%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM224_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 : n003.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 4.50s 1.33s
% Output : CNFRefutation 4.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 52 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 181 ( 41 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 91 ( 36 ~; 23 |; 24 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 74 ( 74 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 : 48 ( 48 usr; 9 con; 0-3 aty)
% Number of variables : 46 ( 0 sgn 40 !; 6 ?; 46 :)
% 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: vTerm > 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: vOptTerm > 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: vOptTerm > vTerm ).
tff(f36,axiom,
! [X0: vTerm,X1: vTerm] :
( ( vsomeTerm(X0) = vsomeTerm(X1) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-someTerm') ).
tff(f42,axiom,
! [X0: vTerm] :
( visNV(vSucc(X0))
<=> visNV(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','isNV-1') ).
tff(f66,axiom,
! [X0: vTerm] :
( visNV(X0)
=> ( vreduce(vPred(vSucc(X0))) = vsomeTerm(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reduce-7') ).
tff(f94,axiom,
! [X0: vTerm] :
( vptchecksimple(vSucc(X0),vNat)
=> vptchecksimple(X0,vNat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','TSucc_inv2') ).
tff(f97,axiom,
! [X0: vTerm,X1: vTy] :
( vptchecksimple(vPred(X0),X1)
=> ( X1 = vNat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','TPred_inv2') ).
tff(f106,axiom,
! [X0: vTerm] :
( visNV(X0)
=> vptchecksimple(X0,vNat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isNVisNat) ).
tff(f107,conjecture,
! [X0: vTerm,X1: vTy,X2: vTerm] :
( ( ( vreduce(vPred(vt1)) = vsomeTerm(X2) )
& vptchecksimple(vPred(vt1),X1)
& ( vt1 = vSucc(X0) )
& ( vt1 != vZero )
& visNV(X0) )
=> vptchecksimple(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Preservation-Pred-Succ-isNV-True') ).
tff(f108,negated_conjecture,
~ ! [X0: vTerm,X1: vTy,X2: vTerm] :
( ( ( vreduce(vPred(vt1)) = vsomeTerm(X2) )
& vptchecksimple(vPred(vt1),X1)
& ( vt1 = vSucc(X0) )
& ( vt1 != vZero )
& visNV(X0) )
=> vptchecksimple(X2,X1) ),
inference(negated_conjecture,[status(cth)],[f107]) ).
tff(f111,plain,
? [X0: vTerm,X1: vTy,X2: vTerm] :
( ( vreduce(vPred(vt1)) = vsomeTerm(X2) )
& vptchecksimple(vPred(vt1),X1)
& ( vt1 = vSucc(X0) )
& ( vt1 != vZero )
& visNV(X0)
& ~ vptchecksimple(X2,X1) ),
inference(ennf_transformation,[],[f108]) ).
tff(f112,plain,
? [X0: vTerm,X1: vTy,X2: vTerm] :
( ( vreduce(vPred(vt1)) = vsomeTerm(X2) )
& vptchecksimple(vPred(vt1),X1)
& ( vt1 = vSucc(X0) )
& ( vt1 != vZero )
& visNV(X0)
& ~ vptchecksimple(X2,X1) ),
inference(flattening,[],[f111]) ).
tff(f114,plain,
! [X0: vTerm] :
( ~ visNV(X0)
| vptchecksimple(X0,vNat) ),
inference(ennf_transformation,[],[f106]) ).
tff(f116,plain,
! [X0: vTerm] :
( ~ visNV(X0)
| ( vreduce(vPred(vSucc(X0))) = vsomeTerm(X0) ) ),
inference(ennf_transformation,[],[f66]) ).
tff(f123,plain,
! [X0: vTerm,X1: vTy] :
( ~ vptchecksimple(vPred(X0),X1)
| ( X1 = vNat ) ),
inference(ennf_transformation,[],[f97]) ).
tff(f134,plain,
! [X0: vTerm,X1: vTerm] :
( ( vsomeTerm(X1) != vsomeTerm(X0) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f36]) ).
tff(f140,plain,
! [X0: vTerm] :
( ~ vptchecksimple(vSucc(X0),vNat)
| vptchecksimple(X0,vNat) ),
inference(ennf_transformation,[],[f94]) ).
tff(f165,plain,
( ( vreduce(vPred(vt1)) = vsomeTerm(sK3) )
& vptchecksimple(vPred(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)],[f112]) ).
