%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM223_1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n002.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 : Fri Sep 25 01:04:36 PM UTC 2026
% Result : Theorem 14.76s 4.71s
% Output : CNFRefutation 14.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 91 ( 39 unt; 0 typ; 4 def)
% Number of atoms : 463 ( 57 equ)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 171 ( 73 ~; 61 |; 27 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 274 ( 274 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 44 ( 42 usr; 10 prp; 0-3 aty)
% Number of functors : 87 ( 87 usr; 3 con; 0-3 aty)
% Number of variables : 92 ( 0 sgn 86 !; 6 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
vNat: vTy ).
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: ( vTy * vTerm ) > $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(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(f36,axiom,
! [X0: vTerm,X1: vTerm] :
( ( vsomeTerm(X0) = vsomeTerm(X1) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-someTerm') ).
tff(f40,axiom,
! [X0: vTerm] : ( vgetTerm(vsomeTerm(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','getTerm-0') ).
tff(f53,axiom,
! [X0: vOptTerm] :
( visSomeTerm(X0)
=> ? [X1: vTerm] : ( X0 = vsomeTerm(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','isSomeTerm-true-INV') ).
tff(f78,axiom,
! [X0: vTerm,X1: vTerm] :
( ( visSomeTerm(vreduce(X1))
& ~ visNV(X1)
& visNV(X0) )
=> ( vreduce(vPlus(X0,X1)) = vsomeTerm(vPlus(X0,vgetTerm(vreduce(X1)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reduce-19') ).
tff(f101,axiom,
! [X0: vTerm,X1: vTerm] :
( ( vptchecksimple(X1,vNat)
& vptchecksimple(X0,vNat) )
=> vptchecksimple(vPlus(X0,X1),vNat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','TPlus') ).
tff(f102,axiom,
! [X0: vTerm,X1: vTerm,X2: vTy] :
( vptchecksimple(vPlus(X0,X1),X2)
=> ( X2 = vNat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','TPlus_inv0') ).
tff(f103,axiom,
! [X0: vTerm,X1: vTerm] :
( vptchecksimple(vPlus(X0,X1),vNat)
=> vptchecksimple(X0,vNat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','TPlus_inv1') ).
tff(f104,axiom,
! [X0: vTerm,X1: vTerm] :
( vptchecksimple(vPlus(X0,X1),vNat)
=> vptchecksimple(X1,vNat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','TPlus_inv2') ).
tff(f106,axiom,
! [X0: vTy,X1: vTerm] :
( ( ( vreduce(vt2) = vsomeTerm(X1) )
& vptchecksimple(vt2,X0) )
=> vptchecksimple(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Preservation-Plus-IH1') ).
tff(f108,conjecture,
! [X0: vTy,X1: vTerm] :
( ( ( vreduce(vPlus(vt1,vt2)) = vsomeTerm(X1) )
& vptchecksimple(vPlus(vt1,vt2),X0)
& visNV(vt1)
& ~ visNV(vt2)
& visSomeTerm(vreduce(vt2)) )
=> vptchecksimple(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Preservation-Plus-isNV-True-isNV-False-isSomeTerm-True') ).
tff(f109,negated_conjecture,
~ ! [X0: vTy,X1: vTerm] :
( ( ( vreduce(vPlus(vt1,vt2)) = vsomeTerm(X1) )
& vptchecksimple(vPlus(vt1,vt2),X0)
& visNV(vt1)
& ~ visNV(vt2)
& visSomeTerm(vreduce(vt2)) )
=> vptchecksimple(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f108]) ).
tff(f117,plain,
! [X0: vTerm,X1: vTerm] :
( ( vsomeTerm(X1) != vsomeTerm(X0) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f36]) ).
tff(f129,plain,
! [X0: vOptTerm] :
( ~ visSomeTerm(X0)
| ? [X1: vTerm] : ( X0 = vsomeTerm(X1) ) ),
inference(ennf_transformation,[],[f53]) ).
