TSTP Solution File: NUM331+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM331+1 : TPTP v8.2.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n027.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 May 21 01:49:34 EDT 2024
% Result : Theorem 108.39s 15.87s
% Output : Refutation 108.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 61 ( 30 unt; 0 def)
% Number of atoms : 142 ( 15 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 143 ( 62 ~; 43 |; 25 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 138 ( 132 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1001674,plain,
$false,
inference(subsumption_resolution,[],[f1001673,f135594]) ).
fof(f135594,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n7),rdnn(n6),rdn(rdnn(n3),rdnn(n1))),
inference(unit_resulting_resolution,[],[f761,f93830,f916]) ).
fof(f916,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ sP16(X5,X3,X4,X0)
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X3),rdnn(X5))
| rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdn(rdnn(X4),rdnn(n1))) ),
inference(general_splitting,[],[f883,f915_D]) ).
fof(f915,plain,
! [X3,X0,X6,X4,X5] :
( ~ rdn_digit_add(rdnn(X5),rdnn(X6),rdnn(n1),rdnn(n0))
| ~ rdn_digit_add(rdnn(X3),rdnn(X0),rdnn(X4),rdnn(X6))
| sP16(X5,X3,X4,X0) ),
inference(cnf_transformation,[],[f915_D]) ).
fof(f915_D,plain,
! [X0,X4,X3,X5] :
( ! [X6] :
( ~ rdn_digit_add(rdnn(X5),rdnn(X6),rdnn(n1),rdnn(n0))
| ~ rdn_digit_add(rdnn(X3),rdnn(X0),rdnn(X4),rdnn(X6)) )
<=> ~ sP16(X5,X3,X4,X0) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP16])]) ).
fof(f883,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdn(rdnn(X4),rdnn(n1)))
| ~ rdn_digit_add(rdnn(X5),rdnn(X6),rdnn(n1),rdnn(n0))
| ~ rdn_digit_add(rdnn(X3),rdnn(X0),rdnn(X4),rdnn(X6))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X3),rdnn(X5)) ),
inference(cnf_transformation,[],[f469]) ).
fof(f469,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdn(rdnn(X4),rdnn(n1)))
| ~ rdn_digit_add(rdnn(X5),rdnn(X6),rdnn(n1),rdnn(n0))
| ~ rdn_digit_add(rdnn(X3),rdnn(X0),rdnn(X4),rdnn(X6))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X3),rdnn(X5)) ),
inference(flattening,[],[f468]) ).
fof(f468,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdn(rdnn(X4),rdnn(n1)))
| ~ rdn_digit_add(rdnn(X5),rdnn(X6),rdnn(n1),rdnn(n0))
| ~ rdn_digit_add(rdnn(X3),rdnn(X0),rdnn(X4),rdnn(X6))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X3),rdnn(X5)) ),
inference(ennf_transformation,[],[f423]) ).
fof(f423,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( rdn_digit_add(rdnn(X5),rdnn(X6),rdnn(n1),rdnn(n0))
& rdn_digit_add(rdnn(X3),rdnn(X0),rdnn(X4),rdnn(X6))
& rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X3),rdnn(X5)) )
=> rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdn(rdnn(X4),rdnn(n1))) ),
inference(rectify,[],[f298]) ).
fof(f298,axiom,
! [X20,X21,X22,X24,X23,X25,X26] :
( ( rdn_digit_add(rdnn(X25),rdnn(X26),rdnn(n1),rdnn(n0))
& rdn_digit_add(rdnn(X24),rdnn(X20),rdnn(X23),rdnn(X26))
& rdn_digit_add(rdnn(X21),rdnn(X22),rdnn(X24),rdnn(X25)) )
=> rdn_add_with_carry(rdnn(X20),rdnn(X21),rdnn(X22),rdn(rdnn(X23),rdnn(n1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_digit_digit_rdn) ).
fof(f93830,plain,
sP16(n1,n3,n3,n0),
inference(unit_resulting_resolution,[],[f743,f797,f915]) ).
fof(f797,plain,
rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0)),
inference(cnf_transformation,[],[f312]) ).
fof(f312,axiom,
rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n1_n0_n1_n0) ).
fof(f743,plain,
rdn_digit_add(rdnn(n3),rdnn(n0),rdnn(n3),rdnn(n0)),
inference(cnf_transformation,[],[f332]) ).
fof(f332,axiom,
rdn_digit_add(rdnn(n3),rdnn(n0),rdnn(n3),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n3_n0_n3_n0) ).
fof(f761,plain,
rdn_digit_add(rdnn(n7),rdnn(n6),rdnn(n3),rdnn(n1)),
inference(cnf_transformation,[],[f378]) ).
fof(f378,axiom,
rdn_digit_add(rdnn(n7),rdnn(n6),rdnn(n3),rdnn(n1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n7_n6_n3_n1) ).
