TSTP Solution File: KLE040+2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE040+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 : n007.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 7.55s 1.44s
% Output : Refutation 7.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 50 ( 36 unt; 0 def)
% Number of atoms : 68 ( 28 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 22 ~; 11 |; 4 &)
% ( 1 <=>; 2 =>; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 83 ( 81 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f50445,plain,
$false,
inference(subsumption_resolution,[],[f50444,f49061]) ).
fof(f49061,plain,
! [X0] : leq(multiplication(addition(one,X0),star(X0)),star(X0)),
inference(superposition,[],[f187,f48739]) ).
fof(f48739,plain,
! [X0] : star(X0) = addition(one,multiplication(addition(one,X0),star(X0))),
inference(forward_demodulation,[],[f48515,f4477]) ).
fof(f4477,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f42,f32]) ).
fof(f32,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(f42,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(f48515,plain,
! [X0] : star(X0) = addition(one,addition(star(X0),multiplication(X0,star(X0)))),
inference(superposition,[],[f92,f14891]) ).
fof(f14891,plain,
! [X2,X0,X1] : addition(X1,addition(X0,X2)) = addition(addition(X1,X2),X0),
inference(superposition,[],[f1045,f36]) ).
fof(f36,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(f1045,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[],[f127,f39]) ).
fof(f39,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(f127,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(superposition,[],[f39,f36]) ).
fof(f92,plain,
! [X0] : star(X0) = addition(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(unit_resulting_resolution,[],[f34,f37]) ).
fof(f37,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(f34,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(f187,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(superposition,[],[f162,f36]) ).
fof(f162,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(unit_resulting_resolution,[],[f126,f38]) ).
fof(f38,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f126,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f39,f33]) ).
fof(f33,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(f50444,plain,
~ leq(multiplication(addition(one,sK0),star(sK0)),star(sK0)),
inference(forward_demodulation,[],[f50443,f4477]) ).
fof(f50443,plain,
~ leq(addition(star(sK0),multiplication(sK0,star(sK0))),star(sK0)),
inference(forward_demodulation,[],[f50433,f36]) ).
fof(f50433,plain,
~ leq(addition(multiplication(sK0,star(sK0)),star(sK0)),star(sK0)),
inference(unit_resulting_resolution,[],[f49491,f44]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ~ leq(addition(multiplication(X0,X1),X2),X1)
| leq(multiplication(star(X0),X2),X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X0,X1),X2),X1)
=> leq(multiplication(star(X0),X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction_left) ).
fof(f49491,plain,
~ leq(multiplication(star(sK0),star(sK0)),star(sK0)),
inference(unit_resulting_resolution,[],[f48978,f27]) ).
fof(f27,plain,
( ~ leq(multiplication(star(sK0),star(sK0)),star(sK0))
| ~ leq(star(sK0),multiplication(star(sK0),star(sK0))) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
( ~ leq(star(sK0),multiplication(star(sK0),star(sK0)))
| ~ leq(multiplication(star(sK0),star(sK0)),star(sK0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f21,f24]) ).
fof(f24,plain,
( ? [X0] :
( ~ leq(star(X0),multiplication(star(X0),star(X0)))
| ~ leq(multiplication(star(X0),star(X0)),star(X0)) )
=> ( ~ leq(star(sK0),multiplication(star(sK0),star(sK0)))
| ~ leq(multiplication(star(sK0),star(sK0)),star(sK0)) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
? [X0] :
( ~ leq(star(X0),multiplication(star(X0),star(X0)))
| ~ leq(multiplication(star(X0),star(X0)),star(X0)) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
~ ! [X0] :
( leq(star(X0),multiplication(star(X0),star(X0)))
& leq(multiplication(star(X0),star(X0)),star(X0)) ),
inference(rectify,[],[f18]) ).
fof(f18,negated_conjecture,
~ ! [X3] :
( leq(star(X3),multiplication(star(X3),star(X3)))
& leq(multiplication(star(X3),star(X3)),star(X3)) ),
inference(negated_conjecture,[],[f17]) ).
fof(f17,conjecture,
! [X3] :
( leq(star(X3),multiplication(star(X3),star(X3)))
& leq(multiplication(star(X3),star(X3)),star(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f48978,plain,
! [X0,X1] : leq(X1,multiplication(X1,star(X0))),
inference(superposition,[],[f2789,f48739]) ).
fof(f2789,plain,
! [X0,X1] : leq(X0,multiplication(X0,addition(one,X1))),
inference(superposition,[],[f1985,f31]) ).
fof(f31,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(f1985,plain,
! [X2,X0,X1] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(superposition,[],[f162,f41]) ).
fof(f41,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) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : KLE040+2 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n007.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 04:53:18 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (6080)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (6083)WARNING: value z3 for option sas not known
% 0.15/0.38 % (6087)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 % (6084)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (6082)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 % (6085)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 % (6086)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 % (6083)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 % (6081)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]
% 0.15/0.38 TRYING [3]
% 0.21/0.39 TRYING [1]
% 0.21/0.39 TRYING [2]
% 0.21/0.39 TRYING [4]
% 0.21/0.40 TRYING [3]
% 0.21/0.42 TRYING [5]
% 0.21/0.43 TRYING [4]
% 0.21/0.51 TRYING [6]
% 1.22/0.53 TRYING [5]
% 1.98/0.64 TRYING [1]
% 1.98/0.64 TRYING [2]
% 1.98/0.65 TRYING [3]
% 1.98/0.65 TRYING [4]
% 2.38/0.69 TRYING [5]
% 2.86/0.75 TRYING [7]
% 3.45/0.86 TRYING [6]
% 3.45/0.91 TRYING [6]
% 6.39/1.27 TRYING [7]
% 6.87/1.33 TRYING [8]
% 7.55/1.44 % (6087)First to succeed.
% 7.55/1.44 % (6087)Refutation found. Thanks to Tanya!
% 7.55/1.44 % SZS status Theorem for theBenchmark
% 7.55/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 7.55/1.45 % (6087)------------------------------
% 7.55/1.45 % (6087)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 7.55/1.45 % (6087)Termination reason: Refutation
% 7.55/1.45
% 7.55/1.45 % (6087)Memory used [KB]: 8488
% 7.55/1.45 % (6087)Time elapsed: 1.066 s
% 7.55/1.45 % (6087)Instructions burned: 2502 (million)
% 7.55/1.45 % (6087)------------------------------
% 7.55/1.45 % (6087)------------------------------
% 7.55/1.45 % (6080)Success in time 1.07 s
%------------------------------------------------------------------------------