%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG429-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 09:20:00 AM UTC 2026
% Result : Unsatisfiable 2.62s 1.05s
% Output : Refutation 2.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of formulae : 86 ( 12 unt; 9 def)
% Number of atoms : 240 ( 49 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 248 ( 94 ~; 145 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 9 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 13 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1486,axiom,
v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pe_0) ).
fof(f1487,plain,
c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p,
inference(reorient_equations,[],[f1486]) ).
fof(f1492,axiom,
! [X0] :
( c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X0,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_4) ).
fof(f1493,plain,
! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q,X0,tc_Complex_Ocomplex) ),
inference(reorient_equations,[],[f1492]) ).
fof(f1496,axiom,
( c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_2) ).
fof(f1497,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(reorient_equations,[],[f1496]) ).
fof(f1500,axiom,
( v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f1501,plain,
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) ),
inference(reorient_equations,[],[f1500]) ).
fof(f1504,axiom,
! [X0] :
( c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X0,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_4_02) ).
fof(f1505,plain,
! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q,X0,tc_Complex_Ocomplex) ),
inference(reorient_equations,[],[f1504]) ).
fof(f1508,axiom,
( c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_2_04) ).
fof(f1509,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(reorient_equations,[],[f1508]) ).
fof(f1512,axiom,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_06) ).
fof(f1513,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) != c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) ),
inference(reorient_equations,[],[f1512]) ).
fof(f1514,negated_conjecture,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1515,plain,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) ),
inference(reorient_equations,[],[f1514]) ).
fof(f1516,negated_conjecture,
( c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1517,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(reorient_equations,[],[f1516]) ).
fof(f1522,negated_conjecture,
! [X0] :
( c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_q,X0,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f1523,plain,
! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q,X0,tc_Complex_Ocomplex) ),
inference(reorient_equations,[],[f1522]) ).
fof(f1709,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f2270,plain,
~ sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),
inference(equality_proxy_replacement,[],[f1487,f1709]) ).
fof(f2273,plain,
! [X0] :
( ~ sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex))
| sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q,X0,tc_Complex_Ocomplex)) ),
inference(equality_proxy_replacement,[],[f1493,f1709,f1709,f1709]) ).
fof(f2275,plain,
( ~ sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex))
| sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex))
| sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(equality_proxy_replacement,[],[f1497,f1709,f1709,f1709]) ).
fof(f2277,plain,
( sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex))
| sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)) ),
inference(equality_proxy_replacement,[],[f1501,f1709,f1709,f1709]) ).
fof(f2279,plain,
! [X0] :
( ~ sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex))
| sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q,X0,tc_Complex_Ocomplex)) ),
inference(equality_proxy_replacement,[],[f1505,f1709,f1709,f1709]) ).
fof(f2281,plain,
( ~ sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex))
| ~ sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex))
| sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(equality_proxy_replacement,[],[f1509,f1709,f1709,f1709]) ).
fof(f2283,plain,
( ~ sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex))
| sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex)) ),
inference(equality_proxy_replacement,[],[f1513,f1709,f1709,f1709]) ).
fof(f2284,plain,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex)) ),
inference(equality_proxy_replacement,[],[f1515,f1709]) ).
fof(f2285,plain,
( ~ sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(equality_proxy_replacement,[],[f1517,f1709]) ).
fof(f2288,plain,
! [X0] :
( ~ sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex))
| sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q,X0,tc_Complex_Ocomplex)) ),
inference(equality_proxy_replacement,[],[f1523,f1709,f1709,f1709]) ).
fof(f2296,definition,
( spl1_1
<=> c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f2302,definition,
( spl1_3
<=> ! [X0] :
( ~ sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex))
| sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q,X0,tc_Complex_Ocomplex)) ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f2303,plain,
( ! [X0] :
( sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q,X0,tc_Complex_Ocomplex))
| ~ sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex)) )
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f2302]) ).
fof(f2306,definition,
( spl1_4
<=> sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f2308,plain,
( spl1_1
| spl1_4
| spl1_3 ),
inference(avatar_split_clause,[],[f2288,f2302,f2306,f2296]) ).
fof(f2310,definition,
( spl1_5
<=> sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex)) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f2311,plain,
( ~ sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex))
| spl1_5 ),
inference(avatar_component_clause,[],[f2310]) ).
fof(f2316,definition,
( spl1_6
<=> sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex)) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f2317,plain,
( sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex))
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f2316]) ).
fof(f2320,plain,
( ~ spl1_1
| ~ spl1_5 ),
inference(avatar_split_clause,[],[f2285,f2310,f2296]) ).