tff(f169,plain,
! [X0: vTerm] :
( ( ~ visNV(vSucc(X0))
| visNV(X0) )
& ( ~ visNV(X0)
| visNV(vSucc(X0)) ) ),
inference(nnf_transformation,[],[f42]) ).
tff(f180,plain,
vreduce(vPred(vt1)) = vsomeTerm(sK3),
inference(cnf_transformation,[],[f165]) ).
tff(f181,plain,
vptchecksimple(vPred(vt1),sK2),
inference(cnf_transformation,[],[f165]) ).
tff(f182,plain,
vt1 = vSucc(sK1),
inference(cnf_transformation,[],[f165]) ).
tff(f184,plain,
visNV(sK1),
inference(cnf_transformation,[],[f165]) ).
tff(f185,plain,
~ vptchecksimple(sK3,sK2),
inference(cnf_transformation,[],[f165]) ).
tff(f188,plain,
! [X0: vTerm] :
( ~ visNV(X0)
| vptchecksimple(X0,vNat) ),
inference(cnf_transformation,[],[f114]) ).
tff(f190,plain,
! [X0: vTerm] :
( ~ visNV(X0)
| ( vsomeTerm(X0) = vreduce(vPred(vSucc(X0))) ) ),
inference(cnf_transformation,[],[f116]) ).
tff(f201,plain,
! [X0: vTerm] :
( ~ visNV(X0)
| visNV(vSucc(X0)) ),
inference(cnf_transformation,[],[f169]) ).
tff(f203,plain,
! [X0: vTerm,X1: vTy] :
( ~ vptchecksimple(vPred(X0),X1)
| ( vNat = X1 ) ),
inference(cnf_transformation,[],[f123]) ).
tff(f224,plain,
! [X0: vTerm,X1: vTerm] :
( ( vsomeTerm(X1) != vsomeTerm(X0) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f134]) ).
tff(f229,plain,
! [X0: vTerm] :
( ~ vptchecksimple(vSucc(X0),vNat)
| vptchecksimple(X0,vNat) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_49,negated_conjecture,
~ vptchecksimple(sK3,sK2),
inference(cnf_transformation,[],[f185]) ).
tcf(c_50,negated_conjecture,
visNV(sK1),
inference(cnf_transformation,[],[f184]) ).
tcf(c_52,negated_conjecture,
vSucc(sK1) = vt1,
inference(cnf_transformation,[],[f182]) ).
tcf(c_53,negated_conjecture,
vptchecksimple(vPred(vt1),sK2),
inference(cnf_transformation,[],[f181]) ).
tcf(c_54,negated_conjecture,
vreduce(vPred(vt1)) = vsomeTerm(sK3),
inference(cnf_transformation,[],[f180]) ).
tcf(c_57,plain,
! [X0_vTerm: vTerm] :
( vptchecksimple(X0_vTerm,vNat)
| ~ visNV(X0_vTerm) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_59,plain,
! [X0_vTerm: vTerm] :
( ( vreduce(vPred(vSucc(X0_vTerm))) = vsomeTerm(X0_vTerm) )
| ~ visNV(X0_vTerm) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_69,plain,
! [X0_vTerm: vTerm] :
( visNV(vSucc(X0_vTerm))
| ~ visNV(X0_vTerm) ),
inference(cnf_transformation,[],[f201]) ).
tcf(c_72,plain,
! [X0_vTerm: vTerm,X0_vTy: vTy] :
( ( X0_vTy = vNat )
| ~ vptchecksimple(vPred(X0_vTerm),X0_vTy) ),
inference(cnf_transformation,[],[f203]) ).
tcf(c_93,plain,
! [X0_vTerm: vTerm,X1_vTerm: vTerm] :
( ( X0_vTerm = X1_vTerm )
| ( vsomeTerm(X0_vTerm) != vsomeTerm(X1_vTerm) ) ),
inference(cnf_transformation,[],[f224]) ).
tcf(c_98,plain,
! [X0_vTerm: vTerm] :
( vptchecksimple(X0_vTerm,vNat)
| ~ vptchecksimple(vSucc(X0_vTerm),vNat) ),
inference(cnf_transformation,[],[f229]) ).
tcf(c_2480,plain,
( visNV(vt1)
| ~ visNV(sK1) ),
inference(superposition,[status(thm)],[c_52,c_69]) ).
tcf(c_2481,plain,
visNV(vt1),
inference(forward_subsumption_resolution,[status(thm)],[c_2480,c_50]) ).
