%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SCT159+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n014.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 02:40:54 PM UTC 2026
% Result : Theorem 10.31s 2.76s
% Output : CNFRefutation 10.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 15 unt; 0 def)
% Number of atoms : 78 ( 3 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 77 ( 35 ~; 29 |; 6 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-4 aty)
% Number of variables : 92 ( 0 sgn 86 !; 6 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__indi) ).
fof(f13,axiom,
! [X0,X1,X2,X3] :
( c_Finite__Set_Ofinite(X3,X2)
=> c_Finite__Set_Ofinite(X1,c_Set_Oimage(X3,X1,X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageI) ).
fof(f110,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
=> ( c_Finite__Set_Ofinite(X2,X0)
=> c_Finite__Set_Ofinite(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__subset) ).
fof(f173,axiom,
! [X0] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
<=> ? [X1] :
! [X2] :
( c_member(tc_Nat_Onat,X2,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).
fof(f195,axiom,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__UNIV) ).
fof(f209,axiom,
! [X0,X1,X2,X3,X4] :
( X4 = hAPP(X3,X2)
=> c_member(X1,X4,c_Set_Oimage(X0,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__eqI) ).
fof(f243,axiom,
! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(f580,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(X3,X2) != X4
| c_member(X1,X4,c_Set_Oimage(X0,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))) ),
inference(ennf_transformation,[],[f209]) ).
fof(f590,plain,
! [X0,X1,X2,X3] :
( ~ c_Finite__Set_Ofinite(X3,X2)
| c_Finite__Set_Ofinite(X1,c_Set_Oimage(X3,X1,X0,X2)) ),
inference(ennf_transformation,[],[f13]) ).
fof(f716,plain,
! [X0] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
<=> ? [X1] :
! [X2] :
( ~ c_member(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
inference(ennf_transformation,[],[f173]) ).
fof(f720,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| ~ c_Finite__Set_Ofinite(X2,X0)
| c_Finite__Set_Ofinite(X2,X1) ),
inference(ennf_transformation,[],[f110]) ).
fof(f721,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| ~ c_Finite__Set_Ofinite(X2,X0)
| c_Finite__Set_Ofinite(X2,X1) ),
inference(flattening,[],[f720]) ).
fof(f991,plain,
! [X0] :
( ( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ? [X1] :
! [X2] :
( ~ c_member(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) )
& ( ! [X1] :
? [X2] :
( c_member(tc_Nat_Onat,X2,X0)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) )
| c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ) ),
inference(nnf_transformation,[],[f716]) ).
fof(f992,plain,
! [X0] :
( ( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ? [X3] :
! [X4] :
( ~ c_member(tc_Nat_Onat,X4,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ) )
& ( ! [X1] :
? [X2] :
( c_member(tc_Nat_Onat,X2,X0)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) )
| c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ) ),
inference(rectify,[],[f991]) ).
fof(f993,plain,
! [X0] :
( ( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ! [X4] :
( ~ c_member(tc_Nat_Onat,X4,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,sK23(X0)) ) )
& ( ! [X1] :
( c_member(tc_Nat_Onat,sK22(X0,X1),X0)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK22(X0,X1),X1) )
| c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22,sK23]),skolemize(X2,sK22(X0,X1)),skolemize(X3,sK23(X0))],[f992]) ).
fof(f1109,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(X3,X2) != X4
| c_member(X1,X4,c_Set_Oimage(X0,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))) ),
inference(cnf_transformation,[],[f580]) ).
fof(f1127,plain,
! [X2,X3,X0,X1] :
( ~ c_Finite__Set_Ofinite(X3,X2)
| c_Finite__Set_Ofinite(X1,c_Set_Oimage(X3,X1,X0,X2)) ),
inference(cnf_transformation,[],[f590]) ).
fof(f1180,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
inference(cnf_transformation,[],[f195]) ).
fof(f1232,plain,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
inference(cnf_transformation,[],[f12]) ).
fof(f1333,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X0),X0),
inference(cnf_transformation,[],[f243]) ).
fof(f1396,plain,
! [X0,X4] :
( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ~ c_member(tc_Nat_Onat,X4,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,sK23(X0)) ),
inference(cnf_transformation,[],[f993]) ).
fof(f1403,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| ~ c_Finite__Set_Ofinite(X2,X0)
| c_Finite__Set_Ofinite(X2,X1) ),
inference(cnf_transformation,[],[f721]) ).
