%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWW186+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 : n007.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 03:29:13 PM UTC 2026
% Result : Theorem 58.12s 14.46s
% Output : CNFRefutation 58.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 65 ( 22 unt; 0 def)
% Number of atoms : 130 ( 82 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 117 ( 52 ~; 46 |; 8 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 76 ( 0 sgn 76 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__0(X1)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__0) ).
fof(f5,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(X3,X0,X1)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
=> X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__eq__0__lemma) ).
fof(f12,axiom,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( c_Polynomial_OpCons(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
<=> ( X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
& X1 = c_Groups_Ozero__class_Ozero(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).
fof(f14,axiom,
! [X0,X1] :
( class_Groups_Ocomm__monoid__add(X1)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__poly__code_I1_J) ).
fof(f16,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__0(X1)
=> c_Polynomial_Osmult(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__0__right) ).
fof(f997,axiom,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Groups_Ocomm__monoid__add(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add) ).
fof(f1003,axiom,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Groups_Ozero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Ocomm__semiring__0__Groups_Ozero) ).
fof(f1179,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1180,axiom,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(f1181,conjecture,
( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
& v_a = c_Groups_Ozero__class_Ozero(t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
fof(f1182,negated_conjecture,
~ ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
& v_a = c_Groups_Ozero__class_Ozero(t_a) ),
inference(negated_conjecture,[status(cth)],[f1181]) ).
fof(f1183,axiom,
class_Rings_Ocomm__semiring__0(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).
fof(f1215,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(ennf_transformation,[],[f1179]) ).
fof(f1216,plain,
( v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| v_a != c_Groups_Ozero__class_Ozero(t_a) ),
inference(ennf_transformation,[],[f1182]) ).
fof(f1228,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(ennf_transformation,[],[f2]) ).
fof(f1240,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| ( c_Polynomial_OpCons(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
<=> ( X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
& X1 = c_Groups_Ozero__class_Ozero(X2) ) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f1244,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(X3,X0,X1)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f1245,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(X3,X0,X1)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(flattening,[],[f1244]) ).
fof(f1256,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Polynomial_Osmult(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f1319,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__0(X0)
| class_Groups_Ozero(X0) ),
inference(ennf_transformation,[],[f1003]) ).
fof(f1696,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__0(X0)
| class_Groups_Ocomm__monoid__add(X0) ),
inference(ennf_transformation,[],[f997]) ).
fof(f1708,plain,
! [X0,X1] :
( ~ class_Groups_Ocomm__monoid__add(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = X0 ),
inference(ennf_transformation,[],[f14]) ).
fof(f1753,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0)
| ( X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
& X1 = c_Groups_Ozero__class_Ozero(X2) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1
| c_Polynomial_OpCons(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) ) ),
inference(nnf_transformation,[],[f1240]) ).
fof(f1754,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0)
| ( X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
& X1 = c_Groups_Ozero__class_Ozero(X2) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1
| c_Polynomial_OpCons(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) ) ),
inference(flattening,[],[f1753]) ).
fof(f1909,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(cnf_transformation,[],[f1215]) ).
fof(f1910,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),
inference(cnf_transformation,[],[f1180]) ).
fof(f1911,plain,
( v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| v_a != c_Groups_Ozero__class_Ozero(t_a) ),
inference(cnf_transformation,[],[f1216]) ).
fof(f1912,plain,
class_Rings_Ocomm__semiring__0(t_a),
inference(cnf_transformation,[],[f1183]) ).
fof(f1952,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) ),
inference(cnf_transformation,[],[f1228]) ).
fof(f1967,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ozero(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(X2) = X1 ),
inference(cnf_transformation,[],[f1754]) ).
fof(f1971,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(X3,X0,X1)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1 ),
inference(cnf_transformation,[],[f1245]) ).
fof(f1980,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
inference(cnf_transformation,[],[f1256]) ).
fof(f2099,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__0(X0)
| class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f1319]) ).
fof(f2645,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__0(X0)
| class_Groups_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[],[f1696]) ).
fof(f2653,plain,
! [X0,X1] :
( ~ class_Groups_Ocomm__monoid__add(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = X0 ),
inference(cnf_transformation,[],[f1708]) ).
tcf(c_49,plain,
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = v_p )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
inference(cnf_transformation,[],[f1909]) ).
tcf(c_50,plain,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(cnf_transformation,[],[f1910]) ).
tcf(c_51,negated_conjecture,
( ( c_Groups_Ozero__class_Ozero(t_a) != v_a )
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != v_p ) ),
inference(cnf_transformation,[],[f1911]) ).
