%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM225_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 : n007.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 4.18s 1.31s
% Output : CNFRefutation 4.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 39 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 275 ( 70 equ)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 181 ( 72 ~; 79 |; 26 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 127 ( 127 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 5 prp; 0-3 aty)
% Number of functors : 49 ( 49 usr; 10 con; 0-3 aty)
% Number of variables : 64 ( 0 sgn 56 !; 8 ?; 64 :)
% 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 * vTerm ) ) > $o ).
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,
vB: vTy ).
tff(func_def_11,type,
vIfelse: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_12,type,
vt1: vTerm ).
tff(func_def_13,type,
vreduce: vTerm > vOptTerm ).
tff(func_def_14,type,
vplusop: ( vTerm * vTerm ) > vTerm ).
tff(func_def_15,type,
vgetTerm: vOptTerm > vTerm ).
tff(func_def_16,type,
sK1: vTy ).
tff(func_def_17,type,
sK2: vTerm ).
tff(func_def_18,type,
sK3: vTerm > vTerm ).
tff(func_def_19,type,
sK4: vTerm > vTerm ).
tff(func_def_20,type,
sK5: vTerm > vTerm ).
tff(func_def_21,type,
sK6: vTerm > vTerm ).
tff(func_def_22,type,
sK7: vTerm > vTerm ).
tff(func_def_23,type,
sK8: vTerm > vTerm ).
tff(func_def_24,type,
sK9: vTerm > vTerm ).
tff(func_def_25,type,
sK10: vTerm > vTerm ).
tff(func_def_26,type,
sK11: vOptTerm > vTerm ).
tff(func_def_27,type,
sK12: vTerm > vTerm ).
tff(func_def_28,type,
sK13: vTerm > vTerm ).
tff(func_def_29,type,
sK14: vTerm > vTerm ).
tff(func_def_30,type,
sK15: vTerm > vTerm ).
tff(func_def_31,type,
sK16: vTerm ).
tff(func_def_32,type,
sK17: vTerm ).
tff(func_def_33,type,
sK18: vTerm > vTerm ).
tff(func_def_34,type,
sK19: vTerm > vTerm ).
tff(func_def_35,type,
sK20: vTerm > vTerm ).
tff(func_def_36,type,
sK21: vTerm > vTerm ).
tff(func_def_37,type,
sK22: vTerm > vTerm ).
tff(func_def_38,type,
sK23: vTerm > vTerm ).
tff(func_def_39,type,
sK24: vTerm > vTerm ).
tff(func_def_40,type,
sK25: vTerm > vTerm ).
tff(func_def_41,type,
sK26: vTerm > vTerm ).
tff(func_def_42,type,
sK27: vTerm > vTerm ).
tff(func_def_43,type,
sK28: vTerm > vTerm ).
tff(func_def_44,type,
sK29: vTerm > vTerm ).
tff(func_def_45,type,
sK30: vTerm > vTerm ).
tff(func_def_46,type,
sK31: vTerm > vTerm ).
tff(func_def_47,type,
sK32: vTerm > vTerm ).
tff(func_def_48,type,
sK33: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_49,type,
sK34: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_50,type,
sK35: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_51,type,
sK36: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_52,type,
sK37: vTerm > vTerm ).
tff(func_def_53,type,
sK38: vOptTerm > vTerm ).
tff(f106,axiom,
! [X0: vTy,X1: vTerm] :
( ( ( vreduce(vPred(vt1)) = vsomeTerm(X1) )
& vptchecksimple(vPred(vt1),X0)
& ! [X2: vTerm] : ( vt1 != vSucc(X2) )
& ( vt1 != vZero )
& visSomeTerm(vreduce(vt1)) )
=> vptchecksimple(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Preservation-Pred-t1-isSomeTerm-True') ).
tff(f107,axiom,
! [X0: vTy,X1: vTerm] :
( ( ( vreduce(vPred(vt1)) = vsomeTerm(X1) )
& vptchecksimple(vPred(vt1),X0)
& ! [X2: vTerm] : ( vt1 != vSucc(X2) )
& ( vt1 != vZero )
& ~ visSomeTerm(vreduce(vt1)) )
=> vptchecksimple(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Preservation-Pred-t1-isSomeTerm-False') ).
tff(f108,conjecture,
! [X0: vTy,X1: vTerm] :
( ( ( vreduce(vPred(vt1)) = vsomeTerm(X1) )
& vptchecksimple(vPred(vt1),X0)
& ! [X2: vTerm] : ( vt1 != vSucc(X2) )
& ( vt1 != vZero ) )
=> vptchecksimple(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Preservation-Pred-t1') ).
