%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW224+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 : n026.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 03:10:07 PM UTC 2026
% Result : Theorem 12.40s 2.30s
% Output : CNFRefutation 12.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 22
% Syntax : Number of formulae : 88 ( 37 unt; 0 def)
% Number of atoms : 215 ( 27 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 214 ( 87 ~; 83 |; 14 &)
% ( 8 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 138 ( 0 sgn 87 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_less__le__not__le,axiom,
! [X16,X6,X7] :
( class_Orderings_Opreorder(X7)
=> ( c_Orderings_Oord__class_Oless(X7,X6,X16)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(X7,X16,X6)
& c_Orderings_Oord__class_Oless__eq(X7,X6,X16) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_real__le__trans,axiom,
! [X21,X22,X23] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X23,X22)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X22,X21)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X23,X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__trans) ).
fof(conj_1,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
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(conj_0,hypothesis,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m,v_x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_real__le__linear,axiom,
! [X20,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X20,X13)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__linear) ).
fof(conj_2,conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)),v_e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
fof(fact_not__leE,axiom,
! [X12,X14,X7] :
( class_Orderings_Olinorder(X7)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X7,X14,X12)
=> c_Orderings_Oord__class_Oless(X7,X12,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__leE) ).
fof(fact_xt1_I7_J,axiom,
! [X13,X12,X14,X7] :
( class_Orderings_Oorder(X7)
=> ( c_Orderings_Oord__class_Oless(X7,X14,X12)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X13,X14)
=> c_Orderings_Oord__class_Oless(X7,X13,X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_xt1_I10_J,axiom,
! [X13,X12,X14,X7] :
( class_Orderings_Oorder(X7)
=> ( c_Orderings_Oord__class_Oless(X7,X14,X12)
=> ( c_Orderings_Oord__class_Oless(X7,X13,X14)
=> c_Orderings_Oord__class_Oless(X7,X13,X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_real__norm__def,axiom,
! [X31] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X31) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X31),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(fact_linorder__antisym__conv2,axiom,
! [X16,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X6,X16)
=> ( ~ c_Orderings_Oord__class_Oless(X7,X6,X16)
<=> X6 = X16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
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__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(fact_add__strict__right__mono,axiom,
! [X11,X8,X9,X7] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X7)
=> ( c_Orderings_Oord__class_Oless(X7,X9,X8)
=> c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X9,X11),c_Groups_Oplus__class_Oplus(X7,X8,X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
fof(fact_abs__diff__less__iff,axiom,
! [X4,X5,X6,X7] :
( class_Rings_Olinordered__idom(X7)
=> ( c_Orderings_Oord__class_Oless(X7,c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,X6,X5)),X4)
<=> ( c_Orderings_Oord__class_Oless(X7,X6,c_Groups_Oplus__class_Oplus(X7,X5,X4))
& c_Orderings_Oord__class_Oless(X7,c_Groups_Ominus__class_Ominus(X7,X5,X4),X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__diff__less__iff) ).
fof(fact_real__less__def,axiom,
! [X16,X6] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X6,X16)
<=> ( X6 != X16
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__less__def) ).
fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(fact_diff__add__cancel,axiom,
! [X8,X9,X7] :
( class_Groups_Ogroup__add(X7)
=> c_Groups_Oplus__class_Oplus(X7,c_Groups_Ominus__class_Ominus(X7,X9,X8),X8) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(fact_less__eq__real__def,axiom,
! [X16,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,X16)
<=> ( X6 = X16
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X6,X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
fof(c_0_22,plain,
! [X16,X6,X7] :
( class_Orderings_Opreorder(X7)
=> ( c_Orderings_Oord__class_Oless(X7,X6,X16)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(X7,X16,X6)
& c_Orderings_Oord__class_Oless__eq(X7,X6,X16) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(c_0_23,plain,
! [X364,X365,X366] :
( ( ~ class_Orderings_Opreorder(X366)
| c_Orderings_Oord__class_Oless(X366,X365,X364)
| c_Orderings_Oord__class_Oless__eq(X366,X364,X365)
| ~ c_Orderings_Oord__class_Oless__eq(X366,X365,X364) )
& ( ~ class_Orderings_Opreorder(X366)
| ~ c_Orderings_Oord__class_Oless(X366,X365,X364)
| ~ c_Orderings_Oord__class_Oless__eq(X366,X364,X365) )
& ( ~ class_Orderings_Opreorder(X366)
| ~ c_Orderings_Oord__class_Oless(X366,X365,X364)
| c_Orderings_Oord__class_Oless__eq(X366,X365,X364) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])]) ).
fof(c_0_24,plain,
! [X304,X305,X306] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X306,X304)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X305,X304)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X306,X305) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__trans])])]) ).
