%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM215_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 : n017.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 09:39:48 AM UTC 2026
% Result : Theorem 2.76s 1.15s
% Output : Refutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 11 unt; 0 typ; 1 def)
% Number of atoms : 46 ( 24 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 36 ( 13 ~; 11 |; 9 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 41 ( 39 usr; 1 prp; 0-2 aty)
% Number of functors : 72 ( 72 usr; 8 con; 0-3 aty)
% Number of variables : 24 ( 20 !; 4 ?; 24 :)
% 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,
vreduce: vTerm > vOptTerm ).
tff(func_def_14,type,
vplusop: ( vTerm * vTerm ) > vTerm ).
tff(func_def_15,type,
vgetTerm: vOptTerm > vTerm ).
tff(func_def_16,type,
sK23: vTerm ).
tff(func_def_17,type,
sK24: vTerm > vTerm ).
tff(func_def_18,type,
sK25: vTerm > vTerm ).
tff(func_def_19,type,
sK26: vTerm > vTerm ).
tff(func_def_20,type,
sK27: vTerm > vOptTerm ).
tff(func_def_21,type,
sK28: vTerm > vTerm ).
tff(func_def_22,type,
sK29: vTerm > vOptTerm ).
tff(func_def_23,type,
sK30: vTerm > vTerm ).
tff(func_def_24,type,
sK31: vTerm > vTerm ).
tff(func_def_25,type,
sK32: vTerm > vTerm ).
tff(func_def_26,type,
sK33: vTerm > vOptTerm ).
tff(func_def_27,type,
sK34: vTerm > vTerm ).
tff(func_def_28,type,
sK35: vTerm > vOptTerm ).
tff(func_def_29,type,
sK36: vTerm > vTerm ).
tff(func_def_30,type,
sK37: vTerm > vOptTerm ).
tff(func_def_31,type,
sK38: vTerm > vTerm ).
tff(func_def_32,type,
sK39: vTerm > vOptTerm ).
tff(func_def_33,type,
sK40: vTerm > vTerm ).
tff(func_def_34,type,
sK41: vTerm > vTerm ).
tff(func_def_35,type,
sK42: vTerm > vOptTerm ).
tff(func_def_36,type,
sK43: vTerm > vTerm ).
tff(func_def_37,type,
sK44: vTerm > vTerm ).
tff(func_def_38,type,
sK45: vTerm > vOptTerm ).
tff(func_def_39,type,
sK46: vTerm > vTerm ).
tff(func_def_40,type,
sK47: vTerm > vTerm ).
tff(func_def_41,type,
sK48: vTerm > vTerm ).
tff(func_def_42,type,
sK49: vTerm > vOptTerm ).
tff(func_def_43,type,
sK50: vTerm > vTerm ).
tff(func_def_44,type,
sK51: vTerm > vTerm ).
tff(func_def_45,type,
sK52: vTerm > vTerm ).
tff(func_def_46,type,
sK53: vTerm > vOptTerm ).
tff(func_def_47,type,
sK54: vTerm > vTerm ).
tff(func_def_48,type,
sK55: vTerm > vOptTerm ).
tff(func_def_49,type,
sK56: vTerm > vTerm ).
tff(func_def_50,type,
sK57: vTerm > vOptTerm ).
tff(func_def_51,type,
sK58: vTerm > vTerm ).
tff(func_def_52,type,
sK59: vTerm > vOptTerm ).
tff(func_def_53,type,
sK60: vTerm > vTerm ).
tff(func_def_54,type,
sK61: vTerm > vOptTerm ).
tff(func_def_55,type,
sK62: vTerm > vTerm ).
tff(func_def_56,type,
sK63: vTerm > vTerm ).
tff(func_def_57,type,
sK64: vTerm > vOptTerm ).
tff(func_def_58,type,
sK65: vTerm > vTerm ).
tff(func_def_59,type,
sK66: vTerm > vTerm ).
tff(func_def_60,type,
sK67: vTerm > vOptTerm ).
tff(func_def_61,type,
sK68: vTerm > vTerm ).
tff(func_def_62,type,
sK69: vTerm > vTerm ).
tff(func_def_63,type,
sK70: vTerm > vTerm ).
tff(func_def_64,type,
sK71: vTerm > vTerm ).
tff(func_def_65,type,
sK72: vTerm > vTerm ).
tff(func_def_66,type,
sK73: ( vTerm * vTerm ) > vTerm ).
tff(func_def_67,type,
sK74: ( vTerm * vTerm ) > vTerm ).
tff(func_def_68,type,
sK75: ( vTerm * vTerm ) > vTerm ).
tff(func_def_69,type,
sK76: ( vTerm * vTerm ) > vTerm ).
tff(func_def_70,type,
sK77: ( vTerm * vTerm ) > vTerm ).
