TSTP Solution File: KLE041+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE041+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 : 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 : Tue Apr 30 13:11:46 EDT 2024
% Result : Theorem 6.90s 1.33s
% Output : Refutation 6.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 13
% Syntax : Number of formulae : 87 ( 68 unt; 0 def)
% Number of atoms : 110 ( 50 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 19 ~; 12 |; 5 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 125 ( 121 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f46496,plain,
$false,
inference(resolution,[],[f46495,f28]) ).
fof(f28,plain,
~ leq(star(sK0),star(sK1)),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
( ~ leq(star(sK0),star(sK1))
& leq(sK0,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f21,f24]) ).
fof(f24,plain,
( ? [X0,X1] :
( ~ leq(star(X0),star(X1))
& leq(X0,X1) )
=> ( ~ leq(star(sK0),star(sK1))
& leq(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
? [X0,X1] :
( ~ leq(star(X0),star(X1))
& leq(X0,X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
~ ! [X0,X1] :
( leq(X0,X1)
=> leq(star(X0),star(X1)) ),
inference(rectify,[],[f18]) ).
fof(f18,negated_conjecture,
~ ! [X3,X4] :
( leq(X3,X4)
=> leq(star(X3),star(X4)) ),
inference(negated_conjecture,[],[f17]) ).
fof(f17,conjecture,
! [X3,X4] :
( leq(X3,X4)
=> leq(star(X3),star(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f46495,plain,
leq(star(sK0),star(sK1)),
inference(forward_demodulation,[],[f46491,f33]) ).
fof(f33,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(f46491,plain,
leq(multiplication(one,star(sK0)),star(sK1)),
inference(resolution,[],[f46473,f918]) ).
fof(f918,plain,
! [X2,X0,X1] :
( ~ leq(addition(X2,multiplication(X0,X1)),X0)
| leq(multiplication(X2,star(X1)),X0) ),
inference(superposition,[],[f44,f37]) ).
fof(f37,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(f44,plain,
! [X2,X0,X1] :
( ~ leq(addition(multiplication(X0,X1),X2),X0)
| leq(multiplication(X2,star(X1)),X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X0,X1),X2),X0)
=> leq(multiplication(X2,star(X1)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction_right) ).
fof(f46473,plain,
leq(addition(one,multiplication(star(sK1),sK0)),star(sK1)),
inference(forward_demodulation,[],[f46472,f35192]) ).
fof(f35192,plain,
! [X0] : star(X0) = addition(one,star(X0)),
inference(superposition,[],[f103,f4911]) ).
fof(f4911,plain,
! [X0] : star(X0) = addition(one,multiplication(addition(one,X0),star(X0))),
inference(forward_demodulation,[],[f4910,f763]) ).
fof(f763,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f43,f33]) ).
fof(f43,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(f4910,plain,
! [X0] : star(X0) = addition(one,addition(star(X0),multiplication(X0,star(X0)))),
inference(forward_demodulation,[],[f4872,f37]) ).
fof(f4872,plain,
! [X0] : star(X0) = addition(one,addition(multiplication(X0,star(X0)),star(X0))),
inference(superposition,[],[f76,f40]) ).
fof(f40,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f20]) ).
fof(f20,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(f76,plain,
! [X0] : star(X0) = addition(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(resolution,[],[f35,f38]) ).
fof(f38,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f35,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold_right) ).
fof(f103,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f40,f34]) ).
fof(f34,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(f46472,plain,
leq(addition(one,multiplication(addition(one,star(sK1)),sK0)),star(sK1)),
inference(forward_demodulation,[],[f46471,f763]) ).
fof(f46471,plain,
leq(addition(one,addition(sK0,multiplication(star(sK1),sK0))),star(sK1)),
inference(forward_demodulation,[],[f46470,f40]) ).
fof(f46470,plain,
leq(addition(addition(one,sK0),multiplication(star(sK1),sK0)),star(sK1)),
inference(forward_demodulation,[],[f46408,f37]) ).
