%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM237_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 : n015.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 01:04:38 PM UTC 2026
% Result : Theorem 0.93s 1.30s
% Output : CNFRefutation 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 33 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 393 ( 59 equ)
% Maximal formula atoms : 6 ( 11 avg)
% Number of connectives : 151 ( 65 ~; 56 |; 26 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 1 ( 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 : 40 ( 38 usr; 7 prp; 0-3 aty)
% Number of functors : 87 ( 87 usr; 4 con; 0-3 aty)
% Number of variables : 34 ( 0 sgn 28 !; 6 ?; 34 :)
% 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,
sK39: vTerm > vTerm ).
tff(func_def_31,type,
sK40: vOptTerm > vTerm ).
tff(func_def_32,type,
sK41: vTerm > vTerm ).
tff(func_def_33,type,
sK42: ( vTerm * vTerm ) > vTerm ).
tff(func_def_34,type,
sK43: ( vTerm * vTerm ) > vTerm ).
tff(func_def_35,type,
sK44: ( vTerm * vTerm ) > vTerm ).
tff(func_def_36,type,
sK45: ( vTerm * vTerm ) > vTerm ).
tff(func_def_37,type,
sK46: ( vTerm * vTerm ) > vTerm ).
tff(func_def_38,type,
sK47: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_39,type,
sK48: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_40,type,
sK49: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_41,type,
sK50: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_42,type,
sK51: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_43,type,
sK52: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_44,type,
sK53: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_45,type,
sK54: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_46,type,
sK55: vTerm > vTerm ).
tff(func_def_47,type,
sK56: vTerm > vTerm ).
tff(func_def_48,type,
sK57: vTerm > vTerm ).
tff(func_def_49,type,
sK58: vTerm > vTerm ).
tff(func_def_50,type,
sK59: vTerm > vTerm ).
tff(func_def_51,type,
sK60: vTerm > vTerm ).
tff(func_def_52,type,
sK61: vTerm > vTerm ).
tff(func_def_53,type,
sK62: vTerm > vTerm ).
tff(func_def_54,type,
sK63: vTerm > vTerm ).
tff(func_def_55,type,
sK64: vTerm > vTerm ).
tff(func_def_56,type,
sK65: vTerm > vTerm ).
tff(func_def_57,type,
sK66: vTerm > vTerm ).
tff(func_def_58,type,
sK67: vTerm > vTerm ).
tff(func_def_59,type,
sK68: vTerm > vTerm ).
tff(func_def_60,type,
sK69: vTerm > vTerm ).
tff(func_def_61,type,
sK70: vTerm > vTerm ).
tff(func_def_62,type,
sK71: vTerm > vTerm ).
tff(func_def_63,type,
sK72: vTerm > vTerm ).
tff(func_def_64,type,
sK73: vTerm > vTerm ).
tff(func_def_65,type,
sK74: vTerm > vTerm ).
tff(func_def_66,type,
sK75: vTerm > vTerm ).
tff(func_def_67,type,
sK76: vTerm > vOptTerm ).
tff(func_def_68,type,
sK77: vTerm > vTerm ).
tff(func_def_69,type,
sK78: vTerm > vOptTerm ).
tff(func_def_70,type,
sK79: vTerm > vTerm ).
tff(func_def_71,type,
sK80: vTerm > vTerm ).
tff(func_def_72,type,
sK81: vTerm > vTerm ).
tff(func_def_73,type,
sK82: vTerm > vOptTerm ).
tff(func_def_74,type,
sK83: vTerm > vTerm ).
tff(func_def_75,type,
sK84: vTerm > vOptTerm ).
tff(func_def_76,type,
sK85: vTerm > vTerm ).
tff(func_def_77,type,
sK86: vTerm > vOptTerm ).
tff(func_def_78,type,
sK87: vTerm > vTerm ).
tff(func_def_79,type,
sK88: vTerm > vOptTerm ).
tff(func_def_80,type,
sK89: vTerm > vTerm ).
tff(func_def_81,type,
sK90: vTerm > vTerm ).
tff(func_def_82,type,
sK91: vTerm > vOptTerm ).
tff(func_def_83,type,
sK92: vTerm > vTerm ).
tff(func_def_84,type,
sK93: vTerm > vTerm ).
tff(func_def_85,type,
sK94: vTerm > vOptTerm ).
