%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ALG386-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 12:52:26 PM UTC 2026
% Result : Unsatisfiable 91.53s 13.72s
% Output : Proof 91.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 10 unt; 0 def)
% Number of atoms : 46 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 16 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 27 ( 2 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f397,axiom,
( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mi_h116b3b148411c36c(V_a,V_d,V_p),c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(V_d,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__infinity_0) ).
fof(f397_nnf,plain,
! [V_d,V_a,V_p,V_z] :
( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mi_h116b3b148411c36c(V_a,V_d,V_p),c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(V_d,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(nnf_transformation,[status(thm)],[f397]) ).
fof(f397_sk,plain,
! [V_d,V_a,V_p,V_z] :
( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mi_h116b3b148411c36c(V_a,V_d,V_p),c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(V_d,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(skolemisation,[status(esa)],[f397_nnf]) ).
cnf(c397,plain,
( X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mi_h116b3b148411c36c(X1,X0,X2),c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X2,tc_Complex_Ocomplex),X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(esa)],[f397_sk]) ).
cnf(f422,negated_conjecture,
( c_lessequals(V_xa,c_RealVector_Onorm__class_Onorm(v_x(V_xa),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f422_nnf,plain,
! [V_xa] :
( c_lessequals(V_xa,c_RealVector_Onorm__class_Onorm(v_x(V_xa),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_thesis____ ),
inference(nnf_transformation,[status(thm)],[f422]) ).
fof(f422_sk,plain,
! [V_xa] :
( c_lessequals(V_xa,c_RealVector_Onorm__class_Onorm(v_x(V_xa),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_thesis____ ),
inference(skolemisation,[status(esa)],[f422_nnf]) ).
cnf(c422,plain,
( c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_thesis____ ),
inference(cnf_transformation,[status(esa)],[f422_sk]) ).
cnf(p2783,plain,
( v_thesis____
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X2,tc_Complex_Ocomplex),v_x(v_sko__Fundamental__Theorem__Algebra__Mi_h116b3b148411c36c(X1,X0,X2)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c397,c422]) ).
cnf(f423,negated_conjecture,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f423_nnf,plain,
! [V_xa] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_thesis____ ),
inference(nnf_transformation,[status(thm)],[f423]) ).
fof(f423_sk,plain,
! [V_xa] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_thesis____ ),
inference(skolemisation,[status(esa)],[f423_nnf]) ).
cnf(c423,plain,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_x(X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_thesis____ ),
inference(cnf_transformation,[status(esa)],[f423_sk]) ).
cnf(p3006,plain,
( v_thesis____
| v_thesis____
| v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(resolution,[status(thm)],[p2783,c423]) ).
cnf(p3009,plain,
( v_thesis____
| v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(factoring,[status(thm)],[p3006]) ).
cnf(f196,axiom,
v_cs____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cs0_0) ).
fof(f196_nnf,plain,
v_cs____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(nnf_transformation,[status(thm)],[f196]) ).
fof(f196_sk,plain,
v_cs____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(skolemisation,[status(esa)],[f196_nnf]) ).
cnf(c196,plain,
v_cs____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cnf_transformation,[status(esa)],[f196_sk]) ).
cnf(p3010,plain,
v_thesis____,
inference(resolution,[status(thm)],[p3009,c196]) ).
cnf(f421,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f421_nnf,plain,
~ v_thesis____,
inference(nnf_transformation,[status(thm)],[f421]) ).
fof(f421_sk,plain,
~ v_thesis____,
inference(skolemisation,[status(esa)],[f421_nnf]) ).
cnf(c421,plain,
~ v_thesis____,
inference(cnf_transformation,[status(esa)],[f421_sk]) ).
cnf(p3011,plain,
$false,
inference(resolution,[status(thm)],[p3010,c421]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ALG386-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Fri Sep 25 05:31:20 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 91.53/13.72 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 91.53/13.72 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------