%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM219_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 3.24s 1.18s
% Output : CNFRefutation 3.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 41 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 271 ( 62 equ)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 186 ( 75 ~; 74 |; 33 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 119 ( 119 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 7 prp; 0-3 aty)
% Number of functors : 48 ( 48 usr; 9 con; 0-3 aty)
% Number of variables : 60 ( 0 sgn 54 !; 6 ?; 60 :)
% 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: vTerm ).
tff(func_def_17,type,
sK2: vTy ).
tff(func_def_18,type,
sK3: 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: vOptTerm > vTerm ).
tff(func_def_24,type,
sK9: vTerm > vTerm ).
tff(func_def_25,type,
sK10: vTerm > vTerm ).
tff(func_def_26,type,
sK11: vTerm > 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 > vTerm ).
tff(func_def_32,type,
sK17: vTerm > 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 * vTerm ) ) > vTerm ).
tff(func_def_47,type,
sK32: ( vTerm * ( vTerm * 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 ).
tff(func_def_51,type,
sK36: vTerm > vTerm ).
tff(func_def_52,type,
sK37: vOptTerm > vTerm ).
tff(f106,axiom,
! [X0: vTerm,X1: vTy,X2: vTerm] :
( ( ( vreduce(vIszero(vt1)) = vsomeTerm(X2) )
& vptchecksimple(vIszero(vt1),X1)
& ( vt1 = vSucc(X0) )
& ( vt1 != vZero )
& ~ visNV(X0)
& visSomeTerm(vreduce(vSucc(X0))) )
=> vptchecksimple(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Preservation-Iszero-Succ-isNV-False-isSomeTerm-True') ).
tff(f107,axiom,
! [X0: vTerm,X1: vTy,X2: vTerm] :
( ( ( vreduce(vIszero(vt1)) = vsomeTerm(X2) )
& vptchecksimple(vIszero(vt1),X1)
& ( vt1 = vSucc(X0) )
& ( vt1 != vZero )
& ~ visNV(X0)
& ~ visSomeTerm(vreduce(vSucc(X0))) )
=> vptchecksimple(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Preservation-Iszero-Succ-isNV-False-isSomeTerm-False') ).
tff(f108,conjecture,
! [X0: vTerm,X1: vTy,X2: vTerm] :
( ( ( vreduce(vIszero(vt1)) = vsomeTerm(X2) )
& vptchecksimple(vIszero(vt1),X1)
& ( vt1 = vSucc(X0) )
& ( vt1 != vZero )
& ~ visNV(X0) )
=> vptchecksimple(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Preservation-Iszero-Succ-isNV-False') ).
tff(f109,negated_conjecture,
~ ! [X0: vTerm,X1: vTy,X2: vTerm] :
( ( ( vreduce(vIszero(vt1)) = vsomeTerm(X2) )
& vptchecksimple(vIszero(vt1),X1)
& ( vt1 = vSucc(X0) )
& ( vt1 != vZero )
& ~ visNV(X0) )
=> vptchecksimple(X2,X1) ),
inference(negated_conjecture,[status(cth)],[f108]) ).
tff(f112,plain,
? [X0: vTerm,X1: vTy,X2: vTerm] :
( ( vreduce(vIszero(vt1)) = vsomeTerm(X2) )
& vptchecksimple(vIszero(vt1),X1)
& ( vt1 = vSucc(X0) )
& ( vt1 != vZero )
& ~ visNV(X0)
& ~ vptchecksimple(X2,X1) ),
inference(ennf_transformation,[],[f109]) ).
tff(f113,plain,
? [X0: vTerm,X1: vTy,X2: vTerm] :
( ( vreduce(vIszero(vt1)) = vsomeTerm(X2) )
& vptchecksimple(vIszero(vt1),X1)
& ( vt1 = vSucc(X0) )
& ( vt1 != vZero )
& ~ visNV(X0)
& ~ vptchecksimple(X2,X1) ),
inference(flattening,[],[f112]) ).
