%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM221_1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 09:39:49 AM UTC 2026
% Result : Theorem 3.77s 1.54s
% Output : Refutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 65 ( 17 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 72 ( 29 ~; 27 |; 12 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 10 con; 0-3 aty)
% Number of variables : 31 ( 27 !; 4 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
vTerm: $tType ).
tff(type_def_6,type,
vOptTerm: $tType ).
tff(type_def_7,type,
vTy: $tType ).
tff(func_def_0,type,
vNat: vTy ).
tff(func_def_1,type,
vSucc: vTerm > vTerm ).
tff(func_def_2,type,
vPred: vTerm > vTerm ).
tff(func_def_3,type,
vsomeTerm: vTerm > vOptTerm ).
tff(func_def_4,type,
vZero: vTerm ).
tff(func_def_5,type,
vIszero: vTerm > vTerm ).
tff(func_def_6,type,
vTrue: vTerm ).
tff(func_def_7,type,
vFalse: vTerm ).
tff(func_def_8,type,
vnoTerm: vOptTerm ).
tff(func_def_9,type,
vPlus: ( vTerm * vTerm ) > vTerm ).
tff(func_def_10,type,
vt2: vTerm ).
tff(func_def_11,type,
vB: vTy ).
tff(func_def_12,type,
vIfelse: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_13,type,
vt1: vTerm ).
tff(func_def_14,type,
vreduce: vTerm > vOptTerm ).
tff(func_def_15,type,
vplusop: ( vTerm * vTerm ) > vTerm ).
tff(func_def_16,type,
vgetTerm: vOptTerm > vTerm ).
tff(func_def_17,type,
sK0: vTy ).
tff(func_def_18,type,
sK1: vTerm ).
tff(func_def_19,type,
sK2: vTerm > vTerm ).
tff(func_def_20,type,
sK3: vTerm > vTerm ).
tff(func_def_21,type,
sK4: vTerm > vTerm ).
tff(func_def_22,type,
sK5: vTerm > vTerm ).
tff(pred_def_1,type,
visValue: vTerm > $o ).
tff(pred_def_2,type,
visNV: vTerm > $o ).
tff(pred_def_3,type,
visSomeTerm: vOptTerm > $o ).
tff(pred_def_4,type,
vptchecksimple: ( vTerm * vTy ) > $o ).
tff(f107,axiom,
! [X0: vTy,X1: vTerm] :
( ( visNV(vt1)
& vptchecksimple(vPlus(vt1,vt2),X0)
& ( vreduce(vPlus(vt1,vt2)) = vsomeTerm(X1) ) )
=> vptchecksimple(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Preservation-Plus-isNV-True') ).
tff(f108,axiom,
! [X0: vTy,X1: vTerm] :
( ( ~ visNV(vt1)
& vptchecksimple(vPlus(vt1,vt2),X0)
& ( vreduce(vPlus(vt1,vt2)) = vsomeTerm(X1) ) )
=> vptchecksimple(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Preservation-Plus-isNV-False') ).
tff(f109,conjecture,
! [X0: vTy,X1: vTerm] :
( ( vptchecksimple(vPlus(vt1,vt2),X0)
& ( vreduce(vPlus(vt1,vt2)) = vsomeTerm(X1) ) )
=> vptchecksimple(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Preservation-Plus') ).
tff(f110,negated_conjecture,
~ ! [X0: vTy,X1: vTerm] :
( ( vptchecksimple(vPlus(vt1,vt2),X0)
& ( vreduce(vPlus(vt1,vt2)) = vsomeTerm(X1) ) )
=> vptchecksimple(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f109]) ).
tff(f111,plain,
? [X0: vTy,X1: vTerm] :
( ~ vptchecksimple(X1,X0)
& vptchecksimple(vPlus(vt1,vt2),X0)
& ( vreduce(vPlus(vt1,vt2)) = vsomeTerm(X1) ) ),
inference(ennf_transformation,[],[f110]) ).
tff(f112,plain,
? [X0: vTy,X1: vTerm] :
( ~ vptchecksimple(X1,X0)
& vptchecksimple(vPlus(vt1,vt2),X0)
& ( vreduce(vPlus(vt1,vt2)) = vsomeTerm(X1) ) ),
inference(flattening,[],[f111]) ).
tff(f115,plain,
! [X0: vTy,X1: vTerm] :
( vptchecksimple(X1,X0)
| visNV(vt1)
| ~ vptchecksimple(vPlus(vt1,vt2),X0)
| ( vsomeTerm(X1) != vreduce(vPlus(vt1,vt2)) ) ),
inference(ennf_transformation,[],[f108]) ).
tff(f116,plain,
! [X0: vTy,X1: vTerm] :
( vptchecksimple(X1,X0)
| visNV(vt1)
| ~ vptchecksimple(vPlus(vt1,vt2),X0)
| ( vsomeTerm(X1) != vreduce(vPlus(vt1,vt2)) ) ),
inference(flattening,[],[f115]) ).
tff(f117,plain,
! [X0: vTy,X1: vTerm] :
( vptchecksimple(X1,X0)
| ~ visNV(vt1)
| ~ vptchecksimple(vPlus(vt1,vt2),X0)
| ( vsomeTerm(X1) != vreduce(vPlus(vt1,vt2)) ) ),
inference(ennf_transformation,[],[f107]) ).