cnf(c_0_25,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_23]) ).
cnf(c_0_26,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e)),
inference(split_conjunct,[status(thm)],[conj_1]) ).
cnf(c_0_27,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
cnf(c_0_28,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,hypothesis,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m,v_x),
inference(split_conjunct,[status(thm)],[conj_0]) ).
cnf(c_0_30,hypothesis,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_x),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_31,hypothesis,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,v_m)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,v_x) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_32,plain,
! [X307,X308] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X307,X308)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X308,X307) ),
inference(variable_rename,[status(thm)],[fact_real__le__linear]) ).
fof(c_0_33,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)),v_e),
inference(assume_negation,[status(cth)],[conj_2]) ).
fof(c_0_34,plain,
! [X12,X14,X7] :
( class_Orderings_Olinorder(X7)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X7,X14,X12)
=> c_Orderings_Oord__class_Oless(X7,X12,X14) ) ),
inference(fof_simplification,[status(thm)],[fact_not__leE]) ).
cnf(c_0_35,hypothesis,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_m),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_37,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)),v_e),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_38,plain,
! [X320,X321,X322,X323] :
( c_Orderings_Oord__class_Oless(X323,X320,X321)
| ~ c_Orderings_Oord__class_Oless__eq(X323,X320,X322)
| ~ c_Orderings_Oord__class_Oless(X323,X322,X321)
| ~ class_Orderings_Oorder(X323) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])])]) ).
fof(c_0_39,plain,
! [X355,X356,X357] :
( c_Orderings_Oord__class_Oless(X357,X355,X356)
| c_Orderings_Oord__class_Oless__eq(X357,X356,X355)
| ~ class_Orderings_Olinorder(X357) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])]) ).
fof(c_0_40,plain,
! [X211,X212,X213,X214] :
( c_Orderings_Oord__class_Oless(X214,X211,X212)
| ~ c_Orderings_Oord__class_Oless(X214,X211,X213)
| ~ c_Orderings_Oord__class_Oless(X214,X213,X212)
| ~ class_Orderings_Oorder(X214) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])])]) ).
cnf(c_0_41,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_42,hypothesis,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_43,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)),v_e),
inference(fof_nnf,[status(thm)],[c_0_37]) ).
fof(c_0_44,plain,
! [X1325] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1325) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1325),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
fof(c_0_45,plain,
! [X16,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X6,X16)
=> ( ~ c_Orderings_Oord__class_Oless(X7,X6,X16)
<=> X6 = X16 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).
cnf(c_0_46,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_47,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).
cnf(c_0_48,plain,
( ~ class_Orderings_Olinorder(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_39]) ).
cnf(c_0_49,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
cnf(c_0_50,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X4,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_51,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_27])]),c_0_35]) ).
fof(c_0_52,plain,
! [X425,X426,X427,X428] :
( c_Orderings_Oord__class_Oless(X428,c_Groups_Oplus__class_Oplus(X428,X427,X425),c_Groups_Oplus__class_Oplus(X428,X426,X425))
| ~ c_Orderings_Oord__class_Oless(X428,X427,X426)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X428) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])])]) ).
fof(c_0_53,plain,
! [X102,X103,X104,X105] :
( ( ~ class_Rings_Olinordered__idom(X105)
| c_Orderings_Oord__class_Oless(X105,c_Groups_Oabs__class_Oabs(X105,c_Groups_Ominus__class_Ominus(X105,X104,X103)),X102)
| ~ c_Orderings_Oord__class_Oless(X105,X104,c_Groups_Oplus__class_Oplus(X105,X103,X102))
| ~ c_Orderings_Oord__class_Oless(X105,c_Groups_Ominus__class_Ominus(X105,X103,X102),X104) )
& ( ~ class_Rings_Olinordered__idom(X105)
| ~ c_Orderings_Oord__class_Oless(X105,c_Groups_Oabs__class_Oabs(X105,c_Groups_Ominus__class_Ominus(X105,X104,X103)),X102)
| c_Orderings_Oord__class_Oless(X105,X104,c_Groups_Oplus__class_Oplus(X105,X103,X102)) )
& ( ~ class_Rings_Olinordered__idom(X105)
| ~ c_Orderings_Oord__class_Oless(X105,c_Groups_Oabs__class_Oabs(X105,c_Groups_Ominus__class_Ominus(X105,X104,X103)),X102)
| c_Orderings_Oord__class_Oless(X105,c_Groups_Ominus__class_Ominus(X105,X103,X102),X104) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__diff__less__iff])])])]) ).
