%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COM222_1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 09:40:31 AM UTC 2026
% Result : Theorem 0.22s 0.32s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 48 ( 16 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 51 ( 22 ~; 7 |; 19 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 31 ( 29 usr; 1 prp; 0-3 aty)
% Number of functors : 116 ( 116 usr; 10 con; 0-3 aty)
% Number of variables : 20 ( 16 !; 4 ?; 20 :)
% 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,
sK25: vTerm > vTerm ).
tff(func_def_18,type,
sK26: vTerm > vTerm ).
tff(func_def_19,type,
sK27: vTerm > vTerm ).
tff(func_def_20,type,
sK28: vTerm > vTerm ).
tff(func_def_21,type,
sK29: vTerm > vTerm ).
tff(func_def_22,type,
sK30: vTerm > vTerm ).
tff(func_def_23,type,
sK31: vTerm > vTerm ).
tff(func_def_24,type,
sK32: vTerm > vTerm ).
tff(func_def_25,type,
sK33: vOptTerm > vTerm ).
tff(func_def_26,type,
sK34: vTerm > vTerm ).
tff(func_def_27,type,
sK35: vTerm > vTerm ).
tff(func_def_28,type,
sK36: vTerm > vTerm ).
tff(func_def_29,type,
sK37: vTerm > vTerm ).
tff(func_def_30,type,
sK38: vTerm > vTerm ).
tff(func_def_31,type,
sK39: vTerm > vTerm ).
tff(func_def_32,type,
sK40: vOptTerm > vTerm ).
tff(func_def_33,type,
sK41: vTerm > vTerm ).
tff(func_def_34,type,
sK42: ( vTerm * vTerm ) > vTerm ).
tff(func_def_35,type,
sK43: ( vTerm * vTerm ) > vTerm ).
tff(func_def_36,type,
sK44: ( vTerm * vTerm ) > vTerm ).
tff(func_def_37,type,
sK45: ( vTerm * vTerm ) > vTerm ).
tff(func_def_38,type,
sK46: ( vTerm * vTerm ) > vTerm ).
tff(func_def_39,type,
sK47: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_40,type,
sK48: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_41,type,
sK49: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_42,type,
sK50: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_43,type,
sK51: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_44,type,
sK52: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_45,type,
sK53: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_46,type,
sK54: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_47,type,
sK55: vTerm > vTerm ).
tff(func_def_48,type,
sK56: vTerm > vTerm ).
tff(func_def_49,type,
sK57: vTerm > vTerm ).
tff(func_def_50,type,
sK58: vTerm > vTerm ).
tff(func_def_51,type,
sK59: vTerm > vTerm ).
tff(func_def_52,type,
sK60: vTerm > vTerm ).
tff(func_def_53,type,
sK61: vTerm > vTerm ).
tff(func_def_54,type,
sK62: vTerm > vTerm ).
tff(func_def_55,type,
sK63: vTerm > vTerm ).
tff(func_def_56,type,
sK64: vTerm > vTerm ).
tff(func_def_57,type,
sK65: vTerm > vTerm ).
tff(func_def_58,type,
sK66: vTerm > vTerm ).
tff(func_def_59,type,
sK67: vTerm > vTerm ).
tff(func_def_60,type,
sK68: vTerm > vTerm ).
tff(func_def_61,type,
sK69: vTerm > vTerm ).
tff(func_def_62,type,
sK70: vTerm > vTerm ).
tff(func_def_63,type,
sK71: vTerm > vTerm ).
tff(func_def_64,type,
sK72: vTerm > vTerm ).
tff(func_def_65,type,
sK73: vTerm > vTerm ).
tff(func_def_66,type,
sK74: vTerm > vTerm ).
tff(func_def_67,type,
sK75: vTerm > vTerm ).
tff(func_def_68,type,
sK76: vTerm > vOptTerm ).
tff(func_def_69,type,
sK77: vTerm > vTerm ).
tff(func_def_70,type,
sK78: vTerm > vOptTerm ).
tff(func_def_71,type,
sK79: vTerm > vTerm ).
tff(func_def_72,type,
sK80: vTerm > vTerm ).
tff(func_def_73,type,
sK81: vTerm > vTerm ).
tff(func_def_74,type,
sK82: vTerm > vOptTerm ).
tff(func_def_75,type,
sK83: vTerm > vTerm ).
tff(func_def_76,type,
sK84: vTerm > vOptTerm ).
tff(func_def_77,type,
sK85: vTerm > vTerm ).