fof(f2321,plain,
( spl1_6
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f2284,f2296,f2316]) ).
fof(f2323,definition,
( spl1_7
<=> sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex)) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f2324,plain,
( sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex))
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f2323]) ).
fof(f2326,definition,
( spl1_8
<=> sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f2328,plain,
( spl1_7
| spl1_1
| spl1_4
| ~ spl1_8 ),
inference(avatar_split_clause,[],[f2283,f2326,f2306,f2296,f2323]) ).
fof(f2331,definition,
( spl1_9
<=> sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex)) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
fof(f2332,plain,
( ~ sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex))
| spl1_9 ),
inference(avatar_component_clause,[],[f2331]) ).
fof(f2333,plain,
( spl1_1
| spl1_4
| ~ spl1_8
| ~ spl1_9 ),
inference(avatar_split_clause,[],[f2281,f2331,f2326,f2306,f2296]) ).
fof(f2335,plain,
( ~ spl1_8
| ~ spl1_1
| spl1_3 ),
inference(avatar_split_clause,[],[f2279,f2302,f2296,f2326]) ).
fof(f2338,plain,
( spl1_8
| spl1_7
| spl1_1
| spl1_4 ),
inference(avatar_split_clause,[],[f2277,f2306,f2296,f2323,f2326]) ).
fof(f2340,plain,
( spl1_1
| spl1_4
| spl1_8
| ~ spl1_9 ),
inference(avatar_split_clause,[],[f2275,f2331,f2326,f2306,f2296]) ).
fof(f2342,plain,
( spl1_8
| ~ spl1_1
| spl1_3 ),
inference(avatar_split_clause,[],[f2273,f2302,f2296,f2326]) ).
fof(f2344,plain,
~ spl1_4,
inference(avatar_split_clause,[],[f2270,f2306]) ).
fof(f2352,plain,
( ~ sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex))
| ~ spl1_3
| spl1_9 ),
inference(resolution,[],[f2332,f2303]) ).
fof(f2353,plain,
( $false
| ~ spl1_3
| ~ spl1_7
| spl1_9 ),
inference(resolution,[],[f2352,f2324]) ).
fof(f2354,plain,
( ~ spl1_3
| ~ spl1_7
| spl1_9 ),
inference(avatar_contradiction_clause,[],[f2353]) ).
fof(f2355,plain,
( ~ sQ0_eqProxy(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex))
| ~ spl1_3
| spl1_5 ),
inference(resolution,[],[f2311,f2303]) ).
fof(f2356,plain,
( $false
| ~ spl1_3
| spl1_5
| ~ spl1_6 ),
inference(resolution,[],[f2355,f2317]) ).
fof(f2357,plain,
( ~ spl1_3
| spl1_5
| ~ spl1_6 ),
inference(avatar_contradiction_clause,[],[f2356]) ).
cnf(s2,plain,
( spl1_1
| spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f2308]) ).
cnf(s5,plain,
( ~ spl1_1
| ~ spl1_5 ),
inference(sat_conversion,[],[f2320]) ).
cnf(s6,plain,
( ~ spl1_1
| spl1_6 ),
inference(sat_conversion,[],[f2321]) ).
cnf(s7,plain,
( spl1_1
| spl1_4
| spl1_7
| ~ spl1_8 ),
inference(sat_conversion,[],[f2328]) ).
cnf(s9,plain,
( spl1_1
| spl1_4
| ~ spl1_8
| ~ spl1_9 ),
inference(sat_conversion,[],[f2333]) ).
cnf(s11,plain,
( ~ spl1_1
| spl1_3
| ~ spl1_8 ),
inference(sat_conversion,[],[f2335]) ).
cnf(s13,plain,
( spl1_1
| spl1_4
| spl1_7
| spl1_8 ),
inference(sat_conversion,[],[f2338]) ).
cnf(s15,plain,
( spl1_1
| spl1_4
| spl1_8
| ~ spl1_9 ),
inference(sat_conversion,[],[f2340]) ).
cnf(s17,plain,
( ~ spl1_1
| spl1_3
| spl1_8 ),
inference(sat_conversion,[],[f2342]) ).
cnf(s19,plain,
~ spl1_4,
inference(sat_conversion,[],[f2344]) ).
cnf(s21,plain,
( ~ spl1_3
| ~ spl1_7
| spl1_9 ),
inference(sat_conversion,[],[f2354]) ).
cnf(s22,plain,
( ~ spl1_3
| spl1_5
| ~ spl1_6 ),
inference(sat_conversion,[],[f2357]) ).