cnf(c_0_54,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)),v_e),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_55,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_56,plain,
! [X337,X338,X339] :
( ( ~ class_Orderings_Olinorder(X339)
| ~ c_Orderings_Oord__class_Oless__eq(X339,X338,X337)
| ~ c_Orderings_Oord__class_Oless(X339,X338,X337)
| X338 != X337 )
& ( ~ class_Orderings_Olinorder(X339)
| ~ c_Orderings_Oord__class_Oless__eq(X339,X338,X337)
| X338 = X337
| c_Orderings_Oord__class_Oless(X339,X338,X337) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])]) ).
cnf(c_0_57,hypothesis,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_29]),c_0_47])]) ).
cnf(c_0_58,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
fof(c_0_59,plain,
! [X16,X6] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X6,X16)
<=> ( X6 != X16
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,X16) ) ),
inference(fof_simplification,[status(thm)],[fact_real__less__def]) ).
cnf(c_0_60,hypothesis,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_47])]) ).
cnf(c_0_61,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_62,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add]) ).
fof(c_0_63,plain,
! [X450,X451,X452] :
( c_Groups_Oplus__class_Oplus(X452,c_Groups_Ominus__class_Ominus(X452,X451,X450),X450) = X451
| ~ class_Groups_Ogroup__add(X452) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__cancel])])]) ).
cnf(c_0_64,plain,
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X4,X2)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_65,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]) ).
cnf(c_0_66,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)),v_e),
inference(rw,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_67,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_68,hypothesis,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m,X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,v_x) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
fof(c_0_69,plain,
! [X460,X461] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X461,X460)
| X461 = X460
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X461,X460) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X461,X460)
| X461 != X460 )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X461,X460)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X461,X460) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])])])]) ).
cnf(c_0_70,hypothesis,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,v_e)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62])]) ).
cnf(c_0_71,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X3) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_72,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]) ).
cnf(c_0_73,hypothesis,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_m,v_e),v_x),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_26]),c_0_55]),c_0_65])]),c_0_66]) ).
cnf(c_0_74,hypothesis,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,v_x)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m,X1)
| X1 = v_x ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_49])]) ).
cnf(c_0_75,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
fof(c_0_76,plain,
! [X458,X459] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X459,X458)
| X459 != X458 )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X459,X458)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X459,X458) )
& ( X459 = X458
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X459,X458)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X459,X458) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])])]) ).
cnf(c_0_77,hypothesis,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,v_e))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72])]) ).
cnf(c_0_78,hypothesis,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_m,v_e))
| c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_m,v_e) = v_x ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_79,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(er,[status(thm)],[c_0_75]) ).
cnf(c_0_80,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| X1 = X2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_81,hypothesis,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_m,v_e) = v_x,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]) ).
cnf(c_0_82,hypothesis,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m,v_x)
| v_x = v_m ),
inference(spm,[status(thm)],[c_0_80,c_0_29]) ).
cnf(c_0_83,hypothesis,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m,v_x),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_81]),c_0_79]) ).
cnf(c_0_84,hypothesis,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_x,v_e) = v_m,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_81]),c_0_72])]) ).
cnf(c_0_85,hypothesis,
v_x = v_m,
inference(sr,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_86,hypothesis,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e) = v_m,
inference(rw,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_87,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_86]),c_0_79]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW224+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 21 09:45:22 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 12.40/2.30 % Version: 3.5.1
% 12.40/2.30 % Preprocessing class: FMLMSMSMSSSNFFN.
% 12.40/2.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 12.40/2.30 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 12.40/2.30 % Starting new_bool_3 with 300s (1) cores
% 12.40/2.30 % Starting new_bool_1 with 300s (1) cores
% 12.40/2.30 % Starting sh5l with 300s (1) cores
% 12.40/2.30 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1961103 completed with status 0
% 12.40/2.30 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 12.40/2.30 % Preprocessing class: FMLMSMSMSSSNFFN.
% 12.40/2.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 12.40/2.30 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 12.40/2.30 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 12.40/2.30 % No SInE strategy applied
% 12.40/2.30 % Search class: FGHSM-SMLM32-DFFFFFNN
% 12.40/2.30 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 12.40/2.30 % Starting SubtermCWHack with 136s (1) cores
% 12.40/2.30 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 12.40/2.30 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 12.40/2.30 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 12.40/2.30 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 12.40/2.30 % G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 1961114 completed with status 0
% 12.40/2.30 % Result found by G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 12.40/2.30 % Preprocessing class: FMLMSMSMSSSNFFN.
