TSTP Solution File: KLE170+1.002 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE170+1.002 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n013.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 13:12:06 EDT 2024
% Result : Theorem 18.06s 2.90s
% Output : Refutation 18.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 14
% Syntax : Number of formulae : 94 ( 85 unt; 0 def)
% Number of atoms : 105 ( 70 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 11 ~; 8 |; 1 &)
% ( 1 <=>; 1 =>; 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 : 138 ( 138 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f129550,plain,
$false,
inference(resolution,[],[f129489,f24]) ).
fof(f24,plain,
~ leq(multiplication(a,a),star(a)),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
~ leq(multiplication(a,a),star(a)),
inference(flattening,[],[f18]) ).
fof(f18,negated_conjecture,
~ leq(multiplication(a,a),star(a)),
inference(negated_conjecture,[],[f17]) ).
fof(f17,conjecture,
leq(multiplication(a,a),star(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a) ).
fof(f129489,plain,
! [X0] : leq(multiplication(X0,X0),star(X0)),
inference(superposition,[],[f129031,f56712]) ).
fof(f56712,plain,
! [X0] : star(X0) = addition(star(X0),multiplication(X0,star(X0))),
inference(superposition,[],[f35639,f33]) ).
fof(f33,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(f35639,plain,
! [X0] : star(X0) = addition(multiplication(X0,star(X0)),star(X0)),
inference(unit_resulting_resolution,[],[f35403,f34]) ).
fof(f34,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,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/sandbox/benchmark/theBenchmark.p',order) ).
fof(f35403,plain,
! [X0] : leq(multiplication(X0,star(X0)),star(X0)),
inference(superposition,[],[f4464,f32642]) ).
fof(f32642,plain,
! [X0] : star(X0) = multiplication(addition(one,X0),star(X0)),
inference(forward_demodulation,[],[f32641,f32583]) ).
fof(f32583,plain,
! [X0] : star(X0) = addition(multiplication(addition(one,X0),star(X0)),one),
inference(forward_demodulation,[],[f32582,f32579]) ).
fof(f32579,plain,
! [X0] : star(X0) = addition(one,star(X0)),
inference(forward_demodulation,[],[f32578,f28940]) ).
fof(f28940,plain,
! [X0] : star(X0) = addition(one,multiplication(addition(one,X0),star(X0))),
inference(forward_demodulation,[],[f28779,f4422]) ).
fof(f4422,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f39,f29]) ).
fof(f29,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(f39,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(f28779,plain,
! [X0] : star(X0) = addition(one,addition(star(X0),multiplication(X0,star(X0)))),
inference(superposition,[],[f94,f14802]) ).
fof(f14802,plain,
! [X2,X0,X1] : addition(X1,addition(X0,X2)) = addition(addition(X1,X2),X0),
inference(superposition,[],[f1047,f33]) ).
fof(f1047,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[],[f129,f36]) ).
fof(f36,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/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
fof(f129,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(superposition,[],[f36,f33]) ).
fof(f94,plain,
! [X0] : star(X0) = addition(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(unit_resulting_resolution,[],[f31,f34]) ).
fof(f31,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/sandbox/benchmark/theBenchmark.p',star_unfold_right) ).
fof(f32578,plain,
! [X0] : addition(one,star(X0)) = addition(one,multiplication(addition(one,X0),star(X0))),
inference(forward_demodulation,[],[f32399,f6903]) ).
fof(f6903,plain,
one = star(zero),
inference(superposition,[],[f6898,f1676]) ).
fof(f1676,plain,
star(zero) = addition(star(zero),one),
inference(forward_demodulation,[],[f1602,f42]) ).
fof(f42,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f33,f27]) ).
fof(f27,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(f1602,plain,
addition(star(zero),one) = addition(zero,star(zero)),
inference(superposition,[],[f1344,f99]) ).
fof(f99,plain,
star(zero) = addition(one,star(zero)),
inference(unit_resulting_resolution,[],[f98,f34]) ).
fof(f98,plain,
leq(one,star(zero)),
inference(forward_demodulation,[],[f96,f27]) ).
fof(f96,plain,
leq(addition(one,zero),star(zero)),
inference(superposition,[],[f31,f26]) ).
fof(f26,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : zero = multiplication(zero,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
fof(f1344,plain,
! [X0,X1] : addition(X1,X0) = addition(zero,addition(X0,X1)),
inference(superposition,[],[f139,f42]) ).
