TSTP Solution File: SWW254+1 by E---3.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.2.0
% Problem : SWW254+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n032.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 : Mon Jun 24 18:11:24 EDT 2024
% Result : Theorem 8.71s 1.64s
% Output : CNFRefutation 8.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 45 ( 27 unt; 0 def)
% Number of atoms : 161 ( 18 equ)
% Maximal formula atoms : 62 ( 3 avg)
% Number of connectives : 189 ( 73 ~; 72 |; 22 &)
% ( 8 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 49 ( 4 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_less__le__not__le,axiom,
! [X24,X7,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X7,X24)
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X7,X24)
& ~ c_Orderings_Oord__class_Oless__eq(X6,X24,X7) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.DIUXeBFOEP/E---3.1_923.p',fact_less__le__not__le) ).
fof(fact_cq0,axiom,
! [X15] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X15))),
file('/export/starexec/sandbox/tmp/tmp.DIUXeBFOEP/E---3.1_923.p',fact_cq0) ).
fof(conj_0,conjecture,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) ),
file('/export/starexec/sandbox/tmp/tmp.DIUXeBFOEP/E---3.1_923.p',conj_0) ).
fof(fact_pqc0,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/tmp/tmp.DIUXeBFOEP/E---3.1_923.p',fact_pqc0) ).
fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/tmp/tmp.DIUXeBFOEP/E---3.1_923.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
fof(fact_q_I2_J,axiom,
! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X3) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X3)),
file('/export/starexec/sandbox/tmp/tmp.DIUXeBFOEP/E---3.1_923.p',fact_q_I2_J) ).
fof(fact_divide__less__eq,axiom,
! [X8,X33,X9,X6] :
( class_Fields_Olinordered__field__inverse__zero(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Rings_Oinverse__class_Odivide(X6,X9,X33),X8)
<=> ( ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X33)
=> c_Orderings_Oord__class_Oless(X6,X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X8),X33)) )
& ( ~ c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X33)
=> ( ( c_Orderings_Oord__class_Oless(X6,X33,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X8),X33),X9) )
& ( ~ c_Orderings_Oord__class_Oless(X6,X33,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X8) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.DIUXeBFOEP/E---3.1_923.p',fact_divide__less__eq) ).
fof(fact_zero__less__norm__iff,axiom,
! [X7,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X6,X7))
<=> X7 != c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/tmp/tmp.DIUXeBFOEP/E---3.1_923.p',fact_zero__less__norm__iff) ).
fof(fact_real__mult__1,axiom,
! [X19] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X19) = X19,
file('/export/starexec/sandbox/tmp/tmp.DIUXeBFOEP/E---3.1_923.p',fact_real__mult__1) ).
fof(fact_pc0,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/tmp/tmp.DIUXeBFOEP/E---3.1_923.p',fact_pc0) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/tmp/tmp.DIUXeBFOEP/E---3.1_923.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/tmp/tmp.DIUXeBFOEP/E---3.1_923.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(c_0_12,plain,
! [X24,X7,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X7,X24)
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X7,X24)
& ~ c_Orderings_Oord__class_Oless__eq(X6,X24,X7) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(c_0_13,plain,
! [X173] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X173))),
inference(variable_rename,[status(thm)],[fact_cq0]) ).
fof(c_0_14,negated_conjecture,
~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_15,plain,
! [X1311,X1312,X1313] :
( ( c_Orderings_Oord__class_Oless__eq(X1313,X1312,X1311)
| ~ c_Orderings_Oord__class_Oless(X1313,X1312,X1311)
| ~ class_Orderings_Opreorder(X1313) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X1313,X1311,X1312)
| ~ c_Orderings_Oord__class_Oless(X1313,X1312,X1311)
| ~ class_Orderings_Opreorder(X1313) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X1313,X1312,X1311)
| c_Orderings_Oord__class_Oless__eq(X1313,X1311,X1312)
| c_Orderings_Oord__class_Oless(X1313,X1312,X1311)
| ~ class_Orderings_Opreorder(X1313) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
cnf(c_0_16,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X1))),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(split_conjunct,[status(thm)],[fact_pqc0]) ).