% 12.40/2.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 12.40/2.30 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 12.40/2.30 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 12.40/2.30 % No SInE strategy applied
% 12.40/2.30 % Search class: FGHSM-SMLM32-DFFFFFNN
% 12.40/2.30 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 12.40/2.30 % Starting SubtermCWHack with 136s (1) cores
% 12.40/2.30 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 12.40/2.30 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 12.40/2.30 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 12.40/2.30 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 12.40/2.30 % Preprocessing time : 0.027 s
% 12.40/2.30 % Presaturation interreduction done
% 12.40/2.30
% 12.40/2.30 % Proof found!
% 12.40/2.30 % SZS status Theorem
% 12.40/2.30 % SZS output start CNFRefutation
% See solution above
% 12.40/2.31 % Parsed axioms : 1188
% 12.40/2.31 % Removed by relevancy pruning/SinE : 0
% 12.40/2.31 % Initial clauses : 1702
% 12.40/2.31 % Removed in clause preprocessing : 44
% 12.40/2.31 % Initial clauses in saturation : 1658
% 12.40/2.31 % Processed clauses : 8697
% 12.40/2.31 % ...of these trivial : 81
% 12.40/2.31 % ...subsumed : 4778
% 12.40/2.31 % ...remaining for further processing : 3838
% 12.40/2.31 % Other redundant clauses eliminated : 373
% 12.40/2.31 % Clauses deleted for lack of memory : 0
% 12.40/2.31 % Backward-subsumed : 165
% 12.40/2.31 % Backward-rewritten : 496
% 12.40/2.31 % Generated clauses : 52303
% 12.40/2.31 % ...of the previous two non-redundant : 46850
% 12.40/2.31 % ...aggressively subsumed : 0
% 12.40/2.31 % Contextual simplify-reflections : 10
% 12.40/2.31 % Paramodulations : 51917
% 12.40/2.31 % Factorizations : 10
% 12.40/2.31 % NegExts : 0
% 12.40/2.31 % Equation resolutions : 389
% 12.40/2.31 % Disequality decompositions : 0
% 12.40/2.31 % Total rewrite steps : 31568
% 12.40/2.31 % ...of those cached : 29962
% 12.40/2.31 % Propositional unsat checks : 0
% 12.40/2.31 % Propositional check models : 0
% 12.40/2.31 % Propositional check unsatisfiable : 0
% 12.40/2.31 % Propositional clauses : 0
% 12.40/2.31 % Propositional clauses after purity: 0
% 12.40/2.31 % Propositional unsat core size : 0
% 12.40/2.31 % Propositional preprocessing time : 0.000
% 12.40/2.31 % Propositional encoding time : 0.000
% 12.40/2.31 % Propositional solver time : 0.000
% 12.40/2.31 % Success case prop preproc time : 0.000
% 12.40/2.31 % Success case prop encoding time : 0.000
% 12.40/2.31 % Success case prop solver time : 0.000
% 12.40/2.31 % Current number of processed clauses : 1673
% 12.40/2.31 % Positive orientable unit clauses : 398
% 12.40/2.31 % Positive unorientable unit clauses: 17
% 12.40/2.31 % Negative unit clauses : 170
% 12.40/2.31 % Non-unit-clauses : 1088
% 12.40/2.31 % Current number of unprocessed clauses: 41017
% 12.40/2.31 % ...number of literals in the above : 145320
% 12.40/2.31 % Current number of archived formulas : 0
% 12.40/2.31 % Current number of archived clauses : 2035
% 12.40/2.31 % Clause-clause subsumption calls (NU) : 563631
% 12.40/2.31 % Rec. Clause-clause subsumption calls : 366122
% 12.40/2.31 % Non-unit clause-clause subsumptions : 2815
% 12.40/2.31 % Unit Clause-clause subsumption calls : 23370
% 12.40/2.31 % Rewrite failures with RHS unbound : 0
% 12.40/2.31 % BW rewrite match attempts : 2824
% 12.40/2.31 % BW rewrite match successes : 260
% 12.40/2.31 % Condensation attempts : 0
% 12.40/2.31 % Condensation successes : 0
% 12.40/2.31 % Termbank termtop insertions : 1014362
% 12.40/2.31 % Search garbage collected termcells : 20149
% 12.40/2.31
% 12.40/2.31 % -------------------------------------------------
% 12.40/2.31 % User time : 1.719 s
% 12.40/2.31 % System time : 0.062 s
% 12.40/2.31 % Total time : 1.781 s
% 12.40/2.31 % Maximum resident set size: 10108 pages
% 12.40/2.31
% 12.40/2.31 % -------------------------------------------------
% 12.40/2.31 % User time : 8.279 s
% 12.40/2.31 % System time : 0.334 s
% 12.40/2.31 % Total time : 8.613 s
% 12.40/2.31 % Maximum resident set size: 5888 pages
% 12.40/2.31 % E exiting
%------------------------------------------------------------------------------