fof(f139,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(superposition,[],[f36,f33]) ).
fof(f6898,plain,
one = addition(star(zero),one),
inference(unit_resulting_resolution,[],[f6894,f34]) ).
fof(f6894,plain,
leq(star(zero),one),
inference(superposition,[],[f6456,f29]) ).
fof(f6456,plain,
! [X0] : leq(multiplication(X0,star(zero)),X0),
inference(unit_resulting_resolution,[],[f52,f6445]) ).
fof(f6445,plain,
! [X0,X1] :
( ~ leq(X1,X0)
| leq(multiplication(X1,star(zero)),X0) ),
inference(forward_demodulation,[],[f6425,f42]) ).
fof(f6425,plain,
! [X0,X1] :
( ~ leq(addition(zero,X1),X0)
| leq(multiplication(X1,star(zero)),X0) ),
inference(superposition,[],[f40,f25]) ).
fof(f25,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] : zero = multiplication(X0,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ leq(addition(multiplication(X0,X1),X2),X0)
| leq(multiplication(X2,star(X1)),X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f21,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/sandbox/benchmark/theBenchmark.p',star_induction_right) ).
fof(f52,plain,
! [X0] : leq(X0,X0),
inference(unit_resulting_resolution,[],[f30,f35]) ).
fof(f35,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f30,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(f32399,plain,
! [X0] : addition(star(zero),multiplication(addition(one,X0),star(X0))) = addition(star(zero),star(X0)),
inference(superposition,[],[f1043,f28940]) ).
fof(f1043,plain,
! [X0] : addition(star(zero),X0) = addition(star(zero),addition(one,X0)),
inference(superposition,[],[f129,f99]) ).
fof(f32582,plain,
! [X0] : addition(one,star(X0)) = addition(multiplication(addition(one,X0),star(X0)),one),
inference(forward_demodulation,[],[f32402,f6903]) ).
fof(f32402,plain,
! [X0] : addition(multiplication(addition(one,X0),star(X0)),star(zero)) = addition(star(zero),star(X0)),
inference(superposition,[],[f1800,f28940]) ).
fof(f1800,plain,
! [X0] : addition(X0,star(zero)) = addition(star(zero),addition(one,X0)),
inference(superposition,[],[f139,f1676]) ).
fof(f32641,plain,
! [X0] : multiplication(addition(one,X0),star(X0)) = addition(multiplication(addition(one,X0),star(X0)),one),
inference(forward_demodulation,[],[f32492,f12733]) ).
fof(f12733,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(multiplication(addition(one,X1),X0),X0),
inference(superposition,[],[f1668,f4422]) ).
fof(f1668,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),X0),
inference(forward_demodulation,[],[f1592,f42]) ).
fof(f1592,plain,
! [X0,X1] : addition(zero,addition(X0,X1)) = addition(addition(X0,X1),X0),
inference(superposition,[],[f1344,f128]) ).
fof(f128,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f36,f30]) ).
fof(f32492,plain,
! [X0] : addition(multiplication(addition(one,X0),star(X0)),one) = addition(multiplication(addition(one,X0),star(X0)),star(X0)),
inference(superposition,[],[f1348,f28940]) ).
fof(f1348,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X1,X0)),
inference(superposition,[],[f139,f128]) ).
fof(f4464,plain,
! [X2,X0,X1] : leq(multiplication(X2,X1),multiplication(addition(X0,X2),X1)),
inference(superposition,[],[f189,f39]) ).
fof(f189,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(superposition,[],[f164,f33]) ).
fof(f164,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(unit_resulting_resolution,[],[f128,f35]) ).
fof(f129031,plain,
! [X2,X0,X1] : leq(multiplication(X1,X0),addition(X2,multiplication(X1,star(X0)))),
inference(superposition,[],[f1742,f35962]) ).
fof(f35962,plain,
! [X0] : star(X0) = addition(star(X0),X0),
inference(forward_demodulation,[],[f35743,f42]) ).
fof(f35743,plain,
! [X0] : addition(zero,star(X0)) = addition(star(X0),X0),
inference(superposition,[],[f1344,f35573]) ).
fof(f35573,plain,
! [X0] : star(X0) = addition(X0,star(X0)),
inference(forward_demodulation,[],[f35572,f32642]) ).