fof(c_0_18,negated_conjecture,
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])]) ).
cnf(c_0_19,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X1))),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
fof(c_0_22,plain,
! [X182] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X182) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X182)),
inference(variable_rename,[status(thm)],[fact_q_I2_J]) ).
fof(c_0_23,plain,
! [X8,X33,X9,X6] :
( class_Fields_Olinordered__field__inverse__zero(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Rings_Oinverse__class_Odivide(X6,X9,X33),X8)
<=> ( ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X33)
=> c_Orderings_Oord__class_Oless(X6,X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X8),X33)) )
& ( ~ c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X33)
=> ( ( c_Orderings_Oord__class_Oless(X6,X33,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X8),X33),X9) )
& ( ~ c_Orderings_Oord__class_Oless(X6,X33,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X8) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divide__less__eq]) ).
cnf(c_0_24,negated_conjecture,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_26,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X1) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_27,plain,
! [X7,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X6,X7))
<=> X7 != c_Groups_Ozero__class_Ozero(X6) ) ),
inference(fof_simplification,[status(thm)],[fact_zero__less__norm__iff]) ).
fof(c_0_28,plain,
! [X1072,X1073,X1074,X1075] :
( ( ~ c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073)
| c_Orderings_Oord__class_Oless(X1075,X1074,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073))
| ~ c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
| ~ class_Fields_Olinordered__field__inverse__zero(X1075) )
& ( ~ c_Orderings_Oord__class_Oless(X1075,X1073,c_Groups_Ozero__class_Ozero(X1075))
| c_Orderings_Oord__class_Oless(X1075,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073),X1074)
| c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073)
| ~ c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
| ~ class_Fields_Olinordered__field__inverse__zero(X1075) )
& ( c_Orderings_Oord__class_Oless(X1075,X1073,c_Groups_Ozero__class_Ozero(X1075))
| c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1072)
| c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073)
| ~ c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
| ~ class_Fields_Olinordered__field__inverse__zero(X1075) )
& ( ~ c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073)
| c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073)
| c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
| ~ class_Fields_Olinordered__field__inverse__zero(X1075) )
& ( ~ c_Orderings_Oord__class_Oless(X1075,X1073,c_Groups_Ozero__class_Ozero(X1075))
| c_Orderings_Oord__class_Oless(X1075,X1073,c_Groups_Ozero__class_Ozero(X1075))
| c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073)
| c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
| ~ class_Fields_Olinordered__field__inverse__zero(X1075) )
& ( ~ c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1072)
| c_Orderings_Oord__class_Oless(X1075,X1073,c_Groups_Ozero__class_Ozero(X1075))
| c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073)
| c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
| ~ class_Fields_Olinordered__field__inverse__zero(X1075) )
& ( ~ c_Orderings_Oord__class_Oless(X1075,X1073,c_Groups_Ozero__class_Ozero(X1075))
| ~ c_Orderings_Oord__class_Oless(X1075,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073),X1074)
| c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073)
| c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
| ~ class_Fields_Olinordered__field__inverse__zero(X1075) )
& ( ~ c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1072)
| ~ c_Orderings_Oord__class_Oless(X1075,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073),X1074)
| c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073)
| c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
| ~ class_Fields_Olinordered__field__inverse__zero(X1075) )
& ( ~ c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073)
| ~ c_Orderings_Oord__class_Oless(X1075,X1074,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073))
| c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
| ~ class_Fields_Olinordered__field__inverse__zero(X1075) )
& ( ~ c_Orderings_Oord__class_Oless(X1075,X1073,c_Groups_Ozero__class_Ozero(X1075))
| c_Orderings_Oord__class_Oless(X1075,X1073,c_Groups_Ozero__class_Ozero(X1075))
| ~ c_Orderings_Oord__class_Oless(X1075,X1074,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073))
| c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
| ~ class_Fields_Olinordered__field__inverse__zero(X1075) )
& ( ~ c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1072)
| c_Orderings_Oord__class_Oless(X1075,X1073,c_Groups_Ozero__class_Ozero(X1075))
| ~ c_Orderings_Oord__class_Oless(X1075,X1074,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073))
| c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
| ~ class_Fields_Olinordered__field__inverse__zero(X1075) )
& ( ~ c_Orderings_Oord__class_Oless(X1075,X1073,c_Groups_Ozero__class_Ozero(X1075))
| ~ c_Orderings_Oord__class_Oless(X1075,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073),X1074)
| ~ c_Orderings_Oord__class_Oless(X1075,X1074,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073))
| c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
| ~ class_Fields_Olinordered__field__inverse__zero(X1075) )
& ( ~ c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1072)
| ~ c_Orderings_Oord__class_Oless(X1075,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073),X1074)
| ~ c_Orderings_Oord__class_Oless(X1075,X1074,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073))
| c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
| ~ class_Fields_Olinordered__field__inverse__zero(X1075) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])]) ).
