%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW254+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:10:10 PM UTC 2026
% Result : Theorem 15.91s 2.93s
% Output : CNFRefutation 15.91s
% 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,X24,X7)
& c_Orderings_Oord__class_Oless__eq(X6,X7,X24) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.p',fact_pqc0) ).
fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/benchmark/theBenchmark.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,X33,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X8) )
& ( 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,c_Groups_Ozero__class_Ozero(X6),X33)
=> c_Orderings_Oord__class_Oless(X6,X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X8),X33)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.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,X24,X7)
& c_Orderings_Oord__class_Oless__eq(X6,X7,X24) ) ) ),
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] :
( ( ~ class_Orderings_Opreorder(X1313)
| c_Orderings_Oord__class_Oless(X1313,X1312,X1311)
| c_Orderings_Oord__class_Oless__eq(X1313,X1311,X1312)
| ~ c_Orderings_Oord__class_Oless__eq(X1313,X1312,X1311) )
& ( ~ class_Orderings_Opreorder(X1313)
| ~ c_Orderings_Oord__class_Oless(X1313,X1312,X1311)
| ~ c_Orderings_Oord__class_Oless__eq(X1313,X1311,X1312) )
& ( ~ class_Orderings_Opreorder(X1313)
| ~ c_Orderings_Oord__class_Oless(X1313,X1312,X1311)
| c_Orderings_Oord__class_Oless__eq(X1313,X1312,X1311) ) ),
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_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))))
| ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])]) ).
cnf(c_0_19,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
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,X33,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X8) )
& ( 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,c_Groups_Ozero__class_Ozero(X6),X33)
=> c_Orderings_Oord__class_Oless(X6,X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X8),X33)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divide__less__eq]) ).
cnf(c_0_24,negated_conjecture,
( 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)) ),
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] :
( ( ~ class_Fields_Olinordered__field__inverse__zero(X1075)
| c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
| ~ c_Orderings_Oord__class_Oless(X1075,X1074,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073))
| ~ 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),X1072) )
& ( ~ class_Fields_Olinordered__field__inverse__zero(X1075)
| c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
| ~ c_Orderings_Oord__class_Oless(X1075,X1074,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073))
| ~ c_Orderings_Oord__class_Oless(X1075,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073),X1074)
| ~ c_Orderings_Oord__class_Oless(X1075,X1073,c_Groups_Ozero__class_Ozero(X1075)) )
& ( ~ class_Fields_Olinordered__field__inverse__zero(X1075)
| c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
| ~ c_Orderings_Oord__class_Oless(X1075,X1074,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073))
| 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) )
& ( ~ class_Fields_Olinordered__field__inverse__zero(X1075)
| c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
| ~ c_Orderings_Oord__class_Oless(X1075,X1074,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073))
| 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)) )
& ( ~ class_Fields_Olinordered__field__inverse__zero(X1075)
| c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
| ~ c_Orderings_Oord__class_Oless(X1075,X1074,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073))
| ~ c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073) )
& ( ~ class_Fields_Olinordered__field__inverse__zero(X1075)
| c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
| c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073)
| ~ 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),X1072) )
& ( ~ class_Fields_Olinordered__field__inverse__zero(X1075)
| c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
| c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073)
| ~ c_Orderings_Oord__class_Oless(X1075,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073),X1074)
| ~ c_Orderings_Oord__class_Oless(X1075,X1073,c_Groups_Ozero__class_Ozero(X1075)) )
& ( ~ class_Fields_Olinordered__field__inverse__zero(X1075)
| c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
| c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073)
| 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) )
& ( ~ class_Fields_Olinordered__field__inverse__zero(X1075)
| c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
| c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073)
| 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)) )
& ( ~ class_Fields_Olinordered__field__inverse__zero(X1075)
| c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
| 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) )
& ( ~ class_Fields_Olinordered__field__inverse__zero(X1075)
| ~ c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
| 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),X1072)
| c_Orderings_Oord__class_Oless(X1075,X1073,c_Groups_Ozero__class_Ozero(X1075)) )
& ( ~ class_Fields_Olinordered__field__inverse__zero(X1075)
| ~ c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
| c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073)
| c_Orderings_Oord__class_Oless(X1075,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073),X1074)
| ~ c_Orderings_Oord__class_Oless(X1075,X1073,c_Groups_Ozero__class_Ozero(X1075)) )
& ( ~ class_Fields_Olinordered__field__inverse__zero(X1075)
| ~ c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
| c_Orderings_Oord__class_Oless(X1075,X1074,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073))
| ~ c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073) ) ),
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_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_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(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] :
( ( ~ class_RealVector_Oreal__normed__vector(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)) ) ),
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,
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)) ),
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,
( ~ class_RealVector_Oreal__normed__vector(X2)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1))
| X1 = c_Groups_Ozero__class_Ozero(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,
( 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))
| X1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
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
% 0.00/0.03 % Problem : SWW254+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n007.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 21 09:42:05 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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/benchmark/theBenchmark.p
% 15.91/2.93 % Version: 3.5.1
% 15.91/2.93 % Preprocessing class: FMLMSMSMSSSNFFN.
% 15.91/2.93 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.91/2.93 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 15.91/2.93 % Starting new_bool_3 with 300s (1) cores
% 15.91/2.93 % Starting new_bool_1 with 300s (1) cores
% 15.91/2.93 % Starting sh5l with 300s (1) cores
% 15.91/2.93 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 771025 completed with status 0
% 15.91/2.93 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 15.91/2.93 % Preprocessing class: FMLMSMSMSSSNFFN.