fof(f35572,plain,
! [X0] : multiplication(addition(one,X0),star(X0)) = addition(X0,star(X0)),
inference(forward_demodulation,[],[f35571,f32579]) ).
fof(f35571,plain,
! [X0] : multiplication(addition(one,X0),star(X0)) = addition(X0,addition(one,star(X0))),
inference(forward_demodulation,[],[f35570,f14799]) ).
fof(f14799,plain,
! [X2,X0,X1] : addition(X1,addition(X0,X2)) = addition(X1,addition(X2,X0)),
inference(superposition,[],[f1047,f139]) ).
fof(f35570,plain,
! [X0] : multiplication(addition(one,X0),star(X0)) = addition(X0,addition(star(X0),one)),
inference(forward_demodulation,[],[f35569,f139]) ).
fof(f35569,plain,
! [X0] : multiplication(addition(one,X0),star(X0)) = addition(star(X0),addition(one,X0)),
inference(forward_demodulation,[],[f35568,f33]) ).
fof(f35568,plain,
! [X0] : multiplication(addition(one,X0),star(X0)) = addition(addition(one,X0),star(X0)),
inference(forward_demodulation,[],[f35463,f32579]) ).
fof(f35463,plain,
! [X0] : addition(addition(one,X0),star(X0)) = multiplication(addition(one,X0),addition(one,star(X0))),
inference(superposition,[],[f1714,f32642]) ).
fof(f1714,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f38,f28]) ).
fof(f28,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(f38,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',right_distributivity) ).
fof(f1742,plain,
! [X2,X3,X0,X1] : leq(multiplication(X0,X2),addition(X3,multiplication(X0,addition(X1,X2)))),
inference(superposition,[],[f207,f38]) ).
fof(f207,plain,
! [X2,X0,X1] : leq(X2,addition(X0,addition(X1,X2))),
inference(superposition,[],[f189,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : KLE170+1.002 : TPTP v8.1.2. Released v5.2.0.
% 0.11/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n013.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Apr 30 04:58:19 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % (26737)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.34 % (26740)WARNING: value z3 for option sas not known
% 0.16/0.34 % (26741)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.34 % (26740)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)
% 0.16/0.34 % (26743)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)
% 0.16/0.34 % (26738)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.34 % (26739)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.34 % (26744)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)
% 0.16/0.34 % (26742)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)
% 0.16/0.34 TRYING [1]
% 0.16/0.34 TRYING [2]
% 0.16/0.34 TRYING [3]
% 0.16/0.34 TRYING [1]
% 0.16/0.35 TRYING [2]
% 0.16/0.35 TRYING [4]
% 0.16/0.36 TRYING [3]
% 0.16/0.38 TRYING [5]
% 0.16/0.39 TRYING [4]
% 0.16/0.46 TRYING [6]
% 0.16/0.51 TRYING [5]
% 2.24/0.68 TRYING [7]
% 4.10/0.92 TRYING [6]
% 6.07/1.19 TRYING [8]
% 7.48/1.44 TRYING [1]
% 7.48/1.44 TRYING [2]
% 7.48/1.44 TRYING [3]
% 7.48/1.45 TRYING [4]
% 8.41/1.52 TRYING [5]
% 9.10/1.67 TRYING [6]
% 12.36/2.12 TRYING [7]
% 14.00/2.36 TRYING [9]
% 15.25/2.55 TRYING [7]
% 17.36/2.89 % (26744)First to succeed.
% 18.06/2.90 % (26744)Refutation found. Thanks to Tanya!
% 18.06/2.90 % SZS status Theorem for theBenchmark
% 18.06/2.90 % SZS output start Proof for theBenchmark
% See solution above
% 18.06/2.90 % (26744)------------------------------
% 18.06/2.90 % (26744)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 18.06/2.90 % (26744)Termination reason: Refutation
% 18.06/2.90
% 18.06/2.90 % (26744)Memory used [KB]: 20216
% 18.06/2.90 % (26744)Time elapsed: 2.556 s
% 18.06/2.90 % (26744)Instructions burned: 5375 (million)
% 18.06/2.90 % (26744)------------------------------
% 18.06/2.90 % (26744)------------------------------
% 18.06/2.90 % (26737)Success in time 2.534 s
%------------------------------------------------------------------------------