fof(f46408,plain,
leq(addition(multiplication(star(sK1),sK0),addition(one,sK0)),star(sK1)),
inference(superposition,[],[f42947,f35555]) ).
fof(f35555,plain,
star(sK1) = addition(multiplication(star(sK1),sK0),star(sK1)),
inference(resolution,[],[f35453,f38]) ).
fof(f35453,plain,
leq(multiplication(star(sK1),sK0),star(sK1)),
inference(superposition,[],[f9161,f35261]) ).
fof(f35261,plain,
! [X0] : star(X0) = addition(multiplication(star(X0),X0),star(X0)),
inference(backward_demodulation,[],[f5155,f35192]) ).
fof(f5155,plain,
! [X0] : star(X0) = addition(multiplication(star(X0),X0),addition(one,star(X0))),
inference(superposition,[],[f81,f104]) ).
fof(f104,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(superposition,[],[f40,f37]) ).
fof(f81,plain,
! [X0] : star(X0) = addition(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(resolution,[],[f36,f38]) ).
fof(f36,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold_left) ).
fof(f9161,plain,
! [X0,X1] : leq(multiplication(X1,sK0),addition(multiplication(X1,sK1),X0)),
inference(superposition,[],[f9116,f37]) ).
fof(f9116,plain,
! [X0,X1] : leq(multiplication(X0,sK0),addition(X1,multiplication(X0,sK1))),
inference(superposition,[],[f827,f8328]) ).
fof(f8328,plain,
! [X0] : multiplication(X0,sK1) = addition(multiplication(X0,sK0),multiplication(X0,sK1)),
inference(resolution,[],[f8301,f38]) ).
fof(f8301,plain,
! [X0] : leq(multiplication(X0,sK0),multiplication(X0,sK1)),
inference(trivial_inequality_removal,[],[f8282]) ).
fof(f8282,plain,
! [X0] :
( multiplication(X0,sK1) != multiplication(X0,sK1)
| leq(multiplication(X0,sK0),multiplication(X0,sK1)) ),
inference(superposition,[],[f359,f54]) ).
fof(f54,plain,
sK1 = addition(sK0,sK1),
inference(resolution,[],[f38,f27]) ).
fof(f27,plain,
leq(sK0,sK1),
inference(cnf_transformation,[],[f25]) ).
fof(f359,plain,
! [X2,X0,X1] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(superposition,[],[f39,f42]) ).
fof(f42,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(f39,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f827,plain,
! [X2,X0,X1] : leq(X1,addition(X2,addition(X1,X0))),
inference(superposition,[],[f814,f37]) ).
fof(f814,plain,
! [X2,X0,X1] : leq(X2,addition(X0,addition(X1,X2))),
inference(superposition,[],[f793,f40]) ).
fof(f793,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(superposition,[],[f753,f37]) ).
fof(f753,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(trivial_inequality_removal,[],[f743]) ).
fof(f743,plain,
! [X0,X1] :
( addition(X0,X1) != addition(X0,X1)
| leq(X0,addition(X0,X1)) ),
inference(superposition,[],[f39,f103]) ).
fof(f42947,plain,
! [X0] : leq(addition(X0,addition(one,sK0)),addition(X0,star(sK1))),
inference(superposition,[],[f797,f42852]) ).
fof(f42852,plain,
star(sK1) = addition(addition(one,sK0),star(sK1)),
inference(forward_demodulation,[],[f42851,f42639]) ).
fof(f42639,plain,
star(sK1) = multiplication(addition(one,sK0),star(sK1)),
inference(superposition,[],[f35859,f5748]) ).
fof(f5748,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(multiplication(X1,X0),X0),
inference(superposition,[],[f771,f33]) ).
fof(f771,plain,
! [X2,X0,X1] : multiplication(addition(X0,X2),X1) = addition(multiplication(X2,X1),multiplication(X0,X1)),
inference(superposition,[],[f43,f37]) ).