tcf(c_52,plain,
class_Rings_Ocomm__semiring__0(t_a),
inference(cnf_transformation,[],[f1912]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f1952]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ~ class_Groups_Ozero(X0)
| ( c_Polynomial_OpCons(X0,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ) ),
inference(cnf_transformation,[],[f1967]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 )
| ~ class_Rings_Ocomm__semiring__0(X0)
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X1,X2),c_Polynomial_OpCons(X0,X3,X2)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ) ),
inference(cnf_transformation,[],[f1971]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_Osmult(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f1980]) ).
tcf(c_232,plain,
! [X0: $i] :
( class_Groups_Ozero(X0)
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2099]) ).
tcf(c_745,plain,
! [X0: $i] :
( class_Groups_Ocomm__monoid__add(X0)
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2645]) ).
tcf(c_753,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1) = X1 )
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[],[f2653]) ).
tcf(c_103863,plain,
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_Rings_Ocomm__semiring__0(t_a) ),
inference(superposition,[status(thm)],[c_50,c_106]) ).
tcf(c_103877,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(forward_subsumption_resolution,[status(thm)],[c_103863,c_52]) ).
tcf(c_103899,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = v_p,
inference(backward_subsumption_resolution,[status(thm)],[c_49,c_103877]) ).
tcf(c_103901,plain,
c_Groups_Ozero__class_Ozero(t_a) != v_a,
inference(backward_subsumption_resolution,[status(thm)],[c_51,c_103899]) ).
tcf(c_182732,negated_conjecture,
c_Groups_Ozero__class_Ozero(t_a) != v_a,
inference(global_subsumption_just,[status(thm)],[c_51,c_103901]) ).
tcf(c_182736,plain,
class_Groups_Ozero(t_a),
inference(superposition,[status(thm)],[c_52,c_232]) ).
tcf(c_182744,plain,
class_Groups_Ocomm__monoid__add(t_a),
inference(superposition,[status(thm)],[c_52,c_745]) ).
tcf(c_185643,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),X0) = X0,
inference(superposition,[status(thm)],[c_182744,c_753]) ).
tcf(c_186324,plain,
! [X0: $i] : c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(superposition,[status(thm)],[c_52,c_88]) ).
tcf(c_186371,plain,
! [X0: $i] : c_Polynomial_Osmult(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(superposition,[status(thm)],[c_52,c_115]) ).
tcf(c_192651,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = v_p,
inference(global_subsumption_just,[status(thm)],[c_49,c_103899]) ).
tcf(c_192657,plain,
! [X0: $i] : c_Polynomial_Osmult(t_a,X0,v_p) = v_p,
inference(demodulation,[status(thm)],[c_186371,c_192651]) ).
tcf(c_192658,plain,
! [X0: $i] : c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,X0) = v_p,
inference(demodulation,[status(thm)],[c_186324,c_192651]) ).
tcf(c_192659,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),v_p,X0) = X0,
inference(demodulation,[status(thm)],[c_185643,c_192651]) ).
tcf(c_220179,plain,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) = v_p,
inference(light_normalisation,[status(thm)],[c_50,c_192651]) ).
tcf(c_220180,plain,
c_Polynomial_OpCons(t_a,v_a,v_p) = v_p,
inference(demodulation,[status(thm)],[c_220179,c_192657,c_192658,c_192659]) ).
tcf(c_220183,plain,
( ( c_Groups_Ozero__class_Ozero(t_a) = v_a )
| ~ class_Groups_Ozero(t_a)
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != v_p ) ),
inference(superposition,[status(thm)],[c_220180,c_102]) ).
tcf(c_220194,plain,
( ( c_Groups_Ozero__class_Ozero(t_a) = v_a )
| ~ class_Groups_Ozero(t_a) ),
inference(ground_joinability,[status(thm)],[c_220183,c_192651]) ).