tff(f118,plain,
! [X0: vTy,X1: vTerm] :
( vptchecksimple(X1,X0)
| ~ visNV(vt1)
| ~ vptchecksimple(vPlus(vt1,vt2),X0)
| ( vsomeTerm(X1) != vreduce(vPlus(vt1,vt2)) ) ),
inference(flattening,[],[f117]) ).
tff(f130,plain,
( ~ vptchecksimple(sK1,sK0)
& vptchecksimple(vPlus(vt1,vt2),sK0)
& ( vreduce(vPlus(vt1,vt2)) = vsomeTerm(sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f112]) ).
tff(f135,plain,
vreduce(vPlus(vt1,vt2)) = vsomeTerm(sK1),
inference(cnf_transformation,[],[f130]) ).
tff(f136,plain,
vptchecksimple(vPlus(vt1,vt2),sK0),
inference(cnf_transformation,[],[f130]) ).
tff(f137,plain,
~ vptchecksimple(sK1,sK0),
inference(cnf_transformation,[],[f130]) ).
tff(f143,plain,
! [X0: vTy,X1: vTerm] :
( vptchecksimple(X1,X0)
| visNV(vt1)
| ~ vptchecksimple(vPlus(vt1,vt2),X0)
| ( vsomeTerm(X1) != vreduce(vPlus(vt1,vt2)) ) ),
inference(cnf_transformation,[],[f116]) ).
tff(f144,plain,
! [X0: vTy,X1: vTerm] :
( vptchecksimple(X1,X0)
| ~ visNV(vt1)
| ~ vptchecksimple(vPlus(vt1,vt2),X0)
| ( vsomeTerm(X1) != vreduce(vPlus(vt1,vt2)) ) ),
inference(cnf_transformation,[],[f118]) ).
tff(f215,plain,
! [X0: vTy,X1: vTerm] :
( ( vsomeTerm(X1) != vsomeTerm(sK1) )
| vptchecksimple(X1,X0)
| visNV(vt1)
| ~ vptchecksimple(vPlus(vt1,vt2),X0) ),
inference(forward_demodulation,[],[f143,f135]) ).
tff(f219,plain,
! [X0: vTy,X1: vTerm] :
( ( vsomeTerm(X1) != vsomeTerm(sK1) )
| vptchecksimple(X1,X0)
| ~ visNV(vt1)
| ~ vptchecksimple(vPlus(vt1,vt2),X0) ),
inference(forward_demodulation,[],[f144,f135]) ).
tff(f220,plain,
! [X0: vTy,X1: vTerm] :
( ( vsomeTerm(X1) != vsomeTerm(sK1) )
| vptchecksimple(X1,X0)
| ~ vptchecksimple(vPlus(vt1,vt2),X0) ),
inference(forward_subsumption_resolution,[],[f219,f215]) ).
tff(f221,plain,
! [X0: vTy] :
( ~ vptchecksimple(vPlus(vt1,vt2),X0)
| vptchecksimple(sK1,X0) ),
inference(equality_resolution,[],[f220]) ).
tff(f222,plain,
vptchecksimple(sK1,sK0),
inference(resolution,[],[f221,f136]) ).
tff(f223,plain,
$false,
inference(forward_subsumption_resolution,[],[f222,f137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM221_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.25 % Computer : n008.cluster.edu
% 0.12/0.25 % Model : x86_64 x86_64
% 0.12/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.25 % Memory : 8046.5625MB
% 0.12/0.25 % OS : Linux 6.8.0-71-generic
% 0.12/0.25 % CPULimit : 300
% 0.12/0.25 % WCLimit : 300
% 0.12/0.25 % DateTime : Mon Sep 28 22:02:55 UTC 2026
% 0.12/0.25 % CPUTime :
% 0.12/0.25 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.31 Running first-order theorem proving
% 0.26/0.31 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
% 3.77/1.54 % (2703174)Detected formulas, will run a generic FOF schedule.
% 3.77/1.54 % (2703197)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1554926313:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.77/1.54 % (2703196)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4053993088:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.77/1.54 % (2703196)First to succeed.
% 3.77/1.54 % (2703196)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2703174"
% 3.77/1.54 % (2703197)Also succeeded, but the first one will report.
% 3.77/1.54 % (2703195)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3087667024:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.77/1.54 % (2703194)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=1668423227:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.77/1.54 % (2703195)Also succeeded, but the first one will report.
% 3.77/1.54 % (2703192)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=2018692996:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.77/1.54 % (2703193)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=2079189327:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.77/1.54 % (2703198)dis-21_1_sil=8000:lcm=predicate:random_seed=1481037217: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)
% 3.77/1.54 % (2703198)Also succeeded, but the first one will report.
% 3.77/1.54 % (2703196)Refutation found. Thanks to Tanya!
% 3.77/1.54 % SZS status Theorem for theBenchmark
% 3.77/1.54 % SZS output start Proof for theBenchmark
% See solution above
% 3.77/1.54 % (2703196)------------------------------
% 3.77/1.54 % (2703196)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.54 % (2703196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.54 % (2703196)CaDiCaL version: 2.1.3
% 3.77/1.54 % (2703196)Termination reason: Refutation
% 3.77/1.54 % (2703196)Time elapsed: 0.004 s
% 3.77/1.54 % (2703196)Peak memory usage: 88 MB
% 3.77/1.54 % (2703196)Instructions burned: 5 (million)
% 3.77/1.54 % (2703196)------------------------------
% 3.77/1.54 % (2703196)------------------------------
% 3.77/1.54 % (2703174)Success in time 0.402 s
% 3.77/1.54 % Vampire exiting
%------------------------------------------------------------------------------