TSTP Solution File: SWW231+1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SWW231+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n010.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 21 06:41:56 EDT 2024
% Result : Theorem 100.39s 13.28s
% Output : CNFRefutation 100.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 24
% Syntax : Number of formulae : 85 ( 66 unt; 0 def)
% Number of atoms : 105 ( 74 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 20 ~; 14 |; 0 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 5 con; 0-3 aty)
% Number of variables : 120 ( 1 sgn 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_mult__right_Ominus,axiom,
! [X5,X23,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X23),c_Groups_Ouminus__class_Ouminus(X10,X5)) = c_Groups_Ouminus__class_Ouminus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X23),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ominus) ).
fof(conj_0,conjecture,
c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) = c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_rcis__def,axiom,
! [X9,X44] : c_Complex_Orcis(X44,X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,X44)),c_Complex_Ocis(X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rcis__def) ).
fof(fact_of__real__minus,axiom,
! [X5,X10] :
( class_RealVector_Oreal__algebra__1(X10)
=> c_RealVector_Oof__real(X10,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X5)) = c_Groups_Ouminus__class_Ouminus(X10,c_RealVector_Oof__real(X10,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__minus) ).
fof(fact_mult__left_Ominus,axiom,
! [X4,X5,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ouminus__class_Ouminus(X10,X5)),X4) = c_Groups_Ouminus__class_Ouminus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X5),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ominus) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(fact_real__sqrt__mult,axiom,
! [X4,X5] : c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(X5)),c_NthRoot_Osqrt(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__mult) ).
fof(fact_real__sqrt__abs2,axiom,
! [X5] : c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5),X5)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__abs2) ).
fof(fact_abs__norm__cancel,axiom,
! [X9,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X9)) = c_RealVector_Onorm__class_Onorm(X10,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__norm__cancel) ).
fof(fact_complex__mod__rcis,axiom,
! [X9,X44] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(X44,X9)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X44),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__rcis) ).
fof(fact_complex__surj,axiom,
! [X17] : c_Complex_Ocomplex_OComplex(c_Complex_ORe(X17),c_Complex_OIm(X17)) = X17,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__surj) ).
fof(fact_Im__rcis,axiom,
! [X9,X44] : c_Complex_OIm(c_Complex_Orcis(X44,X9)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X44),c_Transcendental_Osin(X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Im__rcis) ).
fof(fact_Re__rcis,axiom,
! [X9,X44] : c_Complex_ORe(c_Complex_Orcis(X44,X9)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X44),c_Transcendental_Ocos(X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Re__rcis) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [X9,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oone__class_Oone(X10)),X9) = X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__algebra__1,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(fact_cos__periodic__pi,axiom,
! [X5] : c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cos__periodic__pi) ).
fof(fact_real__mult__1,axiom,
! [X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X17) = X17,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__1) ).
fof(fact_sin__periodic__pi,axiom,
! [X5] : c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sin__periodic__pi) ).
fof(fact_cis__def,axiom,
! [X9] : c_Complex_Ocis(X9) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(X9),c_Transcendental_Osin(X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cis__def) ).
fof(fact_cis__rcis__eq,axiom,
! [X9] : c_Complex_Ocis(X9) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cis__rcis__eq) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X12,X9,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oplus__class_Oplus(X10,X9,X12) = c_Groups_Oplus__class_Oplus(X10,X12,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(c_0_24,plain,
! [X142,X143,X144] :
( ~ class_RealVector_Oreal__normed__algebra(X144)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X144),X143),c_Groups_Ouminus__class_Ouminus(X144,X142)) = c_Groups_Ouminus__class_Ouminus(X144,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X144),X143),X142)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Ominus])])]) ).
fof(c_0_25,negated_conjecture,
c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) != c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
fof(c_0_26,plain,
! [X97,X98] : c_Complex_Orcis(X98,X97) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,X98)),c_Complex_Ocis(X97)),
inference(variable_rename,[status(thm)],[fact_rcis__def]) ).
fof(c_0_27,plain,
! [X962,X963] :
( ~ class_RealVector_Oreal__algebra__1(X963)
| c_RealVector_Oof__real(X963,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X962)) = c_Groups_Ouminus__class_Ouminus(X963,c_RealVector_Oof__real(X963,X962)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__minus])])]) ).
