%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWW198+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n015.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 03:29:14 PM UTC 2026
% Result : Theorem 8.01s 9.25s
% Output : CNFRefutation 8.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 17 unt; 0 def)
% Number of atoms : 39 ( 24 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 10 |; 3 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 25 ( 0 sgn 20 !; 5 ?; 2 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o) ).
fof(f49,axiom,
! [X0] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0)
<=> ? [X1] : X0 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__Suc__mult__two__ex) ).
fof(f224,axiom,
! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(f736,axiom,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(f741,axiom,
! [X0] : c_Int_OBit1(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(f1186,conjecture,
? [X0] : v_na____ = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1187,negated_conjecture,
~ ? [X0] : v_na____ = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0)),
inference(negated_conjecture,[status(cth)],[f1186]) ).
fof(f2197,plain,
! [X0] : v_na____ != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0)),
inference(ennf_transformation,[],[f1187]) ).
fof(f2241,plain,
! [X0] :
( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0)
| ? [X1] : X0 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)) )
& ( ! [X1] : c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)) != X0
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0) ) ),
inference(nnf_transformation,[],[f49]) ).
fof(f2242,plain,
! [X0] :
( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0)
| ? [X2] : c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = X0 )
& ( ! [X1] : c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)) != X0
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0) ) ),
inference(rectify,[],[f2241]) ).
fof(f2243,plain,
! [X0] :
( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0)
| c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),sK14(X0))) = X0 )
& ( ! [X1] : c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)) != X0
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X2,sK14(X0))],[f2242]) ).
fof(f2661,plain,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
inference(cnf_transformation,[],[f1]) ).
fof(f2725,plain,
! [X0] :
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0)
| c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),sK14(X0))) = X0 ),
inference(cnf_transformation,[],[f2243]) ).
fof(f2971,plain,
! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
inference(cnf_transformation,[],[f224]) ).
fof(f3741,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f736]) ).
fof(f3746,plain,
! [X0] : c_Int_OBit1(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
inference(cnf_transformation,[],[f741]) ).
fof(f4434,plain,
! [X0] : v_na____ != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0)),
inference(cnf_transformation,[],[f2197]) ).
fof(f4472,plain,
! [X0] :
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),sK14(X0))) = X0 ),
inference(definition_unfolding,[],[f2725,f3741,f2971,f3746]) ).
fof(f4783,plain,
! [X0] : v_na____ != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X0)),
inference(definition_unfolding,[],[f4434,f3741,f2971,f3746]) ).
tcf(c_49,negated_conjecture,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
inference(cnf_transformation,[],[f2661]) ).
tcf(c_105,plain,
! [X0: $i] :
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),sK14(X0))) = X0 ) ),
inference(cnf_transformation,[],[f4472]) ).
tcf(c_1752,negated_conjecture,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X0)) != v_na____,
inference(cnf_transformation,[],[f4783]) ).
tcf(c_3245,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),sK14(v_na____))) = v_na____ ) ),
inference(instantiation,[status(thm)],[c_105]) ).
tcf(c_6885,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),sK14(v_na____))) != v_na____,
inference(instantiation,[status(thm)],[c_1752]) ).
tcf(c_6886,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_6885,c_3245,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW198+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.38 % Computer : n015.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Thu Sep 24 21:46:22 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 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
% 0.15/5.43
% 0.15/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.43
% 0.15/5.44 % Detected problem language: tptp
% 0.15/5.45 % Proving...
% 8.01/9.25 % SZS status Started for theBenchmark.p
% 8.01/9.25 % SZS status Theorem for theBenchmark.p
% 8.01/9.25
% 8.01/9.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.01/9.25
% 8.01/9.25 % ------ iProver source info
% 8.01/9.25
% 8.01/9.25 % git: date: 2026-07-19 20:42:38 +0200
% 8.01/9.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.01/9.25 % git: non_committed_changes: false
% 8.01/9.25
% 8.01/9.25 % ------ Parsing...
% 8.01/9.25 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.01/9.25
% 8.01/9.25 % ------ Preprocessing... sup_sim: 0 sf_s rm: 31 0s sf_e sup_sim: 0 sf_s rm: 6 0s sf_e %
% 8.01/9.25
% 8.01/9.25 % ------ Preprocessing...%
% 8.01/9.25
% 8.01/9.25 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.01/9.25 % ------ Proving...
% 8.01/9.25 % ------ Problem Properties
% 8.01/9.25
% 8.01/9.25 %
% 8.01/9.25 % clauses 1419
% 8.01/9.25 % conjectures 71
% 8.01/9.25 % EPR 242
% 8.01/9.25 % Horn 1207
% 8.01/9.25 % unary 374
% 8.01/9.25 % binary 437
% 8.01/9.25 % lits 3520
% 8.01/9.25 % lits eq 664
% 8.01/9.25 % fd_pure 0
% 8.01/9.25 % fd_pseudo 0
% 8.01/9.25 % fd_cond 53
% 8.01/9.25 % fd_pseudo_cond 96
% 8.01/9.25 % AC symbols 0
% 8.01/9.25
% 8.01/9.25 % ------ Input Options Time Limit: Unbounded
% 8.01/9.25
% 8.01/9.25
% 8.01/9.25 % ------
% 8.01/9.25 % Current options:
% 8.01/9.25 % ------
% 8.01/9.25
% 8.01/9.25
% 8.01/9.25 %
% 8.01/9.25
% 8.01/9.25 % ------ Proving...
% 8.01/9.25 %
% 8.01/9.25
% 8.01/9.25 % SZS status Theorem for theBenchmark.p
% 8.01/9.25
% 8.01/9.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.01/9.25
% 8.01/9.25
%------------------------------------------------------------------------------