tff(f128,plain,
! [X0: vTerm,X1: vTy,X2: vTerm] :
( ( vreduce(vIszero(vt1)) != vsomeTerm(X2) )
| ~ vptchecksimple(vIszero(vt1),X1)
| ( vSucc(X0) != vt1 )
| ( vZero = vt1 )
| visNV(X0)
| visSomeTerm(vreduce(vSucc(X0)))
| vptchecksimple(X2,X1) ),
inference(ennf_transformation,[],[f107]) ).
tff(f129,plain,
! [X0: vTerm,X1: vTy,X2: vTerm] :
( ( vreduce(vIszero(vt1)) != vsomeTerm(X2) )
| ~ vptchecksimple(vIszero(vt1),X1)
| ( vSucc(X0) != vt1 )
| ( vZero = vt1 )
| visNV(X0)
| visSomeTerm(vreduce(vSucc(X0)))
| vptchecksimple(X2,X1) ),
inference(flattening,[],[f128]) ).
tff(f130,plain,
! [X0: vTerm,X1: vTy,X2: vTerm] :
( ( vreduce(vIszero(vt1)) != vsomeTerm(X2) )
| ~ vptchecksimple(vIszero(vt1),X1)
| ( vSucc(X0) != vt1 )
| ( vZero = vt1 )
| visNV(X0)
| ~ visSomeTerm(vreduce(vSucc(X0)))
| vptchecksimple(X2,X1) ),
inference(ennf_transformation,[],[f106]) ).
tff(f131,plain,
! [X0: vTerm,X1: vTy,X2: vTerm] :
( ( vreduce(vIszero(vt1)) != vsomeTerm(X2) )
| ~ vptchecksimple(vIszero(vt1),X1)
| ( vSucc(X0) != vt1 )
| ( vZero = vt1 )
| visNV(X0)
| ~ visSomeTerm(vreduce(vSucc(X0)))
| vptchecksimple(X2,X1) ),
inference(flattening,[],[f130]) ).
tff(f169,plain,
( ( vreduce(vIszero(vt1)) = vsomeTerm(sK3) )
& vptchecksimple(vIszero(vt1),sK2)
& ( vt1 = vSucc(sK1) )
& ( vt1 != vZero )
& ~ visNV(sK1)
& ~ vptchecksimple(sK3,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f113]) ).
tff(f184,plain,
vreduce(vIszero(vt1)) = vsomeTerm(sK3),
inference(cnf_transformation,[],[f169]) ).
tff(f185,plain,
vptchecksimple(vIszero(vt1),sK2),
inference(cnf_transformation,[],[f169]) ).
tff(f186,plain,
vt1 = vSucc(sK1),
inference(cnf_transformation,[],[f169]) ).
tff(f187,plain,
vZero != vt1,
inference(cnf_transformation,[],[f169]) ).
tff(f188,plain,
~ visNV(sK1),
inference(cnf_transformation,[],[f169]) ).
tff(f189,plain,
~ vptchecksimple(sK3,sK2),
inference(cnf_transformation,[],[f169]) ).
tff(f229,plain,
! [X2: vTerm,X0: vTerm,X1: vTy] :
( ( vreduce(vIszero(vt1)) != vsomeTerm(X2) )
| ~ vptchecksimple(vIszero(vt1),X1)
| ( vSucc(X0) != vt1 )
| ( vZero = vt1 )
| visNV(X0)
| visSomeTerm(vreduce(vSucc(X0)))
| vptchecksimple(X2,X1) ),
inference(cnf_transformation,[],[f129]) ).
tff(f230,plain,
! [X2: vTerm,X0: vTerm,X1: vTy] :
( ( vreduce(vIszero(vt1)) != vsomeTerm(X2) )
| ~ vptchecksimple(vIszero(vt1),X1)
| ( vSucc(X0) != vt1 )
| ( vZero = vt1 )
| visNV(X0)
| ~ visSomeTerm(vreduce(vSucc(X0)))
| vptchecksimple(X2,X1) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_49,negated_conjecture,
~ vptchecksimple(sK3,sK2),
inference(cnf_transformation,[],[f189]) ).
tcf(c_50,negated_conjecture,
~ visNV(sK1),
inference(cnf_transformation,[],[f188]) ).