fof(c_0_28,plain,
! [X136,X137,X138] :
( ~ class_RealVector_Oreal__normed__algebra(X138)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X138),c_Groups_Ouminus__class_Ouminus(X138,X137)),X136) = c_Groups_Ouminus__class_Ouminus(X138,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X138),X137),X136)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Ominus])])]) ).
cnf(c_0_29,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra]) ).
fof(c_0_31,negated_conjecture,
c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) != c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a),
inference(fof_nnf,[status(thm)],[c_0_25]) ).
fof(c_0_32,plain,
! [X828,X829] : c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X829),X828)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(X829)),c_NthRoot_Osqrt(X828)),
inference(variable_rename,[status(thm)],[fact_real__sqrt__mult]) ).
fof(c_0_33,plain,
! [X248] : c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X248),X248)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X248),
inference(variable_rename,[status(thm)],[fact_real__sqrt__abs2]) ).
fof(c_0_34,plain,
! [X274,X275] :
( ~ class_RealVector_Oreal__normed__vector(X275)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X275,X274)) = c_RealVector_Onorm__class_Onorm(X275,X274) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__norm__cancel])])]) ).
fof(c_0_35,plain,
! [X101,X102] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(X102,X101)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X102),
inference(variable_rename,[status(thm)],[fact_complex__mod__rcis]) ).
fof(c_0_36,plain,
! [X1377] : c_Complex_Ocomplex_OComplex(c_Complex_ORe(X1377),c_Complex_OIm(X1377)) = X1377,
inference(variable_rename,[status(thm)],[fact_complex__surj]) ).
fof(c_0_37,plain,
! [X107,X108] : c_Complex_OIm(c_Complex_Orcis(X108,X107)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X108),c_Transcendental_Osin(X107)),
inference(variable_rename,[status(thm)],[fact_Im__rcis]) ).
fof(c_0_38,plain,
! [X109,X110] : c_Complex_ORe(c_Complex_Orcis(X110,X109)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X110),c_Transcendental_Ocos(X109)),
inference(variable_rename,[status(thm)],[fact_Re__rcis]) ).
fof(c_0_39,plain,
! [X1110,X1111] :
( ~ class_Rings_Ocomm__semiring__1(X1111)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1111),c_Groups_Oone__class_Oone(X1111)),X1110) = X1110 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J])])]) ).
cnf(c_0_40,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra]) ).
cnf(c_0_41,plain,
c_Complex_Orcis(X1,X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,X1)),c_Complex_Ocis(X2)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_42,plain,
( c_RealVector_Oof__real(X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) = c_Groups_Ouminus__class_Ouminus(X1,c_RealVector_Oof__real(X1,X2))
| ~ class_RealVector_Oreal__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_43,plain,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__algebra__1]) ).
cnf(c_0_44,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_45,plain,
c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2)),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_46,negated_conjecture,
c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) != c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_47,plain,
c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1)),c_NthRoot_Osqrt(X2)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_48,plain,
c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_49,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2)) = c_RealVector_Onorm__class_Onorm(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_50,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(X1,X2)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_51,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
cnf(c_0_52,plain,
c_Complex_Ocomplex_OComplex(c_Complex_ORe(X1),c_Complex_OIm(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_53,plain,
c_Complex_OIm(c_Complex_Orcis(X1,X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Transcendental_Osin(X2)),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_54,plain,
c_Complex_ORe(c_Complex_Orcis(X1,X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Transcendental_Ocos(X2)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_55,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_56,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)),
inference(spm,[status(thm)],[c_0_29,c_0_40]) ).
fof(c_0_57,plain,
! [X721] : c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X721,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(X721)),
inference(variable_rename,[status(thm)],[fact_cos__periodic__pi]) ).
fof(c_0_58,plain,
! [X407] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X407) = X407,
inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).
fof(c_0_59,plain,
! [X723] : c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X723,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(X723)),
inference(variable_rename,[status(thm)],[fact_sin__periodic__pi]) ).
fof(c_0_60,plain,
! [X932] : c_Complex_Ocis(X932) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(X932),c_Transcendental_Osin(X932)),
inference(variable_rename,[status(thm)],[fact_cis__def]) ).
cnf(c_0_61,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,X1))),c_Complex_Ocis(X2)) = c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).
cnf(c_0_62,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_30]),c_0_45]) ).
cnf(c_0_63,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,X1)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Ocis(X2))) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Orcis(X1,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_41]),c_0_30])]) ).
fof(c_0_64,plain,
! [X103] : c_Complex_Ocis(X103) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X103),
inference(variable_rename,[status(thm)],[fact_cis__rcis__eq]) ).
