TSTP Solution File: NUM335+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM335+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n016.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 14:14:16 EDT 2024
% Result : Theorem 11.38s 2.06s
% Output : Refutation 11.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 48 ( 19 unt; 0 def)
% Number of atoms : 113 ( 12 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 116 ( 51 ~; 38 |; 15 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 113 ( 111 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f170088,plain,
$false,
inference(subsumption_resolution,[],[f170087,f95763]) ).
fof(f95763,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n3),rdnn(n2),rdnn(n5)),
inference(unit_resulting_resolution,[],[f761,f763,f874]) ).
fof(f874,plain,
! [X2,X3,X0,X1,X4] :
( ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
| rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) ),
inference(cnf_transformation,[],[f456]) ).
fof(f456,plain,
! [X0,X1,X2,X3,X4] :
( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
| ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) ),
inference(flattening,[],[f455]) ).
fof(f455,plain,
! [X0,X1,X2,X3,X4] :
( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
| ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) ),
inference(ennf_transformation,[],[f416]) ).
fof(f416,plain,
! [X0,X1,X2,X3,X4] :
( ( rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
& rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) )
=> rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3)) ),
inference(rectify,[],[f297]) ).
fof(f297,axiom,
! [X20,X21,X22,X23,X24] :
( ( rdn_digit_add(rdnn(X24),rdnn(X20),rdnn(X23),rdnn(n0))
& rdn_digit_add(rdnn(X21),rdnn(X22),rdnn(X24),rdnn(n0)) )
=> rdn_add_with_carry(rdnn(X20),rdnn(X21),rdnn(X22),rdnn(X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_digit_digit_digit) ).
fof(f763,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f352]) ).
fof(f352,axiom,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n5_n0_n5_n0) ).
fof(f761,plain,
rdn_digit_add(rdnn(n3),rdnn(n2),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f334]) ).
fof(f334,axiom,
rdn_digit_add(rdnn(n3),rdnn(n2),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n3_n2_n5_n0) ).
fof(f170087,plain,
~ rdn_add_with_carry(rdnn(n0),rdnn(n3),rdnn(n2),rdnn(n5)),
inference(unit_resulting_resolution,[],[f512,f134823,f910]) ).
fof(f910,plain,
! [X3,X0,X4,X5] :
( ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X0,rdn_pos(X3))
| sP14(X4,X0,X5) ),
inference(cnf_transformation,[],[f910_D]) ).
fof(f910_D,plain,
! [X5,X0,X4] :
( ! [X3] :
( ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X0,rdn_pos(X3)) )
<=> ~ sP14(X4,X0,X5) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP14])]) ).
fof(f134823,plain,
~ sP14(rdnn(n2),n3,rdnn(n5)),
inference(unit_resulting_resolution,[],[f513,f129637,f911]) ).
fof(f911,plain,
! [X0,X1,X4,X5] :
( ~ sP14(X4,X0,X5)
| ~ sP13(X0,X5,X1)
| ~ rdn_translate(X1,rdn_pos(X4)) ),
inference(general_splitting,[],[f909,f910_D]) ).
fof(f909,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))
| ~ sP13(X0,X5,X1) ),
inference(general_splitting,[],[f879,f908_D]) ).
fof(f908,plain,
! [X2,X0,X1,X5] :
( ~ rdn_translate(X2,rdn_pos(X5))
| sum(X0,X1,X2)
| sP13(X0,X5,X1) ),
inference(cnf_transformation,[],[f908_D]) ).
fof(f908_D,plain,
! [X1,X5,X0] :
( ! [X2] :
( ~ rdn_translate(X2,rdn_pos(X5))
| sum(X0,X1,X2) )
<=> ~ sP13(X0,X5,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP13])]) ).
fof(f879,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(f129637,plain,
sP13(n3,rdnn(n5),n2),
inference(unit_resulting_resolution,[],[f511,f96505,f908]) ).
fof(f96505,plain,
~ sum(n3,n2,n5),
inference(unit_resulting_resolution,[],[f478,f41242,f871]) ).
fof(f871,plain,
! [X2,X3,X0,X1] :
( ~ sum(X0,X2,X3)
| X1 = X2
| ~ sum(X0,X1,X3) ),
inference(cnf_transformation,[],[f450]) ).
fof(f450,plain,
! [X0,X1,X2,X3] :
( X1 = X2
| ~ sum(X0,X2,X3)
| ~ sum(X0,X1,X3) ),
inference(flattening,[],[f449]) ).
