%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM239_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 01:04:38 PM UTC 2026
% Result : Theorem 22.87s 4.47s
% Output : CNFRefutation 22.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 313 ( 66 equ)
% Maximal formula atoms : 6 ( 9 avg)
% Number of connectives : 97 ( 40 ~; 29 |; 25 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 222 ( 222 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 42 ( 40 usr; 7 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: vTy ).
tff(f37,axiom,
! [X0: vTerm] : ( vnoTerm != vsomeTerm(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-noTerm-someTerm') ).
tff(f69,axiom,
! [X0: vTerm] :
( ( visSomeTerm(vreduce(X0))
& ! [X1: vTerm] : ( X0 != vSucc(X1) )
& ( X0 != vZero ) )
=> ( vreduce(vPred(X0)) = vsomeTerm(vPred(vgetTerm(vreduce(X0)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reduce-10') ).
tff(f106,conjecture,
! [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,negated_conjecture,
~ ! [X0: vTy] :
( ( ~ visValue(vPred(vt1))
& vptchecksimple(vPred(vt1),X0)
& ! [X1: vTerm] : ( vt1 != vSucc(X1) )
& ( vt1 != vZero )
& visSomeTerm(vreduce(vt1)) )
=> ( vreduce(vPred(vt1)) != vnoTerm ) ),
inference(negated_conjecture,[status(cth)],[f106]) ).
tff(f142,plain,
! [X0: vTerm] :
( ~ visSomeTerm(vreduce(X0))
| ? [X1: vTerm] : ( vSucc(X1) = X0 )
| ( vZero = X0 )
| ( vreduce(vPred(X0)) = vsomeTerm(vPred(vgetTerm(vreduce(X0)))) ) ),
inference(ennf_transformation,[],[f69]) ).
tff(f143,plain,
! [X0: vTerm] :
( ~ visSomeTerm(vreduce(X0))
| ? [X1: vTerm] : ( vSucc(X1) = X0 )
| ( vZero = X0 )
| ( vreduce(vPred(X0)) = vsomeTerm(vPred(vgetTerm(vreduce(X0)))) ) ),
inference(flattening,[],[f142]) ).
tff(f189,plain,
? [X0: vTy] :
( ~ visValue(vPred(vt1))
& vptchecksimple(vPred(vt1),X0)
& ! [X1: vTerm] : ( vt1 != vSucc(X1) )
& ( vt1 != vZero )
& visSomeTerm(vreduce(vt1))
& ( vnoTerm = vreduce(vPred(vt1)) ) ),
inference(ennf_transformation,[],[f107]) ).
tff(f190,plain,
? [X0: vTy] :
( ~ visValue(vPred(vt1))
& vptchecksimple(vPred(vt1),X0)
& ! [X1: vTerm] : ( vt1 != vSucc(X1) )
& ( vt1 != vZero )
& visSomeTerm(vreduce(vt1))
& ( vnoTerm = vreduce(vPred(vt1)) ) ),
inference(flattening,[],[f189]) ).
tff(f246,plain,
! [X0: vTerm] :
( ~ visSomeTerm(vreduce(X0))
| ( vSucc(sK55(X0)) = X0 )
| ( vZero = X0 )
| ( vreduce(vPred(X0)) = vsomeTerm(vPred(vgetTerm(vreduce(X0)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(X1,sK55(X0))],[f143]) ).
tff(f313,plain,
( ~ visValue(vPred(vt1))
& vptchecksimple(vPred(vt1),sK122)
& ! [X1: vTerm] : ( vt1 != vSucc(X1) )
& ( vt1 != vZero )
& visSomeTerm(vreduce(vt1))
& ( vnoTerm = vreduce(vPred(vt1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(X0,sK122)],[f190]) ).
tff(f353,plain,
! [X0: vTerm] : ( vnoTerm != vsomeTerm(X0) ),
inference(cnf_transformation,[],[f37]) ).
tff(f419,plain,
! [X0: vTerm] :
( ~ visSomeTerm(vreduce(X0))
| ( vSucc(sK55(X0)) = X0 )
| ( vZero = X0 )
| ( vreduce(vPred(X0)) = vsomeTerm(vPred(vgetTerm(vreduce(X0)))) ) ),
inference(cnf_transformation,[],[f246]) ).
tff(f576,plain,
! [X1: vTerm] : ( vSucc(X1) != vt1 ),
inference(cnf_transformation,[],[f313]) ).
tff(f577,plain,
vZero != vt1,
inference(cnf_transformation,[],[f313]) ).
tff(f578,plain,
visSomeTerm(vreduce(vt1)),
inference(cnf_transformation,[],[f313]) ).
tff(f579,plain,
vnoTerm = vreduce(vPred(vt1)),
inference(cnf_transformation,[],[f313]) ).
tcf(c_88,negated_conjecture,
! [X0_vTerm: vTerm] : vsomeTerm(X0_vTerm) != vnoTerm,
inference(cnf_transformation,[],[f353]) ).
tcf(c_154,plain,
! [X0_vTerm: vTerm] :
( ( X0_vTerm = vZero )
| ( vSucc(sK55(X0_vTerm)) = X0_vTerm )
| ( vsomeTerm(vPred(vgetTerm(vreduce(X0_vTerm)))) = vreduce(vPred(X0_vTerm)) )
| ~ visSomeTerm(vreduce(X0_vTerm)) ),
inference(cnf_transformation,[],[f419]) ).
tcf(c_309,negated_conjecture,
vreduce(vPred(vt1)) = vnoTerm,
inference(cnf_transformation,[],[f579]) ).