tff(func_def_71,type,
sK78: 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 > $o ).
tff(pred_def_6,type,
sP1: vTerm > $o ).
tff(pred_def_7,type,
sP2: vTerm > $o ).
tff(pred_def_8,type,
sP3: vTerm > $o ).
tff(pred_def_9,type,
sP4: vTerm > $o ).
tff(pred_def_10,type,
sP5: vTerm > $o ).
tff(pred_def_11,type,
sP6: vTerm > $o ).
tff(pred_def_12,type,
sP7: vTerm > $o ).
tff(pred_def_13,type,
sP8: vTerm > $o ).
tff(pred_def_14,type,
sP9: vTerm > $o ).
tff(pred_def_15,type,
sP10: vTerm > $o ).
tff(pred_def_16,type,
sP11: vTerm > $o ).
tff(pred_def_17,type,
sP12: vTerm > $o ).
tff(pred_def_18,type,
sP13: vTerm > $o ).
tff(pred_def_19,type,
sP14: vTerm > $o ).
tff(pred_def_20,type,
sP15: vTerm > $o ).
tff(pred_def_21,type,
sP16: vTerm > $o ).
tff(pred_def_22,type,
sP17: vTerm > $o ).
tff(pred_def_23,type,
sP18: vTerm > $o ).
tff(pred_def_24,type,
sP19: vTerm > $o ).
tff(pred_def_25,type,
sP20: vTerm > $o ).
tff(pred_def_26,type,
sP21: ( vTerm * vTerm ) > $o ).
tff(pred_def_27,type,
sP22: ( vTerm * vTerm ) > $o ).
tff(pred_def_28,type,
sP79: vTerm > $o ).
tff(pred_def_29,type,
sP80: vTerm > $o ).
tff(pred_def_30,type,
sP81: vTerm > $o ).
tff(pred_def_31,type,
sP82: vTerm > $o ).
tff(pred_def_32,type,
sP83: vTerm > $o ).
tff(pred_def_33,type,
sP84: vTerm > $o ).
tff(pred_def_34,type,
sP85: vTerm > $o ).
tff(pred_def_35,type,
sP86: vTerm > $o ).
tff(pred_def_36,type,
sP87: vTerm > $o ).
tff(pred_def_37,type,
sP88: vTerm > $o ).
tff(pred_def_38,type,
sP89: vTerm > $o ).
tff(pred_def_39,type,
sP90: vTerm > $o ).
tff(f26,axiom,
! [X0: vTerm] : ( vZero != vPred(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-Zero-Pred') ).
tff(f29,axiom,
! [X0: vTerm,X1: vTerm] : ( vSucc(X0) != vPred(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-Succ-Pred') ).
tff(f57,axiom,
! [X0: vTerm,X1: vTerm] :
( ( ( X0 != vZero )
& ! [X2: vTerm] : ( X0 != vSucc(X2) ) )
=> ( vplusop(X1,X0) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','plusop-2') ).
tff(f106,conjecture,
! [X0: vTerm] :
( ( vptchecksimple(X0,vNat)
& vptchecksimple(vPred(vt2),vNat) )
=> vptchecksimple(vplusop(X0,vPred(vt2)),vNat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','PlusPreservation-Pred') ).
tff(f107,negated_conjecture,
~ ! [X0: vTerm] :
( ( vptchecksimple(X0,vNat)
& vptchecksimple(vPred(vt2),vNat) )
=> vptchecksimple(vplusop(X0,vPred(vt2)),vNat) ),
inference(negated_conjecture,[status(cth)],[f106]) ).
tff(f108,plain,
? [X0: vTerm] :
( ~ vptchecksimple(vplusop(X0,vPred(vt2)),vNat)
& vptchecksimple(X0,vNat)
& vptchecksimple(vPred(vt2),vNat) ),
inference(ennf_transformation,[],[f107]) ).
tff(f109,plain,
? [X0: vTerm] :
( ~ vptchecksimple(vplusop(X0,vPred(vt2)),vNat)
& vptchecksimple(X0,vNat)
& vptchecksimple(vPred(vt2),vNat) ),
inference(flattening,[],[f108]) ).
tff(f127,plain,
! [X0: vTerm,X1: vTerm] :
( ( vplusop(X1,X0) = X0 )
| ( vZero = X0 )
| ? [X2: vTerm] : ( vSucc(X2) = X0 ) ),
inference(ennf_transformation,[],[f57]) ).
tff(f128,plain,
! [X0: vTerm,X1: vTerm] :
( ( vplusop(X1,X0) = X0 )
| ( vZero = X0 )
| ? [X2: vTerm] : ( vSucc(X2) = X0 ) ),
inference(flattening,[],[f127]) ).
tff(f154,plain,
( ~ vptchecksimple(vplusop(sK23,vPred(vt2)),vNat)
& vptchecksimple(sK23,vNat)
& vptchecksimple(vPred(vt2),vNat) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(X0,sK23)],[f109]) ).