fof(f449,plain,
! [X0,X1,X2,X3] :
( X1 = X2
| ~ sum(X0,X2,X3)
| ~ sum(X0,X1,X3) ),
inference(ennf_transformation,[],[f413]) ).
fof(f413,plain,
! [X0,X1,X2,X3] :
( ( sum(X0,X2,X3)
& sum(X0,X1,X3) )
=> X1 = X2 ),
inference(rectify,[],[f295]) ).
fof(f295,axiom,
! [X0,X18,X19,X2] :
( ( sum(X0,X19,X2)
& sum(X0,X18,X2) )
=> X18 = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_RHS) ).
fof(f41242,plain,
sum(n3,sK0,n5),
inference(unit_resulting_resolution,[],[f477,f865]) ).
fof(f865,plain,
! [X2,X0,X1] :
( ~ difference(X0,X1,X2)
| sum(X1,X2,X0) ),
inference(cnf_transformation,[],[f476]) ).
fof(f476,plain,
! [X0,X1,X2] :
( ( sum(X1,X2,X0)
| ~ difference(X0,X1,X2) )
& ( difference(X0,X1,X2)
| ~ sum(X1,X2,X0) ) ),
inference(nnf_transformation,[],[f296]) ).
fof(f296,axiom,
! [X0,X1,X2] :
( sum(X1,X2,X0)
<=> difference(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minus_entry_point) ).
fof(f477,plain,
difference(n5,n3,sK0),
inference(cnf_transformation,[],[f473]) ).
fof(f473,plain,
( n2 != sK0
& difference(n5,n3,sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f426,f472]) ).
fof(f472,plain,
( ? [X0] :
( n2 != X0
& difference(n5,n3,X0) )
=> ( n2 != sK0
& difference(n5,n3,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f426,plain,
? [X0] :
( n2 != X0
& difference(n5,n3,X0) ),
inference(ennf_transformation,[],[f403]) ).
fof(f403,negated_conjecture,
~ ! [X0] :
( difference(n5,n3,X0)
=> n2 = X0 ),
inference(negated_conjecture,[],[f402]) ).
fof(f402,conjecture,
! [X0] :
( difference(n5,n3,X0)
=> n2 = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diff_n5_n3_only_n2) ).
fof(f478,plain,
n2 != sK0,
inference(cnf_transformation,[],[f473]) ).
fof(f511,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn5) ).
fof(f513,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn2) ).
fof(f512,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM335+1 : TPTP v8.1.2. Released v3.1.0.
% 0.04/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Apr 29 23:57:55 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (8467)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.39 % (8470)WARNING: value z3 for option sas not known
% 0.21/0.39 % (8468)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.39 % (8469)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.39 % (8471)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.39 % (8470)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)
% 0.21/0.39 % (8472)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)
% 0.21/0.39 % (8473)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)
% 0.21/0.39 % (8474)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)
% 0.21/0.43 TRYING [1]
% 0.21/0.44 TRYING [2]
% 0.21/0.47 TRYING [1]
% 0.21/0.48 TRYING [2]
% 0.21/0.49 TRYING [3]
% 1.30/0.56 TRYING [3]
% 1.95/0.64 TRYING [4]
% 3.59/0.88 TRYING [4]
% 6.70/1.32 TRYING [5]
% 7.91/1.51 TRYING [1]
% 7.91/1.51 TRYING [2]
% 8.28/1.54 TRYING [3]
% 8.92/1.67 TRYING [4]
% 10.26/1.82 TRYING [5]
% 11.38/2.05 % (8474)First to succeed.
% 11.38/2.06 % (8474)Refutation found. Thanks to Tanya!
% 11.38/2.06 % SZS status Theorem for theBenchmark
% 11.38/2.06 % SZS output start Proof for theBenchmark
% See solution above
% 11.38/2.06 % (8474)------------------------------
% 11.38/2.06 % (8474)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 11.38/2.06 % (8474)Termination reason: Refutation
% 11.38/2.06
% 11.38/2.06 % (8474)Memory used [KB]: 39899
% 11.38/2.06 % (8474)Time elapsed: 1.663 s
% 11.38/2.06 % (8474)Instructions burned: 5267 (million)
% 11.38/2.06 % (8474)------------------------------
% 11.38/2.06 % (8474)------------------------------
% 11.38/2.06 % (8467)Success in time 1.678 s
%------------------------------------------------------------------------------