TSTP Solution File: RNG006-3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : RNG006-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n020.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 14:50:13 EDT 2024
% Result : Unsatisfiable 2.43s 0.74s
% Output : Refutation 2.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of formulae : 45 ( 29 unt; 0 def)
% Number of atoms : 78 ( 8 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 72 ( 39 ~; 30 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 93 ( 93 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f35131,plain,
$false,
inference(subsumption_resolution,[],[f35097,f22]) ).
fof(f22,axiom,
~ product(a,bS_Ic,aPb_S_IaPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_times_bS_Ic_is_aPb_S__IaPc) ).
fof(f35097,plain,
product(a,bS_Ic,aPb_S_IaPc),
inference(superposition,[],[f3,f34913]) ).
fof(f34913,plain,
aPb_S_IaPc = multiply(a,bS_Ic),
inference(forward_demodulation,[],[f34905,f114]) ).
fof(f114,plain,
aPb_S_IaPc = add(additive_inverse(aPc),aPb),
inference(unit_resulting_resolution,[],[f4,f53,f16]) ).
fof(f16,axiom,
! [X2,X0,X1,X4] :
( ~ sum(X0,X1,X4)
| X2 = X4
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
fof(f53,plain,
sum(additive_inverse(aPc),aPb,aPb_S_IaPc),
inference(unit_resulting_resolution,[],[f21,f9]) ).
fof(f9,axiom,
! [X3,X0,X1] :
( ~ sum(X0,X1,X3)
| sum(X1,X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_addition) ).
fof(f21,axiom,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aPb_plus_IaPc) ).
fof(f4,axiom,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
fof(f34905,plain,
add(additive_inverse(aPc),aPb) = multiply(a,bS_Ic),
inference(unit_resulting_resolution,[],[f33481,f122]) ).
fof(f122,plain,
! [X2,X0,X1] :
( ~ sum(X2,X1,X0)
| add(X1,X2) = X0 ),
inference(resolution,[],[f16,f51]) ).
fof(f51,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(unit_resulting_resolution,[],[f4,f9]) ).
fof(f33481,plain,
sum(aPb,additive_inverse(aPc),multiply(a,bS_Ic)),
inference(unit_resulting_resolution,[],[f4188,f33472,f27]) ).
fof(f27,plain,
! [X2,X3,X0,X1,X5] :
( ~ sum(X0,X1,X2)
| sum(X2,X3,X5)
| sP2(X3,X0,X5,X1) ),
inference(cnf_transformation,[],[f27_D]) ).
fof(f27_D,plain,
! [X1,X5,X0,X3] :
( ! [X2] :
( ~ sum(X0,X1,X2)
| sum(X2,X3,X5) )
<=> ~ sP2(X3,X0,X5,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP2])]) ).
fof(f33472,plain,
sum(multiply(a,bS_Ic),aPc,aPb),
inference(forward_demodulation,[],[f33470,f281]) ).
fof(f281,plain,
aPb = multiply(a,b),
inference(unit_resulting_resolution,[],[f19,f3,f17]) ).
fof(f17,axiom,
! [X2,X0,X1,X4] :
( ~ product(X0,X1,X4)
| X2 = X4
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
fof(f19,axiom,
product(a,b,aPb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
fof(f33470,plain,
sum(multiply(a,bS_Ic),aPc,multiply(a,b)),
inference(unit_resulting_resolution,[],[f3,f33185,f34]) ).
fof(f34,plain,
! [X0,X8,X6,X9,X7] :
( ~ sP5(X0,X8,X6,X7)
| sum(X6,X7,X9)
| ~ product(X0,X8,X9) ),
inference(general_splitting,[],[f32,f33_D]) ).
fof(f33,plain,
! [X0,X1,X8,X6,X7] :
( ~ sP4(X0,X8,X1,X7)
| ~ product(X0,X1,X6)
| sP5(X0,X8,X6,X7) ),
inference(cnf_transformation,[],[f33_D]) ).
fof(f33_D,plain,
! [X7,X6,X8,X0] :
( ! [X1] :
( ~ sP4(X0,X8,X1,X7)
| ~ product(X0,X1,X6) )
<=> ~ sP5(X0,X8,X6,X7) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP5])]) ).
fof(f32,plain,
! [X0,X1,X8,X6,X9,X7] :
( ~ product(X0,X1,X6)
| ~ product(X0,X8,X9)
| sum(X6,X7,X9)
| ~ sP4(X0,X8,X1,X7) ),
inference(general_splitting,[],[f12,f31_D]) ).
