TSTP Solution File: NUM928_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM928_5 : TPTP v8.1.2. Released v6.0.0.
% 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 : Sun May 5 08:43:55 EDT 2024
% Result : Theorem 5.77s 1.17s
% Output : Refutation 5.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 61
% Syntax : Number of formulae : 87 ( 22 unt; 53 typ; 0 def)
% Number of atoms : 52 ( 22 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 31 ( 13 ~; 10 |; 3 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 37 ( 27 >; 10 *; 0 +; 0 <<)
% Number of predicates : 27 ( 25 usr; 1 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 5 con; 0-5 aty)
% Number of variables : 110 ( 50 !; 10 ?; 110 :)
% ( 50 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
fun: ( $tType * $tType ) > $tType ).
tff(type_def_8,type,
product_prod: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
minus_minus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_1,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_2,type,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_3,type,
uminus_uminus:
!>[X0: $tType] : ( X0 > X0 ) ).
tff(func_def_4,type,
min: int ).
tff(func_def_5,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_6,type,
ring_1_of_int:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_7,type,
product_Pair:
!>[X0: $tType,X1: $tType] : ( ( X0 * X1 ) > product_prod(X0,X1) ) ).
tff(func_def_8,type,
product_prod_rec:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).
tff(func_def_9,type,
twoSqu196287499sum2sq: product_prod(int,int) > int ).
tff(func_def_10,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_11,type,
fFalse: bool ).
tff(func_def_12,type,
fTrue: bool ).
tff(func_def_13,type,
x: int ).
tff(func_def_14,type,
y: int ).
tff(func_def_15,type,
sK0: int > int ).
tff(func_def_16,type,
sK1: int > int ).
tff(func_def_17,type,
sK2:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_18,type,
sK3:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).
tff(func_def_19,type,
sK4:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).
tff(func_def_20,type,
sK5:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).
tff(func_def_21,type,
sK6:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_22,type,
sK7:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).
tff(func_def_23,type,
sK8:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
ring:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
cl_Groups_Ominus:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
ring_1:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
semiring:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
comm_ring:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
group_add:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
ab_group_add:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
comm_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
ab_semigroup_mult:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
boolean_algebra:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_18,type,
ab_sem1668676832m_mult:
!>[X0: $tType] : $o ).
tff(pred_def_19,type,
semiri456707255roduct:
!>[X0: $tType] : $o ).
tff(pred_def_20,type,
abel_semigroup:
!>[X0: $tType] : ( fun(X0,fun(X0,X0)) > $o ) ).
tff(pred_def_21,type,
comm_monoid:
!>[X0: $tType] : ( ( fun(X0,fun(X0,X0)) * X0 ) > $o ) ).
tff(pred_def_22,type,
semigroup:
!>[X0: $tType] : ( fun(X0,fun(X0,X0)) > $o ) ).
tff(pred_def_23,type,
semilattice:
!>[X0: $tType] : ( fun(X0,fun(X0,X0)) > $o ) ).
tff(pred_def_24,type,
twoSqu1567020053sum2sq: int > $o ).
tff(pred_def_25,type,
pp: bool > $o ).
tff(f15669,plain,
$false,
inference(subsumption_resolution,[],[f15668,f346]) ).
tff(f346,plain,
~ twoSqu1567020053sum2sq(times_times(int,x,y)),
inference(cnf_transformation,[],[f126]) ).
tff(f126,plain,
~ twoSqu1567020053sum2sq(times_times(int,x,y)),
inference(flattening,[],[f125]) ).
tff(f125,negated_conjecture,
~ twoSqu1567020053sum2sq(times_times(int,x,y)),
inference(negated_conjecture,[],[f124]) ).
tff(f124,conjecture,
twoSqu1567020053sum2sq(times_times(int,x,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
tff(f15668,plain,
twoSqu1567020053sum2sq(times_times(int,x,y)),
inference(forward_demodulation,[],[f15666,f524]) ).
tff(f524,plain,
! [X0: int,X1: int] : ( times_times(int,X1,X0) = times_times(int,X0,X1) ),
inference(resolution,[],[f430,f366]) ).