tff(f159,plain,
! [X0: vTerm,X1: vTerm] :
( ~ visSomeTerm(vreduce(X1))
| visNV(X1)
| ~ visNV(X0)
| ( vreduce(vPlus(X0,X1)) = vsomeTerm(vPlus(X0,vgetTerm(vreduce(X1)))) ) ),
inference(ennf_transformation,[],[f78]) ).
tff(f160,plain,
! [X0: vTerm,X1: vTerm] :
( ~ visSomeTerm(vreduce(X1))
| visNV(X1)
| ~ visNV(X0)
| ( vreduce(vPlus(X0,X1)) = vsomeTerm(vPlus(X0,vgetTerm(vreduce(X1)))) ) ),
inference(flattening,[],[f159]) ).
tff(f184,plain,
! [X0: vTerm,X1: vTerm] :
( ~ vptchecksimple(X1,vNat)
| ~ vptchecksimple(X0,vNat)
| vptchecksimple(vPlus(X0,X1),vNat) ),
inference(ennf_transformation,[],[f101]) ).
tff(f185,plain,
! [X0: vTerm,X1: vTerm] :
( ~ vptchecksimple(X1,vNat)
| ~ vptchecksimple(X0,vNat)
| vptchecksimple(vPlus(X0,X1),vNat) ),
inference(flattening,[],[f184]) ).
tff(f186,plain,
! [X0: vTerm,X1: vTerm,X2: vTy] :
( ~ vptchecksimple(vPlus(X0,X1),X2)
| ( X2 = vNat ) ),
inference(ennf_transformation,[],[f102]) ).
tff(f187,plain,
! [X0: vTerm,X1: vTerm] :
( ~ vptchecksimple(vPlus(X0,X1),vNat)
| vptchecksimple(X0,vNat) ),
inference(ennf_transformation,[],[f103]) ).
tff(f188,plain,
! [X0: vTerm,X1: vTerm] :
( ~ vptchecksimple(vPlus(X0,X1),vNat)
| vptchecksimple(X1,vNat) ),
inference(ennf_transformation,[],[f104]) ).
tff(f191,plain,
! [X0: vTy,X1: vTerm] :
( ( vsomeTerm(X1) != vreduce(vt2) )
| ~ vptchecksimple(vt2,X0)
| vptchecksimple(X1,X0) ),
inference(ennf_transformation,[],[f106]) ).
tff(f192,plain,
! [X0: vTy,X1: vTerm] :
( ( vsomeTerm(X1) != vreduce(vt2) )
| ~ vptchecksimple(vt2,X0)
| vptchecksimple(X1,X0) ),
inference(flattening,[],[f191]) ).
tff(f194,plain,
? [X0: vTy,X1: vTerm] :
( ( vreduce(vPlus(vt1,vt2)) = vsomeTerm(X1) )
& vptchecksimple(vPlus(vt1,vt2),X0)
& visNV(vt1)
& ~ visNV(vt2)
& visSomeTerm(vreduce(vt2))
& ~ vptchecksimple(X1,X0) ),
inference(ennf_transformation,[],[f109]) ).
tff(f195,plain,
? [X0: vTy,X1: vTerm] :
( ( vreduce(vPlus(vt1,vt2)) = vsomeTerm(X1) )
& vptchecksimple(vPlus(vt1,vt2),X0)
& visNV(vt1)
& ~ visNV(vt2)
& visSomeTerm(vreduce(vt2))
& ~ vptchecksimple(X1,X0) ),
inference(flattening,[],[f194]) ).
tff(f234,plain,
! [X0: vOptTerm] :
( ~ visSomeTerm(X0)
| ( vsomeTerm(sK40(X0)) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(X1,sK40(X0))],[f129]) ).
tff(f318,plain,
( ( vreduce(vPlus(vt1,vt2)) = vsomeTerm(sK123) )
& vptchecksimple(vPlus(vt1,vt2),sK122)
& visNV(vt1)
& ~ visNV(vt2)
& visSomeTerm(vreduce(vt2))
& ~ vptchecksimple(sK123,sK122) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK122,sK123]),skolemize(X0,sK122),skolemize(X1,sK123)],[f195]) ).