fof(f31,plain,
! [X3,X0,X1,X8,X7] :
( ~ product(X0,X3,X7)
| ~ sum(X1,X3,X8)
| sP4(X0,X8,X1,X7) ),
inference(cnf_transformation,[],[f31_D]) ).
fof(f31_D,plain,
! [X7,X1,X8,X0] :
( ! [X3] :
( ~ product(X0,X3,X7)
| ~ sum(X1,X3,X8) )
<=> ~ sP4(X0,X8,X1,X7) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP4])]) ).
fof(f12,axiom,
! [X3,X0,X1,X8,X6,X9,X7] :
( ~ product(X0,X1,X6)
| ~ product(X0,X8,X9)
| ~ product(X0,X3,X7)
| ~ sum(X1,X3,X8)
| sum(X6,X7,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
fof(f33185,plain,
sP5(a,b,multiply(a,bS_Ic),aPc),
inference(unit_resulting_resolution,[],[f3,f6934,f33]) ).
fof(f6934,plain,
sP4(a,b,bS_Ic,aPc),
inference(unit_resulting_resolution,[],[f4595,f20,f31]) ).
fof(f20,axiom,
product(a,c,aPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c) ).
fof(f4595,plain,
sum(bS_Ic,c,b),
inference(unit_resulting_resolution,[],[f4191,f3414]) ).
fof(f3414,plain,
! [X0,X1] :
( sP2(X0,b,X1,additive_inverse(c))
| sum(bS_Ic,X0,X1) ),
inference(resolution,[],[f27,f18]) ).
fof(f18,axiom,
sum(b,additive_inverse(c),bS_Ic),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_plus_inverse_c) ).
fof(f4191,plain,
! [X0,X1] : ~ sP2(X0,X1,X1,additive_inverse(X0)),
inference(forward_demodulation,[],[f4148,f96]) ).
fof(f96,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(unit_resulting_resolution,[],[f2,f51,f16]) ).
fof(f2,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
fof(f4148,plain,
! [X0,X1] : ~ sP2(X0,X1,add(additive_identity,X1),additive_inverse(X0)),
inference(unit_resulting_resolution,[],[f51,f5,f28]) ).
fof(f28,plain,
! [X3,X0,X1,X4,X5] :
( ~ sP2(X3,X0,X5,X1)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X4,X5) ),
inference(general_splitting,[],[f8,f27_D]) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| sum(X2,X3,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_addition2) ).
fof(f5,axiom,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f4188,plain,
! [X0,X1] : ~ sP2(additive_inverse(X0),X1,X1,X0),
inference(forward_demodulation,[],[f4153,f96]) ).
fof(f4153,plain,
! [X0,X1] : ~ sP2(additive_inverse(X0),X1,add(additive_identity,X1),X0),
inference(unit_resulting_resolution,[],[f51,f6,f28]) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f3,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG006-3 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n020.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 02:08:02 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (3683)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (3686)WARNING: value z3 for option sas not known
% 0.15/0.38 % (3686)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 % (3687)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (3684)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (3685)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 % (3688)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 % (3689)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 % (3690)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 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [3]
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.22/0.40 TRYING [3]
% 0.22/0.40 TRYING [4]
% 0.22/0.46 TRYING [4]
% 0.22/0.48 TRYING [5]
% 1.32/0.62 TRYING [6]
% 2.43/0.73 % (3690)First to succeed.
% 2.43/0.74 % (3690)Refutation found. Thanks to Tanya!
% 2.43/0.74 % SZS status Unsatisfiable for theBenchmark
% 2.43/0.74 % SZS output start Proof for theBenchmark
% See solution above
% 2.43/0.74 % (3690)------------------------------
% 2.43/0.74 % (3690)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 2.43/0.74 % (3690)Termination reason: Refutation
% 2.43/0.74
% 2.43/0.74 % (3690)Memory used [KB]: 5673
% 2.43/0.74 % (3690)Time elapsed: 0.355 s
% 2.43/0.74 % (3690)Instructions burned: 934 (million)
% 2.43/0.74 % (3690)------------------------------
% 2.43/0.74 % (3690)------------------------------
% 2.43/0.74 % (3683)Success in time 0.363 s
%------------------------------------------------------------------------------