%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM215_1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n008.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 01:04:35 PM UTC 2026
% Result : Theorem 1.19s 1.29s
% Output : CNFRefutation 1.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 132 ( 28 equ)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 40 ( 15 ~; 13 |; 9 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 83 ( 83 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 39 ( 37 usr; 6 prp; 0-3 aty)
% Number of functors : 85 ( 85 usr; 2 con; 0-3 aty)
% Number of variables : 28 ( 0 sgn 24 !; 4 ?; 28 :)
% 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(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] :
( ( ! [X2: vTerm] : ( X0 != vSucc(X2) )
& ( X0 != vZero ) )
=> ( vplusop(X1,X0) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','plusop-2') ).
tff(f106,conjecture,
! [X0: vTerm] :
( ( vptchecksimple(vPred(vt2),vNat)
& vptchecksimple(X0,vNat) )
=> vptchecksimple(vplusop(X0,vPred(vt2)),vNat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','PlusPreservation-Pred') ).
tff(f107,negated_conjecture,
~ ! [X0: vTerm] :
( ( vptchecksimple(vPred(vt2),vNat)
& vptchecksimple(X0,vNat) )
=> vptchecksimple(vplusop(X0,vPred(vt2)),vNat) ),
inference(negated_conjecture,[status(cth)],[f106]) ).
tff(f129,plain,
! [X0: vTerm,X1: vTerm] :
( ? [X2: vTerm] : ( vSucc(X2) = X0 )
| ( vZero = X0 )
| ( vplusop(X1,X0) = X0 ) ),
inference(ennf_transformation,[],[f57]) ).
tff(f130,plain,
! [X0: vTerm,X1: vTerm] :
( ? [X2: vTerm] : ( vSucc(X2) = X0 )
| ( vZero = X0 )
| ( vplusop(X1,X0) = X0 ) ),
inference(flattening,[],[f129]) ).
tff(f189,plain,
? [X0: vTerm] :
( vptchecksimple(vPred(vt2),vNat)
& vptchecksimple(X0,vNat)
& ~ vptchecksimple(vplusop(X0,vPred(vt2)),vNat) ),
inference(ennf_transformation,[],[f107]) ).
tff(f190,plain,
? [X0: vTerm] :
( vptchecksimple(vPred(vt2),vNat)
& vptchecksimple(X0,vNat)
& ~ vptchecksimple(vplusop(X0,vPred(vt2)),vNat) ),
inference(flattening,[],[f189]) ).
tff(f230,plain,
! [X0: vTerm,X1: vTerm] :
( ( vSucc(sK41(X0)) = X0 )
| ( vZero = X0 )
| ( vplusop(X1,X0) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(X2,sK41(X0))],[f130]) ).
tff(f313,plain,
( vptchecksimple(vPred(vt2),vNat)
& vptchecksimple(sK122,vNat)
& ~ vptchecksimple(vplusop(sK122,vPred(vt2)),vNat) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(X0,sK122)],[f190]) ).
tff(f342,plain,
! [X0: vTerm] : ( vZero != vPred(X0) ),
inference(cnf_transformation,[],[f26]) ).
tff(f345,plain,
! [X0: vTerm,X1: vTerm] : ( vPred(X1) != vSucc(X0) ),
inference(cnf_transformation,[],[f29]) ).
tff(f387,plain,
! [X0: vTerm,X1: vTerm] :
( ( vSucc(sK41(X0)) = X0 )
| ( vZero = X0 )
| ( vplusop(X1,X0) = X0 ) ),
inference(cnf_transformation,[],[f230]) ).
tff(f574,plain,
vptchecksimple(vPred(vt2),vNat),
inference(cnf_transformation,[],[f313]) ).
tff(f576,plain,
~ vptchecksimple(vplusop(sK122,vPred(vt2)),vNat),
inference(cnf_transformation,[],[f313]) ).
tcf(c_77,plain,
! [X0_vTerm: vTerm] : vPred(X0_vTerm) != vZero,
inference(cnf_transformation,[],[f342]) ).
tcf(c_80,plain,
! [X0_vTerm: vTerm,X1_vTerm: vTerm] : vSucc(X0_vTerm) != vPred(X1_vTerm),
inference(cnf_transformation,[],[f345]) ).
tcf(c_122,plain,
! [X0_vTerm: vTerm,X1_vTerm: vTerm] :
( ( X1_vTerm = vZero )
| ( vSucc(sK41(X1_vTerm)) = X1_vTerm )
| ( vplusop(X0_vTerm,X1_vTerm) = X1_vTerm ) ),
inference(cnf_transformation,[],[f387]) ).
tcf(c_309,negated_conjecture,
~ vptchecksimple(vplusop(sK122,vPred(vt2)),vNat),
inference(cnf_transformation,[],[f576]) ).
tcf(c_311,negated_conjecture,
vptchecksimple(vPred(vt2),vNat),
inference(cnf_transformation,[],[f574]) ).
tcf(c_422,plain,
( ( vPred(vt2) = vZero )
| ( vSucc(sK41(vPred(vt2))) = vPred(vt2) )
| ~ vptchecksimple(vPred(vt2),vNat) ),
inference(superposition,[status(thm)],[c_122,c_309]) ).
tcf(c_424,plain,
( ( vPred(vt2) = vZero )
| ( vSucc(sK41(vPred(vt2))) = vPred(vt2) ) ),
inference(global_subsumption_just,[status(thm)],[c_422,c_311,c_422]) ).
tcf(c_428,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_424,c_77,c_80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM215_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 08:01:24 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.19/1.29 % SZS status Started for theBenchmark.p
% 1.19/1.29 % SZS status Theorem for theBenchmark.p
% 1.19/1.29
% 1.19/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.19/1.29
% 1.19/1.29 % ------ iProver source info
% 1.19/1.29
% 1.19/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.19/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.19/1.29 % git: non_committed_changes: false
% 1.19/1.29
% 1.19/1.29 % ------ Parsing...
% 1.19/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.19/1.29 % ------ Proving...
% 1.19/1.29 % ------ Problem Properties
% 1.19/1.29
% 1.19/1.29 %
% 1.19/1.29 % clauses 263
% 1.19/1.29 % conjectures 3
% 1.19/1.29 % EPR 20
% 1.19/1.29 % Horn 213
% 1.19/1.29 % unary 48
% 1.19/1.29 % binary 164
% 1.19/1.29 % lits 730
% 1.19/1.29 % lits eq 280
% 1.19/1.29 % fd_pure 1
% 1.19/1.29 % fd_pseudo 0
% 1.19/1.29 % fd_cond 19
% 1.19/1.29 % fd_pseudo_cond 9
% 1.19/1.29 % AC symbols 0
% 1.19/1.29
% 1.19/1.29 % ------ Input Options Time Limit: Unbounded
% 1.19/1.29
% 1.19/1.29
% 1.19/1.29 % ------
% 1.19/1.29 % Current options:
% 1.19/1.29 % ------
% 1.19/1.29
% 1.19/1.29
% 1.19/1.29 %
% 1.19/1.29
% 1.19/1.29 % ------ Proving...
% 1.19/1.29 %
% 1.19/1.29
% 1.19/1.29 % SZS status Theorem for theBenchmark.p
% 1.19/1.29
% 1.19/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.19/1.29
% 1.19/1.29
%------------------------------------------------------------------------------