%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG380-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n008.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 04:08:36 PM UTC 2026
% Result : Unsatisfiable 1.28s 1.99s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of clauses : 21 ( 17 unt; 2 nHn; 9 RR)
% Number of literals : 25 ( 15 equ; 8 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-3 aty)
% Number of variables : 27 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
c_HOL_Otimes__class_Otimes(c_Complex_Orcis(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Complex_Orcis(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_Complex_Ocomplex) != c_Complex_Orcis(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),v_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_rcis__mult_0,axiom,
c_HOL_Otimes__class_Otimes(c_Complex_Orcis(X1,X2),c_Complex_Orcis(X3,X4),tc_Complex_Ocomplex) = c_Complex_Orcis(c_HOL_Otimes__class_Otimes(X1,X3,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X2,X4,tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rcis__mult_0) ).
cnf(cls_real__sqrt__mult_0,axiom,
c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__mult_0) ).
cnf(cls_real__sqrt__abs2_0,axiom,
c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal)) = c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__abs2_0) ).
cnf(cls_real__sum__of__halves_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__of__halves_0) ).
cnf(cls_norm__not__less__zero_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X2,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__not__less__zero_0) ).
cnf(cls_complex__mod__rcis_0,axiom,
c_RealVector_Onorm__class_Onorm(c_Complex_Orcis(X1,X2),tc_Complex_Ocomplex) = c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__mod__rcis_0) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
cnf(cls_real__abs__def_1,axiom,
( c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__abs__def_1) ).
cnf(c_0_9,negated_conjecture,
c_HOL_Otimes__class_Otimes(c_Complex_Orcis(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Complex_Orcis(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_Complex_Ocomplex) != c_Complex_Orcis(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),v_a),
cls_conjecture_0 ).
cnf(c_0_10,axiom,
c_HOL_Otimes__class_Otimes(c_Complex_Orcis(X1,X2),c_Complex_Orcis(X3,X4),tc_Complex_Ocomplex) = c_Complex_Orcis(c_HOL_Otimes__class_Otimes(X1,X3,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X2,X4,tc_RealDef_Oreal)),
cls_rcis__mult_0 ).
cnf(c_0_11,axiom,
c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal),
cls_real__sqrt__mult_0 ).
cnf(c_0_12,axiom,
c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal)) = c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),
cls_real__sqrt__abs2_0 ).
cnf(c_0_13,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = X1,
cls_real__sum__of__halves_0 ).
cnf(c_0_14,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X2,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_norm__not__less__zero_0 ).
cnf(c_0_15,axiom,
c_RealVector_Onorm__class_Onorm(c_Complex_Orcis(X1,X2),tc_Complex_Ocomplex) = c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),
cls_complex__mod__rcis_0 ).
cnf(c_0_16,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector ).
cnf(c_0_17,negated_conjecture,
c_Complex_Orcis(c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),tc_RealDef_Oreal),v_a) != c_Complex_Orcis(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),v_a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12]),c_0_13]) ).
cnf(c_0_18,axiom,
( c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_real__abs__def_1 ).
cnf(c_0_19,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.20 % Problem : ALG380-1 : TPTP v9.2.1. Released v4.1.0.
% 0.03/0.20 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.11/0.42 % Computer : n008.cluster.edu
% 0.11/0.42 % Model : x86_64 x86_64
% 0.11/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.42 % Memory : 8042.1875MB
% 0.11/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.42 % CPULimit : 300
% 0.11/0.42 % WCLimit : 300
% 0.11/0.42 % DateTime : Tue May 5 10:32:58 EDT 2026
% 0.11/0.44 % CPUTime :
% 0.14/0.47 % start to proof: theBenchmark
% 1.28/1.99 % Version : CSE_E---1.7
% 1.28/1.99 % Problem : theBenchmark.p
% 1.28/1.99 % SZS status Unsatisfiable for theBenchmark.p
% 1.28/1.99 % SZS output start CNFRefutation
% See solution above
% 1.28/2.00 % Total time : 1.451s
%------------------------------------------------------------------------------