tcf(c_51,negated_conjecture,
vZero != vt1,
inference(cnf_transformation,[],[f187]) ).
tcf(c_52,negated_conjecture,
vSucc(sK1) = vt1,
inference(cnf_transformation,[],[f186]) ).
tcf(c_53,negated_conjecture,
vptchecksimple(vIszero(vt1),sK2),
inference(cnf_transformation,[],[f185]) ).
tcf(c_54,negated_conjecture,
vreduce(vIszero(vt1)) = vsomeTerm(sK3),
inference(cnf_transformation,[],[f184]) ).
tcf(c_94,plain,
! [X0_vTerm: vTerm,X0_vTy: vTy,X1_vTerm: vTerm] :
( visNV(X1_vTerm)
| vptchecksimple(X0_vTerm,X0_vTy)
| visSomeTerm(vreduce(vSucc(X1_vTerm)))
| ( vZero = vt1 )
| ~ vptchecksimple(vIszero(vt1),X0_vTy)
| ( vSucc(X1_vTerm) != vt1 )
| ( vreduce(vIszero(vt1)) != vsomeTerm(X0_vTerm) ) ),
inference(cnf_transformation,[],[f229]) ).
tcf(c_95,plain,
! [X0_vTerm: vTerm,X0_vTy: vTy,X1_vTerm: vTerm] :
( visNV(X1_vTerm)
| vptchecksimple(X0_vTerm,X0_vTy)
| ( vZero = vt1 )
| ~ vptchecksimple(vIszero(vt1),X0_vTy)
| ~ visSomeTerm(vreduce(vSucc(X1_vTerm)))
| ( vSucc(X1_vTerm) != vt1 )
| ( vreduce(vIszero(vt1)) != vsomeTerm(X0_vTerm) ) ),
inference(cnf_transformation,[],[f230]) ).
tcf(c_209,plain,
! [X0_vTerm: vTerm,X0_vTy: vTy,X1_vTerm: vTerm] :
( visNV(X1_vTerm)
| vptchecksimple(X0_vTerm,X0_vTy)
| ~ vptchecksimple(vIszero(vt1),X0_vTy)
| ( vSucc(X1_vTerm) != vt1 )
| ( vreduce(vIszero(vt1)) != vsomeTerm(X0_vTerm) ) ),
inference(global_subsumption_just,[status(thm)],[c_94,c_51,c_94,c_95]) ).
tcf(c_211,plain,
! [X0_vTerm: vTerm,X0_vTy: vTy,X1_vTerm: vTerm] :
( visNV(X1_vTerm)
| vptchecksimple(X0_vTerm,X0_vTy)
| ( vSucc(X1_vTerm) != vt1 )
| ( vreduce(vIszero(vt1)) != vsomeTerm(X0_vTerm) )
| ~ vptchecksimple(vIszero(vt1),X0_vTy) ),
inference(global_subsumption_just,[status(thm)],[c_95,c_209]) ).
tcf(c_212,plain,
! [X0_vTerm: vTerm,X0_vTy: vTy,X1_vTerm: vTerm] :
( visNV(X1_vTerm)
| vptchecksimple(X0_vTerm,X0_vTy)
| ~ vptchecksimple(vIszero(vt1),X0_vTy)
| ( vSucc(X1_vTerm) != vt1 )
| ( vreduce(vIszero(vt1)) != vsomeTerm(X0_vTerm) ) ),
inference(renaming,[status(thm)],[c_211]) ).
tcf(c_1128,plain,
! [X0_vTerm: vTerm,X0_vTy: vTy,X1_vTerm: vTerm] :
( visNV(X0_vTerm)
| vptchecksimple(X1_vTerm,X0_vTy)
| ~ vptchecksimple(vIszero(vt1),X0_vTy)
| ( vsomeTerm(X1_vTerm) != vsomeTerm(sK3) )
| ( vSucc(X0_vTerm) != vt1 ) ),
inference(light_normalisation,[status(thm)],[c_212,c_54]) ).