tff(func_def_78,type,
sK86: vTerm > vOptTerm ).
tff(func_def_79,type,
sK87: vTerm > vTerm ).
tff(func_def_80,type,
sK88: vTerm > vOptTerm ).
tff(func_def_81,type,
sK89: vTerm > vTerm ).
tff(func_def_82,type,
sK90: vTerm > vTerm ).
tff(func_def_83,type,
sK91: vTerm > vOptTerm ).
tff(func_def_84,type,
sK92: vTerm > vTerm ).
tff(func_def_85,type,
sK93: vTerm > vTerm ).
tff(func_def_86,type,
sK94: vTerm > vOptTerm ).
tff(func_def_87,type,
sK95: vTerm > vTerm ).
tff(func_def_88,type,
sK96: vTerm > vTerm ).
tff(func_def_89,type,
sK97: vTerm > vTerm ).
tff(func_def_90,type,
sK98: vTerm > vOptTerm ).
tff(func_def_91,type,
sK99: vTerm > vTerm ).
tff(func_def_92,type,
sK100: vTerm > vTerm ).
tff(func_def_93,type,
sK101: vTerm > vTerm ).
tff(func_def_94,type,
sK102: vTerm > vOptTerm ).
tff(func_def_95,type,
sK103: vTerm > vTerm ).
tff(func_def_96,type,
sK104: vTerm > vOptTerm ).
tff(func_def_97,type,
sK105: vTerm > vTerm ).
tff(func_def_98,type,
sK106: vTerm > vOptTerm ).
tff(func_def_99,type,
sK107: vTerm > vTerm ).
tff(func_def_100,type,
sK108: vTerm > vOptTerm ).
tff(func_def_101,type,
sK109: vTerm > vTerm ).
tff(func_def_102,type,
sK110: vTerm > vOptTerm ).
tff(func_def_103,type,
sK111: vTerm > vTerm ).
tff(func_def_104,type,
sK112: vTerm > vTerm ).
tff(func_def_105,type,
sK113: vTerm > vOptTerm ).
tff(func_def_106,type,
sK114: vTerm > vTerm ).
tff(func_def_107,type,
sK115: vTerm > vTerm ).
tff(func_def_108,type,
sK116: vTerm > vOptTerm ).
tff(func_def_109,type,
sK117: vTerm > vTerm ).
tff(func_def_110,type,
sK118: vTerm > vTerm ).
tff(func_def_111,type,
sK119: vTerm > vTerm ).
tff(func_def_112,type,
sK120: vTerm > vTerm ).
tff(func_def_113,type,
sK121: vTerm > vTerm ).
tff(func_def_114,type,
sK122: vTy ).
tff(func_def_115,type,
sK123: 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(f37,axiom,
! [X0: vTerm] : ( vnoTerm != vsomeTerm(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-noTerm-someTerm') ).
tff(f81,axiom,
! [X0: vTerm,X1: vTerm] :
( ( ~ visNV(X0)
& ~ visSomeTerm(vreduce(X0)) )
=> ( vreduce(vPlus(X0,X1)) = vnoTerm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reduce-22') ).
tff(f108,conjecture,
! [X0: vTy,X1: vTerm] :
( ( ~ visSomeTerm(vreduce(vt1))
& ~ 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-isSomeTerm-False') ).
tff(f109,negated_conjecture,
~ ! [X0: vTy,X1: vTerm] :
( ( ~ visSomeTerm(vreduce(vt1))
& ~ visNV(vt1)
& vptchecksimple(vPlus(vt1,vt2),X0)
& ( vreduce(vPlus(vt1,vt2)) = vsomeTerm(X1) ) )
=> vptchecksimple(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f108]) ).
tff(f165,plain,
! [X0: vTerm,X1: vTerm] :
( ( vreduce(vPlus(X0,X1)) = vnoTerm )
| visNV(X0)
| visSomeTerm(vreduce(X0)) ),
inference(ennf_transformation,[],[f81]) ).
tff(f166,plain,
! [X0: vTerm,X1: vTerm] :
( ( vreduce(vPlus(X0,X1)) = vnoTerm )
| visNV(X0)
| visSomeTerm(vreduce(X0)) ),
inference(flattening,[],[f165]) ).
tff(f194,plain,
? [X0: vTy,X1: vTerm] :
( ~ vptchecksimple(X1,X0)
& ~ visSomeTerm(vreduce(vt1))
& ~ visNV(vt1)
& vptchecksimple(vPlus(vt1,vt2),X0)
& ( vreduce(vPlus(vt1,vt2)) = vsomeTerm(X1) ) ),
inference(ennf_transformation,[],[f109]) ).
