%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM855+2 : TPTP v9.2.1. Released v4.1.0.
% 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 : n008.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 04:58:45 PM UTC 2026
% Result : