%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM212_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 : n009.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 0.64s 0.92s
% Output : Refutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 16 unt; 0 typ; 3 def)
% Number of atoms : 62 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 54 ( 28 ~; 18 |; 2 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 36 ( 34 usr; 3 prp; 0-3 aty)
% Number of functors : 112 ( 112 usr; 6 con; 0-3 aty)
% Number of variables : 17 ( 0 sgn 15 !; 2 ?; 17 :)
% 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,
vB: vTy ).
tff(func_def_11,type,
vIfelse: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_12,type,
vreduce: vTerm > vOptTerm ).
tff(func_def_13,type,
vplusop: ( vTerm * vTerm ) > vTerm ).
tff(func_def_14,type,
vgetTerm: vOptTerm > vTerm ).
tff(func_def_15,type,
sK25: vTerm > vTerm ).
tff(func_def_16,type,
sK26: vTerm > vTerm ).
tff(func_def_17,type,
sK27: vTerm > vTerm ).
tff(func_def_18,type,
sK28: vTerm > vTerm ).
tff(func_def_19,type,
sK29: vTerm > vTerm ).
tff(func_def_20,type,
sK30: vTerm > vTerm ).
tff(func_def_21,type,
sK31: vTerm > vTerm ).
tff(func_def_22,type,
sK32: vTerm > vTerm ).
tff(func_def_23,type,
sK33: vOptTerm > vTerm ).
tff(func_def_24,type,
sK34: vTerm > vTerm ).
tff(func_def_25,type,
sK35: vTerm > vTerm ).
tff(func_def_26,type,
sK36: vTerm > vTerm ).
tff(func_def_27,type,
sK37: vTerm > vTerm ).
tff(func_def_28,type,
sK38: vTerm > vTerm ).
tff(func_def_29,type,
sK39: vTerm > vTerm ).
tff(func_def_30,type,
sK40: vOptTerm > vTerm ).
tff(func_def_31,type,
sK41: vTerm > vTerm ).
tff(func_def_32,type,
sK42: ( vTerm * vTerm ) > vTerm ).
tff(func_def_33,type,
sK43: ( vTerm * vTerm ) > vTerm ).
tff(func_def_34,type,
sK44: ( vTerm * vTerm ) > vTerm ).
tff(func_def_35,type,
sK45: ( vTerm * vTerm ) > vTerm ).
tff(func_def_36,type,
sK46: ( vTerm * vTerm ) > vTerm ).
tff(func_def_37,type,
sK47: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_38,type,
sK48: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_39,type,
sK49: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_40,type,
sK50: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_41,type,
sK51: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_42,type,
sK52: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_43,type,
sK53: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_44,type,
sK54: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_45,type,
sK55: vTerm > vTerm ).
tff(func_def_46,type,
sK56: vTerm > vTerm ).
tff(func_def_47,type,
sK57: vTerm > vTerm ).
tff(func_def_48,type,
sK58: vTerm > vTerm ).
tff(func_def_49,type,
sK59: vTerm > vTerm ).
tff(func_def_50,type,
sK60: vTerm > vTerm ).
tff(func_def_51,type,
sK61: vTerm > vTerm ).
tff(func_def_52,type,
sK62: vTerm > vTerm ).
tff(func_def_53,type,
sK63: vTerm > vTerm ).
tff(func_def_54,type,
sK64: vTerm > vTerm ).
tff(func_def_55,type,
sK65: vTerm > vTerm ).
tff(func_def_56,type,
sK66: vTerm > vTerm ).
tff(func_def_57,type,
sK67: vTerm > vTerm ).
tff(func_def_58,type,
sK68: vTerm > vTerm ).
tff(func_def_59,type,
sK69: vTerm > vTerm ).
tff(func_def_60,type,
sK70: vTerm > vTerm ).
tff(func_def_61,type,
sK71: vTerm > vTerm ).
tff(func_def_62,type,
sK72: vTerm > vTerm ).
tff(func_def_63,type,
sK73: vTerm > vTerm ).
tff(func_def_64,type,
sK74: vTerm > vTerm ).
tff(func_def_65,type,
sK75: vTerm > vTerm ).
tff(func_def_66,type,
sK76: vTerm > vOptTerm ).
tff(func_def_67,type,
sK77: vTerm > vTerm ).
tff(func_def_68,type,
sK78: vTerm > vOptTerm ).
tff(func_def_69,type,
sK79: vTerm > vTerm ).
tff(func_def_70,type,
sK80: vTerm > vTerm ).
tff(func_def_71,type,
sK81: vTerm > vTerm ).
tff(func_def_72,type,
sK82: vTerm > vOptTerm ).
tff(func_def_73,type,
sK83: vTerm > vTerm ).
tff(func_def_74,type,
sK84: vTerm > vOptTerm ).
tff(func_def_75,type,
sK85: vTerm > vTerm ).
tff(func_def_76,type,
sK86: vTerm > vOptTerm ).
tff(func_def_77,type,
sK87: vTerm > vTerm ).
tff(func_def_78,type,
sK88: vTerm > vOptTerm ).
tff(func_def_79,type,
sK89: vTerm > vTerm ).
tff(func_def_80,type,
sK90: vTerm > vTerm ).
tff(func_def_81,type,
sK91: vTerm > vOptTerm ).
tff(func_def_82,type,
sK92: vTerm > vTerm ).
tff(func_def_83,type,
sK93: vTerm > vTerm ).
tff(func_def_84,type,
sK94: vTerm > vOptTerm ).
tff(func_def_85,type,
sK95: vTerm > vTerm ).
tff(func_def_86,type,
sK96: vTerm > vTerm ).
tff(func_def_87,type,
sK97: vTerm > vTerm ).
tff(func_def_88,type,
sK98: vTerm > vOptTerm ).
tff(func_def_89,type,
sK99: vTerm > vTerm ).
tff(func_def_90,type,
sK100: vTerm > vTerm ).
tff(func_def_91,type,
sK101: vTerm > vTerm ).
tff(func_def_92,type,
sK102: vTerm > vOptTerm ).
tff(func_def_93,type,
sK103: vTerm > vTerm ).
tff(func_def_94,type,
sK104: vTerm > vOptTerm ).
tff(func_def_95,type,
sK105: vTerm > vTerm ).
tff(func_def_96,type,
sK106: vTerm > vOptTerm ).
tff(func_def_97,type,
sK107: vTerm > vTerm ).
tff(func_def_98,type,
sK108: vTerm > vOptTerm ).
tff(func_def_99,type,
sK109: vTerm > vTerm ).
tff(func_def_100,type,
sK110: vTerm > vOptTerm ).
tff(func_def_101,type,
sK111: vTerm > vTerm ).
tff(func_def_102,type,
sK112: vTerm > vTerm ).
tff(func_def_103,type,
sK113: vTerm > vOptTerm ).
tff(func_def_104,type,
sK114: vTerm > vTerm ).
tff(func_def_105,type,
sK115: vTerm > vTerm ).
tff(func_def_106,type,
sK116: vTerm > vOptTerm ).
tff(func_def_107,type,
sK117: vTerm > vTerm ).
tff(func_def_108,type,
sK118: vTerm > vTerm ).
tff(func_def_109,type,
sK119: vTerm > vTerm ).
tff(func_def_110,type,
sK120: vTerm > vTerm ).
tff(func_def_111,type,
sK121: 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 ) > $o ).
tff(pred_def_6,type,
sP1: ( vTerm * vTerm ) > $o ).
tff(pred_def_7,type,
sP2: ( vTerm * vTerm * vTerm ) > $o ).
tff(pred_def_8,type,
sP3: ( vTerm * vTerm * 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 > $o ).
tff(pred_def_27,type,
sP22: vTerm > $o ).
tff(pred_def_28,type,
sP23: vTerm > $o ).
tff(pred_def_29,type,
sP24: vTerm > $o ).
tff(pred_def_30,type,
sQ122_eqProxy: ( vTerm * vTerm ) > $o ).
tff(pred_def_31,type,
sQ123_eqProxy: ( vOptTerm * vOptTerm ) > $o ).
tff(pred_def_32,type,
sQ124_eqProxy: ( vTy * vTy ) > $o ).
tff(f15,axiom,
vFalse != vZero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-False-Zero') ).
tff(f16,axiom,
! [X0: vTerm] : ( vFalse != vSucc(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-False-Succ') ).
tff(f43,axiom,
! [X0: vTerm] :
( ( ( X0 != vZero )
& ! [X1: vTerm] : ( X0 != vSucc(X1) ) )
=> ~ visNV(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','isNV-2') ).
tff(f105,conjecture,
( visNV(vFalse)
=> vptchecksimple(vFalse,vNat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','isNVisNat-False') ).
tff(f106,negated_conjecture,
~ ( visNV(vFalse)
=> vptchecksimple(vFalse,vNat) ),
inference(negated_conjecture,[status(cth)],[f105]) ).
tff(f115,plain,
! [X0: vTerm] :
( ~ visNV(X0)
| ( vZero = X0 )
| ? [X1: vTerm] : ( vSucc(X1) = X0 ) ),
inference(ennf_transformation,[],[f43]) ).
tff(f116,plain,
! [X0: vTerm] :
( ~ visNV(X0)
| ( vZero = X0 )
| ? [X1: vTerm] : ( vSucc(X1) = X0 ) ),
inference(flattening,[],[f115]) ).
tff(f186,plain,
( ~ vptchecksimple(vFalse,vNat)
& visNV(vFalse) ),
inference(ennf_transformation,[],[f106]) ).
tff(f219,plain,
! [X0: vTerm] :
( ~ visNV(X0)
| ( vZero = X0 )
| ( vSucc(sK34(X0)) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(X1,sK34(X0))],[f116]) ).
tff(f326,plain,
vFalse != vZero,
inference(cnf_transformation,[],[f15]) ).
tff(f327,plain,
! [X0: vTerm] : ( vFalse != vSucc(X0) ),
inference(cnf_transformation,[],[f16]) ).
tff(f355,plain,
! [X0: vTerm] :
( ~ visNV(X0)
| ( vZero = X0 )
| ( vSucc(sK34(X0)) = X0 ) ),
inference(cnf_transformation,[],[f219]) ).
tff(f568,plain,
visNV(vFalse),
inference(cnf_transformation,[],[f186]) ).
tff(f578,definition,
! [X0: vTerm,X1: vTerm] :
( sQ122_eqProxy(X0,X1)
<=> ( X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ122_eqProxy])],[equality_proxy_definition]) ).
tff(f596,plain,
~ sQ122_eqProxy(vFalse,vZero),
inference(equality_proxy_replacement,[],[f326,f578]) ).
tff(f597,plain,
! [X0: vTerm] : ~ sQ122_eqProxy(vFalse,vSucc(X0)),
inference(equality_proxy_replacement,[],[f327,f578]) ).
tff(f624,plain,
! [X0: vTerm] :
( sQ122_eqProxy(vSucc(sK34(X0)),X0)
| sQ122_eqProxy(vZero,X0)
| ~ visNV(X0) ),
inference(equality_proxy_replacement,[],[f355,f578,f578]) ).
tff(f791,plain,
! [X0: vTerm,X1: vTerm] :
( sQ122_eqProxy(X1,X0)
| ~ sQ122_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f578]) ).
tff(f824,plain,
! [X0: vTerm] : ~ sQ122_eqProxy(vSucc(X0),vFalse),
inference(resolution,[],[f791,f597]) ).
tff(f826,plain,
~ sQ122_eqProxy(vZero,vFalse),
inference(resolution,[],[f791,f596]) ).
tff(f961,definition,
( spl125_1
<=> visNV(vFalse) ),
introduced(definition,[new_symbols(definition,[spl125_1])],[avatar_definition]) ).
tff(f962,plain,
( ~ visNV(vFalse)
| spl125_1 ),
inference(avatar_component_clause,[],[f961]) ).
tff(f974,plain,
( $false
| spl125_1 ),
inference(resolution,[],[f962,f568]) ).
tff(f975,plain,
spl125_1,
inference(avatar_contradiction_clause,[],[f974]) ).
tff(f1103,plain,
( sQ122_eqProxy(vZero,vFalse)
| ~ visNV(vFalse) ),
inference(resolution,[],[f624,f824]) ).
tff(f1111,definition,
( spl125_5
<=> sQ122_eqProxy(vZero,vFalse) ),
introduced(definition,[new_symbols(definition,[spl125_5])],[avatar_definition]) ).
tff(f1112,plain,
( sQ122_eqProxy(vZero,vFalse)
| ~ spl125_5 ),
inference(avatar_component_clause,[],[f1111]) ).
tff(f1113,plain,
( ~ spl125_1
| spl125_5 ),
inference(avatar_split_clause,[],[f1103,f1111,f961]) ).
tff(f1114,plain,
( $false
| ~ spl125_5 ),
inference(resolution,[],[f1112,f826]) ).
tff(f1115,plain,
~ spl125_5,
inference(avatar_contradiction_clause,[],[f1114]) ).
cnf(s3,plain,
spl125_1,
inference(sat_conversion,[],[f975]) ).
cnf(s4,plain,
( ~ spl125_1
| spl125_5 ),
inference(sat_conversion,[],[f1113]) ).
cnf(s5,plain,
~ spl125_5,
inference(sat_conversion,[],[f1115]) ).
cnf(s6,plain,
~ spl125_1,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s3,s6]) ).
tff(f1116,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM212_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n009.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 22:02:00 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 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
% 0.64/0.92 % (3538470)Detected formulas, will run a generic FOF schedule.
% 0.64/0.92 % (3538530)dis-21_1_sil=8000:lcm=predicate:random_seed=648553088: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)
% 0.64/0.92 % (3538530)First to succeed.
% 0.64/0.92 % (3538530)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3538470"
% 0.64/0.92 % (3538529)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3006558402:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.64/0.92 % (3538524)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=1413089489:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.64/0.92 % (3538528)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3142754291:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.64/0.92 % (3538527)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=903028875:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.64/0.92 % (3538526)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=369568944:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.64/0.92 % (3538525)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=4181052787:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.64/0.92 % (3538527)Refutation not found, incomplete strategy
% 0.64/0.92 % (3538527)------------------------------
% 0.64/0.92 % (3538527)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.64/0.92 % (3538527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.92 % (3538527)CaDiCaL version: 2.1.3
% 0.64/0.92 % (3538527)Termination reason: Refutation not found, incomplete strategy
% 0.64/0.92 % (3538527)Time elapsed: 0.002 s
% 0.64/0.92 % (3538527)Peak memory usage: 88 MB
% 0.64/0.92 % (3538527)Instructions burned: 2 (million)
% 0.64/0.92 % (3538528)Also succeeded, but the first one will report.
% 0.64/0.92 % (3538529)Also succeeded, but the first one will report.
% 0.64/0.92 % (3538530)Refutation found. Thanks to Tanya!
% 0.64/0.92 % SZS status Theorem for theBenchmark
% 0.64/0.92 % SZS output start Proof for theBenchmark
% See solution above
% 0.64/1.02 % (3538530)------------------------------
% 0.64/1.02 % (3538530)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.64/1.02 % (3538530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/1.02 % (3538530)CaDiCaL version: 2.1.3
% 0.64/1.02 % (3538530)Termination reason: Refutation
% 0.64/1.02 % (3538530)Time elapsed: 0.008 s
% 0.64/1.02 % (3538530)Peak memory usage: 89 MB
% 0.64/1.02 % (3538530)Instructions burned: 22 (million)
% 0.64/1.02 % (3538530)------------------------------
% 0.64/1.02 % (3538530)------------------------------
% 0.64/1.02 % (3538470)Success in time 0.276 s
% 0.64/1.02 % Vampire exiting
%------------------------------------------------------------------------------