%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM228_1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 09:39:50 AM UTC 2026
% Result : Theorem 3.81s 1.48s
% Output : Refutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 109 ( 50 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 139 ( 59 ~; 50 |; 26 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 55 ( 55 usr; 10 con; 0-3 aty)
% Number of variables : 21 ( 19 !; 2 ?; 21 :)
% 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,
vt3: vTerm ).
tff(func_def_9,type,
vnoTerm: vOptTerm ).
tff(func_def_10,type,
vPlus: ( vTerm * vTerm ) > vTerm ).
tff(func_def_11,type,
vt2: vTerm ).
tff(func_def_12,type,
vB: vTy ).
tff(func_def_13,type,
vIfelse: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_14,type,
vt1: vTerm ).
tff(func_def_15,type,
vreduce: vTerm > vOptTerm ).
tff(func_def_16,type,
vplusop: ( vTerm * vTerm ) > vTerm ).
tff(func_def_17,type,
vgetTerm: vOptTerm > vTerm ).
tff(func_def_18,type,
sK1: vTy ).
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(func_def_23,type,
sK6: vTerm > vTerm ).
tff(func_def_24,type,
sK7: vTerm > vTerm ).
tff(func_def_25,type,
sK8: vTerm > vTerm ).
tff(func_def_26,type,
sK9: vTerm > vTerm ).
tff(func_def_27,type,
sK10: vTerm > vTerm ).
tff(func_def_28,type,
sK11: vTerm > vTerm ).
tff(func_def_29,type,
sK12: vTerm > vTerm ).
tff(func_def_30,type,
sK13: vTerm > vTerm ).
tff(func_def_31,type,
sK14: vTerm > vTerm ).
tff(func_def_32,type,
sK15: vTerm > vTerm ).
tff(func_def_33,type,
sK16: vTerm > vTerm ).
tff(func_def_34,type,
sK17: vTerm > vTerm ).
tff(func_def_35,type,
sK18: vTerm > vTerm ).
tff(func_def_36,type,
sK19: vTerm > vTerm ).
tff(func_def_37,type,
sK20: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_38,type,
sK21: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_39,type,
sK22: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_40,type,
sK23: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_41,type,
sK24: vOptTerm > vTerm ).
tff(func_def_42,type,
sK25: vTerm > vTerm ).
tff(func_def_43,type,
sK26: vTerm > vTerm ).
tff(func_def_44,type,
sK27: vTerm > vTerm ).
tff(func_def_45,type,
sK28: vTerm > vTerm ).
tff(func_def_46,type,
sK29: vOptTerm > vTerm ).
tff(func_def_47,type,
sK30: vTerm > vTerm ).
tff(func_def_48,type,
sK31: vTerm > vTerm ).
tff(func_def_49,type,
sK32: vTerm > vTerm ).
tff(func_def_50,type,
sK33: vTerm > vTerm ).
tff(func_def_51,type,
sK34: vTerm > vTerm ).
tff(func_def_52,type,
sK35: vTerm > vTerm ).
tff(func_def_53,type,
sK36: vTerm > vTerm ).
tff(func_def_54,type,
sK37: 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(pred_def_5,type,
sP0: ( vTerm * vTerm * vTerm ) > $o ).
tff(f107,axiom,
! [X0: vTy] :
( ( ~ visSomeTerm(vreduce(vt1))
& ( vt1 != vTrue )
& ( vt1 != vFalse )
& vptchecksimple(vIfelse(vt1,vt2,vt3),X0)
& ~ visValue(vIfelse(vt1,vt2,vt3)) )
=> ( vreduce(vIfelse(vt1,vt2,vt3)) != vnoTerm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Progress-Ifelse-t1-isSomeTerm-False') ).
tff(f108,axiom,
! [X0: vTy] :
( ( visSomeTerm(vreduce(vt1))
& ( vt1 != vTrue )
& ( vt1 != vFalse )
& vptchecksimple(vIfelse(vt1,vt2,vt3),X0)
& ~ visValue(vIfelse(vt1,vt2,vt3)) )
=> ( vreduce(vIfelse(vt1,vt2,vt3)) != vnoTerm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Progress-Ifelse-t1-isSomeTerm-True') ).
tff(f110,conjecture,
! [X0: vTy] :
( ( ( vt1 != vTrue )
& ( vt1 != vFalse )
& vptchecksimple(vIfelse(vt1,vt2,vt3),X0)
& ~ visValue(vIfelse(vt1,vt2,vt3)) )
=> ( vreduce(vIfelse(vt1,vt2,vt3)) != vnoTerm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Progress-Ifelse-t1') ).
tff(f111,negated_conjecture,
~ ! [X0: vTy] :
( ( ( vt1 != vTrue )
& ( vt1 != vFalse )
& vptchecksimple(vIfelse(vt1,vt2,vt3),X0)
& ~ visValue(vIfelse(vt1,vt2,vt3)) )
=> ( vreduce(vIfelse(vt1,vt2,vt3)) != vnoTerm ) ),
inference(negated_conjecture,[status(cth)],[f110]) ).