tff(f357,plain,
! [X0: vTerm,X1: vTerm] :
( ( vsomeTerm(X1) != vsomeTerm(X0) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f117]) ).
tff(f361,plain,
! [X0: vTerm] : ( vgetTerm(vsomeTerm(X0)) = X0 ),
inference(cnf_transformation,[],[f40]) ).
tff(f388,plain,
! [X0: vOptTerm] :
( ~ visSomeTerm(X0)
| ( vsomeTerm(sK40(X0)) = X0 ) ),
inference(cnf_transformation,[],[f234]) ).
tff(f433,plain,
! [X0: vTerm,X1: vTerm] :
( ~ visSomeTerm(vreduce(X1))
| visNV(X1)
| ~ visNV(X0)
| ( vreduce(vPlus(X0,X1)) = vsomeTerm(vPlus(X0,vgetTerm(vreduce(X1)))) ) ),
inference(cnf_transformation,[],[f160]) ).
tff(f574,plain,
! [X0: vTerm,X1: vTerm] :
( ~ vptchecksimple(X1,vNat)
| ~ vptchecksimple(X0,vNat)
| vptchecksimple(vPlus(X0,X1),vNat) ),
inference(cnf_transformation,[],[f185]) ).
tff(f575,plain,
! [X2: vTy,X0: vTerm,X1: vTerm] :
( ~ vptchecksimple(vPlus(X0,X1),X2)
| ( vNat = X2 ) ),
inference(cnf_transformation,[],[f186]) ).
tff(f576,plain,
! [X0: vTerm,X1: vTerm] :
( ~ vptchecksimple(vPlus(X0,X1),vNat)
| vptchecksimple(X0,vNat) ),
inference(cnf_transformation,[],[f187]) ).
tff(f577,plain,
! [X0: vTerm,X1: vTerm] :
( ~ vptchecksimple(vPlus(X0,X1),vNat)
| vptchecksimple(X1,vNat) ),
inference(cnf_transformation,[],[f188]) ).
tff(f579,plain,
! [X0: vTy,X1: vTerm] :
( ( vsomeTerm(X1) != vreduce(vt2) )
| ~ vptchecksimple(vt2,X0)
| vptchecksimple(X1,X0) ),
inference(cnf_transformation,[],[f192]) ).
tff(f581,plain,
vreduce(vPlus(vt1,vt2)) = vsomeTerm(sK123),
inference(cnf_transformation,[],[f318]) ).
tff(f582,plain,
vptchecksimple(vPlus(vt1,vt2),sK122),
inference(cnf_transformation,[],[f318]) ).
tff(f583,plain,
visNV(vt1),
inference(cnf_transformation,[],[f318]) ).
tff(f584,plain,
~ visNV(vt2),
inference(cnf_transformation,[],[f318]) ).
tff(f585,plain,
visSomeTerm(vreduce(vt2)),
inference(cnf_transformation,[],[f318]) ).
tff(f586,plain,
~ vptchecksimple(sK123,sK122),
inference(cnf_transformation,[],[f318]) ).
tcf(c_87,plain,
! [X0_vTerm: vTerm,X1_vTerm: vTerm] :
( ( X0_vTerm = X1_vTerm )
| ( vsomeTerm(X0_vTerm) != vsomeTerm(X1_vTerm) ) ),
inference(cnf_transformation,[],[f357]) ).
tcf(c_91,plain,
! [X0_vTerm: vTerm] : vgetTerm(vsomeTerm(X0_vTerm)) = X0_vTerm,
inference(cnf_transformation,[],[f361]) ).
tcf(c_118,plain,
! [X0_vOptTerm: vOptTerm] :
( ( vsomeTerm(sK40(X0_vOptTerm)) = X0_vOptTerm )
| ~ visSomeTerm(X0_vOptTerm) ),
inference(cnf_transformation,[],[f388]) ).
