%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW215+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:30:04 PM UTC 2026
% Result : Theorem 15.22s 9.72s
% Output : CNFRefutation 15.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 12 unt; 0 def)
% Number of atoms : 67 ( 3 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 68 ( 28 ~; 26 |; 6 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 38 ( 0 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_real__le__linear,axiom,
! [X12,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,X12)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12,X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__linear) ).
fof(fact_less__le__not__le,axiom,
! [X21,X17,X4] :
( class_Orderings_Opreorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X17,X21)
<=> ( c_Orderings_Oord__class_Oless__eq(X4,X17,X21)
& ~ c_Orderings_Oord__class_Oless__eq(X4,X21,X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_order__trans,axiom,
! [X13,X22,X7,X4] :
( class_Orderings_Opreorder(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X7,X22)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X22,X13)
=> c_Orderings_Oord__class_Oless__eq(X4,X7,X13) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).
fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
fof(fact_H_I5_J,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),v_da____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_H_I5_J) ).
fof(fact_less__eq__real__def,axiom,
! [X21,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X17,X21)
<=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X17,X21)
| X17 = X21 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
fof(fact_H_I2_J,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_H_I2_J) ).
fof(c_0_8,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
fof(c_0_9,plain,
! [X3126,X3127] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3127,X3126)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3126,X3127) ),
inference(variable_rename,[status(thm)],[fact_real__le__linear]) ).
fof(c_0_10,plain,
! [X21,X17,X4] :
( class_Orderings_Opreorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X17,X21)
<=> ( c_Orderings_Oord__class_Oless__eq(X4,X17,X21)
& ~ c_Orderings_Oord__class_Oless__eq(X4,X21,X17) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(c_0_11,plain,
! [X3299,X3300,X3301,X3302] :
( ~ class_Orderings_Opreorder(X3302)
| ~ c_Orderings_Oord__class_Oless__eq(X3302,X3301,X3300)
| ~ c_Orderings_Oord__class_Oless__eq(X3302,X3300,X3299)
| c_Orderings_Oord__class_Oless__eq(X3302,X3301,X3299) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).
cnf(c_0_12,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,plain,
! [X3260,X3261,X3262] :
( ( c_Orderings_Oord__class_Oless__eq(X3262,X3261,X3260)
| ~ c_Orderings_Oord__class_Oless(X3262,X3261,X3260)
| ~ class_Orderings_Opreorder(X3262) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3262,X3260,X3261)
| ~ c_Orderings_Oord__class_Oless(X3262,X3261,X3260)
| ~ class_Orderings_Opreorder(X3262) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3262,X3261,X3260)
| c_Orderings_Oord__class_Oless__eq(X3262,X3260,X3261)
| c_Orderings_Oord__class_Oless(X3262,X3261,X3260)
| ~ class_Orderings_Opreorder(X3262) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
cnf(c_0_15,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
cnf(c_0_18,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_14]) ).
cnf(c_0_19,negated_conjecture,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
cnf(c_0_20,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_17])]) ).
cnf(c_0_21,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),v_da____),
inference(split_conjunct,[status(thm)],[fact_H_I5_J]) ).
fof(c_0_22,plain,
! [X3280,X3281] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3281,X3280)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3281,X3280)
| X3281 = X3280 )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3281,X3280)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3281,X3280) )
& ( X3281 != X3280
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3281,X3280) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])]) ).
cnf(c_0_23,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[fact_H_I2_J]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW215+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n009.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 06:26:41 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 15.22/9.72 % Version : CSE_E---1.7
% 15.22/9.72 % Problem : theBenchmark.p
% 15.22/9.72 % SZS status Theorem for theBenchmark.p
% 15.22/9.72 % SZS output start CNFRefutation
% See solution above
% 15.22/9.78 % Total time : 6.573s
%------------------------------------------------------------------------------