tff(f114,plain,
? [X0: vTy] :
( ( vnoTerm = vreduce(vIfelse(vt1,vt2,vt3)) )
& ( vt1 != vTrue )
& ( vt1 != vFalse )
& vptchecksimple(vIfelse(vt1,vt2,vt3),X0)
& ~ visValue(vIfelse(vt1,vt2,vt3)) ),
inference(ennf_transformation,[],[f111]) ).
tff(f115,plain,
? [X0: vTy] :
( ( vnoTerm = vreduce(vIfelse(vt1,vt2,vt3)) )
& ( vt1 != vTrue )
& ( vt1 != vFalse )
& vptchecksimple(vIfelse(vt1,vt2,vt3),X0)
& ~ visValue(vIfelse(vt1,vt2,vt3)) ),
inference(flattening,[],[f114]) ).
tff(f123,plain,
! [X0: vTy] :
( ( vreduce(vIfelse(vt1,vt2,vt3)) != vnoTerm )
| ~ visSomeTerm(vreduce(vt1))
| ( vTrue = vt1 )
| ( vFalse = vt1 )
| ~ vptchecksimple(vIfelse(vt1,vt2,vt3),X0)
| visValue(vIfelse(vt1,vt2,vt3)) ),
inference(ennf_transformation,[],[f108]) ).
tff(f124,plain,
! [X0: vTy] :
( ( vreduce(vIfelse(vt1,vt2,vt3)) != vnoTerm )
| ~ visSomeTerm(vreduce(vt1))
| ( vTrue = vt1 )
| ( vFalse = vt1 )
| ~ vptchecksimple(vIfelse(vt1,vt2,vt3),X0)
| visValue(vIfelse(vt1,vt2,vt3)) ),
inference(flattening,[],[f123]) ).
tff(f125,plain,
! [X0: vTy] :
( ( vreduce(vIfelse(vt1,vt2,vt3)) != vnoTerm )
| visSomeTerm(vreduce(vt1))
| ( vTrue = vt1 )
| ( vFalse = vt1 )
| ~ vptchecksimple(vIfelse(vt1,vt2,vt3),X0)
| visValue(vIfelse(vt1,vt2,vt3)) ),
inference(ennf_transformation,[],[f107]) ).
tff(f126,plain,
! [X0: vTy] :
( ( vreduce(vIfelse(vt1,vt2,vt3)) != vnoTerm )
| visSomeTerm(vreduce(vt1))
| ( vTrue = vt1 )
| ( vFalse = vt1 )
| ~ vptchecksimple(vIfelse(vt1,vt2,vt3),X0)
| visValue(vIfelse(vt1,vt2,vt3)) ),
inference(flattening,[],[f125]) ).
tff(f168,plain,
( ( vnoTerm = vreduce(vIfelse(vt1,vt2,vt3)) )
& ( vt1 != vTrue )
& ( vt1 != vFalse )
& vptchecksimple(vIfelse(vt1,vt2,vt3),sK1)
& ~ visValue(vIfelse(vt1,vt2,vt3)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f115]) ).
tff(f186,plain,
~ visValue(vIfelse(vt1,vt2,vt3)),
inference(cnf_transformation,[],[f168]) ).
tff(f187,plain,
vptchecksimple(vIfelse(vt1,vt2,vt3),sK1),
inference(cnf_transformation,[],[f168]) ).
tff(f188,plain,
vFalse != vt1,
inference(cnf_transformation,[],[f168]) ).
tff(f189,plain,
vTrue != vt1,
inference(cnf_transformation,[],[f168]) ).
tff(f190,plain,
vnoTerm = vreduce(vIfelse(vt1,vt2,vt3)),
inference(cnf_transformation,[],[f168]) ).
tff(f213,plain,
! [X0: vTy] :
( ( vnoTerm != vreduce(vIfelse(vt1,vt2,vt3)) )
| ~ visSomeTerm(vreduce(vt1))
| ( vTrue = vt1 )
| ( vFalse = vt1 )
| ~ vptchecksimple(vIfelse(vt1,vt2,vt3),X0)
| visValue(vIfelse(vt1,vt2,vt3)) ),
inference(cnf_transformation,[],[f124]) ).
tff(f214,plain,
! [X0: vTy] :
( ( vnoTerm != vreduce(vIfelse(vt1,vt2,vt3)) )
| visSomeTerm(vreduce(vt1))
| ( vTrue = vt1 )
| ( vFalse = vt1 )
| ~ vptchecksimple(vIfelse(vt1,vt2,vt3),X0)
| visValue(vIfelse(vt1,vt2,vt3)) ),
inference(cnf_transformation,[],[f126]) ).
tff(f508,plain,
! [X0: vTy] :
( ~ visSomeTerm(vreduce(vt1))
| ( vTrue = vt1 )
| ( vFalse = vt1 )
| ~ vptchecksimple(vIfelse(vt1,vt2,vt3),X0)
| visValue(vIfelse(vt1,vt2,vt3)) ),
inference(forward_subsumption_resolution,[],[f213,f190]) ).