fof(f1001673,plain,
~ rdn_add_with_carry(rdnn(n0),rdnn(n7),rdnn(n6),rdn(rdnn(n3),rdnn(n1))),
inference(unit_resulting_resolution,[],[f515,f1001672,f909]) ).
fof(f909,plain,
! [X3,X0,X4,X5] :
( ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X0,rdn_pos(X3))
| sP13(X4,X0,X5) ),
inference(cnf_transformation,[],[f909_D]) ).
fof(f909_D,plain,
! [X5,X0,X4] :
( ! [X3] :
( ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X0,rdn_pos(X3)) )
<=> ~ sP13(X4,X0,X5) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP13])]) ).
fof(f1001672,plain,
~ sP13(rdnn(n6),n7,rdn(rdnn(n3),rdnn(n1))),
inference(unit_resulting_resolution,[],[f514,f1001661,f910]) ).
fof(f910,plain,
! [X0,X1,X4,X5] :
( ~ sP13(X4,X0,X5)
| ~ sP12(X0,X5,X1)
| ~ rdn_translate(X1,rdn_pos(X4)) ),
inference(general_splitting,[],[f908,f909_D]) ).
fof(f908,plain,
! [X3,X0,X1,X4,X5] :
( ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ rdn_translate(X0,rdn_pos(X3))
| ~ sP12(X0,X5,X1) ),
inference(general_splitting,[],[f881,f907_D]) ).
fof(f907,plain,
! [X2,X0,X1,X5] :
( ~ rdn_translate(X2,rdn_pos(X5))
| sum(X0,X1,X2)
| sP12(X0,X5,X1) ),
inference(cnf_transformation,[],[f907_D]) ).
fof(f907_D,plain,
! [X1,X5,X0] :
( ! [X2] :
( ~ rdn_translate(X2,rdn_pos(X5))
| sum(X0,X1,X2) )
<=> ~ sP12(X0,X5,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP12])]) ).
fof(f881,plain,
! [X2,X3,X0,X1,X4,X5] :
( sum(X0,X1,X2)
| ~ rdn_translate(X2,rdn_pos(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ rdn_translate(X0,rdn_pos(X3)) ),
inference(cnf_transformation,[],[f465]) ).
fof(f465,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X1,X2)
| ~ rdn_translate(X2,rdn_pos(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ rdn_translate(X0,rdn_pos(X3)) ),
inference(flattening,[],[f464]) ).
fof(f464,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X1,X2)
| ~ rdn_translate(X2,rdn_pos(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ rdn_translate(X0,rdn_pos(X3)) ),
inference(ennf_transformation,[],[f421]) ).
fof(f421,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( rdn_translate(X2,rdn_pos(X5))
& rdn_add_with_carry(rdnn(n0),X3,X4,X5)
& rdn_translate(X1,rdn_pos(X4))
& rdn_translate(X0,rdn_pos(X3)) )
=> sum(X0,X1,X2) ),
inference(rectify,[],[f287]) ).
fof(f287,axiom,
! [X0,X1,X2,X9,X10,X11] :
( ( rdn_translate(X2,rdn_pos(X11))
& rdn_add_with_carry(rdnn(n0),X9,X10,X11)
& rdn_translate(X1,rdn_pos(X10))
& rdn_translate(X0,rdn_pos(X9)) )
=> sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_entry_point_pos_pos) ).
fof(f1001661,plain,
sP12(n7,rdn(rdnn(n3),rdnn(n1)),n6),
inference(unit_resulting_resolution,[],[f607,f1001657,f907]) ).
fof(f1001657,plain,
~ sum(n7,n6,n13),
inference(superposition,[],[f88637,f1001648]) ).
fof(f1001648,plain,
n13 = sK0,
inference(unit_resulting_resolution,[],[f479,f1001639,f875]) ).
fof(f875,plain,
! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X3)
| X2 = X3
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f454]) ).
fof(f454,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(flattening,[],[f453]) ).
fof(f453,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(ennf_transformation,[],[f415]) ).
fof(f415,plain,
! [X0,X1,X2,X3] :
( ( sum(X0,X1,X3)
& sum(X0,X1,X2) )
=> X2 = X3 ),
inference(rectify,[],[f293]) ).
fof(f293,axiom,
! [X0,X1,X14,X15] :
( ( sum(X0,X1,X15)
& sum(X0,X1,X14) )
=> X14 = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_sum) ).
fof(f1001639,plain,
sum(n6,n7,n13),
inference(unit_resulting_resolution,[],[f607,f1001635,f907]) ).
fof(f1001635,plain,
~ sP12(n6,rdn(rdnn(n3),rdnn(n1)),n7),
inference(unit_resulting_resolution,[],[f515,f1001508,f910]) ).
fof(f1001508,plain,
sP13(rdnn(n7),n6,rdn(rdnn(n3),rdnn(n1))),
inference(unit_resulting_resolution,[],[f514,f135593,f909]) ).