tff(f109,negated_conjecture,
~ ! [X0: vTy,X1: vTerm] :
( ( ( vreduce(vPred(vt1)) = vsomeTerm(X1) )
& vptchecksimple(vPred(vt1),X0)
& ! [X2: vTerm] : ( vt1 != vSucc(X2) )
& ( vt1 != vZero ) )
=> vptchecksimple(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f108]) ).
tff(f112,plain,
? [X0: vTy,X1: vTerm] :
( ( vreduce(vPred(vt1)) = vsomeTerm(X1) )
& vptchecksimple(vPred(vt1),X0)
& ! [X2: vTerm] : ( vt1 != vSucc(X2) )
& ( vt1 != vZero )
& ~ vptchecksimple(X1,X0) ),
inference(ennf_transformation,[],[f109]) ).
tff(f113,plain,
? [X0: vTy,X1: vTerm] :
( ( vreduce(vPred(vt1)) = vsomeTerm(X1) )
& vptchecksimple(vPred(vt1),X0)
& ! [X2: vTerm] : ( vt1 != vSucc(X2) )
& ( vt1 != vZero )
& ~ vptchecksimple(X1,X0) ),
inference(flattening,[],[f112]) ).
tff(f131,plain,
! [X0: vTy,X1: vTerm] :
( ( vsomeTerm(X1) != vreduce(vPred(vt1)) )
| ~ vptchecksimple(vPred(vt1),X0)
| ? [X2: vTerm] : ( vSucc(X2) = vt1 )
| ( vZero = vt1 )
| visSomeTerm(vreduce(vt1))
| vptchecksimple(X1,X0) ),
inference(ennf_transformation,[],[f107]) ).
tff(f132,plain,
! [X0: vTy,X1: vTerm] :
( ( vsomeTerm(X1) != vreduce(vPred(vt1)) )
| ~ vptchecksimple(vPred(vt1),X0)
| ? [X2: vTerm] : ( vSucc(X2) = vt1 )
| ( vZero = vt1 )
| visSomeTerm(vreduce(vt1))
| vptchecksimple(X1,X0) ),
inference(flattening,[],[f131]) ).
tff(f133,plain,
! [X0: vTy,X1: vTerm] :
( ( vsomeTerm(X1) != vreduce(vPred(vt1)) )
| ~ vptchecksimple(vPred(vt1),X0)
| ? [X2: vTerm] : ( vSucc(X2) = vt1 )
| ( vZero = vt1 )
| ~ visSomeTerm(vreduce(vt1))
| vptchecksimple(X1,X0) ),
inference(ennf_transformation,[],[f106]) ).
tff(f134,plain,
! [X0: vTy,X1: vTerm] :
( ( vsomeTerm(X1) != vreduce(vPred(vt1)) )
| ~ vptchecksimple(vPred(vt1),X0)
| ? [X2: vTerm] : ( vSucc(X2) = vt1 )
| ( vZero = vt1 )
| ~ visSomeTerm(vreduce(vt1))
| vptchecksimple(X1,X0) ),
inference(flattening,[],[f133]) ).
tff(f169,plain,
( ( vreduce(vPred(vt1)) = vsomeTerm(sK2) )
& vptchecksimple(vPred(vt1),sK1)
& ! [X2: vTerm] : ( vt1 != vSucc(X2) )
& ( vt1 != vZero )
& ~ vptchecksimple(sK2,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f113]) ).
tff(f175,plain,
! [X0: vTy,X1: vTerm] :
( ( vsomeTerm(X1) != vreduce(vPred(vt1)) )
| ~ vptchecksimple(vPred(vt1),X0)
| ( vt1 = vSucc(sK16) )
| ( vZero = vt1 )
| visSomeTerm(vreduce(vt1))
| vptchecksimple(X1,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X2,sK16)],[f132]) ).
tff(f176,plain,
! [X0: vTy,X1: vTerm] :
( ( vsomeTerm(X1) != vreduce(vPred(vt1)) )
| ~ vptchecksimple(vPred(vt1),X0)
| ( vt1 = vSucc(sK17) )
| ( vZero = vt1 )
| ~ visSomeTerm(vreduce(vt1))
| vptchecksimple(X1,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X2,sK17)],[f134]) ).
tff(f186,plain,
vreduce(vPred(vt1)) = vsomeTerm(sK2),
inference(cnf_transformation,[],[f169]) ).
tff(f187,plain,
vptchecksimple(vPred(vt1),sK1),
inference(cnf_transformation,[],[f169]) ).
tff(f188,plain,
! [X2: vTerm] : ( vSucc(X2) != vt1 ),
inference(cnf_transformation,[],[f169]) ).
tff(f189,plain,
vZero != vt1,
inference(cnf_transformation,[],[f169]) ).
tff(f190,plain,
~ vptchecksimple(sK2,sK1),
inference(cnf_transformation,[],[f169]) ).