tff(f509,plain,
! [X0: vTy] :
( ~ visSomeTerm(vreduce(vt1))
| ( vFalse = vt1 )
| ~ vptchecksimple(vIfelse(vt1,vt2,vt3),X0)
| visValue(vIfelse(vt1,vt2,vt3)) ),
inference(forward_subsumption_resolution,[],[f508,f189]) ).
tff(f510,plain,
! [X0: vTy] :
( ~ visSomeTerm(vreduce(vt1))
| ~ vptchecksimple(vIfelse(vt1,vt2,vt3),X0)
| visValue(vIfelse(vt1,vt2,vt3)) ),
inference(forward_subsumption_resolution,[],[f509,f188]) ).
tff(f511,plain,
! [X0: vTy] :
( ~ vptchecksimple(vIfelse(vt1,vt2,vt3),X0)
| ~ visSomeTerm(vreduce(vt1)) ),
inference(forward_subsumption_resolution,[],[f510,f186]) ).
tff(f512,plain,
~ visSomeTerm(vreduce(vt1)),
inference(resolution,[],[f511,f187]) ).
tff(f513,plain,
! [X0: vTy] :
( visSomeTerm(vreduce(vt1))
| ( vTrue = vt1 )
| ( vFalse = vt1 )
| ~ vptchecksimple(vIfelse(vt1,vt2,vt3),X0)
| visValue(vIfelse(vt1,vt2,vt3)) ),
inference(forward_subsumption_resolution,[],[f214,f190]) ).
tff(f514,plain,
! [X0: vTy] :
( ( vTrue = vt1 )
| ( vFalse = vt1 )
| ~ vptchecksimple(vIfelse(vt1,vt2,vt3),X0)
| visValue(vIfelse(vt1,vt2,vt3)) ),
inference(forward_subsumption_resolution,[],[f513,f512]) ).
tff(f515,plain,
! [X0: vTy] :
( ( vFalse = vt1 )
| ~ vptchecksimple(vIfelse(vt1,vt2,vt3),X0)
| visValue(vIfelse(vt1,vt2,vt3)) ),
inference(forward_subsumption_resolution,[],[f514,f189]) ).
tff(f516,plain,
! [X0: vTy] :
( ~ vptchecksimple(vIfelse(vt1,vt2,vt3),X0)
| visValue(vIfelse(vt1,vt2,vt3)) ),
inference(forward_subsumption_resolution,[],[f515,f188]) ).
tff(f517,plain,
! [X0: vTy] : ~ vptchecksimple(vIfelse(vt1,vt2,vt3),X0),
inference(forward_subsumption_resolution,[],[f516,f186]) ).
tff(f518,plain,
$false,
inference(resolution,[],[f517,f187]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COM228_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.27 % Computer : n019.cluster.edu
% 0.11/0.27 % Model : x86_64 x86_64
% 0.11/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.27 % Memory : 8046.5625MB
% 0.11/0.27 % OS : Linux 6.8.0-71-generic
% 0.11/0.27 % CPULimit : 300
% 0.11/0.27 % WCLimit : 300
% 0.11/0.27 % DateTime : Mon Sep 28 22:02:33 UTC 2026
% 0.12/0.27 % CPUTime :
% 0.12/0.27 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.32 Running first-order theorem proving
% 0.12/0.32 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
% 3.81/1.48 % (321554)Detected formulas, will run a generic FOF schedule.
% 3.81/1.48 % (321568)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=889091351:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.81/1.48 % (321571)dis-21_1_sil=8000:lcm=predicate:random_seed=1812779887: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)
% 3.81/1.48 % (321568)First to succeed.
% 3.81/1.48 % (321568)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-321554"
% 3.81/1.48 % (321571)Also succeeded, but the first one will report.
% 3.81/1.48 % (321565)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=590008303:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.81/1.48 % (321567)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1201736453:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.81/1.48 % (321566)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=1364105587:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.81/1.48 % (321564)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=3210582996:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.81/1.48 % (321567)Also succeeded, but the first one will report.
% 3.81/1.48 % (321569)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=507117325:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.81/1.48 % (321569)Also succeeded, but the first one will report.
% 3.81/1.48 % (321568)Refutation found. Thanks to Tanya!
% 3.81/1.48 % SZS status Theorem for theBenchmark
% 3.81/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.81/1.48 % (321568)------------------------------
% 3.81/1.48 % (321568)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.48 % (321568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.48 % (321568)CaDiCaL version: 2.1.3
% 3.81/1.48 % (321568)Termination reason: Refutation
% 3.81/1.48 % (321568)Time elapsed: 0.011 s
% 3.81/1.48 % (321568)Peak memory usage: 88 MB
% 3.81/1.48 % (321568)Instructions burned: 18 (million)
% 3.81/1.48 % (321568)------------------------------
% 3.81/1.48 % (321568)------------------------------
% 3.81/1.48 % (321554)Success in time 0.444 s
% 3.81/1.48 % Vampire exiting
%------------------------------------------------------------------------------