tff(f366,plain,
comm_semiring_1(int),
inference(cnf_transformation,[],[f106]) ).
tff(f106,axiom,
comm_semiring_1(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
tff(f430,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ~ comm_semiring_1(X0)
| ( times_times(X0,X2,X1) = times_times(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f280]) ).
tff(f280,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( times_times(X0,X2,X1) = times_times(X0,X1,X2) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0] : ( times_times(X0,X2,X1) = times_times(X0,X1,X2) ) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X3: X0,X4: X0] : ( times_times(X0,X4,X3) = times_times(X0,X3,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
tff(f15666,plain,
twoSqu1567020053sum2sq(times_times(int,y,x)),
inference(superposition,[],[f15653,f630]) ).
tff(f630,plain,
x = twoSqu196287499sum2sq(product_Pair(int,int,sK0(x),sK1(x))),
inference(resolution,[],[f454,f348]) ).
tff(f348,plain,
twoSqu1567020053sum2sq(x),
inference(cnf_transformation,[],[f122]) ).
tff(f122,axiom,
twoSqu1567020053sum2sq(x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f454,plain,
! [X0: int] :
( ~ twoSqu1567020053sum2sq(X0)
| ( twoSqu196287499sum2sq(product_Pair(int,int,sK0(X0),sK1(X0))) = X0 ) ),
inference(cnf_transformation,[],[f331]) ).
tff(f331,plain,
! [X0: int] :
( ( twoSqu1567020053sum2sq(X0)
| ! [X1: int,X2: int] : ( twoSqu196287499sum2sq(product_Pair(int,int,X1,X2)) != X0 ) )
& ( ( twoSqu196287499sum2sq(product_Pair(int,int,sK0(X0),sK1(X0))) = X0 )
| ~ twoSqu1567020053sum2sq(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f329,f330]) ).
tff(f330,plain,
! [X0: int] :
( ? [X3: int,X4: int] : ( twoSqu196287499sum2sq(product_Pair(int,int,X3,X4)) = X0 )
=> ( twoSqu196287499sum2sq(product_Pair(int,int,sK0(X0),sK1(X0))) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f329,plain,
! [X0: int] :
( ( twoSqu1567020053sum2sq(X0)
| ! [X1: int,X2: int] : ( twoSqu196287499sum2sq(product_Pair(int,int,X1,X2)) != X0 ) )
& ( ? [X3: int,X4: int] : ( twoSqu196287499sum2sq(product_Pair(int,int,X3,X4)) = X0 )
| ~ twoSqu1567020053sum2sq(X0) ) ),
inference(rectify,[],[f328]) ).
tff(f328,plain,
! [X0: int] :
( ( twoSqu1567020053sum2sq(X0)
| ! [X1: int,X2: int] : ( twoSqu196287499sum2sq(product_Pair(int,int,X1,X2)) != X0 ) )
& ( ? [X1: int,X2: int] : ( twoSqu196287499sum2sq(product_Pair(int,int,X1,X2)) = X0 )
| ~ twoSqu1567020053sum2sq(X0) ) ),
inference(nnf_transformation,[],[f199]) ).
tff(f199,plain,
! [X0: int] :
( twoSqu1567020053sum2sq(X0)
<=> ? [X1: int,X2: int] : ( twoSqu196287499sum2sq(product_Pair(int,int,X1,X2)) = X0 ) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X16: int] :
( twoSqu1567020053sum2sq(X16)
<=> ? [X17: int,X18: int] : ( twoSqu196287499sum2sq(product_Pair(int,int,X17,X18)) = X16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_is__sum2sq__def) ).
tff(f15653,plain,
! [X0: int,X1: int] : twoSqu1567020053sum2sq(times_times(int,y,twoSqu196287499sum2sq(product_Pair(int,int,X0,X1)))),
inference(superposition,[],[f9359,f629]) ).
tff(f629,plain,
y = twoSqu196287499sum2sq(product_Pair(int,int,sK0(y),sK1(y))),
inference(resolution,[],[f454,f347]) ).