tff(f195,plain,
? [X0: vTy,X1: vTerm] :
( ~ vptchecksimple(X1,X0)
& ~ visSomeTerm(vreduce(vt1))
& ~ visNV(vt1)
& vptchecksimple(vPlus(vt1,vt2),X0)
& ( vreduce(vPlus(vt1,vt2)) = vsomeTerm(X1) ) ),
inference(flattening,[],[f194]) ).
tff(f318,plain,
( ~ vptchecksimple(sK123,sK122)
& ~ visSomeTerm(vreduce(vt1))
& ~ visNV(vt1)
& vptchecksimple(vPlus(vt1,vt2),sK122)
& ( vreduce(vPlus(vt1,vt2)) = vsomeTerm(sK123) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK122,sK123]),skolemize(X0,sK122),skolemize(X1,sK123)],[f195]) ).
tff(f358,plain,
! [X0: vTerm] : ( vnoTerm != vsomeTerm(X0) ),
inference(cnf_transformation,[],[f37]) ).
tff(f436,plain,
! [X0: vTerm,X1: vTerm] :
( visSomeTerm(vreduce(X0))
| visNV(X0)
| ( vnoTerm = vreduce(vPlus(X0,X1)) ) ),
inference(cnf_transformation,[],[f166]) ).
tff(f581,plain,
vreduce(vPlus(vt1,vt2)) = vsomeTerm(sK123),
inference(cnf_transformation,[],[f318]) ).
tff(f583,plain,
~ visNV(vt1),
inference(cnf_transformation,[],[f318]) ).
tff(f584,plain,
~ visSomeTerm(vreduce(vt1)),
inference(cnf_transformation,[],[f318]) ).
tff(f587,plain,
vnoTerm != vreduce(vPlus(vt1,vt2)),
inference(superposition,[],[f358,f581]) ).
tff(f1295,plain,
! [X0: vTerm] :
( visNV(vt1)
| ( vnoTerm = vreduce(vPlus(vt1,X0)) ) ),
inference(resolution,[],[f436,f584]) ).
tff(f1312,plain,
! [X0: vTerm] : ( vnoTerm = vreduce(vPlus(vt1,X0)) ),
inference(forward_subsumption_resolution,[],[f1295,f583]) ).
tff(f1413,plain,
vnoTerm != vnoTerm,
inference(superposition,[],[f587,f1312]) ).
tff(f1423,plain,
$false,
inference(trivial_inequality_removal,[],[f1413]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM222_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n014.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 22:02:00 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.32 % (2227421)Will run a generic schedule for satisfiability detection.
% 0.22/0.32 % (2227440)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3864295401_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.32 % (2227441)% WARNING: option uhcvi not known.
% 0.22/0.32 % (2227442)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3157424034:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.32 % (2227441)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3802059418:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.32 % (2227443)dis+10_1_sil=32000:sp=arity:random_seed=1721484971:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.32 % (2227444)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3393648079:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.32 % (2227445)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=228227781:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.32 % (2227447)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3025903670:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.32 % Detected minimum model sizes of [1,3,1]
% 0.22/0.32 % Detected maximum model sizes of [3,max,max]
% 0.22/0.32 % TRYING [1,3,1]
% 0.22/0.32 % TRYING [1,3,2]
% 0.22/0.32 % TRYING [1,3,3]
% 0.22/0.32 % (2227445) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2227421-2227445"...
% 0.22/0.32 % TRYING [1,4,3]
% 0.22/0.32 % (2227445)...printing done.
% 0.22/0.32 % (2227445)Refutation found. Thanks to Tanya!
% 0.22/0.32 % SZS status Theorem for theBenchmark
% 0.22/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.32 % (2227445)------------------------------
% 0.22/0.32 % (2227445)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (2227445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (2227445)CaDiCaL version: 2.1.3
% 0.22/0.32 % (2227445)Termination reason: Refutation
% 0.22/0.32 % (2227445)Time elapsed: 0.034 s
% 0.22/0.32 % (2227445)Peak memory usage: 13 MB
% 0.22/0.32 % (2227445)Instructions burned: 48 (million)
% 0.22/0.32 % (2227421)Success in time 0.083 s
% 0.22/0.32 % Vampire exiting
%------------------------------------------------------------------------------