%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG356-1 : 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 : n029.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 04:08:32 PM UTC 2026
% Result : Unsatisfiable 6.56s 4.71s
% Output : CNFRefutation 6.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 12
% Syntax : Number of clauses : 33 ( 21 unt; 4 nHn; 19 RR)
% Number of literals : 49 ( 26 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_norm__divide_0,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__divide_0) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
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_abs__norm__cancel_0,axiom,
( c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__norm__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_norm__one_0,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__one_0) ).
cnf(cls_right__inverse__eq_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Oinverse__class_Odivide(X2,X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
cnf(cls_conjecture_0,negated_conjecture,
c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_b_0,axiom,
v_b != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_b_0) ).
cnf(c_0_12,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
cls_norm__divide_0 ).
cnf(c_0_13,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field ).
cnf(c_0_14,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero ).
cnf(c_0_15,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_16,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1 ).
cnf(c_0_17,plain,
c_HOL_Oinverse__class_Odivide(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_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).
cnf(c_0_18,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_15,c_0_16]) ).
cnf(c_0_19,axiom,
( c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_abs__norm__cancel_0 ).
cnf(c_0_20,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector ).
cnf(c_0_21,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
cls_norm__one_0 ).
cnf(c_0_22,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Oinverse__class_Odivide(X2,X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_right__inverse__eq_1 ).
cnf(c_0_23,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ofield ).
cnf(c_0_24,negated_conjecture,
c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
cls_conjecture_0 ).
cnf(c_0_25,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,plain,
c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_21,c_0_16]) ).
cnf(c_0_28,plain,
( c_HOL_Oinverse__class_Odivide(X1,X1,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,negated_conjecture,
c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(v_b,v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_17]) ).
cnf(c_0_30,plain,
( c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(X1,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,axiom,
v_b != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
cls_b_0 ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG356-1 : 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
% 0.16/0.33 % Computer : n029.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 10:32:59 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 6.56/4.71 % Version : CSE_E---1.7
% 6.56/4.71 % Problem : theBenchmark.p
% 6.56/4.71 % SZS status Unsatisfiable for theBenchmark.p
% 6.56/4.71 % SZS output start CNFRefutation
% See solution above
% 6.56/4.73 % Total time : 3.432s
%------------------------------------------------------------------------------