tff(func_def_86,type,
sK95: vTerm > vTerm ).
tff(func_def_87,type,
sK96: vTerm > vTerm ).
tff(func_def_88,type,
sK97: vTerm > vTerm ).
tff(func_def_89,type,
sK98: vTerm > vOptTerm ).
tff(func_def_90,type,
sK99: vTerm > vTerm ).
tff(func_def_91,type,
sK100: vTerm > vTerm ).
tff(func_def_92,type,
sK101: vTerm > vTerm ).
tff(func_def_93,type,
sK102: vTerm > vOptTerm ).
tff(func_def_94,type,
sK103: vTerm > vTerm ).
tff(func_def_95,type,
sK104: vTerm > vOptTerm ).
tff(func_def_96,type,
sK105: vTerm > vTerm ).
tff(func_def_97,type,
sK106: vTerm > vOptTerm ).
tff(func_def_98,type,
sK107: vTerm > vTerm ).
tff(func_def_99,type,
sK108: vTerm > vOptTerm ).
tff(func_def_100,type,
sK109: vTerm > vTerm ).
tff(func_def_101,type,
sK110: vTerm > vOptTerm ).
tff(func_def_102,type,
sK111: vTerm > vTerm ).
tff(func_def_103,type,
sK112: vTerm > vTerm ).
tff(func_def_104,type,
sK113: vTerm > vOptTerm ).
tff(func_def_105,type,
sK114: vTerm > vTerm ).
tff(func_def_106,type,
sK115: vTerm > vTerm ).
tff(func_def_107,type,
sK116: vTerm > vOptTerm ).
tff(func_def_108,type,
sK117: vTerm > vTerm ).
tff(func_def_109,type,
sK118: vTerm > vTerm ).
tff(func_def_110,type,
sK119: vTerm > vTerm ).
tff(func_def_111,type,
sK120: vTerm > vTerm ).
tff(func_def_112,type,
sK121: vTerm > vTerm ).
tff(func_def_113,type,
sK122: vTerm ).
tff(func_def_114,type,
sK123: vTerm ).
tff(func_def_115,type,
sK124: vTy ).
tff(f106,axiom,
! [X0: vTy] :
( ( ~ visValue(vPred(vt1))
& vptchecksimple(vPred(vt1),X0)
& ! [X1: vTerm] : ( vt1 != vSucc(X1) )
& ( vt1 != vZero )
& visSomeTerm(vreduce(vt1)) )
=> ( vreduce(vPred(vt1)) != vnoTerm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Progress-Pred-t1-isSomeTerm-True') ).
tff(f107,axiom,
! [X0: vTy] :
( ( ~ visValue(vPred(vt1))
& vptchecksimple(vPred(vt1),X0)
& ! [X1: vTerm] : ( vt1 != vSucc(X1) )
& ( vt1 != vZero )
& ~ visSomeTerm(vreduce(vt1)) )
=> ( vreduce(vPred(vt1)) != vnoTerm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Progress-Pred-t1-isSomeTerm-False') ).
tff(f108,conjecture,
! [X0: vTy] :
( ( ~ visValue(vPred(vt1))
& vptchecksimple(vPred(vt1),X0)
& ! [X1: vTerm] : ( vt1 != vSucc(X1) )
& ( vt1 != vZero ) )
=> ( vreduce(vPred(vt1)) != vnoTerm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Progress-Pred-t1') ).
tff(f109,negated_conjecture,
~ ! [X0: vTy] :
( ( ~ visValue(vPred(vt1))
& vptchecksimple(vPred(vt1),X0)
& ! [X1: vTerm] : ( vt1 != vSucc(X1) )
& ( vt1 != vZero ) )
=> ( vreduce(vPred(vt1)) != vnoTerm ) ),
inference(negated_conjecture,[status(cth)],[f108]) ).
tff(f191,plain,
! [X0: vTy] :
( visValue(vPred(vt1))
| ~ vptchecksimple(vPred(vt1),X0)
| ? [X1: vTerm] : ( vSucc(X1) = vt1 )
| ( vZero = vt1 )
| ~ visSomeTerm(vreduce(vt1))
| ( vreduce(vPred(vt1)) != vnoTerm ) ),
inference(ennf_transformation,[],[f106]) ).
