%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SCT179_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 12:37:43 PM UTC 2026
% Result : Theorem 0.17s 0.51s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 6 ~; 3 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 20 ( 19 usr; 1 prp; 0-6 aty)
% Number of functors : 34 ( 34 usr; 6 con; 0-5 aty)
% Number of variables : 20 ( 18 !; 2 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
arrow_411405190le_alt: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(type_def_8,type,
fun: ( $tType * $tType ) > $tType ).
tff(type_def_9,type,
product_prod: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
arrow_1985332922le_Lin: fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool) ).
tff(func_def_1,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * fun(X2,X0) ) > fun(X2,X1) ) ).
tff(func_def_2,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * X1 ) > fun(X0,X2) ) ).
tff(func_def_3,type,
combk:
!>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).
tff(func_def_4,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).
tff(func_def_5,type,
minus_minus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_6,type,
order_215145569der_on:
!>[X0: $tType] : ( fun(X0,bool) > fun(fun(product_prod(X0,X0),bool),bool) ) ).
tff(func_def_7,type,
bot_bot:
!>[X0: $tType] : X0 ).
tff(func_def_8,type,
top_top:
!>[X0: $tType] : X0 ).
tff(func_def_9,type,
domain:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > fun(X0,bool) ) ).
tff(func_def_10,type,
id:
!>[X0: $tType] : fun(product_prod(X0,X0),bool) ).
tff(func_def_11,type,
id_on:
!>[X0: $tType] : ( fun(X0,bool) > fun(product_prod(X0,X0),bool) ) ).
tff(func_def_12,type,
range:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > fun(X1,bool) ) ).
tff(func_def_13,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_14,type,
lex_prod:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X0),bool) * fun(product_prod(X1,X1),bool) ) > fun(product_prod(product_prod(X0,X1),product_prod(X0,X1)),bool) ) ).
tff(func_def_15,type,
measure:
!>[X0: $tType] : ( fun(X0,nat) > fun(product_prod(X0,X0),bool) ) ).
tff(func_def_16,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_17,type,
fFalse: bool ).
tff(func_def_18,type,
fNot: fun(bool,bool) ).
tff(func_def_19,type,
fTrue: bool ).
tff(func_def_20,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_21,type,
member:
!>[X0: $tType] : fun(X0,fun(fun(X0,bool),bool)) ).
tff(func_def_22,type,
r: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_23,type,
sK0:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_24,type,
sK1:
!>[X0: $tType] : X0 ).
tff(func_def_25,type,
sK2:
!>[X0: $tType] : ( fun(X0,bool) > fun(product_prod(X0,X0),bool) ) ).
tff(func_def_26,type,
sK3:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_27,type,
sK4:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_28,type,
sK5:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_29,type,
sK6:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_30,type,
sK7:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_31,type,
sK8:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(pred_def_1,type,
cl_Groups_Ominus:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
bot:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
top:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
group_add:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
preorder:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
ordered_ab_group_add:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
order_1409979114der_on:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) ) > $o ) ).
tff(pred_def_8,type,
order_915043626der_on:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) ) > $o ) ).
tff(pred_def_9,type,
order_preorder_on:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) ) > $o ) ).
tff(pred_def_10,type,
order_well_order_on:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) ) > $o ) ).
tff(pred_def_11,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_12,type,
inv_imagep:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X0,bool)) * fun(X1,X0) * X1 * X1 ) > $o ) ).
tff(pred_def_13,type,
antisym:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).
tff(pred_def_14,type,
irrefl:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).
tff(pred_def_15,type,
refl_on:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) ) > $o ) ).
tff(pred_def_16,type,
total_on:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) ) > $o ) ).
tff(pred_def_17,type,
trans:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).
tff(pred_def_18,type,
wf:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).
tff(pred_def_19,type,
pp: bool > $o ).
tff(f1,axiom,
! [X0: $tType,X3: fun(product_prod(X0,X0),bool),X4: fun(X0,bool)] :
( order_1409979114der_on(X0,X4,X3)
=> pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X4),minus_minus(fun(product_prod(X0,X0),bool),X3,id(X0)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_strict__linear__order__on__diff__Id) ).
tff(f124,axiom,
order_1409979114der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f126,conjecture,
? [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
tff(f127,negated_conjecture,
~ ? [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),X0)),
inference(negated_conjecture,[status(cth)],[f126]) ).
tff(f128,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( order_1409979114der_on(X0,X2,X1)
=> pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0)))) ),
inference(rectify,[],[f1]) ).
tff(f132,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0))))
| ~ order_1409979114der_on(X0,X2,X1) ),
inference(ennf_transformation,[],[f128]) ).
tff(f186,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : ~ pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),X0)),
inference(ennf_transformation,[],[f127]) ).
tff(f187,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( ~ order_1409979114der_on(X0,X2,X1)
| pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0)))) ),
inference(cnf_transformation,[],[f132]) ).
tff(f334,plain,
order_1409979114der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),r),
inference(cnf_transformation,[],[f124]) ).
tff(f336,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : ~ pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),X0)),
inference(cnf_transformation,[],[f186]) ).
tff(f349,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0))))
| order_1409979114der_on(X0,X2,X1) ),
inference(consistent_polarity_flipping,[],[f187]) ).
tff(f388,plain,
~ order_1409979114der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),r),
inference(consistent_polarity_flipping,[],[f334]) ).
tff(f1415,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : order_1409979114der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),X0),
inference(resolution,[],[f349,f336]) ).
tff(f1433,plain,
$false,
inference(backward_subsumption_resolution,[],[f388,f1415]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT179_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 % Computer : n006.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Sun Sep 27 23:57:26 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.43 Running first-order model finding
% 0.11/0.43 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.51 % (3458535)Will run a generic schedule for satisfiability detection.
% 0.17/0.51 % (3458546)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3124598482:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.51 % (3458545)% WARNING: option uhcvi not known.
% 0.17/0.51 % (3458544)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4215844423_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.51 % (3458547)dis+10_1_sil=32000:sp=arity:random_seed=2533675666:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.51 % (3458545)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2578307586:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.51 % (3458549)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1943798451:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.51 % (3458548)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3928551723:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.51 % (3458550)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3961441053:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.51 % Exception at run slice level
% 0.17/0.51 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.51 % (3458561)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3850458166:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.17/0.51 % Exception at run slice level
% 0.17/0.51 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.51 % (3458545) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3458535-3458545"...
% 0.17/0.51 % (3458547) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3458535-3458547"...
% 0.17/0.51 % (3458545)...printing done.
% 0.17/0.51 % (3458545)Refutation found. Thanks to Tanya!
% 0.17/0.51 % SZS status Theorem for theBenchmark
% 0.17/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.51 % (3458545)------------------------------
% 0.17/0.51 % (3458545)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.51 % (3458545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.51 % (3458545)CaDiCaL version: 2.1.3
% 0.17/0.51 % (3458545)Termination reason: Refutation
% 0.17/0.51 % (3458545)Time elapsed: 0.037 s
% 0.17/0.51 % (3458545)Peak memory usage: 12 MB
% 0.17/0.51 % (3458545)Instructions burned: 54 (million)
% 0.17/0.51 % (3458535)Success in time 0.065 s
% 0.17/0.51 % Vampire exiting
%------------------------------------------------------------------------------