%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT242_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 12:37:19 PM UTC 2026
% Result : Theorem 1.29s 1.69s
% Output : Refutation 5.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 15 unt; 0 typ; 2 def)
% Number of atoms : 52 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 21 ~; 15 |; 3 &)
% ( 1 <=>; 3 =>; 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 : 11 ( 9 usr; 3 prp; 0-5 aty)
% Number of functors : 26 ( 26 usr; 10 con; 0-6 aty)
% Number of variables : 17 ( 0 sgn 15 !; 2 ?; 17 :)
% 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,
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,
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(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_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,
product_Pair:
!>[X0: $tType,X1: $tType] : fun(X0,fun(X1,product_prod(X0,X1))) ).
tff(func_def_7,type,
product_apfst:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * product_prod(X0,X2) ) > product_prod(X1,X2) ) ).
tff(func_def_8,type,
product_apsnd:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * product_prod(X2,X0) ) > product_prod(X2,X1) ) ).
tff(func_def_9,type,
product_curry:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X0,X1),X2) > fun(X0,fun(X1,X2)) ) ).
tff(func_def_10,type,
produc1605651328_split:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2)) ).
tff(func_def_11,type,
product_prod_case:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2)) ).
tff(func_def_12,type,
product_prod_rec:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).
tff(func_def_13,type,
product_scomp:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( fun(X0,product_prod(X1,X2)) * fun(X1,fun(X2,X3)) ) > fun(X0,X3) ) ).
tff(func_def_14,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_15,type,
fFalse: bool ).
tff(func_def_16,type,
fTrue: bool ).
tff(func_def_17,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_18,type,
lab: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_19,type,
a: arrow_411405190le_alt ).
tff(func_def_20,type,
b: arrow_411405190le_alt ).
tff(func_def_21,type,
sK0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_22,type,
sK1: ( arrow_411405190le_alt * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_23,type,
sK2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(pred_def_1,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_2,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_3,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_4,type,
in_rel:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X1),bool) * X0 * X1 ) > $o ) ).
tff(pred_def_5,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_6,type,
pp: bool > $o ).
tff(pred_def_8,type,
sP3: arrow_411405190le_alt > $o ).
tff(f2,axiom,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096a_A_126_061_Ab_096) ).
tff(f8,axiom,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( X1 != X0 )
=> ? [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_complete__Lin) ).
tff(f81,axiom,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),X0)
=> ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
=> thesis ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f82,conjecture,
thesis,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(f83,negated_conjecture,
~ thesis,
inference(negated_conjecture,[status(cth)],[f82]) ).
tff(f84,plain,
~ thesis,
inference(flattening,[],[f83]) ).
tff(f85,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( thesis
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),X0) ),
inference(ennf_transformation,[],[f81]) ).
tff(f86,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( thesis
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),X0) ),
inference(flattening,[],[f85]) ).
tff(f87,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ? [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f8]) ).
tff(f94,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),sK1(X0,X1),arrow_1985332922le_Lin)
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),sK1(X0,X1)) )
| ( X0 = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f87]) ).
tff(f97,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( thesis
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),X0) ),
inference(cnf_transformation,[],[f86]) ).
tff(f98,plain,
~ thesis,
inference(cnf_transformation,[],[f84]) ).
tff(f100,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),sK1(X0,X1))
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f94]) ).
tff(f101,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),sK1(X0,X1),arrow_1985332922le_Lin)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f94]) ).
tff(f107,plain,
a != b,
inference(cnf_transformation,[],[f2]) ).
tff(f108,definition,
~ sP3(a),
introduced(definition,[new_symbols(definition,[sP3])],[inequality_splitting_name_introduction]) ).
tff(f109,plain,
sP3(b),
inference(inequality_splitting,[],[f107,f108]) ).
tff(f110,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),X0)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin) ),
inference(forward_subsumption_resolution,[],[f97,f98]) ).
tff(f111,plain,
( ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),sK1(a,b),arrow_1985332922le_Lin)
| ( a = b ) ),
inference(resolution,[],[f110,f100]) ).
tff(f115,definition,
( spl4_1
<=> ( a = b ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
tff(f117,plain,
( ( a = b )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f115]) ).
tff(f122,plain,
a = b,
inference(forward_subsumption_resolution,[],[f111,f101]) ).
tff(f123,plain,
spl4_1,
inference(avatar_split_clause,[],[f122,f115]) ).
tff(f125,plain,
( sP3(a)
| ~ spl4_1 ),
inference(superposition,[],[f109,f117]) ).
tff(f127,plain,
( $false
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f125,f108]) ).
tff(f128,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f127]) ).
cnf(s2,plain,
spl4_1,
inference(sat_conversion,[],[f123]) ).
cnf(s3,plain,
~ spl4_1,
inference(sat_conversion,[],[f128]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s2,s3]) ).
tff(f129,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SCT242_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.44 % Computer : n004.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Mon Sep 28 00:01:22 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.45 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.51 Running first-order theorem proving
% 0.21/0.51 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.29/1.69 % (4017023)Detected formulas, will run a generic FOF schedule.
% 1.29/1.69 % (4017029)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=2838605525:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.29/1.69 % (4017032)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3596356840:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.29/1.69 % (4017033)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=307574661:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.29/1.69 % (4017031)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2226456662:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.29/1.69 % (4017028)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=3401587803:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.29/1.69 % (4017030)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=165084536:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.29/1.69 % (4017031)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.29/1.69 % (4017031)First to succeed.
% 1.29/1.69 % (4017032)Also succeeded, but the first one will report.
% 1.29/1.69 % (4017031)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4017023"
% 1.29/1.69 % (4017030)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.29/1.69 % (4017034)dis-21_1_sil=8000:lcm=predicate:random_seed=3188034665: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)
% 1.29/1.69 % (4017033)Also succeeded, but the first one will report.
% 1.29/1.69 % (4017034)Also succeeded, but the first one will report.
% 1.29/1.69 % Exception at run slice level
% 1.29/1.69 User error: GNN currently only supports monomorphic FOL.
% 1.29/1.69 % (4017031)Refutation found. Thanks to Tanya!
% 1.29/1.69 % SZS status Theorem for theBenchmark
% 1.29/1.69 % SZS output start Proof for theBenchmark
% See solution above
% 5.67/1.93 % (4017031)------------------------------
% 5.67/1.93 % (4017031)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.67/1.93 % (4017031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.67/1.93 % (4017031)CaDiCaL version: 2.1.3
% 5.67/1.93 % (4017031)Termination reason: Refutation
% 5.67/1.93 % (4017031)Time elapsed: 0.006 s
% 5.67/1.93 % (4017031)Peak memory usage: 90 MB
% 5.67/1.93 % (4017031)Instructions burned: 3 (million)
% 5.67/1.93 % (4017031)------------------------------
% 5.67/1.93 % (4017031)------------------------------
% 5.67/1.93 % (4017023)Success in time 0.708 s
% 5.67/1.93 % Vampire exiting
%------------------------------------------------------------------------------