%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW287+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 : Tue Sep 29 01:30:01 PM UTC 2026
% Result : Theorem 3.48s 1.18s
% Output : Refutation 3.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 77 ( 16 unt; 9 def)
% Number of atoms : 215 ( 98 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 225 ( 87 ~; 97 |; 22 &)
% ( 11 <=>; 7 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 15 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pe) ).
fof(f3,axiom,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dp) ).
fof(f4,axiom,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Nat_OSuc(v_n____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n) ).
fof(f6,axiom,
! [X0] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____))))
=> ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bx_O_A_091_124_Ap_Advd_Aq_A_094_ASuc_An_059_Apoly_Ap_Ax_A_061_A0_059_Apoly_Aq_Ax_A_126_061_A0_A_124_093_A_061_061_062_AFalse_096) ).
fof(f7,axiom,
( ! [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
=> ( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_091_124_AALL_Ax_O_Apoly_Ap_Ax_A_061_A0_A_N_N_062_Apoly_Aq_Ax_A_061_A0_059_Adegree_Ap_A_061_Adegree_Ap_059_Adegree_Ap_A_126_061_A0_A_124_093_061_061_062_Ap_Advd_Aq_A_094_Adegree_Ap_096) ).
fof(f1206,conjecture,
( ! [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1207,negated_conjecture,
~ ( ! [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
inference(negated_conjecture,[status(cth)],[f1206]) ).
fof(f1257,plain,
! [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____)))) ),
inference(ennf_transformation,[],[f6]) ).
fof(f1258,plain,
! [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____)))) ),
inference(flattening,[],[f1257]) ).
fof(f1259,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
& hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f1260,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
& hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(flattening,[],[f1259]) ).
fof(f2424,plain,
( ! [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<~> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
inference(ennf_transformation,[],[f1207]) ).
fof(f2433,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK4)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X0,sK4)],[f1260]) ).
fof(f2763,plain,
( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
& ( v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q ) )
| ? [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
& hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ! [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
inference(nnf_transformation,[],[f2424]) ).
fof(f2764,plain,
( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
& ( v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q ) )
| ? [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
& hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ! [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
inference(flattening,[],[f2763]) ).
fof(f2765,plain,
( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
& ( v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q ) )
| ? [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
& hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1) ) ) ),
inference(rectify,[],[f2764]) ).
fof(f2766,plain,
( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
& ( v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q ) )
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK21)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK21) ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(X0,sK21)],[f2765]) ).
fof(f2768,plain,
v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cnf_transformation,[],[f2]) ).
fof(f2769,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f3]) ).
fof(f2770,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Nat_OSuc(v_n____),
inference(cnf_transformation,[],[f4]) ).
fof(f2777,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____)))) ),
inference(cnf_transformation,[],[f1258]) ).
fof(f2778,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK4) ),
inference(cnf_transformation,[],[f2433]) ).
fof(f2779,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK4) ),
inference(cnf_transformation,[],[f2433]) ).
fof(f4321,plain,
! [X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1) ),
inference(cnf_transformation,[],[f2766]) ).
fof(f4324,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK21) ),
inference(cnf_transformation,[],[f2766]) ).
fof(f4325,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK21) ),
inference(cnf_transformation,[],[f2766]) ).
fof(f4579,definition,
( spl22_1
<=> ! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1) ) ),
introduced(definition,[new_symbols(definition,[spl22_1])],[avatar_definition]) ).
fof(f4580,plain,
( ! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1) )
| ~ spl22_1 ),
inference(avatar_component_clause,[],[f4579]) ).
fof(f4586,definition,
( spl22_3
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ),
introduced(definition,[new_symbols(definition,[spl22_3])],[avatar_definition]) ).
fof(f4588,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ~ spl22_3 ),
inference(avatar_component_clause,[],[f4586]) ).
fof(f4591,definition,
( spl22_4
<=> v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
introduced(definition,[new_symbols(definition,[spl22_4])],[avatar_definition]) ).
fof(f4594,plain,
( spl22_1
| spl22_4
| spl22_3 ),
inference(avatar_split_clause,[],[f4321,f4586,f4591,f4579]) ).
fof(f4596,definition,
( spl22_5
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK21) ),
introduced(definition,[new_symbols(definition,[spl22_5])],[avatar_definition]) ).
fof(f4598,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK21)
| ~ spl22_5 ),
inference(avatar_component_clause,[],[f4596]) ).
fof(f4601,definition,
( spl22_6
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK21) ),
introduced(definition,[new_symbols(definition,[spl22_6])],[avatar_definition]) ).
fof(f4603,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK21)
| spl22_6 ),
inference(avatar_component_clause,[],[f4601]) ).
fof(f4605,plain,
( spl22_5
| ~ spl22_3 ),
inference(avatar_split_clause,[],[f4324,f4586,f4596]) ).
fof(f4606,plain,
( ~ spl22_6
| ~ spl22_3 ),
inference(avatar_split_clause,[],[f4325,f4586,f4601]) ).