cnf(c_0_65,negated_conjecture,
c_Complex_Orcis(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) != c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_66,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51])]) ).
cnf(c_0_67,plain,
c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Transcendental_Ocos(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Transcendental_Osin(X2))) = c_Complex_Orcis(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]) ).
cnf(c_0_68,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X2) = c_Groups_Ouminus__class_Ouminus(X1,X2)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_55]) ).
cnf(c_0_69,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_40]),c_0_56]) ).
cnf(c_0_70,plain,
c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(X1)),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_71,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_72,plain,
c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(X1)),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_73,plain,
c_Complex_Ocis(X1) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(X1),c_Transcendental_Osin(X1)),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_74,plain,
c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Orcis(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).
cnf(c_0_75,plain,
c_Complex_Ocis(X1) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_76,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).
fof(c_0_77,plain,
! [X1582,X1583,X1584] :
( ~ class_Rings_Ocomm__semiring__1(X1584)
| c_Groups_Oplus__class_Oplus(X1584,X1583,X1582) = c_Groups_Oplus__class_Oplus(X1584,X1582,X1583) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])])]) ).
cnf(c_0_78,negated_conjecture,
c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a) != c_Complex_Orcis(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)),
inference(rw,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_79,plain,
c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Ocis(X1)) = c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Transcendental_Opi)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]),c_0_70]),c_0_71]),c_0_72]),c_0_73]),c_0_74]),c_0_75]),c_0_76]),c_0_40])]) ).
cnf(c_0_80,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X3,X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_81,negated_conjecture,
c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Orcis(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r),v_a)) != c_Complex_Orcis(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)),
inference(rw,[status(thm)],[c_0_78,c_0_74]) ).
cnf(c_0_82,plain,
c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Orcis(X1,X2)) = c_Complex_Orcis(X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Transcendental_Opi)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_79]),c_0_41]) ).
cnf(c_0_83,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),
inference(spm,[status(thm)],[c_0_80,c_0_76]) ).
cnf(c_0_84,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82]),c_0_83])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW231+1 : TPTP v8.2.0. Released v5.2.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.14/0.37 % Computer : n010.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Sat May 18 19:09:53 EDT 2024
% 0.14/0.37 % CPUTime :
% 0.23/0.49 Running first-order theorem proving
% 0.23/0.49 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 100.39/13.28 # Version: 3.1.0
% 100.39/13.28 # Preprocessing class: FMLMSMSMSSSNFFN.
% 100.39/13.28 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 100.39/13.28 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 100.39/13.28 # Starting new_bool_3 with 300s (1) cores
% 100.39/13.28 # Starting new_bool_1 with 300s (1) cores
% 100.39/13.28 # Starting sh5l with 300s (1) cores
% 100.39/13.28 # sh5l with pid 10875 completed with status 0
% 100.39/13.28 # Result found by sh5l
% 100.39/13.28 # Preprocessing class: FMLMSMSMSSSNFFN.
% 100.39/13.28 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 100.39/13.28 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 100.39/13.28 # Starting new_bool_3 with 300s (1) cores
% 100.39/13.28 # Starting new_bool_1 with 300s (1) cores
% 100.39/13.28 # Starting sh5l with 300s (1) cores
% 100.39/13.28 # SinE strategy is gf500_gu_R04_F100_L20000
% 100.39/13.28 # Search class: FGHSM-SSLM31-DFFFFFNN
% 100.39/13.28 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 100.39/13.28 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 163s (1) cores
% 100.39/13.28 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 10878 completed with status 0
% 100.39/13.28 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 100.39/13.28 # Preprocessing class: FMLMSMSMSSSNFFN.
% 100.39/13.28 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 100.39/13.28 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 100.39/13.28 # Starting new_bool_3 with 300s (1) cores
% 100.39/13.28 # Starting new_bool_1 with 300s (1) cores
% 100.39/13.28 # Starting sh5l with 300s (1) cores
% 100.39/13.28 # SinE strategy is gf500_gu_R04_F100_L20000
% 100.39/13.28 # Search class: FGHSM-SSLM31-DFFFFFNN
% 100.39/13.28 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 100.39/13.28 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 163s (1) cores
% 100.39/13.28 # Preprocessing time : 0.015 s
% 100.39/13.28 # Presaturation interreduction done
% 100.39/13.28
% 100.39/13.28 # Proof found!