tff(f347,plain,
twoSqu1567020053sum2sq(y),
inference(cnf_transformation,[],[f123]) ).
tff(f123,axiom,
twoSqu1567020053sum2sq(y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(f9359,plain,
! [X2: int,X3: int,X0: int,X1: int] : twoSqu1567020053sum2sq(times_times(int,twoSqu196287499sum2sq(product_Pair(int,int,X0,X2)),twoSqu196287499sum2sq(product_Pair(int,int,X1,X3)))),
inference(superposition,[],[f497,f472]) ).
tff(f472,plain,
! [X2: int,X3: int,X0: int,X1: int] : ( times_times(int,twoSqu196287499sum2sq(product_Pair(int,int,X3,X2)),twoSqu196287499sum2sq(product_Pair(int,int,X1,X0))) = twoSqu196287499sum2sq(product_Pair(int,int,plus_plus(int,times_times(int,X3,X1),times_times(int,X2,X0)),minus_minus(int,times_times(int,X3,X0),times_times(int,X2,X1)))) ),
inference(cnf_transformation,[],[f215]) ).
tff(f215,plain,
! [X0: int,X1: int,X2: int,X3: int] : ( times_times(int,twoSqu196287499sum2sq(product_Pair(int,int,X3,X2)),twoSqu196287499sum2sq(product_Pair(int,int,X1,X0))) = twoSqu196287499sum2sq(product_Pair(int,int,plus_plus(int,times_times(int,X3,X1),times_times(int,X2,X0)),minus_minus(int,times_times(int,X3,X0),times_times(int,X2,X1)))) ),
inference(rectify,[],[f75]) ).
tff(f75,axiom,
! [X42: int,X43: int,X3: int,X4: int] : ( times_times(int,twoSqu196287499sum2sq(product_Pair(int,int,X4,X3)),twoSqu196287499sum2sq(product_Pair(int,int,X43,X42))) = twoSqu196287499sum2sq(product_Pair(int,int,plus_plus(int,times_times(int,X4,X43),times_times(int,X3,X42)),minus_minus(int,times_times(int,X4,X42),times_times(int,X3,X43)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_mult__sum2sq) ).
tff(f497,plain,
! [X2: int,X1: int] : twoSqu1567020053sum2sq(twoSqu196287499sum2sq(product_Pair(int,int,X1,X2))),
inference(equality_resolution,[],[f455]) ).
tff(f455,plain,
! [X2: int,X0: int,X1: int] :
( twoSqu1567020053sum2sq(X0)
| ( twoSqu196287499sum2sq(product_Pair(int,int,X1,X2)) != X0 ) ),
inference(cnf_transformation,[],[f331]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM928_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n007.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 14:22:38 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % (27942)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (27946)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37 % Exception at run slice level
% 0.15/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.37 % (27945)WARNING: value z3 for option sas not known
% 0.15/0.38 % (27943)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (27944)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 % (27945)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 % (27947)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 % (27948)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 % (27949)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 % Exception at run slice level
% 0.15/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.38 % Exception at run slice level
% 0.15/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.38 % (27949)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.38 % (27950)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.15/0.38 % (27950)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.38 % Exception at run slice level
% 0.15/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39 % (27953)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.15/0.40 % (27951)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.15/0.40 % (27952)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.15/0.40 % (27951)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.77/1.17 % (27952)First to succeed.
% 5.77/1.17 % (27952)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-27942"
% 5.77/1.17 % (27952)Refutation found. Thanks to Tanya!
% 5.77/1.17 % SZS status Theorem for theBenchmark
% 5.77/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 5.77/1.17 % (27952)------------------------------
% 5.77/1.17 % (27952)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 5.77/1.17 % (27952)Termination reason: Refutation
% 5.77/1.17
% 5.77/1.17 % (27952)Memory used [KB]: 6098
% 5.77/1.17 % (27952)Time elapsed: 0.776 s
% 5.77/1.17 % (27952)Instructions burned: 1502 (million)
% 5.77/1.17 % (27942)Success in time 0.807 s
%------------------------------------------------------------------------------