X0)) = strong_iteration(strong_iteration(star(X0))),
inference(superposition,[],[f23995,f10365]) ).
fof(f10365,plain,
! [X0] : strong_iteration(X0) = addition(strong_iteration(X0),X0),
inference(forward_demodulation,[],[f10282,f50]) ).
fof(f50,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f40,f32]) ).
fof(f32,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
fof(f10282,plain,
! [X0] : addition(zero,strong_iteration(X0)) = addition(strong_iteration(X0),X0),
inference(superposition,[],[f5053,f10215]) ).
fof(f10215,plain,
! [X0] : strong_iteration(X0) = addition(X0,strong_iteration(X0)),
inference(unit_resulting_resolution,[],[f10209,f41]) ).
fof(f10209,plain,
! [X0] : leq(X0,strong_iteration(X0)),
inference(superposition,[],[f10123,f97]) ).
fof(f10123,plain,
! [X2,X0,X1] : leq(X1,addition(X2,multiplication(X1,strong_iteration(X0)))),
inference(superposition,[],[f9842,f213]) ).
fof(f9842,plain,
! [X2,X0,X1] : leq(X0,addition(X2,multiplication(X0,addition(one,X1)))),
inference(superposition,[],[f302,f2775]) ).
fof(f2775,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f45,f33]) ).
fof(f45,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',distributivity1) ).
fof(f302,plain,
! [X2,X0,X1] : leq(X1,addition(X2,addition(X1,X0))),
inference(superposition,[],[f258,f40]) ).
fof(f258,plain,
! [X2,X0,X1] : leq(X2,addition(X0,addition(X1,X2))),
inference(superposition,[],[f231,f43]) ).
fof(f231,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(superposition,[],[f202,f40]) ).
fof(f5053,plain,
! [X0,X1] : addition(X1,X0) = addition(zero,addition(X0,X1)),
inference(superposition,[],[f192,f50]) ).
fof(f192,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(superposition,[],[f43,f40]) ).
fof(f23995,plain,
! [X0,X1] : strong_iteration(star(X0)) = addition(X1,strong_iteration(star(X0))),
inference(unit_resulting_resolution,[],[f23961,f41]) ).
fof(f23961,plain,
! [X0,X1] : leq(X1,strong_iteration(star(X0))),
inference(superposition,[],[f23947,f37]) ).
fof(f37,plain,
! [X0] : star(X0) = addition(one,multiplication(X0,star(X0))),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : star(X0) = addition(one,multiplication(X0,star(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold1) ).
fof(f30,plain,
strong_iteration(one) != strong_iteration(star(sK0)),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
strong_iteration(one) != strong_iteration(star(sK0)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f23,f27]) ).
fof(f27,plain,
( ? [X0] : strong_iteration(one) != strong_iteration(star(X0))
=> strong_iteration(one) != strong_iteration(star(sK0)) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
? [X0] : strong_iteration(one) != strong_iteration(star(X0)),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
~ ! [X0] : strong_iteration(one) = strong_iteration(star(X0)),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ! [X3] : strong_iteration(star(X3)) = strong_iteration(one),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
! [X3] : strong_iteration(star(X3)) = strong_iteration(one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE144+1 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n012.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 : Tue Apr 30 04:57:42 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.21/0.35 % (32621)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.36 % (32627)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)
% 0.21/0.37 % (32624)WARNING: value z3 for option sas not known
% 0.21/0.37 % (32622)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.37 % (32623)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.37 % (32625)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.37 % (32626)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)
% 0.21/0.37 % (32624)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)
% 0.21/0.37 % (32628)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)
% 0.21/0.37 TRYING [1]
% 0.21/0.37 TRYING [2]
% 0.21/0.37 TRYING [3]
% 0.21/0.38 TRYING [1]
% 0.21/0.38 TRYING [2]
% 0.21/0.39 TRYING [4]
% 0.21/0.39 TRYING [3]
% 0.21/0.43 TRYING [5]
% 0.21/0.44 TRYING [4]
% 0.21/0.52 TRYING [6]
% 0.21/0.54 TRYING [5]
% 2.23/0.69 % (32628)First to succeed.
% 2.23/0.69 % (32628)Refutation found. Thanks to Tanya!
% 2.23/0.69 % SZS status Theorem for theBenchmark
% 2.23/0.69 % SZS output start Proof for theBenchmark
% See solution above
% 2.23/0.69 % (32628)------------------------------
% 2.23/0.69 % (32628)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 2.23/0.69 % (32628)Termination reason: Refutation
% 2.23/0.69
% 2.23/0.69 % (32628)Memory used [KB]: 6078
% 2.23/0.69 % (32628)Time elapsed: 0.319 s
% 2.23/0.69 % (32628)Instructions burned: 837 (million)
% 2.23/0.69 % (32628)------------------------------
% 2.23/0.69 % (32628)------------------------------
% 2.23/0.69 % (32621)Success in time 0.334 s
%------------------------------------------------------------------------------