fof(f1620,plain,
! [X2,X3,X0,X1] : c_member(X1,hAPP(X3,X2),c_Set_Oimage(X0,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))),
inference(equality_resolution,[],[f1109]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_member(X0,hAPP(X1,X2),c_Set_Oimage(X3,X0,X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f1620]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Finite__Set_Ofinite(X2,c_Set_Oimage(X0,X2,X3,X1))
| ~ c_Finite__Set_Ofinite(X0,X1) ),
inference(cnf_transformation,[],[f1127]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X1,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))),
inference(cnf_transformation,[],[f1180]) ).
tcf(c_219,plain,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
inference(cnf_transformation,[],[f1232]) ).
tcf(c_320,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X0),X0),
inference(cnf_transformation,[],[f1333]) ).
tcf(c_383,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK23(X1))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| ~ c_member(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f1396]) ).
tcf(c_388,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Finite__Set_Ofinite(X0,X1)
| ~ c_Finite__Set_Ofinite(X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X1,X2) ),
inference(cnf_transformation,[],[f1403]) ).
tcf(c_25793,plain,
! [X0: $i] :
( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ~ c_member(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK23(X0)),X0) ),
inference(superposition,[status(thm)],[c_383,c_320]) ).
tcf(c_26122,plain,
! [X0: $i,X1: $i] :
( c_Finite__Set_Ofinite(X0,X1)
| ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) ),
inference(superposition,[status(thm)],[c_167,c_388]) ).
tcf(c_26178,plain,
! [X0: $i] : c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,X0),
inference(superposition,[status(thm)],[c_219,c_26122]) ).
tcf(c_36939,plain,
! [X0: $i] : ~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Set_Oimage(X0,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))),
inference(superposition,[status(thm)],[c_96,c_25793]) ).
tcf(c_36956,plain,
! [X0: $i] : ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))),
inference(superposition,[status(thm)],[c_114,c_36939]) ).
tcf(c_36967,plain,
$false,
inference(superposition,[status(thm)],[c_26178,c_36956]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT159+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n014.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Thu Sep 24 08:54:48 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 0.09/0.43
% 0.09/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.43
% 0.09/0.43 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 10.31/2.76 % SZS status Started for theBenchmark.p
% 10.31/2.76 % SZS status Theorem for theBenchmark.p
% 10.31/2.76
% 10.31/2.76 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.31/2.76
% 10.31/2.76 % ------ iProver source info
% 10.31/2.76
% 10.31/2.76 % git: date: 2026-07-19 20:42:38 +0200
% 10.31/2.76 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.31/2.76 % git: non_committed_changes: false
% 10.31/2.76
% 10.31/2.76 % ------ Parsing...
% 10.31/2.76 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.31/2.76
% 10.31/2.76 % ------ Preprocessing... sup_sim: 28 sf_s rm: 2 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 2 sf_s rm: 3 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 10.31/2.76
% 10.31/2.76 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.31/2.76
% 10.31/2.76 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.31/2.76 % ------ Proving...
% 10.31/2.76 % ------ Problem Properties
% 10.31/2.76
% 10.31/2.76 %
% 10.31/2.76 % clauses 322
% 10.31/2.76 % conjectures 0
% 10.31/2.76 % EPR 22
% 10.31/2.76 % Horn 241
% 10.31/2.76 % unary 63
% 10.31/2.76 % binary 116
% 10.31/2.76 % lits 777
% 10.31/2.76 % lits eq 218
% 10.31/2.76 % fd_pure 0
% 10.31/2.76 % fd_pseudo 0
% 10.31/2.76 % fd_cond 11
% 10.31/2.76 % fd_pseudo_cond 38
% 10.31/2.76 % AC symbols 0
% 10.31/2.76
% 10.31/2.76 % ------ Schedule dynamic 5 is on
% 10.31/2.76
% 10.31/2.76 % ------ no conjectures: strip conj schedule
% 10.31/2.76
% 10.31/2.76 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 10.31/2.76
% 10.31/2.76
% 10.31/2.76 % ------
% 10.31/2.76 % Current options:
% 10.31/2.76 % ------
% 10.31/2.76
% 10.31/2.76
% 10.31/2.76 %
% 10.31/2.76
% 10.31/2.76 % ------ Proving...
% 10.31/2.76 %
% 10.31/2.76
% 10.31/2.76 % SZS status Theorem for theBenchmark.p
% 10.31/2.76
% 10.31/2.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.31/2.76
% 10.31/2.76
%------------------------------------------------------------------------------