tcf(c_220195,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_220194,c_182732,c_182736]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW186+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n007.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 21:38:54 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.40 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
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 58.12/14.46 % SZS status Started for theBenchmark.p
% 58.12/14.46 ERROR - "ProverProcess:heur/409474:1.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 58.12/14.46 Fatal error: exception Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 58.12/14.46 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 3 --comb_mode clause_based --comb_res_mult 4 --comb_sup_deep_mult 2 --comb_sup_mult 0 --conj_cone_tolerance 3. --demod_completeness_check fast --demod_use_ground true --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 500 --inst_dismatching true --inst_eager_unprocessed_to_passive true --inst_eq_res_simp false --inst_learning_factor 2 --inst_learning_loop_flag true --inst_learning_start 3000 --inst_lit_activity_flag true --inst_lit_sel "[+prop;+sign;+ground;-num_var;-num_symb]" --inst_lit_sel_side num_symb --inst_orphan_elimination true --inst_passive_queue_type priority_queues --inst_passive_queues "[[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]" --inst_passive_queues_freq "[25;2]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew solver --inst_solver_calls_frac 1. --inst_solver_per_active 1400 --inst_sos_flag false --inst_start_prop_sim_after_learn 3 --inst_subs_given false --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 256 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution false --res_forward_subs subset_subsumption --res_forward_subs_resolution true --res_lit_sel pos_max --res_lit_sel_side num_var --res_ordering kbo_pred --res_passive_queue_type priority_queues --res_passive_queues "[[-num_lits];[-conj_symb;-num_symb;+num_symb]]" --res_passive_queues_freq "[15;3]" --res_prop_simpl_given false --res_prop_simpl_new true --res_sim_input true --res_time_limit 202.80 --res_to_prop_solver passive --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[ACNormalisation]" --sup_immed_fw_main "[]" --sup_immed_triv "[]" --sup_indices_passive "[]" --sup_input_bw "[]" --sup_input_fw "[ACNormalisation]" --sup_input_triv "[Unflattening]" --sup_iter_deepening 2 --sup_passive_queue_type priority_queues --sup_passive_queues "[[-conj_dist;-num_symb];[+age;-num_symb];[+score;-num_symb]]" --sup_passive_queues_freq "[8;4;4]" --sup_prop_simpl_given true --sup_prop_simpl_new true --sup_restarts_mult 2 --sup_score sim_d_gen --sup_share_max_num_cl 500 --sup_share_score_frac 0.2 --sup_smt_interval 10000 --sup_symb_ordering invfreq --sup_to_prop_solver passive --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --tptp_safe_out true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 0.33" --time_out_real 1.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_phuw5skl/rrueec1u 2>> /export/starexec/sandbox/tmp/iprover_out_phuw5skl/rrueec1u_error
% 58.12/14.46 % SZS status Theorem for theBenchmark.p
% 58.12/14.46
% 58.12/14.46 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 58.12/14.46
% 58.12/14.46 % ------ iProver source info
% 58.12/14.46
% 58.12/14.46 % git: date: 2026-07-19 20:42:38 +0200
% 58.12/14.46 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 58.12/14.46 % git: non_committed_changes: false
% 58.12/14.46
% 58.12/14.46 % ------ Parsing...
% 58.12/14.46 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 58.12/14.46
% 58.12/14.46 % ------ Preprocessing... sup_sim: 54 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 5 sf_s rm: 2 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 58.12/14.46
% 58.12/14.46 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 58.12/14.46
% 58.12/14.46 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 58.12/14.46 % ------ Proving...
% 58.12/14.46 % ------ Problem Properties
% 58.12/14.46
% 58.12/14.46 %
% 58.12/14.46 % clauses 544
% 58.12/14.46 % conjectures 1
% 58.12/14.46 % EPR 34
% 58.12/14.46 % Horn 483
% 58.12/14.46 % unary 134
% 58.12/14.46 % binary 254
% 58.12/14.46 % lits 1151
% 58.12/14.46 % lits eq 417
% 58.12/14.46 % fd_pure 0
% 58.12/14.46 % fd_pseudo 0
% 58.12/14.46 % fd_cond 31
% 58.12/14.46 % fd_pseudo_cond 47
% 58.12/14.46 % AC symbols 0
% 58.12/14.46
% 58.12/14.46 % ------ Schedule dynamic 5 is on
% 58.12/14.46
% 58.12/14.46 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 58.12/14.46
% 58.12/14.46
% 58.12/14.46 % ------
% 58.12/14.46 % Current options:
% 58.12/14.46 % ------
% 58.12/14.46
% 58.12/14.46
% 58.12/14.46 %
% 58.12/14.46
% 58.12/14.46 % ------ Proving...
% 58.12/14.46 % Proof_search_loop: time out after: 4472 full_loop iterations
% 58.12/14.46
% 58.12/14.46 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 58.12/14.46
% 58.12/14.46
% 58.12/14.46 % ------
% 58.12/14.46 % Current options:
% 58.12/14.46 % ------
% 58.12/14.46
% 58.12/14.46
% 58.12/14.46 %
% 58.12/14.46
% 58.12/14.46 % ------ Proving...
% 58.12/14.46 %
% 58.12/14.46
% 58.12/14.46 % SZS status Theorem for theBenchmark.p
% 58.12/14.46
% 58.12/14.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 58.12/14.46
% 58.12/14.46
%------------------------------------------------------------------------------