fof(f4618,definition,
( spl22_9
<=> c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
introduced(definition,[new_symbols(definition,[spl22_9])],[avatar_definition]) ).
fof(f4636,definition,
( spl22_12
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK4) ),
introduced(definition,[new_symbols(definition,[spl22_12])],[avatar_definition]) ).
fof(f4638,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK4)
| ~ spl22_12 ),
inference(avatar_component_clause,[],[f4636]) ).
fof(f4639,plain,
( spl22_12
| spl22_9
| spl22_3 ),
inference(avatar_split_clause,[],[f2778,f4586,f4618,f4636]) ).
fof(f4641,definition,
( spl22_13
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK4) ),
introduced(definition,[new_symbols(definition,[spl22_13])],[avatar_definition]) ).
fof(f4644,plain,
( ~ spl22_13
| spl22_9
| spl22_3 ),
inference(avatar_split_clause,[],[f2779,f4586,f4618,f4641]) ).
fof(f4646,definition,
( spl22_14
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____)))) ),
introduced(definition,[new_symbols(definition,[spl22_14])],[avatar_definition]) ).
fof(f4649,plain,
( ~ spl22_14
| spl22_1 ),
inference(avatar_split_clause,[],[f2777,f4579,f4646]) ).
fof(f4662,plain,
~ spl22_9,
inference(avatar_split_clause,[],[f2769,f4618]) ).
fof(f4663,plain,
~ spl22_4,
inference(avatar_split_clause,[],[f2768,f4591]) ).
fof(f4664,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____))))
| ~ spl22_3 ),
inference(superposition,[],[f4588,f2770]) ).
fof(f4665,plain,
( spl22_14
| ~ spl22_3 ),
inference(avatar_split_clause,[],[f4664,f4586,f4646]) ).
fof(f4668,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK21)
| ~ spl22_1
| ~ spl22_5 ),
inference(superposition,[],[f4580,f4598]) ).
fof(f4669,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK21)
| ~ spl22_1
| ~ spl22_5 ),
inference(trivial_inequality_removal,[],[f4668]) ).
fof(f4670,plain,
( $false
| ~ spl22_1
| ~ spl22_5
| spl22_6 ),
inference(forward_subsumption_resolution,[],[f4669,f4603]) ).
fof(f4671,plain,
( ~ spl22_1
| ~ spl22_5
| spl22_6 ),
inference(avatar_contradiction_clause,[],[f4670]) ).
fof(f4674,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK4)
| ~ spl22_1
| ~ spl22_12 ),
inference(superposition,[],[f4580,f4638]) ).
fof(f4675,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK4)
| ~ spl22_1
| ~ spl22_12 ),
inference(trivial_inequality_removal,[],[f4674]) ).
fof(f4676,plain,
( spl22_13
| ~ spl22_1
| ~ spl22_12 ),
inference(avatar_split_clause,[],[f4675,f4636,f4579,f4641]) ).
cnf(s2,plain,
( spl22_1
| spl22_3
| spl22_4 ),
inference(sat_conversion,[],[f4594]) ).
cnf(s5,plain,
( ~ spl22_3
| spl22_5 ),
inference(sat_conversion,[],[f4605]) ).
cnf(s6,plain,
( ~ spl22_3
| ~ spl22_6 ),
inference(sat_conversion,[],[f4606]) ).
cnf(s15,plain,
( spl22_3
| spl22_9
| spl22_12 ),
inference(sat_conversion,[],[f4639]) ).
cnf(s16,plain,
( spl22_3
| spl22_9
| ~ spl22_13 ),
inference(sat_conversion,[],[f4644]) ).
cnf(s17,plain,
( spl22_1
| ~ spl22_14 ),
inference(sat_conversion,[],[f4649]) ).
cnf(s22,plain,
~ spl22_9,
inference(sat_conversion,[],[f4662]) ).
cnf(s23,plain,
~ spl22_4,
inference(sat_conversion,[],[f4663]) ).
cnf(s24,plain,
( ~ spl22_3
| spl22_14 ),
inference(sat_conversion,[],[f4665]) ).
cnf(s26,plain,
( ~ spl22_1
| ~ spl22_5
| spl22_6 ),
inference(sat_conversion,[],[f4671]) ).
cnf(s27,plain,
( ~ spl22_1
| ~ spl22_12
| spl22_13 ),
inference(sat_conversion,[],[f4676]) ).
cnf(s28,plain,
( spl22_3
| ~ spl22_13 ),
inference(rat,[],[s16,s22]) ).
cnf(s29,plain,
( spl22_3
| spl22_12 ),
inference(rat,[],[s15,s22]) ).
cnf(s31,plain,
( spl22_1
| spl22_3 ),
inference(rat,[],[s2,s23]) ).
cnf(s32,plain,
spl22_1,
inference(rat,[],[s24,s31,s17]) ).
cnf(s33,plain,
spl22_3,
inference(rat,[],[s27,s29,s28,s32]) ).
cnf(s35,plain,
~ spl22_6,
inference(rat,[],[s6,s33]) ).
cnf(s36,plain,
spl22_5,
inference(rat,[],[s5,s33]) ).
cnf(s37,plain,
$false,
inference(rat,[],[s26,s32,s35,s36]) ).
fof(f4677,plain,
$false,
inference(avatar_sat_refutation,[],[s37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW287+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n013.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 13:29:37 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.48/1.18 % (1178677)Detected formulas, will run a generic FOF schedule.