% 100.39/13.28 # SZS status Theorem
% 100.39/13.28 # SZS output start CNFRefutation
% See solution above
% 100.39/13.28 # Parsed axioms : 1201
% 100.39/13.28 # Removed by relevancy pruning/SinE : 404
% 100.39/13.28 # Initial clauses : 1032
% 100.39/13.28 # Removed in clause preprocessing : 28
% 100.39/13.28 # Initial clauses in saturation : 1004
% 100.39/13.28 # Processed clauses : 42037
% 100.39/13.28 # ...of these trivial : 1989
% 100.39/13.28 # ...subsumed : 27576
% 100.39/13.28 # ...remaining for further processing : 12472
% 100.39/13.28 # Other redundant clauses eliminated : 1652
% 100.39/13.28 # Clauses deleted for lack of memory : 0
% 100.39/13.28 # Backward-subsumed : 167
% 100.39/13.28 # Backward-rewritten : 1372
% 100.39/13.28 # Generated clauses : 335687
% 100.39/13.28 # ...of the previous two non-redundant : 282779
% 100.39/13.28 # ...aggressively subsumed : 0
% 100.39/13.28 # Contextual simplify-reflections : 7
% 100.39/13.28 # Paramodulations : 333999
% 100.39/13.28 # Factorizations : 16
% 100.39/13.28 # NegExts : 0
% 100.39/13.28 # Equation resolutions : 1681
% 100.39/13.28 # Disequality decompositions : 0
% 100.39/13.28 # Total rewrite steps : 359788
% 100.39/13.28 # ...of those cached : 334968
% 100.39/13.28 # Propositional unsat checks : 2
% 100.39/13.28 # Propositional check models : 0
% 100.39/13.28 # Propositional check unsatisfiable : 0
% 100.39/13.28 # Propositional clauses : 0
% 100.39/13.28 # Propositional clauses after purity: 0
% 100.39/13.28 # Propositional unsat core size : 0
% 100.39/13.28 # Propositional preprocessing time : 0.000
% 100.39/13.28 # Propositional encoding time : 0.469
% 100.39/13.28 # Propositional solver time : 0.385
% 100.39/13.28 # Success case prop preproc time : 0.000
% 100.39/13.28 # Success case prop encoding time : 0.000
% 100.39/13.28 # Success case prop solver time : 0.000
% 100.39/13.28 # Current number of processed clauses : 10025
% 100.39/13.28 # Positive orientable unit clauses : 2214
% 100.39/13.28 # Positive unorientable unit clauses: 33
% 100.39/13.28 # Negative unit clauses : 4937
% 100.39/13.28 # Non-unit-clauses : 2841
% 100.39/13.28 # Current number of unprocessed clauses: 241679
% 100.39/13.28 # ...number of literals in the above : 463688
% 100.39/13.28 # Current number of archived formulas : 0
% 100.39/13.28 # Current number of archived clauses : 2364
% 100.39/13.28 # Clause-clause subsumption calls (NU) : 722925
% 100.39/13.28 # Rec. Clause-clause subsumption calls : 577725
% 100.39/13.28 # Non-unit clause-clause subsumptions : 5092
% 100.39/13.28 # Unit Clause-clause subsumption calls : 5897221
% 100.39/13.28 # Rewrite failures with RHS unbound : 0
% 100.39/13.28 # BW rewrite match attempts : 116758
% 100.39/13.28 # BW rewrite match successes : 4205
% 100.39/13.28 # Condensation attempts : 0
% 100.39/13.28 # Condensation successes : 0
% 100.39/13.28 # Termbank termtop insertions : 8005824
% 100.39/13.28 # Search garbage collected termcells : 12992
% 100.39/13.28
% 100.39/13.28 # -------------------------------------------------
% 100.39/13.28 # User time : 12.130 s
% 100.39/13.28 # System time : 0.315 s
% 100.39/13.28 # Total time : 12.445 s
% 100.39/13.28 # Maximum resident set size: 6008 pages
% 100.39/13.28
% 100.39/13.28 # -------------------------------------------------
% 100.39/13.28 # User time : 12.166 s
% 100.39/13.28 # System time : 0.321 s
% 100.39/13.28 # Total time : 12.486 s
% 100.39/13.28 # Maximum resident set size: 3004 pages
% 100.39/13.28 % E---3.1 exiting
% 100.39/13.28 % E exiting
%------------------------------------------------------------------------------