tff(f231,plain,
! [X0: vTy,X1: vTerm] :
( ( vsomeTerm(X1) != vreduce(vPred(vt1)) )
| ~ vptchecksimple(vPred(vt1),X0)
| ( vt1 = vSucc(sK16) )
| ( vZero = vt1 )
| visSomeTerm(vreduce(vt1))
| vptchecksimple(X1,X0) ),
inference(cnf_transformation,[],[f175]) ).
tff(f232,plain,
! [X0: vTy,X1: vTerm] :
( ( vsomeTerm(X1) != vreduce(vPred(vt1)) )
| ~ vptchecksimple(vPred(vt1),X0)
| ( vt1 = vSucc(sK17) )
| ( vZero = vt1 )
| ~ visSomeTerm(vreduce(vt1))
| vptchecksimple(X1,X0) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_49,negated_conjecture,
~ vptchecksimple(sK2,sK1),
inference(cnf_transformation,[],[f190]) ).
tcf(c_50,negated_conjecture,
vZero != vt1,
inference(cnf_transformation,[],[f189]) ).
tcf(c_51,negated_conjecture,
! [X0_vTerm: vTerm] : vSucc(X0_vTerm) != vt1,
inference(cnf_transformation,[],[f188]) ).
tcf(c_52,negated_conjecture,
vptchecksimple(vPred(vt1),sK1),
inference(cnf_transformation,[],[f187]) ).
tcf(c_53,negated_conjecture,
vreduce(vPred(vt1)) = vsomeTerm(sK2),
inference(cnf_transformation,[],[f186]) ).
tcf(c_94,plain,
! [X0_vTerm: vTerm,X0_vTy: vTy] :
( visSomeTerm(vreduce(vt1))
| vptchecksimple(X0_vTerm,X0_vTy)
| ( vZero = vt1 )
| ( vSucc(sK16) = vt1 )
| ~ vptchecksimple(vPred(vt1),X0_vTy)
| ( vreduce(vPred(vt1)) != vsomeTerm(X0_vTerm) ) ),
inference(cnf_transformation,[],[f231]) ).
tcf(c_95,plain,
! [X0_vTerm: vTerm,X0_vTy: vTy] :
( vptchecksimple(X0_vTerm,X0_vTy)
| ( vZero = vt1 )
| ( vSucc(sK17) = vt1 )
| ~ visSomeTerm(vreduce(vt1))
| ~ vptchecksimple(vPred(vt1),X0_vTy)
| ( vreduce(vPred(vt1)) != vsomeTerm(X0_vTerm) ) ),
inference(cnf_transformation,[],[f232]) ).
tcf(c_209,plain,
! [X0_vTerm: vTerm,X0_vTy: vTy] :
( visSomeTerm(vreduce(vt1))
| vptchecksimple(X0_vTerm,X0_vTy)
| ( vreduce(vPred(vt1)) != vsomeTerm(X0_vTerm) )
| ~ vptchecksimple(vPred(vt1),X0_vTy)
| ( vSucc(sK16) = vt1 ) ),
inference(global_subsumption_just,[status(thm)],[c_94,c_50,c_94]) ).
tcf(c_210,plain,
! [X0_vTerm: vTerm,X0_vTy: vTy] :
( visSomeTerm(vreduce(vt1))
| vptchecksimple(X0_vTerm,X0_vTy)
| ( vSucc(sK16) = vt1 )
| ~ vptchecksimple(vPred(vt1),X0_vTy)
| ( vreduce(vPred(vt1)) != vsomeTerm(X0_vTerm) ) ),
inference(renaming,[status(thm)],[c_209]) ).
tcf(c_211,plain,
! [X0_vTerm: vTerm,X0_vTy: vTy] :
( vptchecksimple(X0_vTerm,X0_vTy)
| ( vreduce(vPred(vt1)) != vsomeTerm(X0_vTerm) )
| ~ vptchecksimple(vPred(vt1),X0_vTy)
| ~ visSomeTerm(vreduce(vt1))
| ( vSucc(sK17) = vt1 ) ),
inference(global_subsumption_just,[status(thm)],[c_95,c_50,c_95]) ).
tcf(c_212,plain,
! [X0_vTerm: vTerm,X0_vTy: vTy] :
( vptchecksimple(X0_vTerm,X0_vTy)
| ( vSucc(sK17) = vt1 )
| ~ visSomeTerm(vreduce(vt1))
| ~ vptchecksimple(vPred(vt1),X0_vTy)
| ( vreduce(vPred(vt1)) != vsomeTerm(X0_vTerm) ) ),
inference(renaming,[status(thm)],[c_211]) ).
