%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM213_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 : n005.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 4.40s 1.30s
% Output : CNFRefutation 4.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 76 ( 20 equ)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 33 ( 13 ~; 12 |; 5 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 37 ( 37 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 5 prp; 0-3 aty)
% Number of functors : 45 ( 45 usr; 6 con; 0-3 aty)
% Number of variables : 18 ( 0 sgn 15 !; 3 ?; 18 :)
% 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 > vTerm ).
tff(func_def_17,type,
sK2: vTerm > 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: 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: vOptTerm > vTerm ).
tff(func_def_44,type,
sK29: vTerm > vTerm ).
tff(func_def_45,type,
sK30: ( vTerm * ( vTerm * 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: vOptTerm > vTerm ).
tff(f26,axiom,
! [X0: vTerm] : ( vZero != vPred(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-Zero-Pred') ).
tff(f29,axiom,
! [X0: vTerm,X1: vTerm] : ( vSucc(X0) != vPred(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-Succ-Pred') ).
tff(f44,axiom,
! [X0: vTerm] :
( visNV(X0)
=> ( ? [X1: vTerm] :
( visNV(X1)
& ( X0 = vSucc(X1) ) )
| ( X0 = vZero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','isNV-true-INV') ).
tff(f106,conjecture,
( visNV(vPred(vt1))
=> vptchecksimple(vPred(vt1),vNat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','isNVisNat-Pred') ).
tff(f107,negated_conjecture,
~ ( visNV(vPred(vt1))
=> vptchecksimple(vPred(vt1),vNat) ),
inference(negated_conjecture,[status(cth)],[f106]) ).
tff(f110,plain,
( visNV(vPred(vt1))
& ~ vptchecksimple(vPred(vt1),vNat) ),
inference(ennf_transformation,[],[f107]) ).
tff(f127,plain,
! [X0: vTerm] :
( ~ visNV(X0)
| ? [X1: vTerm] :
( visNV(X1)
& ( X0 = vSucc(X1) ) )
| ( X0 = vZero ) ),
inference(ennf_transformation,[],[f44]) ).
tff(f128,plain,
! [X0: vTerm] :
( ~ visNV(X0)
| ? [X1: vTerm] :
( visNV(X1)
& ( X0 = vSucc(X1) ) )
| ( X0 = vZero ) ),
inference(flattening,[],[f127]) ).
tff(f162,plain,
! [X0: vTerm] :
( ~ visNV(X0)
| ( visNV(sK3(X0))
& ( vSucc(sK3(X0)) = X0 ) )
| ( X0 = vZero ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f128]) ).
tff(f175,plain,
visNV(vPred(vt1)),
inference(cnf_transformation,[],[f110]) ).
tff(f198,plain,
! [X0: vTerm] :
( ~ visNV(X0)
| ( vSucc(sK3(X0)) = X0 )
| ( vZero = X0 ) ),
inference(cnf_transformation,[],[f162]) ).
tff(f209,plain,
! [X0: vTerm,X1: vTerm] : ( vPred(X1) != vSucc(X0) ),
inference(cnf_transformation,[],[f29]) ).
tff(f210,plain,
! [X0: vTerm] : ( vZero != vPred(X0) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_50,negated_conjecture,
visNV(vPred(vt1)),
inference(cnf_transformation,[],[f175]) ).
tcf(c_71,plain,
! [X0_vTerm: vTerm] :
( ( X0_vTerm = vZero )
| ( vSucc(sK3(X0_vTerm)) = X0_vTerm )
| ~ visNV(X0_vTerm) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_83,plain,
! [X0_vTerm: vTerm,X1_vTerm: vTerm] : vSucc(X0_vTerm) != vPred(X1_vTerm),
inference(cnf_transformation,[],[f209]) ).
tcf(c_84,plain,
! [X0_vTerm: vTerm] : vPred(X0_vTerm) != vZero,
inference(cnf_transformation,[],[f210]) ).
tcf(c_3034,plain,
( ( vPred(vt1) = vZero )
| ( vSucc(sK3(vPred(vt1))) = vPred(vt1) ) ),
inference(superposition,[status(thm)],[c_50,c_71]) ).
tcf(c_3039,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3034,c_84,c_83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM213_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 : n005.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 08:00:17 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 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...
% 4.40/1.30 % SZS status Started for theBenchmark.p
% 4.40/1.30 % SZS status Theorem for theBenchmark.p
% 4.40/1.30
% 4.40/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.40/1.30
% 4.40/1.30 % ------ iProver source info
% 4.40/1.30
% 4.40/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 4.40/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.40/1.30 % git: non_committed_changes: false
% 4.40/1.30
% 4.40/1.30 % ------ Parsing...
% 4.40/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 4.40/1.30 %
% 4.40/1.30
% 4.40/1.30 % ------ Preprocessing... sup_sim: 0 pe_s pe_e %
% 4.40/1.30
% 4.40/1.30 % ------ Preprocessing...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 4.40/1.30 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
% 4.40/1.30 %
% 4.40/1.30
% 4.40/1.30 % ------ Preprocessing...
% 4.40/1.30 % ------ Proving...
% 4.40/1.30 % ------ Problem Properties
% 4.40/1.30
% 4.40/1.30 %
% 4.40/1.30 % clauses 93
% 4.40/1.30 % conjectures 2
% 4.40/1.30 % EPR 10
% 4.40/1.30 % Horn 72
% 4.40/1.30 % unary 39
% 4.40/1.30 % binary 33
% 4.40/1.30 % lits 188
% 4.40/1.30 % lits eq 115
% 4.40/1.30 % fd_pure 0
% 4.40/1.30 % fd_pseudo 0
% 4.40/1.30 % fd_cond 8
% 4.40/1.30 % fd_pseudo_cond 9
% 4.40/1.30 % AC symbols 0
% 4.40/1.30
% 4.40/1.30 % ------ Schedule dynamic 5 is on
% 4.40/1.30
% 4.40/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.40/1.30
% 4.40/1.30
% 4.40/1.30 % ------
% 4.40/1.30 % Current options:
% 4.40/1.30 % ------
% 4.40/1.30
% 4.40/1.30
% 4.40/1.30 %
% 4.40/1.30
% 4.40/1.30 % ------ Proving...
% 4.40/1.30 %
% 4.40/1.30
% 4.40/1.30 % SZS status Theorem for theBenchmark.p
% 4.40/1.30
% 4.40/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.40/1.30
% 4.40/1.30
%------------------------------------------------------------------------------