% 15.91/2.93 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.91/2.93 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 15.91/2.93 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 15.91/2.93 % No SInE strategy applied
% 15.91/2.93 % Search class: FGHSM-SMLM32-DFFFFFNN
% 15.91/2.93 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 15.91/2.93 % Starting SubtermCWHack with 136s (1) cores
% 15.91/2.93 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 15.91/2.93 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 15.91/2.93 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 15.91/2.93 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 15.91/2.93 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 771039 completed with status 0
% 15.91/2.93 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 15.91/2.93 % Preprocessing class: FMLMSMSMSSSNFFN.
% 15.91/2.93 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.91/2.93 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 15.91/2.93 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 15.91/2.93 % No SInE strategy applied
% 15.91/2.93 % Search class: FGHSM-SMLM32-DFFFFFNN
% 15.91/2.93 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 15.91/2.93 % Starting SubtermCWHack with 136s (1) cores
% 15.91/2.93 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 15.91/2.93 % Preprocessing time : 0.030 s
% 15.91/2.93 % Presaturation interreduction done
% 15.91/2.93
% 15.91/2.93 % Proof found!
% 15.91/2.93 % SZS status Theorem
% 15.91/2.93 % SZS output start CNFRefutation
% See solution above
% 15.91/2.93 % Parsed axioms : 1245
% 15.91/2.93 % Removed by relevancy pruning/SinE : 0
% 15.91/2.93 % Initial clauses : 1805
% 15.91/2.93 % Removed in clause preprocessing : 83
% 15.91/2.93 % Initial clauses in saturation : 1722
% 15.91/2.93 % Processed clauses : 4798
% 15.91/2.93 % ...of these trivial : 107
% 15.91/2.93 % ...subsumed : 1284
% 15.91/2.93 % ...remaining for further processing : 3407
% 15.91/2.93 % Other redundant clauses eliminated : 346
% 15.91/2.93 % Clauses deleted for lack of memory : 0
% 15.91/2.93 % Backward-subsumed : 12
% 15.91/2.93 % Backward-rewritten : 26
% 15.91/2.93 % Generated clauses : 44036
% 15.91/2.93 % ...of the previous two non-redundant : 38804
% 15.91/2.93 % ...aggressively subsumed : 0
% 15.91/2.93 % Contextual simplify-reflections : 3
% 15.91/2.93 % Paramodulations : 43680
% 15.91/2.93 % Factorizations : 11
% 15.91/2.93 % NegExts : 0
% 15.91/2.93 % Equation resolutions : 360
% 15.91/2.93 % Disequality decompositions : 0
% 15.91/2.93 % Total rewrite steps : 33908
% 15.91/2.93 % ...of those cached : 31390
% 15.91/2.93 % Propositional unsat checks : 0
% 15.91/2.93 % Propositional check models : 0
% 15.91/2.93 % Propositional check unsatisfiable : 0
% 15.91/2.93 % Propositional clauses : 0
% 15.91/2.93 % Propositional clauses after purity: 0
% 15.91/2.93 % Propositional unsat core size : 0
% 15.91/2.93 % Propositional preprocessing time : 0.000
% 15.91/2.93 % Propositional encoding time : 0.000
% 15.91/2.93 % Propositional solver time : 0.000
% 15.91/2.93 % Success case prop preproc time : 0.000
% 15.91/2.93 % Success case prop encoding time : 0.000
% 15.91/2.93 % Success case prop solver time : 0.000
% 15.91/2.93 % Current number of processed clauses : 1748
% 15.91/2.93 % Positive orientable unit clauses : 403
% 15.91/2.93 % Positive unorientable unit clauses: 8
% 15.91/2.93 % Negative unit clauses : 63
% 15.91/2.93 % Non-unit-clauses : 1274
% 15.91/2.93 % Current number of unprocessed clauses: 37199
% 15.91/2.93 % ...number of literals in the above : 129940
% 15.91/2.93 % Current number of archived formulas : 0
% 15.91/2.93 % Current number of archived clauses : 1520
% 15.91/2.93 % Clause-clause subsumption calls (NU) : 414002
% 15.91/2.93 % Rec. Clause-clause subsumption calls : 181407
% 15.91/2.93 % Non-unit clause-clause subsumptions : 502
% 15.91/2.93 % Unit Clause-clause subsumption calls : 2697
% 15.91/2.93 % Rewrite failures with RHS unbound : 0
% 15.91/2.93 % BW rewrite match attempts : 1637
% 15.91/2.93 % BW rewrite match successes : 233
% 15.91/2.93 % Condensation attempts : 0
% 15.91/2.93 % Condensation successes : 0
% 15.91/2.93 % Termbank termtop insertions : 1180593
% 15.91/2.93 % Search garbage collected termcells : 22950
% 15.91/2.93
% 15.91/2.93 % -------------------------------------------------
% 15.91/2.93 % User time : 2.181 s
% 15.91/2.93 % System time : 0.099 s
% 15.91/2.93 % Total time : 2.280 s
% 15.91/2.93 % Maximum resident set size: 10448 pages
% 15.91/2.93
% 15.91/2.93 % -------------------------------------------------
% 15.91/2.93 % User time : 10.550 s
% 15.91/2.93 % System time : 0.416 s
% 15.91/2.93 % Total time : 10.965 s
% 15.91/2.93 % Maximum resident set size: 6144 pages
% 15.91/2.93 % E exiting
%------------------------------------------------------------------------------