tcf(c_498,plain,
! [X0_vTerm: vTerm,X0_vTy: vTy] :
( visSomeTerm(vreduce(vt1))
| vptchecksimple(X0_vTerm,X0_vTy)
| ~ vptchecksimple(vPred(vt1),X0_vTy)
| ( vreduce(vPred(vt1)) != vsomeTerm(X0_vTerm) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_210,c_51]) ).
tcf(c_499,plain,
! [X0_vTerm: vTerm,X0_vTy: vTy] :
( vptchecksimple(X0_vTerm,X0_vTy)
| ~ visSomeTerm(vreduce(vt1))
| ~ vptchecksimple(vPred(vt1),X0_vTy)
| ( vreduce(vPred(vt1)) != vsomeTerm(X0_vTerm) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_212,c_51]) ).
tcf(c_500,plain,
! [X0_vTerm: vTerm,X0_vTy: vTy] :
( ( vreduce(vPred(vt1)) != vsomeTerm(X0_vTerm) )
| ~ vptchecksimple(vPred(vt1),X0_vTy)
| vptchecksimple(X0_vTerm,X0_vTy) ),
inference(global_subsumption_just,[status(thm)],[c_498,c_499,c_498]) ).
tcf(c_501,plain,
! [X0_vTerm: vTerm,X0_vTy: vTy] :
( vptchecksimple(X0_vTerm,X0_vTy)
| ~ vptchecksimple(vPred(vt1),X0_vTy)
| ( vreduce(vPred(vt1)) != vsomeTerm(X0_vTerm) ) ),
inference(renaming,[status(thm)],[c_500]) ).
tcf(c_1088,plain,
! [X0_vTerm: vTerm,X0_vTy: vTy] :
( vptchecksimple(X0_vTerm,X0_vTy)
| ~ vptchecksimple(vPred(vt1),X0_vTy)
| ( vsomeTerm(X0_vTerm) != vsomeTerm(sK2) ) ),
inference(light_normalisation,[status(thm)],[c_501,c_53]) ).
tcf(c_3933,plain,
! [X0_vTy: vTy] :
( vptchecksimple(sK2,X0_vTy)
| ~ vptchecksimple(vPred(vt1),X0_vTy) ),
inference(equality_resolution,[status(thm)],[c_1088]) ).
tcf(c_3941,plain,
vptchecksimple(sK2,sK1),
inference(superposition,[status(thm)],[c_52,c_3933]) ).
tcf(c_3942,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3941,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM225_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n007.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Fri Sep 25 07:58:38 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.43 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
% 0.12/0.44
% 0.12/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.44
% 0.12/0.44 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 4.18/1.31 % SZS status Started for theBenchmark.p
% 4.18/1.31 % SZS status Theorem for theBenchmark.p
% 4.18/1.31
% 4.18/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.18/1.31
% 4.18/1.31 % ------ iProver source info
% 4.18/1.31
% 4.18/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 4.18/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.18/1.31 % git: non_committed_changes: false
% 4.18/1.31
% 4.18/1.31 % ------ Parsing...
% 4.18/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 4.18/1.31 %
% 4.18/1.31
% 4.18/1.31 % ------ Preprocessing... sup_sim: 1 pe_s pe_e sup_sim: 0 pe_s pe_e %
% 4.18/1.31
% 4.18/1.31 % ------ Preprocessing...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 4.18/1.31 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
% 4.18/1.31 %
% 4.18/1.31
% 4.18/1.31 % ------ Preprocessing...
% 4.18/1.31 % ------ Proving...
% 4.18/1.31 % ------ Problem Properties
% 4.18/1.31
% 4.18/1.31 %
% 4.18/1.31 % clauses 97
% 4.18/1.31 % conjectures 5
% 4.18/1.31 % EPR 11
% 4.18/1.31 % Horn 76
% 4.18/1.31 % unary 42
% 4.18/1.31 % binary 32
% 4.18/1.31 % lits 195
% 4.18/1.31 % lits eq 120
% 4.18/1.31 % fd_pure 0
% 4.18/1.31 % fd_pseudo 0
% 4.18/1.31 % fd_cond 8
% 4.18/1.31 % fd_pseudo_cond 9
% 4.18/1.31 % AC symbols 0
% 4.18/1.31
% 4.18/1.31 % ------ Schedule dynamic 5 is on
% 4.18/1.31
% 4.18/1.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.18/1.31
% 4.18/1.31
% 4.18/1.31 % ------
% 4.18/1.31 % Current options:
% 4.18/1.31 % ------
% 4.18/1.31
% 4.18/1.31
% 4.18/1.31 %
% 4.18/1.31
% 4.18/1.31 % ------ Proving...
% 4.18/1.31 %
% 4.18/1.31
% 4.18/1.31 % SZS status Theorem for theBenchmark.p
% 4.18/1.31
% 4.18/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.18/1.31
% 4.18/1.31
%------------------------------------------------------------------------------