tcf(c_2525,plain,
! [X0_vTerm: vTerm] :
( vptchecksimple(X0_vTerm,vNat)
| ~ visNV(vSucc(X0_vTerm)) ),
inference(superposition,[status(thm)],[c_57,c_98]) ).
tcf(c_2550,plain,
( vptchecksimple(sK1,vNat)
| ~ visNV(vt1) ),
inference(superposition,[status(thm)],[c_52,c_2525]) ).
tcf(c_2551,plain,
vptchecksimple(sK1,vNat),
inference(forward_subsumption_resolution,[status(thm)],[c_2550,c_2481]) ).
tcf(c_2565,plain,
vNat = sK2,
inference(superposition,[status(thm)],[c_53,c_72]) ).
tcf(c_2569,plain,
~ vptchecksimple(sK3,vNat),
inference(demodulation,[status(thm)],[c_49,c_2565]) ).
tcf(c_2705,plain,
vreduce(vPred(vSucc(sK1))) = vsomeTerm(sK1),
inference(superposition,[status(thm)],[c_50,c_59]) ).
tcf(c_2710,plain,
vsomeTerm(sK1) = vsomeTerm(sK3),
inference(light_normalisation,[status(thm)],[c_2705,c_52,c_54]) ).
tcf(c_2760,plain,
! [X0_vTerm: vTerm] :
( ( X0_vTerm = sK3 )
| ( vsomeTerm(X0_vTerm) != vsomeTerm(sK1) ) ),
inference(superposition,[status(thm)],[c_2710,c_93]) ).
tcf(c_2800,plain,
sK1 = sK3,
inference(equality_resolution,[status(thm)],[c_2760]) ).
tcf(c_2815,plain,
~ vptchecksimple(sK1,vNat),
inference(demodulation,[status(thm)],[c_2569,c_2800]) ).
tcf(c_2816,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2815,c_2551]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COM224_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.19/0.44 % Computer : n003.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.45 % DateTime : Fri Sep 25 08:02:22 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.23/0.51 Running first-order theorem proving
% 0.23/0.51 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
% 0.23/0.53
% 0.23/0.53 % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.53
% 0.23/0.53 % Detected problem language: tptp
% 0.23/0.55 % Proving...
% 4.50/1.33 % SZS status Started for theBenchmark.p
% 4.50/1.33 % SZS status Theorem for theBenchmark.p
% 4.50/1.33
% 4.50/1.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.50/1.33
% 4.50/1.33 % ------ iProver source info
% 4.50/1.33
% 4.50/1.33 % git: date: 2026-07-19 20:42:38 +0200
% 4.50/1.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.50/1.33 % git: non_committed_changes: false
% 4.50/1.33
% 4.50/1.33 % ------ Parsing...
% 4.50/1.33 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 4.50/1.33 %
% 4.50/1.33
% 4.50/1.33 % ------ Preprocessing... sup_sim: 0 pe_s pe_e %
% 4.50/1.33
% 4.50/1.33 % ------ Preprocessing...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 4.50/1.33 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
% 4.50/1.33 %
% 4.50/1.33
% 4.50/1.33 % ------ Preprocessing...
% 4.50/1.33 % ------ Proving...
% 4.50/1.33 % ------ Problem Properties
% 4.50/1.33
% 4.50/1.33 %
% 4.50/1.33 % clauses 98
% 4.50/1.33 % conjectures 6
% 4.50/1.33 % EPR 13
% 4.50/1.33 % Horn 77
% 4.50/1.33 % unary 43
% 4.50/1.33 % binary 33
% 4.50/1.33 % lits 195
% 4.50/1.33 % lits eq 119
% 4.50/1.33 % fd_pure 0
% 4.50/1.33 % fd_pseudo 0
% 4.50/1.33 % fd_cond 8
% 4.50/1.33 % fd_pseudo_cond 9
% 4.50/1.33 % AC symbols 0
% 4.50/1.33
% 4.50/1.33 % ------ Schedule dynamic 5 is on
% 4.50/1.33
% 4.50/1.33 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.50/1.33
% 4.50/1.33
% 4.50/1.33 % ------
% 4.50/1.33 % Current options:
% 4.50/1.33 % ------
% 4.50/1.33
% 4.50/1.33
% 4.50/1.33 %
% 4.50/1.33
% 4.50/1.33 % ------ Proving...
% 4.50/1.33 %
% 4.50/1.33
% 4.50/1.33 % SZS status Theorem for theBenchmark.p
% 4.50/1.33
% 4.50/1.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.50/1.33
% 4.50/1.33
%------------------------------------------------------------------------------