tcf(c_163,plain,
! [X0_vTerm: vTerm,X1_vTerm: vTerm] :
( visNV(X0_vTerm)
| ( vsomeTerm(vPlus(X1_vTerm,vgetTerm(vreduce(X0_vTerm)))) = vreduce(vPlus(X1_vTerm,X0_vTerm)) )
| ~ visNV(X1_vTerm)
| ~ visSomeTerm(vreduce(X0_vTerm)) ),
inference(cnf_transformation,[],[f433]) ).
tcf(c_304,plain,
! [X0_vTerm: vTerm,X1_vTerm: vTerm] :
( vptchecksimple(vPlus(X0_vTerm,X1_vTerm),vNat)
| ~ vptchecksimple(X1_vTerm,vNat)
| ~ vptchecksimple(X0_vTerm,vNat) ),
inference(cnf_transformation,[],[f574]) ).
tcf(c_305,plain,
! [X0_vTerm: vTerm,X0_vTy: vTy,X1_vTerm: vTerm] :
( ( X0_vTy = vNat )
| ~ vptchecksimple(vPlus(X0_vTerm,X1_vTerm),X0_vTy) ),
inference(cnf_transformation,[],[f575]) ).
tcf(c_306,plain,
! [X0_vTerm: vTerm,X1_vTerm: vTerm] :
( vptchecksimple(X0_vTerm,vNat)
| ~ vptchecksimple(vPlus(X0_vTerm,X1_vTerm),vNat) ),
inference(cnf_transformation,[],[f576]) ).
tcf(c_307,plain,
! [X0_vTerm: vTerm,X1_vTerm: vTerm] :
( vptchecksimple(X1_vTerm,vNat)
| ~ vptchecksimple(vPlus(X0_vTerm,X1_vTerm),vNat) ),
inference(cnf_transformation,[],[f577]) ).
tcf(c_309,plain,
! [X0_vTerm: vTerm,X0_vTy: vTy] :
( vptchecksimple(X0_vTerm,X0_vTy)
| ~ vptchecksimple(vt2,X0_vTy)
| ( vsomeTerm(X0_vTerm) != vreduce(vt2) ) ),
inference(cnf_transformation,[],[f579]) ).
tcf(c_311,negated_conjecture,
~ vptchecksimple(sK123,sK122),
inference(cnf_transformation,[],[f586]) ).
tcf(c_312,negated_conjecture,
visSomeTerm(vreduce(vt2)),
inference(cnf_transformation,[],[f585]) ).
tcf(c_313,negated_conjecture,
~ visNV(vt2),
inference(cnf_transformation,[],[f584]) ).
tcf(c_314,negated_conjecture,
visNV(vt1),
inference(cnf_transformation,[],[f583]) ).
tcf(c_315,negated_conjecture,
vptchecksimple(vPlus(vt1,vt2),sK122),
inference(cnf_transformation,[],[f582]) ).
tcf(c_316,negated_conjecture,
vreduce(vPlus(vt1,vt2)) = vsomeTerm(sK123),
inference(cnf_transformation,[],[f581]) ).
tcf(c_50995,definition,
iPr_def_10 = vPlus(vt1,vt2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_50996,definition,
iPr_def_11 = vreduce(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_50997,definition,
iPr_def_12 = vsomeTerm(sK123),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_50998,definition,
iPr_def_13 = vreduce(vt2),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_50999,negated_conjecture,
iPr_def_11 = iPr_def_12,
inference(demodulation,[status(thm)],[c_316,c_50997,c_50995,c_50996]) ).
tcf(c_51000,negated_conjecture,
vptchecksimple(iPr_def_10,sK122),
inference(demodulation,[status(thm)],[c_315]) ).
tcf(c_51001,negated_conjecture,
visNV(vt1),
inference(demodulation,[status(thm)],[c_314]) ).
tcf(c_51002,negated_conjecture,
~ visNV(vt2),
inference(demodulation,[status(thm)],[c_313]) ).
tcf(c_51003,negated_conjecture,
visSomeTerm(iPr_def_13),
inference(demodulation,[status(thm)],[c_312,c_50998]) ).
tcf(c_51004,negated_conjecture,
~ vptchecksimple(sK123,sK122),
inference(demodulation,[status(thm)],[c_311]) ).