cnf(c_0_29,negated_conjecture,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_17]),c_0_17]) ).
cnf(c_0_30,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____))),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
fof(c_0_31,plain,
! [X1377] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1377) = X1377,
inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).
fof(c_0_32,plain,
! [X102,X103] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X103,X102))
| X102 != c_Groups_Ozero__class_Ozero(X103)
| ~ class_RealVector_Oreal__normed__vector(X103) )
& ( X102 = c_Groups_Ozero__class_Ozero(X103)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X103,X102))
| ~ class_RealVector_Oreal__normed__vector(X103) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])]) ).
fof(c_0_33,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(fof_simplification,[status(thm)],[fact_pc0]) ).
cnf(c_0_34,plain,
( c_Orderings_Oord__class_Oless(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,negated_conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(sr,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,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_31]) ).
cnf(c_0_37,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero]) ).
cnf(c_0_38,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1))
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
fof(c_0_40,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[c_0_33]) ).
cnf(c_0_41,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_37])]),c_0_30]) ).
cnf(c_0_42,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SWW254+1 : TPTP v8.2.0. Released v5.2.0.
% 0.00/0.09 % Command : run_E %s %d THM
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Wed Jun 19 07:04:53 EDT 2024
% 0.13/0.28 % CPUTime :
% 0.14/0.47 Running first-order theorem proving
% 0.14/0.47 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.DIUXeBFOEP/E---3.1_923.p
% 8.71/1.64 # Version: 3.2.0
% 8.71/1.64 # Preprocessing class: FMLMSMSMSSSNFFN.
% 8.71/1.64 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.71/1.64 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.71/1.64 # Starting new_bool_3 with 300s (1) cores
% 8.71/1.64 # Starting new_bool_1 with 300s (1) cores
% 8.71/1.64 # Starting sh5l with 300s (1) cores
% 8.71/1.64 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1055 completed with status 0
% 8.71/1.64 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 8.71/1.64 # Preprocessing class: FMLMSMSMSSSNFFN.
% 8.71/1.64 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.71/1.64 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.71/1.64 # No SInE strategy applied
% 8.71/1.64 # Search class: FGHSM-SMLM32-DFFFFFNN
% 8.71/1.64 # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 8.71/1.64 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with 113s (1) cores
% 8.71/1.64 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 8.71/1.64 # Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 8.71/1.64 # Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 8.71/1.64 # Starting G-E--_208_B00_00_F1_SE_CS_SP_PS_S5PRR_S00EN with 113s (1) cores
% 8.71/1.64 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with pid 1067 completed with status 0
% 8.71/1.64 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y
% 8.71/1.64 # Preprocessing class: FMLMSMSMSSSNFFN.
% 8.71/1.64 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.71/1.64 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.71/1.64 # No SInE strategy applied
% 8.71/1.64 # Search class: FGHSM-SMLM32-DFFFFFNN
% 8.71/1.64 # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 8.71/1.64 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with 113s (1) cores
% 8.71/1.64 # Preprocessing time : 0.024 s
% 8.71/1.64 # Presaturation interreduction done
% 8.71/1.64
% 8.71/1.64 # Proof found!