tff(f192,plain,
! [X0: vTy] :
( visValue(vPred(vt1))
| ~ vptchecksimple(vPred(vt1),X0)
| ? [X1: vTerm] : ( vSucc(X1) = vt1 )
| ( vZero = vt1 )
| ~ visSomeTerm(vreduce(vt1))
| ( vreduce(vPred(vt1)) != vnoTerm ) ),
inference(flattening,[],[f191]) ).
tff(f193,plain,
! [X0: vTy] :
( visValue(vPred(vt1))
| ~ vptchecksimple(vPred(vt1),X0)
| ? [X1: vTerm] : ( vSucc(X1) = vt1 )
| ( vZero = vt1 )
| visSomeTerm(vreduce(vt1))
| ( vreduce(vPred(vt1)) != vnoTerm ) ),
inference(ennf_transformation,[],[f107]) ).
tff(f194,plain,
! [X0: vTy] :
( visValue(vPred(vt1))
| ~ vptchecksimple(vPred(vt1),X0)
| ? [X1: vTerm] : ( vSucc(X1) = vt1 )
| ( vZero = vt1 )
| visSomeTerm(vreduce(vt1))
| ( vreduce(vPred(vt1)) != vnoTerm ) ),
inference(flattening,[],[f193]) ).
tff(f195,plain,
? [X0: vTy] :
( ~ visValue(vPred(vt1))
& vptchecksimple(vPred(vt1),X0)
& ! [X1: vTerm] : ( vt1 != vSucc(X1) )
& ( vt1 != vZero )
& ( vnoTerm = vreduce(vPred(vt1)) ) ),
inference(ennf_transformation,[],[f109]) ).
tff(f196,plain,
? [X0: vTy] :
( ~ visValue(vPred(vt1))
& vptchecksimple(vPred(vt1),X0)
& ! [X1: vTerm] : ( vt1 != vSucc(X1) )
& ( vt1 != vZero )
& ( vnoTerm = vreduce(vPred(vt1)) ) ),
inference(flattening,[],[f195]) ).
tff(f319,plain,
! [X0: vTy] :
( visValue(vPred(vt1))
| ~ vptchecksimple(vPred(vt1),X0)
| ( vt1 = vSucc(sK122) )
| ( vZero = vt1 )
| ~ visSomeTerm(vreduce(vt1))
| ( vreduce(vPred(vt1)) != vnoTerm ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(X1,sK122)],[f192]) ).
tff(f320,plain,
! [X0: vTy] :
( visValue(vPred(vt1))
| ~ vptchecksimple(vPred(vt1),X0)
| ( vt1 = vSucc(sK123) )
| ( vZero = vt1 )
| visSomeTerm(vreduce(vt1))
| ( vreduce(vPred(vt1)) != vnoTerm ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK123]),skolemize(X1,sK123)],[f194]) ).
tff(f321,plain,
( ~ visValue(vPred(vt1))
& vptchecksimple(vPred(vt1),sK124)
& ! [X1: vTerm] : ( vt1 != vSucc(X1) )
& ( vt1 != vZero )
& ( vnoTerm = vreduce(vPred(vt1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK124]),skolemize(X0,sK124)],[f196]) ).
tff(f582,plain,
! [X0: vTy] :
( visValue(vPred(vt1))
| ~ vptchecksimple(vPred(vt1),X0)
| ( vt1 = vSucc(sK122) )
| ( vZero = vt1 )
| ~ visSomeTerm(vreduce(vt1))
| ( vnoTerm != vreduce(vPred(vt1)) ) ),
inference(cnf_transformation,[],[f319]) ).
tff(f583,plain,
! [X0: vTy] :
( visValue(vPred(vt1))
| ~ vptchecksimple(vPred(vt1),X0)
| ( vt1 = vSucc(sK123) )
| ( vZero = vt1 )
| visSomeTerm(vreduce(vt1))
| ( vnoTerm != vreduce(vPred(vt1)) ) ),
inference(cnf_transformation,[],[f320]) ).
tff(f584,plain,
~ visValue(vPred(vt1)),
inference(cnf_transformation,[],[f321]) ).
tff(f585,plain,
vptchecksimple(vPred(vt1),sK124),
inference(cnf_transformation,[],[f321]) ).
