%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT179_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 12:37:11 PM UTC 2026
% Result : Theorem 2.69s 1.36s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 7 ~; 4 |; 3 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 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 : 21 ( 20 usr; 1 prp; 0-6 aty)
% Number of functors : 34 ( 34 usr; 6 con; 0-5 aty)
% Number of variables : 39 ( 36 !; 3 ?; 39 :)
% 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(pred_def_20,type,
sQ9_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $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/sandbox2/benchmark/theBenchmark.p',fact_0_strict__linear__order__on__diff__Id) ).
tff(f10,axiom,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( order_well_order_on(X0,X2,X1)
<=> ( order_1409979114der_on(X0,X2,X1)
& wf(X0,minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_well__order__on__def) ).
tff(f24,axiom,
! [X0: $tType,X1: fun(X0,bool)] :
? [X2: fun(product_prod(X0,X0),bool)] : order_well_order_on(X0,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_well__order__on) ).
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/sandbox2/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(f129,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( order_well_order_on(X0,X2,X1)
=> ( order_1409979114der_on(X0,X2,X1)
& wf(X0,minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0))) ) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
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(f136,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ( order_1409979114der_on(X0,X2,X1)
& wf(X0,minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0))) )
| ~ order_well_order_on(X0,X2,X1) ),
inference(ennf_transformation,[],[f129]) ).
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(f192,plain,
! [X0: $tType,X1: fun(X0,bool)] : order_well_order_on(X0,X1,sK2(X0,X1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f24]) ).
tff(f224,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(f237,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( ~ order_well_order_on(X0,X2,X1)
| order_1409979114der_on(X0,X2,X1) ),
inference(cnf_transformation,[],[f136]) ).
tff(f250,plain,
! [X0: $tType,X1: fun(X0,bool)] : order_well_order_on(X0,X1,sK2(X0,X1)),
inference(cnf_transformation,[],[f192]) ).
tff(f373,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(f444,plain,
! [X0: $tType,X1: fun(X0,bool)] : order_1409979114der_on(X0,X1,sK2(X0,X1)),
inference(resolution,[],[f237,f250]) ).
tff(f619,plain,
! [X0: $tType,X1: fun(X0,bool)] : pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X1),minus_minus(fun(product_prod(X0,X0),bool),sK2(X0,X1),id(X0)))),
inference(resolution,[],[f224,f444]) ).
tff(f689,plain,
$false,
inference(resolution,[],[f619,f373]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT179_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n011.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 23:57:46 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.69/1.36 % (2894470)Detected formulas, will run a generic FOF schedule.
% 2.69/1.36 % (2894481)dis-21_1_sil=8000:lcm=predicate:random_seed=2215968726:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.69/1.36 % (2894481)First to succeed.
% 2.69/1.36 % (2894481)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2894470"
% 2.69/1.36 % (2894475)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2579182460:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.69/1.36 % (2894479)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1051852928:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.69/1.36 % (2894480)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2439230771:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.69/1.36 % (2894477)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1927527798:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.69/1.36 % (2894478)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3826303740:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.69/1.36 % (2894476)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1884405439:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.69/1.36 % (2894478)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.69/1.36 % (2894478)Also succeeded, but the first one will report.
% 2.69/1.36 % (2894477)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.69/1.36 % (2894479)Also succeeded, but the first one will report.
% 2.69/1.36 % (2894480)Also succeeded, but the first one will report.
% 2.69/1.36 % (2894481)Refutation found. Thanks to Tanya!
% 2.69/1.36 % SZS status Theorem for theBenchmark
% 2.69/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.36 % (2894481)------------------------------
% 2.69/1.36 % (2894481)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.36 % (2894481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.36 % (2894481)CaDiCaL version: 2.1.3
% 2.69/1.36 % (2894481)Termination reason: Refutation
% 2.69/1.36 % (2894481)Time elapsed: 0.007 s
% 2.69/1.36 % (2894481)Peak memory usage: 88 MB
% 2.69/1.36 % (2894481)Instructions burned: 18 (million)
% 2.69/1.36 % (2894481)------------------------------
% 2.69/1.36 % (2894481)------------------------------
% 2.69/1.36 % (2894470)Success in time 0.305 s
% 2.69/1.36 % Vampire exiting
%------------------------------------------------------------------------------