fof(f35859,plain,
star(sK1) = addition(multiplication(sK0,star(sK1)),star(sK1)),
inference(resolution,[],[f35747,f38]) ).
fof(f35747,plain,
leq(multiplication(sK0,star(sK1)),star(sK1)),
inference(superposition,[],[f9711,f35262]) ).
fof(f35262,plain,
! [X0] : star(X0) = addition(multiplication(X0,star(X0)),star(X0)),
inference(backward_demodulation,[],[f4871,f35192]) ).
fof(f4871,plain,
! [X0] : star(X0) = addition(multiplication(X0,star(X0)),addition(one,star(X0))),
inference(superposition,[],[f76,f104]) ).
fof(f9711,plain,
! [X0,X1] : leq(multiplication(sK0,X1),addition(multiplication(sK1,X1),X0)),
inference(superposition,[],[f9666,f37]) ).
fof(f9666,plain,
! [X0,X1] : leq(multiplication(sK0,X0),addition(X1,multiplication(sK1,X0))),
inference(superposition,[],[f827,f9013]) ).
fof(f9013,plain,
! [X0] : multiplication(sK1,X0) = addition(multiplication(sK0,X0),multiplication(sK1,X0)),
inference(resolution,[],[f8962,f38]) ).
fof(f8962,plain,
! [X0] : leq(multiplication(sK0,X0),multiplication(sK1,X0)),
inference(trivial_inequality_removal,[],[f8944]) ).
fof(f8944,plain,
! [X0] :
( multiplication(sK1,X0) != multiplication(sK1,X0)
| leq(multiplication(sK0,X0),multiplication(sK1,X0)) ),
inference(superposition,[],[f778,f54]) ).
fof(f778,plain,
! [X2,X0,X1] :
( multiplication(X2,X1) != multiplication(addition(X0,X2),X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(superposition,[],[f39,f43]) ).
fof(f42851,plain,
multiplication(addition(one,sK0),star(sK1)) = addition(addition(one,sK0),star(sK1)),
inference(forward_demodulation,[],[f42797,f35192]) ).
fof(f42797,plain,
addition(addition(one,sK0),star(sK1)) = multiplication(addition(one,sK0),addition(one,star(sK1))),
inference(superposition,[],[f344,f42639]) ).
fof(f344,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f42,f32]) ).
fof(f32,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(f797,plain,
! [X2,X0,X1] : leq(addition(X0,X1),addition(X0,addition(X1,X2))),
inference(superposition,[],[f753,f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KLE041+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % 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 : Tue Apr 30 04:58:18 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (11409)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (11412)WARNING: value z3 for option sas not known
% 0.15/0.37 % (11413)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37 % (11410)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37 % (11412)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 % (11414)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 % (11411)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 % (11416)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)
% 0.15/0.37 % (11415)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 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]
% 0.15/0.39 TRYING [4]
% 0.15/0.40 TRYING [3]
% 0.21/0.43 TRYING [5]
% 0.21/0.44 TRYING [4]
% 0.21/0.50 TRYING [6]
% 0.21/0.54 TRYING [5]
% 2.12/0.66 TRYING [7]
% 4.23/0.95 TRYING [6]
% 4.70/1.03 TRYING [8]
% 6.23/1.32 % (11415)First to succeed.
% 6.90/1.33 % (11415)Refutation found. Thanks to Tanya!
% 6.90/1.33 % SZS status Theorem for theBenchmark
% 6.90/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 6.90/1.33 % (11415)------------------------------
% 6.90/1.33 % (11415)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 6.90/1.33 % (11415)Termination reason: Refutation
% 6.90/1.33
% 6.90/1.33 % (11415)Memory used [KB]: 15081
% 6.90/1.33 % (11415)Time elapsed: 0.956 s
% 6.90/1.33 % (11415)Instructions burned: 2853 (million)
% 6.90/1.33 % (11415)------------------------------
% 6.90/1.33 % (11415)------------------------------
% 6.90/1.33 % (11409)Success in time 0.95 s
%------------------------------------------------------------------------------