%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL894+1 : TPTP v9.2.1. Released v5.5.0.
% 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 : n016.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 04:45:19 PM UTC 2026
% Result : Theorem 1.88s 1.90s
% Output : CNFRefutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 67 ( 30 unt; 0 def)
% Number of atoms : 122 ( 18 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 96 ( 41 ~; 40 |; 7 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 113 ( 9 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_03,axiom,
! [X1] : '+'(X1,'0') = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_03) ).
fof(sos_02,axiom,
! [X1,X2] : '+'(X1,X2) = '+'(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_02) ).
fof(sos_09,axiom,
! [X12,X13,X14] :
( '>='(X12,X13)
=> '>='('+'(X12,X14),'+'(X13,X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_09) ).
fof(sos_08,axiom,
! [X1] : '>='(X1,'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
fof(sos_05,axiom,
! [X4,X5,X6] :
( ( '>='(X4,X5)
& '>='(X5,X6) )
=> '>='(X4,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_05) ).
fof(goals_13,conjecture,
( ( '>='(c,a)
& '>='(c,b) )
<=> '>='(c,'+'(a,'==>'(a,b))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_13) ).
fof(sos_07,axiom,
! [X9,X10,X11] :
( '>='('+'(X9,X10),X11)
<=> '>='(X10,'==>'(X9,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).
fof(sos_04,axiom,
! [X1] : '>='(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_04) ).
fof(sos_06,axiom,
! [X7,X8] :
( ( '>='(X7,X8)
& '>='(X8,X7) )
=> X7 = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_06) ).
fof(sos_10,axiom,
! [X15,X16,X17] :
( '>='(X15,X16)
=> '>='('==>'(X16,X17),'==>'(X15,X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_10) ).
fof(sos_12,axiom,
! [X1,X2] : '+'(X1,'==>'(X1,X2)) = '+'(X2,'==>'(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_12) ).
fof(sos_11,axiom,
! [X18,X19,X20] :
( '>='(X18,X19)
=> '>='('==>'(X20,X18),'==>'(X20,X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_11) ).
fof(c_0_12,plain,
! [X53] : '+'(X53,'0') = X53,
inference(variable_rename,[status(thm)],[sos_03]) ).
fof(c_0_13,plain,
! [X51,X52] : '+'(X51,X52) = '+'(X52,X51),
inference(variable_rename,[status(thm)],[sos_02]) ).
fof(c_0_14,plain,
! [X64,X65,X66] :
( ~ '>='(X64,X65)
| '>='('+'(X64,X66),'+'(X65,X66)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_09])]) ).
cnf(c_0_15,plain,
'+'(X1,'0') = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
'+'(X1,X2) = '+'(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_17,plain,
! [X63] : '>='(X63,'0'),
inference(variable_rename,[status(thm)],[sos_08]) ).
fof(c_0_18,plain,
! [X55,X56,X57] :
( ~ '>='(X55,X56)
| ~ '>='(X56,X57)
| '>='(X55,X57) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_05])]) ).
cnf(c_0_19,plain,
( '>='('+'(X1,X3),'+'(X2,X3))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
'+'('0',X1) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
'>='(X1,'0'),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
( '>='(X1,X3)
| ~ '>='(X1,X2)
| ~ '>='(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
'>='('+'(X1,X2),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
fof(c_0_24,negated_conjecture,
~ ( ( '>='(c,a)
& '>='(c,b) )
<=> '>='(c,'+'(a,'==>'(a,b))) ),
inference(assume_negation,[status(cth)],[goals_13]) ).
cnf(c_0_25,plain,
( '>='(X1,X2)
| ~ '>='(X1,'+'(X3,X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_26,negated_conjecture,
( ( ~ '>='(c,a)
| ~ '>='(c,b)
| ~ '>='(c,'+'(a,'==>'(a,b))) )
& ( '>='(c,a)
| '>='(c,'+'(a,'==>'(a,b))) )
& ( '>='(c,b)
| '>='(c,'+'(a,'==>'(a,b))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])]) ).
fof(c_0_27,plain,
! [X60,X61,X62] :
( ( ~ '>='('+'(X60,X61),X62)
| '>='(X61,'==>'(X60,X62)) )
& ( ~ '>='(X61,'==>'(X60,X62))
| '>='('+'(X60,X61),X62) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_07])]) ).
fof(c_0_28,plain,
! [X54] : '>='(X54,X54),
inference(variable_rename,[status(thm)],[sos_04]) ).
cnf(c_0_29,plain,
( '>='(X1,X2)
| ~ '>='(X1,'+'(X2,X3)) ),
inference(spm,[status(thm)],[c_0_25,c_0_16]) ).
