%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG413-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:08:41 PM UTC 2026
% Result : Unsatisfiable 183.63s 154.24s
% Output : CNFRefutation 183.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 17
% Syntax : Number of clauses : 48 ( 33 unt; 0 nHn; 26 RR)
% Number of literals : 65 ( 36 equ; 21 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 61 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_class__semiring_Omul__c_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
cnf(cls_scaleR__conv__of__real_0,axiom,
( c_RealVector_OscaleR__class_OscaleR(X2,X3,X1) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(X2,X1),X3,X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__conv__of__real_0) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).
cnf(cls_poly__pCons_0,axiom,
( c_Polynomial_Opoly(c_Polynomial_OpCons(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X4,c_Polynomial_Opoly(X3,X4,X1),X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__pCons_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
cnf(cls_norm__mult_0,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__mult_0) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
cnf(cls_norm__of__real_0,axiom,
( c_RealVector_Onorm__class_Onorm(c_RealVector_Oof__real(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__of__real_0) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
cnf(cls_minus__unique_0,axiom,
( c_HOL_Ouminus__class_Ouminus(X2,X1) = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__unique_0) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
cnf(cls_CHAINED_0,axiom,
c_Polynomial_Opoly(c_Polynomial_OpCons(v_d____,v_ds____,tc_Complex_Ocomplex),c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(v_d____,tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_norm__minus__cancel_0,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_RealVector_Onorm__class_Onorm(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__minus__cancel_0) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
cnf(cls_real__mult__commute_0,axiom,
c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X2,X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__commute_0) ).
cnf(c_0_17,axiom,
( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__c_0 ).
cnf(c_0_18,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_19,axiom,
( c_RealVector_OscaleR__class_OscaleR(X2,X3,X1) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(X2,X1),X3,X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
cls_scaleR__conv__of__real_0 ).
cnf(c_0_20,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1 ).
cnf(c_0_21,axiom,
( c_Polynomial_Opoly(c_Polynomial_OpCons(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X4,c_Polynomial_Opoly(X3,X4,X1),X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_poly__pCons_0 ).
cnf(c_0_22,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0 ).
cnf(c_0_23,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
cls_norm__mult_0 ).
cnf(c_0_24,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra ).
cnf(c_0_25,axiom,
( c_RealVector_Onorm__class_Onorm(c_RealVector_Oof__real(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
cls_norm__of__real_0 ).
cnf(c_0_26,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1 ).
cnf(c_0_27,plain,
c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X2,X1,tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_28,plain,
c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_RealVector_OscaleR__class_OscaleR(X1,X2,tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_29,axiom,
( c_HOL_Ouminus__class_Ouminus(X2,X1) = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_minus__unique_0 ).
cnf(c_0_30,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add ).
cnf(c_0_31,axiom,
c_Polynomial_Opoly(c_Polynomial_OpCons(v_d____,v_ds____,tc_Complex_Ocomplex),c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
cls_CHAINED_0 ).
cnf(c_0_32,plain,
c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X2,tc_Complex_Ocomplex),X3,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X3,c_Polynomial_Opoly(X2,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_33,negated_conjecture,
c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(v_d____,tc_Complex_Ocomplex),
cls_conjecture_0 ).
cnf(c_0_34,plain,
c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(X2,tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_35,plain,
c_RealVector_Onorm__class_Onorm(c_RealVector_Oof__real(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_36,plain,
c_HOL_Otimes__class_Otimes(X1,c_RealVector_Oof__real(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_OscaleR__class_OscaleR(X2,X1,tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_37,plain,
( c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex) = X2
| c_HOL_Oplus__class_Oplus(X1,X2,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_38,plain,
c_HOL_Oplus__class_Oplus(v_d____,c_RealVector_OscaleR__class_OscaleR(v_x____,c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_28]) ).
cnf(c_0_39,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_RealVector_Onorm__class_Onorm(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_norm__minus__cancel_0 ).
cnf(c_0_40,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector ).
cnf(c_0_41,negated_conjecture,
c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(v_x____,c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(v_d____,tc_Complex_Ocomplex),
inference(rw,[status(thm)],[c_0_33,c_0_28]) ).
cnf(c_0_42,plain,
c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X2,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_43,axiom,
c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X2,X1,tc_RealDef_Oreal),
cls_real__mult__commute_0 ).
cnf(c_0_44,plain,
c_RealVector_OscaleR__class_OscaleR(v_x____,c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_d____,tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,negated_conjecture,
c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(v_x____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(v_d____,tc_Complex_Ocomplex),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_47,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_44]),c_0_45]),c_0_43]),c_0_46]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG413-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n020.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 10:34:04 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 183.63/154.24 % Version : CSE_E---1.7
% 183.63/154.24 % Problem : theBenchmark.p
% 183.63/154.24 % SZS status Unsatisfiable for theBenchmark.p
% 183.63/154.24 % SZS output start CNFRefutation
% See solution above
% 183.93/154.55 % Total time : 141.401s
%------------------------------------------------------------------------------