cnf(s23,plain,
( spl1_1
| spl1_8
| ~ spl1_9 ),
inference(rat,[],[s15,s19]) ).
cnf(s24,plain,
( spl1_1
| spl1_7
| spl1_8 ),
inference(rat,[],[s13,s19]) ).
cnf(s25,plain,
( spl1_1
| ~ spl1_8
| ~ spl1_9 ),
inference(rat,[],[s9,s19]) ).
cnf(s26,plain,
( spl1_1
| spl1_7
| ~ spl1_8 ),
inference(rat,[],[s7,s19]) ).
cnf(s27,plain,
( spl1_1
| spl1_3 ),
inference(rat,[],[s2,s19]) ).
cnf(s28,plain,
( spl1_7
| spl1_1 ),
inference(rat,[],[s26,s24]) ).
cnf(s29,plain,
( ~ spl1_9
| spl1_1 ),
inference(rat,[],[s25,s23]) ).
cnf(s30,plain,
spl1_1,
inference(rat,[],[s29,s21,s28,s27]) ).
cnf(s31,plain,
spl1_6,
inference(rat,[],[s6,s30]) ).
cnf(s32,plain,
~ spl1_5,
inference(rat,[],[s5,s30]) ).
cnf(s33,plain,
~ spl1_3,
inference(rat,[],[s22,s31,s32]) ).
cnf(s34,plain,
spl1_8,
inference(rat,[],[s17,s30,s33]) ).
cnf(s35,plain,
$false,
inference(rat,[],[s11,s30,s34,s33]) ).
fof(f2358,plain,
$false,
inference(avatar_sat_refutation,[],[s35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG429-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n001.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 20:27:04 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 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
% 2.62/1.05 % (682478)Input is clausal, will run a generic CNF schedule.
% 2.62/1.05 % (682489)dis-21_1_sil=8000:lcm=predicate:random_seed=1493246733:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.62/1.05 % (682489)First to succeed.
% 2.62/1.05 % (682489)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-682478"
% 2.62/1.05 % (682487)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3429781946:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.62/1.05 % (682488)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2966419133:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.62/1.05 % (682485)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3715956457:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.62/1.05 % (682486)lrs+10_1_sil=8000:sp=occurrence:random_seed=3470011715:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.62/1.05 % (682483)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=3470981034:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.62/1.05 % (682484)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1373519301:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.62/1.05 % (682488)Also succeeded, but the first one will report.
% 2.62/1.05 % (682486)Instruction limit reached!
% 2.62/1.05 % (682486)------------------------------
% 2.62/1.05 % (682486)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.05 % (682486)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.05 % (682486)CaDiCaL version: 2.1.3
% 2.62/1.05 % (682486)Termination reason: Instruction limit
% 2.62/1.05 % (682486)Termination phase: Saturation
% 2.62/1.05 % (682486)Time elapsed: 0.071 s
% 2.62/1.05 % (682486)Peak memory usage: 89 MB
% 2.62/1.05 % (682486)Instructions burned: 107 (million)
% 2.62/1.05 % (682487)Instruction limit reached!
% 2.62/1.05 % (682487)------------------------------
% 2.62/1.05 % (682487)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.05 % (682487)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.05 % (682487)CaDiCaL version: 2.1.3
% 2.62/1.05 % (682487)Termination reason: Instruction limit
% 2.62/1.05 % (682487)Termination phase: Saturation
% 2.62/1.05 % (682487)Time elapsed: 0.077 s
% 2.62/1.05 % (682487)Peak memory usage: 89 MB
% 2.62/1.05 % (682487)Instructions burned: 115 (million)
% 2.62/1.05 % (682489)Refutation found. Thanks to Tanya!
% 2.62/1.05 % SZS status Unsatisfiable for theBenchmark
% 2.62/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 2.97/1.23 % (682489)------------------------------
% 2.97/1.23 % (682489)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.97/1.23 % (682489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.97/1.23 % (682489)CaDiCaL version: 2.1.3
% 2.97/1.23 % (682489)Termination reason: Refutation
% 2.97/1.23 % (682489)Time elapsed: 0.011 s
% 2.97/1.23 % (682489)Peak memory usage: 90 MB
% 2.97/1.23 % (682489)Instructions burned: 37 (million)
% 2.97/1.23 % (682489)------------------------------
% 2.97/1.23 % (682489)------------------------------
% 2.97/1.23 % (682478)Success in time 0.369 s
% 2.97/1.23 % Vampire exiting
%------------------------------------------------------------------------------