tcf(c_3154,plain,
! [X0_vTerm: vTerm,X0_vTy: vTy] :
( ~ iPr_def_10
| ( vsomeTerm(X0_vTerm) != vsomeTerm(sK3) )
| ~ vptchecksimple(vIszero(vt1),X0_vTy)
| vptchecksimple(X0_vTerm,X0_vTy) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_1128]) ).
tcf(c_3155,plain,
! [X0_vTerm: vTerm] :
( ~ iPr_def_11
| ( vSucc(X0_vTerm) != vt1 )
| visNV(X0_vTerm) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_1128]) ).
tcf(c_3156,plain,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_1128]) ).
tcf(c_3983,plain,
( visNV(sK1)
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_52,c_3155]) ).
tcf(c_3984,plain,
~ iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_3983,c_50]) ).
tcf(c_3985,plain,
iPr_def_10,
inference(backward_subsumption_resolution,[status(thm)],[c_3156,c_3984]) ).
tcf(c_3987,plain,
! [X0_vTerm: vTerm,X0_vTy: vTy] :
( vptchecksimple(X0_vTerm,X0_vTy)
| ~ vptchecksimple(vIszero(vt1),X0_vTy)
| ( vsomeTerm(X0_vTerm) != vsomeTerm(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_3154,c_3154,c_3985]) ).
tcf(c_3992,plain,
! [X0_vTy: vTy] :
( vptchecksimple(sK3,X0_vTy)
| ~ vptchecksimple(vIszero(vt1),X0_vTy) ),
inference(equality_resolution,[status(thm)],[c_3987]) ).
tcf(c_4000,plain,
vptchecksimple(sK3,sK2),
inference(superposition,[status(thm)],[c_53,c_3992]) ).
tcf(c_4001,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4000,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM219_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 07:58:23 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.42
% 0.14/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.42
% 0.14/0.42 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 3.24/1.18 % SZS status Started for theBenchmark.p
% 3.24/1.18 % SZS status Theorem for theBenchmark.p
% 3.24/1.18
% 3.24/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.24/1.18
% 3.24/1.18 % ------ iProver source info
% 3.24/1.18
% 3.24/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 3.24/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.24/1.18 % git: non_committed_changes: false
% 3.24/1.18
% 3.24/1.18 % ------ Parsing...
% 3.24/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 3.24/1.18 %
% 3.24/1.18
% 3.24/1.18 % ------ Preprocessing... sup_sim: 1 pe_s pe_e sup_sim: 0 pe_s pe_e %
% 3.24/1.18
% 3.24/1.18 % ------ Preprocessing...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 3.24/1.18 gs_s sp: 2 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
% 3.24/1.18 %
% 3.24/1.18
% 3.24/1.18 % ------ Preprocessing...
% 3.24/1.18 % ------ Proving...
% 3.24/1.18 % ------ Problem Properties
% 3.24/1.18
% 3.24/1.18 %
% 3.24/1.18 % clauses 100
% 3.24/1.18 % conjectures 6
% 3.24/1.18 % EPR 13
% 3.24/1.18 % Horn 78
% 3.24/1.18 % unary 43
% 3.24/1.18 % binary 33
% 3.24/1.18 % lits 202
% 3.24/1.18 % lits eq 121
% 3.24/1.18 % fd_pure 0
% 3.24/1.18 % fd_pseudo 0
% 3.24/1.18 % fd_cond 8
% 3.24/1.18 % fd_pseudo_cond 9
% 3.24/1.18 % AC symbols 0
% 3.24/1.18
% 3.24/1.18 % ------ Schedule dynamic 5 is on
% 3.24/1.18
% 3.24/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.24/1.18
% 3.24/1.18
% 3.24/1.18 % ------
% 3.24/1.18 % Current options:
% 3.24/1.18 % ------
% 3.24/1.18
% 3.24/1.18
% 3.24/1.18 %
% 3.24/1.18
% 3.24/1.18 % ------ Proving...
% 3.24/1.18 %
% 3.24/1.18
% 3.24/1.18 % SZS status Theorem for theBenchmark.p
% 3.24/1.18
% 3.24/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.24/1.18
%------------------------------------------------------------------------------