% 3.48/1.18 % (1178686)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2910749510:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.48/1.18 % (1178682)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=94139635:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.48/1.18 % (1178684)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2631578066:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.48/1.18 % (1178685)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1087533643:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.48/1.18 % (1178687)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=451870635:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.48/1.18 % (1178683)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1652786038:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.48/1.18 % (1178688)dis-21_1_sil=8000:lcm=predicate:random_seed=2172604253:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.48/1.18 % (1178686)Instruction limit reached!
% 3.48/1.18 % (1178686)------------------------------
% 3.48/1.18 % (1178686)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.18 % (1178686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.18 % (1178686)CaDiCaL version: 2.1.3
% 3.48/1.18 % (1178686)Termination reason: Instruction limit
% 3.48/1.18 % (1178686)Termination phase: Saturation
% 3.48/1.18 % (1178686)Time elapsed: 0.039 s
% 3.48/1.18 % (1178686)Peak memory usage: 89 MB
% 3.48/1.18 % (1178686)Instructions burned: 122 (million)
% 3.48/1.18 % (1178687)First to succeed.
% 3.48/1.18 % (1178687)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1178677"
% 3.48/1.18 % (1178685)Instruction limit reached!
% 3.48/1.18 % (1178685)------------------------------
% 3.48/1.18 % (1178685)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.18 % (1178685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.18 % (1178685)CaDiCaL version: 2.1.3
% 3.48/1.18 % (1178685)Termination reason: Instruction limit
% 3.48/1.18 % (1178685)Termination phase: Saturation
% 3.48/1.18 % (1178685)Time elapsed: 0.064 s
% 3.48/1.18 % (1178685)Peak memory usage: 90 MB
% 3.48/1.18 % (1178685)Instructions burned: 110 (million)
% 3.48/1.18 % (1178688)Instruction limit reached!
% 3.48/1.18 % (1178688)------------------------------
% 3.48/1.18 % (1178688)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.18 % (1178688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.18 % (1178688)CaDiCaL version: 2.1.3
% 3.48/1.18 % (1178688)Termination reason: Instruction limit
% 3.48/1.18 % (1178688)Termination phase: Saturation
% 3.48/1.18 % (1178688)Time elapsed: 0.067 s
% 3.48/1.18 % (1178688)Peak memory usage: 91 MB
% 3.48/1.18 % (1178688)Instructions burned: 129 (million)
% 3.48/1.18 % (1178696)lrs+10_1_sil=8000:sp=occurrence:random_seed=3842510203:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.48/1.18 % (1178697)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2580686960:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.48/1.18 % (1178696)Also succeeded, but the first one will report.
% 3.48/1.18 % (1178698)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2578367536:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.48/1.18 % (1178698)Also succeeded, but the first one will report.
% 3.48/1.18 % (1178697)Instruction limit reached!
% 3.48/1.18 % (1178697)------------------------------
% 3.48/1.18 % (1178697)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.18 % (1178697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.18 % (1178697)CaDiCaL version: 2.1.3
% 3.48/1.18 % (1178697)Termination reason: Instruction limit
% 3.48/1.18 % (1178697)Termination phase: Saturation
% 3.48/1.18 % (1178697)Time elapsed: 0.093 s
% 3.48/1.18 % (1178697)Peak memory usage: 91 MB
% 3.48/1.18 % (1178697)Instructions burned: 158 (million)
% 3.48/1.18 % (1178687)Refutation found. Thanks to Tanya!
% 3.48/1.18 % SZS status Theorem for theBenchmark
% 3.48/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 3.94/1.37 % (1178687)------------------------------
% 3.94/1.37 % (1178687)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.37 % (1178687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.37 % (1178687)CaDiCaL version: 2.1.3
% 3.94/1.37 % (1178687)Termination reason: Refutation
% 3.94/1.37 % (1178687)Time elapsed: 0.051 s
% 3.94/1.37 % (1178687)Peak memory usage: 91 MB
% 3.94/1.37 % (1178687)Instructions burned: 102 (million)
% 3.94/1.37 % (1178687)------------------------------
% 3.94/1.37 % (1178687)------------------------------
% 3.94/1.37 % (1178677)Success in time 0.518 s
% 3.94/1.37 % Vampire exiting
%------------------------------------------------------------------------------