tcf(c_53640,plain,
vsomeTerm(sK123) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_50997,c_50999]) ).
tcf(c_55388,plain,
vsomeTerm(sK40(iPr_def_13)) = iPr_def_13,
inference(superposition,[status(thm)],[c_51003,c_118]) ).
tcf(c_55417,plain,
vgetTerm(iPr_def_13) = sK40(iPr_def_13),
inference(superposition,[status(thm)],[c_55388,c_91]) ).
tcf(c_55420,plain,
vsomeTerm(vgetTerm(iPr_def_13)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_55388,c_55417]) ).
tcf(c_56099,plain,
( vptchecksimple(vt1,vNat)
| ~ vptchecksimple(iPr_def_10,vNat) ),
inference(superposition,[status(thm)],[c_50995,c_306]) ).
tcf(c_56535,plain,
( vptchecksimple(vt2,vNat)
| ~ vptchecksimple(iPr_def_10,vNat) ),
inference(superposition,[status(thm)],[c_50995,c_307]) ).
tcf(c_57559,plain,
! [X0_vTy: vTy] :
( ( X0_vTy = vNat )
| ~ vptchecksimple(iPr_def_10,X0_vTy) ),
inference(superposition,[status(thm)],[c_50995,c_305]) ).
tcf(c_57575,plain,
vNat = sK122,
inference(superposition,[status(thm)],[c_51000,c_57559]) ).
tcf(c_57651,plain,
~ vptchecksimple(sK123,vNat),
inference(demodulation,[status(thm)],[c_51004,c_57575]) ).
tcf(c_57652,plain,
vptchecksimple(iPr_def_10,vNat),
inference(demodulation,[status(thm)],[c_51000,c_57575]) ).
tcf(c_57653,plain,
vptchecksimple(vt2,vNat),
inference(backward_subsumption_resolution,[status(thm)],[c_56535,c_57652]) ).
tcf(c_57654,plain,
vptchecksimple(vt1,vNat),
inference(backward_subsumption_resolution,[status(thm)],[c_56099,c_57652]) ).
tcf(c_58110,plain,
! [X0_vTerm: vTerm] :
( ( X0_vTerm = sK123 )
| ( vsomeTerm(X0_vTerm) != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_53640,c_87]) ).
tcf(c_61126,plain,
! [X0_vTerm: vTerm,X0_vTy: vTy] :
( vptchecksimple(X0_vTerm,X0_vTy)
| ~ vptchecksimple(vt2,X0_vTy)
| ( vsomeTerm(X0_vTerm) != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_309,c_50998]) ).
tcf(c_61139,plain,
! [X0_vTy: vTy] :
( vptchecksimple(vgetTerm(iPr_def_13),X0_vTy)
| ~ vptchecksimple(vt2,X0_vTy) ),
inference(superposition,[status(thm)],[c_55420,c_61126]) ).
tcf(c_61172,plain,
( vptchecksimple(vgetTerm(iPr_def_13),vNat)
| ~ vptchecksimple(vt2,vNat) ),
inference(instantiation,[status(thm)],[c_61139]) ).
tcf(c_63551,plain,
! [X0_vTerm: vTerm] :
( visNV(vt2)
| ( vsomeTerm(vPlus(X0_vTerm,vgetTerm(vreduce(vt2)))) = vreduce(vPlus(X0_vTerm,vt2)) )
| ~ visSomeTerm(iPr_def_13)
| ~ visNV(X0_vTerm) ),
inference(superposition,[status(thm)],[c_50998,c_163]) ).
tcf(c_63566,plain,
! [X0_vTerm: vTerm] :
( visNV(vt2)
| ( vsomeTerm(vPlus(X0_vTerm,vgetTerm(iPr_def_13))) = vreduce(vPlus(X0_vTerm,vt2)) )
| ~ visSomeTerm(iPr_def_13)
| ~ visNV(X0_vTerm) ),
inference(light_normalisation,[status(thm)],[c_63551,c_50998]) ).
