%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM928_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:26:14 PM UTC 2026
% Result : Theorem 0.87s 0.60s
% Output : Refutation 0.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 2 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 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 : 23 ( 21 !; 2 ?; 23 :)
% 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) > product_prod(X0,X1) ) ).
tff(func_def_18,type,
sK3:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_19,type,
sK4:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).
tff(func_def_20,type,
sK5:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_21,type,
sK6:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).
tff(func_def_22,type,
sK7:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_23,type,
sK8:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > 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(f15,axiom,
! [X0: int] :
( twoSqu1567020053sum2sq(X0)
<=> ? [X1: int,X2: int] : ( twoSqu196287499sum2sq(product_Pair(int,int,X1,X2)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_is__sum2sq__def) ).
tff(f75,axiom,
! [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)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_mult__sum2sq) ).
tff(f122,axiom,
twoSqu1567020053sum2sq(x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f123,axiom,
twoSqu1567020053sum2sq(y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(f124,conjecture,
twoSqu1567020053sum2sq(times_times(int,x,y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
tff(f125,negated_conjecture,
~ twoSqu1567020053sum2sq(times_times(int,x,y)),
inference(negated_conjecture,[status(cth)],[f124]) ).
tff(f127,plain,
~ twoSqu1567020053sum2sq(times_times(int,x,y)),
inference(flattening,[],[f125]) ).
tff(f225,plain,
! [X2: int,X0: int,X1: int] :
( ( twoSqu196287499sum2sq(product_Pair(int,int,X1,X2)) != X0 )
| twoSqu1567020053sum2sq(X0) ),
inference(cnf_transformation,[],[f15]) ).
tff(f226,plain,
! [X0: int] :
( ~ twoSqu1567020053sum2sq(X0)
| ( twoSqu196287499sum2sq(product_Pair(int,int,sK0(X0),sK1(X0))) = X0 ) ),
inference(cnf_transformation,[],[f15]) ).
tff(f294,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,[],[f75]) ).
tff(f346,plain,
twoSqu1567020053sum2sq(x),
inference(cnf_transformation,[],[f122]) ).
tff(f347,plain,
twoSqu1567020053sum2sq(y),
inference(cnf_transformation,[],[f123]) ).
tff(f348,plain,
~ twoSqu1567020053sum2sq(times_times(int,x,y)),
inference(cnf_transformation,[],[f127]) ).
tff(f349,plain,
! [X2: int,X1: int] : twoSqu1567020053sum2sq(twoSqu196287499sum2sq(product_Pair(int,int,X1,X2))),
inference(equality_resolution,[],[f225]) ).
tff(f439,plain,
x = twoSqu196287499sum2sq(product_Pair(int,int,sK0(x),sK1(x))),
inference(resolution,[],[f226,f346]) ).
tff(f440,plain,
y = twoSqu196287499sum2sq(product_Pair(int,int,sK0(y),sK1(y))),
inference(resolution,[],[f226,f347]) ).
tff(f976,plain,
! [X2: int,X3: int,X0: int,X1: int] : twoSqu1567020053sum2sq(times_times(int,twoSqu196287499sum2sq(product_Pair(int,int,X0,X1)),twoSqu196287499sum2sq(product_Pair(int,int,X2,X3)))),
inference(superposition,[],[f349,f294]) ).
tff(f2095,plain,
! [X0: int,X1: int] : twoSqu1567020053sum2sq(times_times(int,x,twoSqu196287499sum2sq(product_Pair(int,int,X0,X1)))),
inference(superposition,[],[f976,f439]) ).
tff(f4121,plain,
twoSqu1567020053sum2sq(times_times(int,x,y)),
inference(superposition,[],[f2095,f440]) ).
tff(f4126,plain,
$false,
inference(forward_subsumption_resolution,[],[f4121,f348]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM928_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n007.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 21:42:56 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.87/0.60 % (1806136)Will run a generic schedule for satisfiability detection.
% 0.87/0.60 % (1806144)dis+10_1_sil=32000:sp=arity:random_seed=2898092686:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.87/0.60 % (1806142)% WARNING: option uhcvi not known.
% 0.87/0.60 % (1806141)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1482140740_2999 on theBenchmark for (2999ds/0Mi)
% 0.87/0.60 % (1806142)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2703387699:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.87/0.60 % (1806143)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=972185362:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.87/0.60 % (1806145)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1383326449:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.87/0.60 % (1806147)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4223249058:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.87/0.60 % (1806146)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1386505688:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.87/0.60 % Exception at run slice level
% 0.87/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.87/0.60 % (1806155)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=506418512:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.87/0.60 % (1806144)Instruction limit reached!
