%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW237+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n006.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 05:30:47 PM UTC 2026
% Result : Theorem 25.16s 15.65s
% Output : CNFRefutation 25.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 53 ( 21 unt; 0 def)
% Number of atoms : 126 ( 9 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 125 ( 52 ~; 49 |; 7 &)
% ( 4 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 78 ( 0 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_leI,axiom,
! [X9,X7,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X7,X9)
=> c_Orderings_Oord__class_Oless__eq(X6,X9,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leI) ).
fof(fact_real__le__trans,axiom,
! [X19,X20,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X20)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X20,X19)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__trans) ).
fof(fact_less__eq__real__def,axiom,
! [X16,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X16)
<=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X15,X16)
| X15 = X16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
fof(conj_2,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_da____,v_mazh),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(fact_less__le__not__le,axiom,
! [X16,X15,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X15,X16)
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X15,X16)
& ~ c_Orderings_Oord__class_Oless__eq(X6,X16,X15) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(conj_0,hypothesis,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_mzh,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_mazh,v_ma)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_xt1_I5_J,axiom,
! [X7,X9,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X9,X7)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X7,X9)
=> X7 = X9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_abs__ge__self,axiom,
! [X5,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,X5,c_Groups_Oabs__class_Oabs(X6,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__ge__self) ).
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_add__less__cancel__right,axiom,
! [X10,X11,X12,X6] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X12,X11),c_Groups_Oplus__class_Oplus(X6,X10,X11))
<=> c_Orderings_Oord__class_Oless(X6,X12,X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(conj_1,hypothesis,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),v_ma),v_mzh),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(c_0_15,plain,
! [X9,X7,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X7,X9)
=> c_Orderings_Oord__class_Oless__eq(X6,X9,X7) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
fof(c_0_16,plain,
! [X3450,X3451,X3452] :
( ~ class_Orderings_Olinorder(X3452)
| c_Orderings_Oord__class_Oless(X3452,X3451,X3450)
| c_Orderings_Oord__class_Oless__eq(X3452,X3450,X3451) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])]) ).
fof(c_0_17,plain,
! [X3166,X3167,X3168] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3168,X3167)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3167,X3166)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3168,X3166) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__trans])]) ).
fof(c_0_18,plain,
! [X3506,X3507] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3507,X3506)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3507,X3506)
| X3507 = X3506 )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3507,X3506)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3507,X3506) )
& ( X3507 != X3506
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3507,X3506) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])]) ).
fof(c_0_19,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_da____,v_mazh),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_2])]) ).
cnf(c_0_20,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
fof(c_0_22,plain,
! [X16,X15,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X15,X16)
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X15,X16)
& ~ c_Orderings_Oord__class_Oless__eq(X6,X16,X15) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
cnf(c_0_23,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
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_18]) ).
cnf(c_0_25,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_da____,v_mazh),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_27,plain,
! [X3456,X3457,X3458] :
( ( c_Orderings_Oord__class_Oless__eq(X3458,X3457,X3456)
| ~ c_Orderings_Oord__class_Oless(X3458,X3457,X3456)
| ~ class_Orderings_Opreorder(X3458) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3458,X3456,X3457)
| ~ c_Orderings_Oord__class_Oless(X3458,X3457,X3456)
| ~ class_Orderings_Opreorder(X3458) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3458,X3457,X3456)
| c_Orderings_Oord__class_Oless__eq(X3458,X3456,X3457)
| c_Orderings_Oord__class_Oless(X3458,X3457,X3456)
| ~ class_Orderings_Opreorder(X3458) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])]) ).
cnf(c_0_28,hypothesis,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_mzh,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_mazh,v_ma)),
inference(split_conjunct,[status(thm)],[conj_0]) ).
fof(c_0_29,plain,
! [X3091,X3092,X3093] :
( ~ class_Orderings_Oorder(X3093)
| ~ c_Orderings_Oord__class_Oless__eq(X3093,X3092,X3091)
| ~ c_Orderings_Oord__class_Oless__eq(X3093,X3091,X3092)
| X3091 = X3092 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).
fof(c_0_30,plain,
! [X3011,X3012] :
( ~ class_Groups_Oordered__ab__group__add__abs(X3012)
| c_Orderings_Oord__class_Oless__eq(X3012,X3011,c_Groups_Oabs__class_Oabs(X3012,X3011)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__self])]) ).
cnf(c_0_31,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_32,negated_conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_mazh,v_da____),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,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_27]) ).
cnf(c_0_34,hypothesis,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_mazh,v_ma))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,v_mzh) ),
inference(spm,[status(thm)],[c_0_23,c_0_28]) ).
cnf(c_0_35,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
fof(c_0_36,plain,
! [X3496,X3497,X3498,X3499] :
( ( ~ c_Orderings_Oord__class_Oless(X3499,c_Groups_Oplus__class_Oplus(X3499,X3498,X3497),c_Groups_Oplus__class_Oplus(X3499,X3496,X3497))
| c_Orderings_Oord__class_Oless(X3499,X3498,X3496)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3499) )
& ( ~ c_Orderings_Oord__class_Oless(X3499,X3498,X3496)
| c_Orderings_Oord__class_Oless(X3499,c_Groups_Oplus__class_Oplus(X3499,X3498,X3497),c_Groups_Oplus__class_Oplus(X3499,X3496,X3497))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3499) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).
cnf(c_0_37,plain,
( X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oabs__class_Oabs(X1,X2))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,negated_conjecture,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,v_da____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,v_mazh) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_40,hypothesis,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_mazh,v_ma),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,v_mzh) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).
cnf(c_0_41,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_42,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le]) ).
cnf(c_0_43,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),X2)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,negated_conjecture,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_mazh,X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,v_da____) ),
inference(spm,[status(thm)],[c_0_39,c_0_26]) ).
cnf(c_0_45,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).
cnf(c_0_46,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs]) ).
cnf(c_0_47,hypothesis,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_mazh,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,v_ma),v_mzh) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).
cnf(c_0_48,hypothesis,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),v_ma),v_mzh),
inference(split_conjunct,[status(thm)],[conj_1]) ).
cnf(c_0_49,negated_conjecture,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____) = v_da____
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_mazh,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46])]) ).
cnf(c_0_50,hypothesis,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_mazh,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____)),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_51,negated_conjecture,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____) = v_da____,
inference(sr,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_52,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWW237+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n006.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 06:29:01 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 25.16/15.65 % Version : CSE_E---1.7
% 25.16/15.65 % Problem : theBenchmark.p
% 25.16/15.65 % SZS status Theorem for theBenchmark.p
% 25.16/15.65 % SZS output start CNFRefutation
% See solution above
% 25.27/15.76 % Total time : 10.579s
%------------------------------------------------------------------------------