tcf(c_63567,plain,
! [X0_vTerm: vTerm] :
( ( vsomeTerm(vPlus(X0_vTerm,vgetTerm(iPr_def_13))) = vreduce(vPlus(X0_vTerm,vt2)) )
| ~ visNV(X0_vTerm) ),
inference(forward_subsumption_resolution,[status(thm)],[c_63566,c_51002,c_51003]) ).
tcf(c_64043,plain,
vsomeTerm(vPlus(vt1,vgetTerm(iPr_def_13))) = vreduce(vPlus(vt1,vt2)),
inference(superposition,[status(thm)],[c_51001,c_63567]) ).
tcf(c_64048,plain,
vsomeTerm(vPlus(vt1,vgetTerm(iPr_def_13))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_64043,c_50995,c_50996]) ).
tcf(c_64769,plain,
vPlus(vt1,vgetTerm(iPr_def_13)) = sK123,
inference(superposition,[status(thm)],[c_64048,c_58110]) ).
tcf(c_65202,plain,
( vptchecksimple(sK123,vNat)
| ~ vptchecksimple(vt1,vNat)
| ~ vptchecksimple(vgetTerm(iPr_def_13),vNat) ),
inference(superposition,[status(thm)],[c_64769,c_304]) ).
tcf(c_65233,plain,
~ vptchecksimple(vgetTerm(iPr_def_13),vNat),
inference(forward_subsumption_resolution,[status(thm)],[c_65202,c_57651,c_57654]) ).
tcf(c_65247,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_65233,c_61172,c_57653]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM223_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 08:03:34 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 14.76/4.71 % SZS status Started for theBenchmark.p
% 14.76/4.71 % SZS status Theorem for theBenchmark.p
% 14.76/4.71
% 14.76/4.71 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 14.76/4.71
% 14.76/4.71 % ------ iProver source info
% 14.76/4.71
% 14.76/4.71 % git: date: 2026-07-19 20:42:38 +0200
% 14.76/4.71 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 14.76/4.71 % git: non_committed_changes: false
% 14.76/4.71
% 14.76/4.71 % ------ Parsing...
% 14.76/4.71 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 14.76/4.71 %
% 14.76/4.71
% 14.76/4.71 % ------ Preprocessing... sup_sim: 0 pe_s pe_e sup_sim: 0 pe_s pe_e %
% 14.76/4.71
% 14.76/4.71 % ------ Preprocessing...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 14.76/4.71 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e % ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 14.76/4.71 %
% 14.76/4.71
% 14.76/4.71 % ------ Preprocessing...
% 14.76/4.71 % ------ Proving...
% 14.76/4.71 % ------ Problem Properties
% 14.76/4.71
% 14.76/4.71 %
% 14.76/4.71 % clauses 268
% 14.76/4.71 % conjectures 6
% 14.76/4.71 % EPR 26
% 14.76/4.71 % Horn 218
% 14.76/4.71 % unary 55
% 14.76/4.71 % binary 161
% 14.76/4.71 % lits 734
% 14.76/4.71 % lits eq 283
% 14.76/4.71 % fd_pure 1
% 14.76/4.71 % fd_pseudo 0
% 14.76/4.71 % fd_cond 19
% 14.76/4.71 % fd_pseudo_cond 9
% 14.76/4.71 % AC symbols 0
% 14.76/4.71
% 14.76/4.71 % ------ Schedule dynamic 5 is on
% 14.76/4.71
% 14.76/4.71 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 14.76/4.71
% 14.76/4.71
% 14.76/4.71 % ------
% 14.76/4.71 % Current options:
% 14.76/4.71 % ------
% 14.76/4.71
% 14.76/4.71
% 14.76/4.71 %
% 14.76/4.71
% 14.76/4.71 % ------ Proving...
% 14.76/4.71 %
% 14.76/4.71
% 14.76/4.71 % SZS status Theorem for theBenchmark.p
% 14.76/4.71
% 14.76/4.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 14.76/4.71
% 14.76/4.71
%------------------------------------------------------------------------------