tcf(c_310,negated_conjecture,
visSomeTerm(vreduce(vt1)),
inference(cnf_transformation,[],[f578]) ).
tcf(c_311,negated_conjecture,
vZero != vt1,
inference(cnf_transformation,[],[f577]) ).
tcf(c_312,negated_conjecture,
! [X0_vTerm: vTerm] : vSucc(X0_vTerm) != vt1,
inference(cnf_transformation,[],[f576]) ).
tcf(c_678,plain,
! [X0_vTerm: vTerm] : X0_vTerm = X0_vTerm,
theory(equality) ).
tcf(c_681,plain,
! [X0_vTerm: vTerm,X1_vTerm: vTerm,X2_vTerm: vTerm] :
( ( X2_vTerm = X0_vTerm )
| ( X2_vTerm != X1_vTerm )
| ( X0_vTerm != X1_vTerm ) ),
theory(equality) ).
tcf(c_926,plain,
vZero = vZero,
inference(instantiation,[status(thm)],[c_678]) ).
tcf(c_2184,plain,
( ( vt1 = vZero )
| ( vSucc(sK55(vt1)) = vt1 )
| ( vsomeTerm(vPred(vgetTerm(vreduce(vt1)))) = vreduce(vPred(vt1)) )
| ~ visSomeTerm(vreduce(vt1)) ),
inference(instantiation,[status(thm)],[c_154]) ).
tcf(c_2240,plain,
! [X0_vTerm: vTerm] :
( ( vZero = vt1 )
| ( vt1 != X0_vTerm )
| ( vZero != X0_vTerm ) ),
inference(instantiation,[status(thm)],[c_681]) ).
tcf(c_2241,plain,
( ( vZero = vt1 )
| ( vt1 != vZero )
| ( vZero != vZero ) ),
inference(instantiation,[status(thm)],[c_2240]) ).
tcf(c_11491,plain,
( ( vZero = vt1 )
| ( vSucc(sK55(vt1)) = vt1 )
| ( vsomeTerm(vPred(vgetTerm(vreduce(vt1)))) = vreduce(vPred(vt1)) ) ),
inference(superposition,[status(thm)],[c_310,c_154]) ).
tcf(c_12596,plain,
( ( vsomeTerm(vPred(vgetTerm(vreduce(vt1)))) = vreduce(vPred(vt1)) )
| ( vSucc(sK55(vt1)) = vt1 ) ),
inference(global_subsumption_just,[status(thm)],[c_11491,c_310,c_311,c_926,c_2184,c_2241]) ).
tcf(c_12597,plain,
( ( vSucc(sK55(vt1)) = vt1 )
| ( vsomeTerm(vPred(vgetTerm(vreduce(vt1)))) = vreduce(vPred(vt1)) ) ),
inference(renaming,[status(thm)],[c_12596]) ).
tcf(c_12610,plain,
( ( vSucc(sK55(vt1)) = vt1 )
| ( vreduce(vPred(vt1)) != vnoTerm ) ),
inference(superposition,[status(thm)],[c_12597,c_88]) ).
tcf(c_12635,plain,
vSucc(sK55(vt1)) = vt1,
inference(global_subsumption_just,[status(thm)],[c_12610,c_309,c_12610]) ).
tcf(c_12661,plain,
$false,
inference(superposition,[status(thm)],[c_12635,c_312]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM239_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n002.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 08:03:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.44
% 0.10/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.44
% 0.10/0.44 % Detected problem language: tptp
% 0.10/0.46 % Proving...
% 22.87/4.47 % SZS status Started for theBenchmark.p
% 22.87/4.47 % SZS status Theorem for theBenchmark.p
% 22.87/4.47
% 22.87/4.47 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 22.87/4.47
% 22.87/4.47 % ------ iProver source info
% 22.87/4.47
% 22.87/4.47 % git: date: 2026-07-19 20:42:38 +0200
% 22.87/4.47 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 22.87/4.47 % git: non_committed_changes: false
% 22.87/4.47
% 22.87/4.47 % ------ Parsing...
% 22.87/4.47 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 22.87/4.47
% 22.87/4.47 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e %
% 22.87/4.47
% 22.87/4.47 % ------ Preprocessing...%
% 22.87/4.47
% 22.87/4.47 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 22.87/4.47 % ------ Proving...
% 22.87/4.47 % ------ Problem Properties
% 22.87/4.47
% 22.87/4.47 %
% 22.87/4.47 % clauses 266
% 22.87/4.47 % conjectures 78
% 22.87/4.47 % EPR 20
% 22.87/4.47 % Horn 216
% 22.87/4.47 % unary 51
% 22.87/4.47 % binary 164
% 22.87/4.47 % lits 733
% 22.87/4.47 % lits eq 284
% 22.87/4.47 % fd_pure 1
% 22.87/4.47 % fd_pseudo 0
% 22.87/4.47 % fd_cond 19
% 22.87/4.47 % fd_pseudo_cond 9
% 22.87/4.47 % AC symbols 0
% 22.87/4.47
% 22.87/4.47 % ------ Input Options Time Limit: Unbounded
% 22.87/4.47
% 22.87/4.47
% 22.87/4.47 % ------
% 22.87/4.47 % Current options:
% 22.87/4.47 % ------
% 22.87/4.47
% 22.87/4.47
% 22.87/4.47 %
% 22.87/4.47
% 22.87/4.47 % ------ Proving...
% 22.87/4.47 %
% 22.87/4.47
% 22.87/4.47 % SZS status Theorem for theBenchmark.p
% 22.87/4.47
% 22.87/4.47 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 22.87/4.47
% 22.87/4.47
%------------------------------------------------------------------------------