tff(f586,plain,
! [X1: vTerm] : ( vSucc(X1) != vt1 ),
inference(cnf_transformation,[],[f321]) ).
tff(f587,plain,
vZero != vt1,
inference(cnf_transformation,[],[f321]) ).
tff(f588,plain,
vnoTerm = vreduce(vPred(vt1)),
inference(cnf_transformation,[],[f321]) ).
tcf(c_309,plain,
! [X0_vTy: vTy] :
( visValue(vPred(vt1))
| ( vZero = vt1 )
| ( vSucc(sK122) = vt1 )
| ~ visSomeTerm(vreduce(vt1))
| ~ vptchecksimple(vPred(vt1),X0_vTy)
| ( vreduce(vPred(vt1)) != vnoTerm ) ),
inference(cnf_transformation,[],[f582]) ).
tcf(c_310,plain,
! [X0_vTy: vTy] :
( visSomeTerm(vreduce(vt1))
| visValue(vPred(vt1))
| ( vZero = vt1 )
| ( vSucc(sK123) = vt1 )
| ~ vptchecksimple(vPred(vt1),X0_vTy)
| ( vreduce(vPred(vt1)) != vnoTerm ) ),
inference(cnf_transformation,[],[f583]) ).
tcf(c_311,negated_conjecture,
vreduce(vPred(vt1)) = vnoTerm,
inference(cnf_transformation,[],[f588]) ).
tcf(c_312,negated_conjecture,
vZero != vt1,
inference(cnf_transformation,[],[f587]) ).
tcf(c_313,negated_conjecture,
! [X0_vTerm: vTerm] : vSucc(X0_vTerm) != vt1,
inference(cnf_transformation,[],[f586]) ).
tcf(c_314,negated_conjecture,
vptchecksimple(vPred(vt1),sK124),
inference(cnf_transformation,[],[f585]) ).
tcf(c_315,negated_conjecture,
~ visValue(vPred(vt1)),
inference(cnf_transformation,[],[f584]) ).
tcf(c_538,plain,
! [X0_vTy: vTy] :
( visSomeTerm(vreduce(vt1))
| ( vSucc(sK123) = vt1 )
| ~ vptchecksimple(vPred(vt1),X0_vTy) ),
inference(global_subsumption_just,[status(thm)],[c_310,c_315,c_312,c_311,c_310]) ).
tcf(c_541,plain,
! [X0_vTy: vTy] :
( ( vSucc(sK122) = vt1 )
| ~ visSomeTerm(vreduce(vt1))
| ~ vptchecksimple(vPred(vt1),X0_vTy) ),
inference(global_subsumption_just,[status(thm)],[c_309,c_315,c_312,c_311,c_309]) ).
tcf(c_1611,plain,
! [X0_vTy: vTy] :
( ~ visSomeTerm(vreduce(vt1))
| ~ vptchecksimple(vPred(vt1),X0_vTy) ),
inference(backward_subsumption_resolution,[status(thm)],[c_541,c_313]) ).
tcf(c_1612,plain,
! [X0_vTy: vTy] :
( visSomeTerm(vreduce(vt1))
| ~ vptchecksimple(vPred(vt1),X0_vTy) ),
inference(backward_subsumption_resolution,[status(thm)],[c_538,c_313]) ).
tcf(c_1615,plain,
! [X0_vTy: vTy] : ~ vptchecksimple(vPred(vt1),X0_vTy),
inference(global_subsumption_just,[status(thm)],[c_1611,c_1612,c_1611]) ).
tcf(c_1620,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_314,c_1615]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM237_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 08:04:27 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 0.93/1.30 % SZS status Started for theBenchmark.p
% 0.93/1.30 % SZS status Theorem for theBenchmark.p
% 0.93/1.30
% 0.93/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.93/1.30
% 0.93/1.30 % ------ iProver source info
% 0.93/1.30
% 0.93/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 0.93/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.93/1.30 % git: non_committed_changes: false
% 0.93/1.30
% 0.93/1.30 % ------ Parsing...
% 0.93/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 0.93/1.30 %
% 0.93/1.30
% 0.93/1.30 % ------ Preprocessing...%
% 0.93/1.30
% 0.93/1.30 % SZS status Theorem for theBenchmark.p
% 0.93/1.30
% 0.93/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.93/1.30
% 0.93/1.30
%------------------------------------------------------------------------------