cnf(c_0_30,negated_conjecture,
( '>='(c,a)
| '>='(c,'+'(a,'==>'(a,b))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_31,plain,
! [X58,X59] :
( ~ '>='(X58,X59)
| ~ '>='(X59,X58)
| X58 = X59 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_06])]) ).
cnf(c_0_32,plain,
( '>='('+'(X2,X1),X3)
| ~ '>='(X1,'==>'(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
'>='(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,negated_conjecture,
'>='(c,a),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( X1 = X2
| ~ '>='(X1,X2)
| ~ '>='(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,plain,
( '>='(X2,'==>'(X1,X3))
| ~ '>='('+'(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,plain,
'>='('+'(X1,'==>'(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( '>='(X1,a)
| ~ '>='(X1,c) ),
inference(spm,[status(thm)],[c_0_22,c_0_34]) ).
cnf(c_0_39,plain,
'>='('+'(X1,X2),X1),
inference(spm,[status(thm)],[c_0_23,c_0_16]) ).
fof(c_0_40,plain,
! [X67,X68,X69] :
( ~ '>='(X67,X68)
| '>='('==>'(X68,X69),'==>'(X67,X69)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_10])]) ).
cnf(c_0_41,plain,
( '==>'(X1,X2) = X3
| ~ '>='('==>'(X1,X2),X3)
| ~ '>='('+'(X1,X3),X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,plain,
'>='('==>'('0',X1),X1),
inference(spm,[status(thm)],[c_0_37,c_0_20]) ).
cnf(c_0_43,plain,
( '>='(X1,'==>'(X2,X3))
| ~ '>='('+'(X2,X4),X3)
| ~ '>='(X1,X4) ),
inference(spm,[status(thm)],[c_0_22,c_0_36]) ).
cnf(c_0_44,negated_conjecture,
'>='('+'(c,X1),a),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,plain,
( '>='('==>'(X2,X3),'==>'(X1,X3))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_46,plain,
'==>'('0',X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_20]),c_0_33])]) ).
cnf(c_0_47,negated_conjecture,
( '>='(X1,'==>'(c,a))
| ~ '>='(X1,X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,plain,
'>='(X1,'==>'(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_21])]) ).
fof(c_0_49,plain,
! [X73,X74] : '+'(X73,'==>'(X73,X74)) = '+'(X74,'==>'(X74,X73)),
inference(variable_rename,[status(thm)],[sos_12]) ).
cnf(c_0_50,plain,
( '0' = X1
| ~ '>='('0',X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_21]) ).
cnf(c_0_51,negated_conjecture,
'>='(X1,'==>'(c,a)),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,plain,
'+'(X1,'==>'(X1,X2)) = '+'(X2,'==>'(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_53,negated_conjecture,
'==>'(c,a) = '0',
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,negated_conjecture,
( ~ '>='(c,a)
| ~ '>='(c,b)
| ~ '>='(c,'+'(a,'==>'(a,b))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_55,plain,
( '>='(X1,X2)
| ~ '>='(X1,'+'(X3,'==>'(X3,X2))) ),
inference(spm,[status(thm)],[c_0_29,c_0_52]) ).
cnf(c_0_56,negated_conjecture,
( '>='(c,b)
| '>='(c,'+'(a,'==>'(a,b))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_57,plain,
( '>='('+'(X1,X2),'+'(X3,X1))
| ~ '>='(X2,X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_58,negated_conjecture,
'+'(a,'==>'(a,c)) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_15]) ).
fof(c_0_59,plain,
! [X70,X71,X72] :
( ~ '>='(X70,X71)
| '>='('==>'(X72,X70),'==>'(X72,X71)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_11])]) ).
cnf(c_0_60,negated_conjecture,
( ~ '>='(c,'+'(a,'==>'(a,b)))
| ~ '>='(c,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_34])]) ).
cnf(c_0_61,negated_conjecture,
'>='(c,b),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_62,negated_conjecture,
( '>='(c,'+'(X1,a))
| ~ '>='('==>'(a,c),X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,plain,
( '>='('==>'(X3,X1),'==>'(X3,X2))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_64,negated_conjecture,
~ '>='(c,'+'(a,'==>'(a,b))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61])]) ).
cnf(c_0_65,negated_conjecture,
( '>='(c,'+'(a,'==>'(a,X1)))
| ~ '>='(c,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_16]) ).
cnf(c_0_66,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_61])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL894+1 : TPTP v9.2.1. Released v5.5.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n016.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 23:18:36 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.88/1.90 % Version : CSE_E---1.7
% 1.88/1.90 % Problem : theBenchmark.p
% 1.88/1.90 % SZS status Theorem for theBenchmark.p
% 1.88/1.90 % SZS output start CNFRefutation
% See solution above
% 1.88/1.90 % Total time : 1.373s
%------------------------------------------------------------------------------