fof(f135593,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n6),rdnn(n7),rdn(rdnn(n3),rdnn(n1))),
inference(unit_resulting_resolution,[],[f759,f93830,f916]) ).
fof(f759,plain,
rdn_digit_add(rdnn(n6),rdnn(n7),rdnn(n3),rdnn(n1)),
inference(cnf_transformation,[],[f369]) ).
fof(f369,axiom,
rdn_digit_add(rdnn(n6),rdnn(n7),rdnn(n3),rdnn(n1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n6_n7_n3_n1) ).
fof(f479,plain,
sum(n6,n7,sK0),
inference(cnf_transformation,[],[f475]) ).
fof(f475,plain,
( sK0 != sK1
& sum(n7,n6,sK1)
& sum(n6,n7,sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f428,f474]) ).
fof(f474,plain,
( ? [X0,X1] :
( X0 != X1
& sum(n7,n6,X1)
& sum(n6,n7,X0) )
=> ( sK0 != sK1
& sum(n7,n6,sK1)
& sum(n6,n7,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f428,plain,
? [X0,X1] :
( X0 != X1
& sum(n7,n6,X1)
& sum(n6,n7,X0) ),
inference(flattening,[],[f427]) ).
fof(f427,plain,
? [X0,X1] :
( X0 != X1
& sum(n7,n6,X1)
& sum(n6,n7,X0) ),
inference(ennf_transformation,[],[f404]) ).
fof(f404,plain,
~ ! [X0,X1] :
( ( sum(n7,n6,X1)
& sum(n6,n7,X0) )
=> X0 = X1 ),
inference(rectify,[],[f403]) ).
fof(f403,negated_conjecture,
~ ! [X14,X15] :
( ( sum(n7,n6,X15)
& sum(n6,n7,X14) )
=> X14 = X15 ),
inference(negated_conjecture,[],[f402]) ).
fof(f402,conjecture,
! [X14,X15] :
( ( sum(n7,n6,X15)
& sum(n6,n7,X14) )
=> X14 = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',communative_sum_n6_n7) ).
fof(f88637,plain,
~ sum(n7,n6,sK0),
inference(unit_resulting_resolution,[],[f481,f480,f875]) ).
fof(f480,plain,
sum(n7,n6,sK1),
inference(cnf_transformation,[],[f475]) ).
fof(f481,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f475]) ).
fof(f607,plain,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
inference(cnf_transformation,[],[f14]) ).
fof(f14,axiom,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn13) ).
fof(f514,plain,
rdn_translate(n6,rdn_pos(rdnn(n6))),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
rdn_translate(n6,rdn_pos(rdnn(n6))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn6) ).
fof(f515,plain,
rdn_translate(n7,rdn_pos(rdnn(n7))),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
rdn_translate(n7,rdn_pos(rdnn(n7))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn7) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : NUM331+1 : TPTP v8.2.0. Released v3.1.0.
% 0.10/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon May 20 05:06:07 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % (12936)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.37 % (12939)WARNING: value z3 for option sas not known
% 0.12/0.37 % (12940)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.37 % (12939)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)
% 0.12/0.37 % (12942)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)
% 0.12/0.37 % (12943)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)
% 0.12/0.37 % (12941)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)
% 0.12/0.37 % (12938)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.38 % (12937)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.40 TRYING [1]
% 0.12/0.40 TRYING [2]
% 0.18/0.45 TRYING [3]
% 0.18/0.46 TRYING [1]
% 0.18/0.47 TRYING [2]
% 0.18/0.56 TRYING [3]
% 2.15/0.68 TRYING [4]
% 4.23/0.96 TRYING [4]
% 7.76/1.48 TRYING [1]
% 7.76/1.49 TRYING [2]
% 8.12/1.52 TRYING [3]
% 9.12/1.66 TRYING [4]
% 11.01/1.93 TRYING [5]
% 16.18/2.69 TRYING [5]
% 30.68/4.74 TRYING [5]
% 55.26/8.28 TRYING [6]
% 59.54/8.87 TRYING [6]
% 108.22/15.84 % (12943)First to succeed.
% 108.22/15.85 % (12943)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-12936"
% 108.39/15.87 % (12943)Refutation found. Thanks to Tanya!
% 108.39/15.87 % SZS status Theorem for theBenchmark
% 108.39/15.87 % SZS output start Proof for theBenchmark
% See solution above
% 108.39/15.87 % (12943)------------------------------
% 108.39/15.87 % (12943)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 108.39/15.87 % (12943)Termination reason: Refutation
% 108.39/15.87
% 108.39/15.87 % (12943)Memory used [KB]: 124395
% 108.39/15.87 % (12943)Time elapsed: 15.488 s
% 108.39/15.87 % (12943)Instructions burned: 30497 (million)
% 108.39/15.87 % (12936)Success in time 15.515 s
%------------------------------------------------------------------------------