% 0.87/0.60 % (1806144)------------------------------
% 0.87/0.60 % (1806144)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.60 % (1806144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.60 % (1806144)CaDiCaL version: 2.1.3
% 0.87/0.60 % (1806144)Termination reason: Instruction limit
% 0.87/0.60 % (1806144)Termination phase: Saturation
% 0.87/0.60 % (1806144)Time elapsed: 0.032 s
% 0.87/0.60 % (1806144)Peak memory usage: 12 MB
% 0.87/0.60 % (1806144)Instructions burned: 107 (million)
% 0.87/0.60 % Exception at run slice level
% 0.87/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.87/0.60 % (1806157)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=992126565:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.87/0.60 % (1806158)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2694581389:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.87/0.60 % (1806145)Instruction limit reached!
% 0.87/0.60 % (1806145)------------------------------
% 0.87/0.60 % (1806145)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.60 % (1806145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.60 % (1806145)CaDiCaL version: 2.1.3
% 0.87/0.60 % (1806145)Termination reason: Instruction limit
% 0.87/0.60 % (1806145)Termination phase: Saturation
% 0.87/0.60 % (1806145)Time elapsed: 0.066 s
% 0.87/0.60 % (1806145)Peak memory usage: 12 MB
% 0.87/0.60 % (1806145)Instructions burned: 116 (million)
% 0.87/0.60 % (1806157)Instruction limit reached!
% 0.87/0.60 % (1806157)------------------------------
% 0.87/0.60 % (1806157)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.60 % (1806157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.60 % (1806157)CaDiCaL version: 2.1.3
% 0.87/0.60 % (1806157)Termination reason: Instruction limit
% 0.87/0.60 % (1806157)Termination phase: Saturation
% 0.87/0.60 % (1806157)Time elapsed: 0.041 s
% 0.87/0.60 % (1806157)Peak memory usage: 13 MB
% 0.87/0.60 % (1806157)Instructions burned: 132 (million)
% 0.87/0.60 % (1806146)Instruction limit reached!
% 0.87/0.60 % (1806146)------------------------------
% 0.87/0.60 % (1806146)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.60 % (1806146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.60 % (1806146)CaDiCaL version: 2.1.3
% 0.87/0.60 % (1806146)Termination reason: Instruction limit
% 0.87/0.60 % (1806146)Termination phase: Saturation
% 0.87/0.60 % (1806146)Time elapsed: 0.076 s
% 0.87/0.60 % (1806146)Peak memory usage: 13 MB
% 0.87/0.60 % (1806146)Instructions burned: 132 (million)
% 0.87/0.60 % (1806161)ott-21_1_sil=16000:fs=off:random_seed=1059232429:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.87/0.60 % (1806162)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1461166107:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.87/0.60 % (1806147)Instruction limit reached!
% 0.87/0.60 % (1806147)------------------------------
% 0.87/0.60 % (1806147)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.60 % (1806147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.60 % (1806147)CaDiCaL version: 2.1.3
% 0.87/0.60 % (1806147)Termination reason: Instruction limit
% 0.87/0.60 % (1806147)Termination phase: Saturation
% 0.87/0.60 % (1806147)Time elapsed: 0.094 s
% 0.87/0.60 % (1806147)Peak memory usage: 13 MB
% 0.87/0.60 % (1806147)Instructions burned: 160 (million)
% 0.87/0.60 % (1806163)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2792728650:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.87/0.60 % Exception at run slice level
% 0.87/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.87/0.60 % (1806166)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=605040987:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 0.87/0.60 % (1806168)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2617310217:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 0.87/0.60 % Exception at run slice level
% 0.87/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.87/0.60 % (1806142) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1806136-1806142"...
% 0.87/0.60 % (1806142)...printing done.
% 0.87/0.60 % (1806142)Refutation found. Thanks to Tanya!
% 0.87/0.60 % SZS status Theorem for theBenchmark
% 0.87/0.60 % SZS output start Proof for theBenchmark
% See solution above
% 0.87/0.60 % (1806142)------------------------------
% 0.87/0.60 % (1806142)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.60 % (1806142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.60 % (1806142)CaDiCaL version: 2.1.3
% 0.87/0.60 % (1806142)Termination reason: Refutation
% 0.87/0.60 % (1806142)Time elapsed: 0.136 s
% 0.87/0.60 % (1806142)Peak memory usage: 14 MB
% 0.87/0.60 % (1806142)Instructions burned: 261 (million)
% 0.87/0.60 % (1806136)Success in time 0.18 s
% 0.87/0.60 % Vampire exiting
%------------------------------------------------------------------------------