%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SCT161+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 : n016.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 31.03s 5.79s
% Output : CNFRefutation 31.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 12 unt; 0 def)
% Number of atoms : 68 ( 3 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 68 ( 31 ~; 24 |; 7 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-4 aty)
% Number of variables : 78 ( 0 sgn 72 !; 6 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
fof(f83,axiom,
! [X0,X1,X2,X3,X4] :
( X4 = hAPP(X3,X2)
=> hBOOL(hAPP(hAPP(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(f149,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(f182,axiom,
! [X0] :
( c_Finite__Set_Ofinite(tc_Option_Ooption(X0),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X0),tc_HOL_Obool)))
<=> c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__option__UNIV) ).
fof(f216,axiom,
! [X0] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
<=> ? [X1] :
! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
fof(f227,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(f384,axiom,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).
fof(f639,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(X3,X2) != X4
| hBOOL(hAPP(hAPP(c_member(X1),X4),c_Set_Oimage(X0,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))))) ),
inference(ennf_transformation,[],[f83]) ).
fof(f710,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,[],[f149]) ).
fof(f815,plain,
! [X0] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
<=> ? [X1] :
! [X2] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ) ),
inference(ennf_transformation,[],[f216]) ).
fof(f1150,plain,
! [X0] :
( ( ~ c_Finite__Set_Ofinite(tc_Option_Ooption(X0),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X0),tc_HOL_Obool)))
| c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) )
& ( ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(tc_Option_Ooption(X0),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X0),tc_HOL_Obool))) ) ),
inference(nnf_transformation,[],[f182]) ).
fof(f1164,plain,
! [X0] :
( ( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ? [X1] :
! [X2] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ) )
& ( ! [X1] :
? [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) )
| c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ) ),
inference(nnf_transformation,[],[f815]) ).
fof(f1165,plain,
! [X0] :
( ( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ? [X3] :
! [X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)) ) )
& ( ! [X1] :
? [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) )
| c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ) ),
inference(rectify,[],[f1164]) ).
fof(f1166,plain,
! [X0] :
( ( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ! [X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),sK31(X0))) ) )
& ( ! [X1] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK30(X0,X1)),X0))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK30(X0,X1)),X1)) )
| c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30,sK31]),skolemize(X2,sK30(X0,X1)),skolemize(X3,sK31(X0))],[f1165]) ).
fof(f1409,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(X3,X2) != X4
| hBOOL(hAPP(hAPP(c_member(X1),X4),c_Set_Oimage(X0,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))))) ),
inference(cnf_transformation,[],[f639]) ).
fof(f1553,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,[],[f710]) ).
fof(f1597,plain,
! [X0] :
( ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(tc_Option_Ooption(X0),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X0),tc_HOL_Obool))) ),
inference(cnf_transformation,[],[f1150]) ).
fof(f1643,plain,
! [X0,X4] :
( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),sK31(X0))) ),
inference(cnf_transformation,[],[f1166]) ).
fof(f1663,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,[],[f227]) ).
fof(f1880,plain,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)),X0)),
inference(cnf_transformation,[],[f384]) ).
fof(f2108,plain,
! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(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,[],[f1409]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(hAPP(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,[],[f2108]) ).
tcf(c_293,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,[],[f1553]) ).
tcf(c_331,plain,
! [X0: $i] :
( c_Finite__Set_Ofinite(tc_Option_Ooption(X0),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X0),tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) ),
inference(cnf_transformation,[],[f1597]) ).
tcf(c_380,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),sK31(X1)))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X0),X1)) ),
inference(cnf_transformation,[],[f1643]) ).
tcf(c_398,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,[],[f1663]) ).
tcf(c_611,negated_conjecture,
! [X0: $i,X1: $i] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X1)),
inference(cnf_transformation,[],[f1880]) ).
tcf(c_33124,plain,
! [X0: $i,X1: $i] :
( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),sK31(X1))),X1)) ),
inference(superposition,[status(thm)],[c_380,c_611]) ).
tcf(c_33651,plain,
! [X0: $i,X1: $i] : ~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Set_Oimage(X0,tc_Nat_Onat,hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))),
inference(superposition,[status(thm)],[c_154,c_33124]) ).
tcf(c_34065,plain,
! [X0: $i] : ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))),
inference(superposition,[status(thm)],[c_293,c_33651]) ).
tcf(c_35200,plain,
! [X0: $i] : ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))),
inference(global_subsumption_just,[status(thm)],[c_331,c_34065]) ).
tcf(c_35206,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_398,c_35200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT161+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 09:00:14 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 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...
% 31.03/5.79 % SZS status Started for theBenchmark.p
% 31.03/5.79 % SZS status Theorem for theBenchmark.p
% 31.03/5.79
% 31.03/5.79 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 31.03/5.79
% 31.03/5.79 % ------ iProver source info
% 31.03/5.79
% 31.03/5.79 % git: date: 2026-07-19 20:42:38 +0200
% 31.03/5.79 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 31.03/5.79 % git: non_committed_changes: false
% 31.03/5.79
% 31.03/5.79 % ------ Parsing...
% 31.03/5.79 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 31.03/5.79
% 31.03/5.79 % ------ Preprocessing... sup_sim: 0 sf_s rm: 3 0s sf_e sup_sim: 0 sf_s rm: 2 0s sf_e %
% 31.03/5.79
% 31.03/5.79 % ------ Preprocessing...%
% 31.03/5.79
% 31.03/5.79 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 31.03/5.79 % ------ Proving...
% 31.03/5.79 % ------ Problem Properties
% 31.03/5.79
% 31.03/5.79 %
% 31.03/5.79 % clauses 579
% 31.03/5.79 % conjectures 42
% 31.03/5.79 % EPR 37
% 31.03/5.79 % Horn 471
% 31.03/5.79 % unary 146
% 31.03/5.79 % binary 187
% 31.03/5.79 % lits 1482
% 31.03/5.79 % lits eq 307
% 31.03/5.79 % fd_pure 0
% 31.03/5.79 % fd_pseudo 0
% 31.03/5.79 % fd_cond 11
% 31.03/5.79 % fd_pseudo_cond 97
% 31.03/5.79 % AC symbols 0
% 31.03/5.79
% 31.03/5.79 % ------ Input Options Time Limit: Unbounded
% 31.03/5.79
% 31.03/5.79
% 31.03/5.79 % ------
% 31.03/5.79 % Current options:
% 31.03/5.79 % ------
% 31.03/5.79
% 31.03/5.79
% 31.03/5.79 %
% 31.03/5.79
% 31.03/5.79 % ------ Proving...
% 31.03/5.79 %
% 31.03/5.79
% 31.03/5.79 % SZS status Theorem for theBenchmark.p
% 31.03/5.79
% 31.03/5.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 31.03/5.79
% 31.03/5.79
%------------------------------------------------------------------------------