% 8.71/1.64 # SZS status Theorem
% 8.71/1.64 # SZS output start CNFRefutation
% See solution above
% 8.71/1.64 # Parsed axioms : 1245
% 8.71/1.64 # Removed by relevancy pruning/SinE : 0
% 8.71/1.64 # Initial clauses : 1805
% 8.71/1.64 # Removed in clause preprocessing : 83
% 8.71/1.64 # Initial clauses in saturation : 1722
% 8.71/1.64 # Processed clauses : 4809
% 8.71/1.64 # ...of these trivial : 132
% 8.71/1.64 # ...subsumed : 1242
% 8.71/1.64 # ...remaining for further processing : 3435
% 8.71/1.64 # Other redundant clauses eliminated : 479
% 8.71/1.64 # Clauses deleted for lack of memory : 0
% 8.71/1.64 # Backward-subsumed : 9
% 8.71/1.64 # Backward-rewritten : 30
% 8.71/1.64 # Generated clauses : 42395
% 8.71/1.64 # ...of the previous two non-redundant : 37943
% 8.71/1.64 # ...aggressively subsumed : 0
% 8.71/1.64 # Contextual simplify-reflections : 2
% 8.71/1.64 # Paramodulations : 41901
% 8.71/1.64 # Factorizations : 11
% 8.71/1.64 # NegExts : 0
% 8.71/1.64 # Equation resolutions : 498
% 8.71/1.64 # Disequality decompositions : 0
% 8.71/1.64 # Total rewrite steps : 29914
% 8.71/1.64 # ...of those cached : 27470
% 8.71/1.64 # Propositional unsat checks : 0
% 8.71/1.64 # Propositional check models : 0
% 8.71/1.64 # Propositional check unsatisfiable : 0
% 8.71/1.64 # Propositional clauses : 0
% 8.71/1.64 # Propositional clauses after purity: 0
% 8.71/1.64 # Propositional unsat core size : 0
% 8.71/1.64 # Propositional preprocessing time : 0.000
% 8.71/1.64 # Propositional encoding time : 0.000
% 8.71/1.64 # Propositional solver time : 0.000
% 8.71/1.64 # Success case prop preproc time : 0.000
% 8.71/1.64 # Success case prop encoding time : 0.000
% 8.71/1.64 # Success case prop solver time : 0.000
% 8.71/1.64 # Current number of processed clauses : 1775
% 8.71/1.64 # Positive orientable unit clauses : 384
% 8.71/1.64 # Positive unorientable unit clauses: 8
% 8.71/1.64 # Negative unit clauses : 66
% 8.71/1.64 # Non-unit-clauses : 1317
% 8.71/1.64 # Current number of unprocessed clauses: 36305
% 8.71/1.64 # ...number of literals in the above : 127553
% 8.71/1.64 # Current number of archived formulas : 0
% 8.71/1.64 # Current number of archived clauses : 1521
% 8.71/1.64 # Clause-clause subsumption calls (NU) : 378701
% 8.71/1.64 # Rec. Clause-clause subsumption calls : 174500
% 8.71/1.64 # Non-unit clause-clause subsumptions : 465
% 8.71/1.64 # Unit Clause-clause subsumption calls : 18152
% 8.71/1.64 # Rewrite failures with RHS unbound : 0
% 8.71/1.64 # BW rewrite match attempts : 1735
% 8.71/1.64 # BW rewrite match successes : 175
% 8.71/1.64 # Condensation attempts : 0
% 8.71/1.64 # Condensation successes : 0
% 8.71/1.64 # Termbank termtop insertions : 1107681
% 8.71/1.64 # Search garbage collected termcells : 22950
% 8.71/1.64
% 8.71/1.64 # -------------------------------------------------
% 8.71/1.64 # User time : 1.040 s
% 8.71/1.64 # System time : 0.049 s
% 8.71/1.64 # Total time : 1.088 s
% 8.71/1.64 # Maximum resident set size: 8612 pages
% 8.71/1.64
% 8.71/1.64 # -------------------------------------------------
% 8.71/1.64 # User time : 4.909 s
% 8.71/1.64 # System time : 0.184 s
% 8.71/1.64 # Total time : 5.093 s
% 8.71/1.64 # Maximum resident set size: 3140 pages
% 8.71/1.64 % E---3.1 exiting
% 8.71/1.64 % E exiting
%------------------------------------------------------------------------------