tff(f224,plain,
! [X0: vTerm,X1: vTerm] :
( ( vplusop(X1,X0) = X0 )
| ( vZero = X0 )
| ( vSucc(sK78(X0)) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(X2,sK78(X0))],[f128]) ).
tff(f225,plain,
vptchecksimple(vPred(vt2),vNat),
inference(cnf_transformation,[],[f154]) ).
tff(f227,plain,
~ vptchecksimple(vplusop(sK23,vPred(vt2)),vNat),
inference(cnf_transformation,[],[f154]) ).
tff(f241,plain,
! [X0: vTerm,X1: vTerm] : ( vPred(X1) != vSucc(X0) ),
inference(cnf_transformation,[],[f29]) ).
tff(f242,plain,
! [X0: vTerm] : ( vZero != vPred(X0) ),
inference(cnf_transformation,[],[f26]) ).
tff(f376,plain,
! [X0: vTerm,X1: vTerm] :
( ( vplusop(X1,X0) = X0 )
| ( vZero = X0 )
| ( vSucc(sK78(X0)) = X0 ) ),
inference(cnf_transformation,[],[f224]) ).
tff(f379,definition,
~ sP79(vZero),
introduced(definition,[new_symbols(definition,[sP79])],[inequality_splitting_name_introduction]) ).
tff(f380,plain,
! [X0: vTerm] : sP79(vPred(X0)),
inference(inequality_splitting,[],[f242,f379]) ).
tff(f412,plain,
( ~ vptchecksimple(vPred(vt2),vNat)
| ( vZero = vPred(vt2) )
| ( vPred(vt2) = vSucc(sK78(vPred(vt2))) ) ),
inference(superposition,[],[f227,f376]) ).
tff(f433,plain,
( ( vZero = vPred(vt2) )
| ( vPred(vt2) = vSucc(sK78(vPred(vt2))) ) ),
inference(forward_subsumption_resolution,[],[f412,f225]) ).
tff(f434,plain,
vZero = vPred(vt2),
inference(forward_subsumption_resolution,[],[f433,f241]) ).
tff(f445,plain,
sP79(vZero),
inference(superposition,[],[f380,f434]) ).
tff(f446,plain,
$false,
inference(forward_subsumption_resolution,[],[f445,f379]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM215_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n017.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Mon Sep 28 21:57:21 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.20 Running first-order theorem proving
% 0.06/0.20 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
% 2.76/1.15 % (4079564)Detected formulas, will run a generic FOF schedule.
% 2.76/1.15 % (4079702)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=658421914:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.76/1.15 % (4079702)First to succeed.
% 2.76/1.15 % (4079702)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4079564"
% 2.76/1.15 % (4079699)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=4150398608:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.76/1.15 % (4079703)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3901599918:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.76/1.15 % (4079701)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=1887678387:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.76/1.15 % (4079704)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1325892117:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.76/1.15 % (4079705)dis-21_1_sil=8000:lcm=predicate:random_seed=1597328058: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)
% 2.76/1.15 % (4079704)Also succeeded, but the first one will report.
% 2.76/1.15 % (4079700)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=3974543745:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.76/1.15 % (4079703)Also succeeded, but the first one will report.
% 2.76/1.15 % (4079705)Instruction limit reached!
% 2.76/1.15 % (4079705)------------------------------
% 2.76/1.15 % (4079705)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.15 % (4079705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.15 % (4079705)CaDiCaL version: 2.1.3
% 2.76/1.15 % (4079705)Termination reason: Instruction limit
% 2.76/1.15 % (4079705)Termination phase: Saturation
% 2.76/1.15 % (4079705)Time elapsed: 0.075 s
% 2.76/1.15 % (4079705)Peak memory usage: 90 MB
% 2.76/1.15 % (4079705)Instructions burned: 131 (million)
% 2.76/1.15 % (4079702)Refutation found. Thanks to Tanya!
% 2.76/1.15 % SZS status Theorem for theBenchmark
% 2.76/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.76/1.15 % (4079702)------------------------------
% 2.76/1.15 % (4079702)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.15 % (4079702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.15 % (4079702)CaDiCaL version: 2.1.3
% 2.76/1.15 % (4079702)Termination reason: Refutation
% 2.76/1.15 % (4079702)Time elapsed: 0.006 s
% 2.76/1.15 % (4079702)Peak memory usage: 89 MB
% 2.76/1.15 % (4079702)Instructions burned: 17 (million)
% 2.76/1.15 % (4079702)------------------------------
% 2.76/1.15 % (4079702)------------------------------
% 2.76/1.15 % (4079564)Success in time 0.309 s
% 2.76/1.15 % Vampire exiting
%------------------------------------------------------------------------------