%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT222_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 : n026.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 12:37:16 PM UTC 2026
% Result : Theorem 3.67s 1.66s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 9 unt; 0 typ; 1 def)
% Number of atoms : 12 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 11 ( 9 ~; 0 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-6 aty)
% Number of functors : 34 ( 34 usr; 11 con; 0-6 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
arrow_411405190le_alt: $tType ).
tff(type_def_6,type,
arrow_159774573e_indi: $tType ).
tff(type_def_7,type,
bool: $tType ).
tff(type_def_8,type,
list: $tType > $tType ).
tff(type_def_9,type,
fun: ( $tType * $tType ) > $tType ).
tff(type_def_10,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,
arrow_610318064e_Prof: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),bool) ).
tff(func_def_2,type,
arrow_1158827142_above: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_3,type,
arrow_319942042_below: fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))) ).
tff(func_def_4,type,
arrow_276188178_mkbot: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_5,type,
arrow_424895264_mktop: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_6,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * fun(X2,X0) ) > fun(X2,X1) ) ).
tff(func_def_7,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * X1 ) > fun(X0,X2) ) ).
tff(func_def_8,type,
combi:
!>[X0: $tType] : fun(X0,X0) ).
tff(func_def_9,type,
combk:
!>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).
tff(func_def_10,type,
pi:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,bool) * fun(X0,fun(X1,bool)) ) > fun(fun(X0,X1),bool) ) ).
tff(func_def_11,type,
insert:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_12,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_13,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_14,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_15,type,
splice:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_16,type,
top_top:
!>[X0: $tType] : X0 ).
tff(func_def_17,type,
product_Pair:
!>[X0: $tType,X1: $tType] : ( ( X0 * X1 ) > product_prod(X0,X1) ) ).
tff(func_def_18,type,
product_curry:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(product_prod(X0,X1),X2) * X0 * X1 ) > X2 ) ).
tff(func_def_19,type,
produc1605651328_split:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).
tff(func_def_20,type,
product_prod_rec:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).
tff(func_def_21,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_22,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_23,type,
fFalse: bool ).
tff(func_def_24,type,
fTrue: bool ).
tff(func_def_25,type,
f: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ).
tff(func_def_26,type,
p1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ).
tff(func_def_27,type,
p: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ).
tff(func_def_28,type,
a: arrow_411405190le_alt ).
tff(func_def_29,type,
b: arrow_411405190le_alt ).
tff(func_def_30,type,
c: arrow_411405190le_alt ).
tff(pred_def_1,type,
top:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
arrow_1958449194le_IIA: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) > $o ).
tff(pred_def_3,type,
arrow_987702531ctator: ( fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_159774573e_indi ) > $o ).
tff(pred_def_4,type,
arrow_2069624013nimity: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) > $o ).
tff(pred_def_5,type,
distinct:
!>[X0: $tType] : ( list(X0) > $o ) ).
tff(pred_def_6,type,
inv_imagep:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X0,bool)) * fun(X1,X0) * X1 * X1 ) > $o ) ).
tff(pred_def_7,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_8,type,
pp: bool > $o ).
tff(pred_def_9,type,
sP0: arrow_411405190le_alt > $o ).
tff(pred_def_10,type,
sP1: arrow_411405190le_alt > $o ).
tff(pred_def_11,type,
sP2: arrow_411405190le_alt > $o ).
tff(pred_def_12,type,
sP3: arrow_411405190le_alt > $o ).
tff(f114,axiom,
( ( a != b )
& ( a != c )
& ( b != c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
tff(f115,conjecture,
b != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
tff(f116,negated_conjecture,
( ( ~ b ) != c ),
inference(negated_conjecture,[status(cth)],[f115]) ).
tff(f117,plain,
b = c,
inference(flattening,[],[f116]) ).
tff(f118,plain,
b != c,
inference(cnf_transformation,[],[f114]) ).
tff(f121,plain,
b = c,
inference(cnf_transformation,[],[f117]) ).
tff(f124,plain,
c != c,
inference(definition_unfolding,[],[f118,f121]) ).
tff(f130,definition,
~ sP2(c),
introduced(definition,[new_symbols(definition,[sP2])],[inequality_splitting_name_introduction]) ).
tff(f131,plain,
sP2(c),
inference(inequality_splitting,[],[f124,f130]) ).
tff(f134,plain,
$false,
inference(forward_subsumption_resolution,[],[f131,f130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT222_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n026.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 28 00:02:42 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.48 Running first-order theorem proving
% 0.17/0.48 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
% 3.67/1.66 % (3346009)Detected formulas, will run a generic FOF schedule.
% 3.67/1.66 % (3346029)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3383938116:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.67/1.66 % (3346029)First to succeed.
% 3.67/1.66 % (3346029)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3346009"
% 3.67/1.66 % (3346032)dis-21_1_sil=8000:lcm=predicate:random_seed=2448616236: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)
% 3.67/1.66 % (3346032)Also succeeded, but the first one will report.
% 3.67/1.66 % (3346030)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2730804982:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.67/1.66 % (3346031)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2410911155:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.67/1.66 % (3346026)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=1552548309:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.67/1.66 % (3346027)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=3460905153:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.67/1.66 % (3346028)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=1851886882:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.67/1.66 % (3346030)Also succeeded, but the first one will report.
% 3.67/1.66 % (3346028)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.67/1.66 % (3346031)Also succeeded, but the first one will report.
% 3.67/1.66 % (3346029)Refutation found. Thanks to Tanya!
% 3.67/1.66 % SZS status Theorem for theBenchmark
% 3.67/1.66 % SZS output start Proof for theBenchmark
% See solution above
% 3.67/1.66 % (3346029)------------------------------
% 3.67/1.66 % (3346029)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.66 % (3346029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.66 % (3346029)CaDiCaL version: 2.1.3
% 3.67/1.66 % (3346029)Termination reason: Refutation
% 3.67/1.66 % (3346029)Time elapsed: 0.002 s
% 3.67/1.66 % (3346029)Peak memory usage: 88 MB
% 3.67/1.66 % (3346029)Instructions burned: 1 (million)
% 3.67/1.66 % (3346029)------------------------------
% 3.67/1.66 % (3346029)------------------------------
% 3.67/1.66 % (3346009)Success in time 0.408 s
% 3.67/1.66 % Vampire exiting
%------------------------------------------------------------------------------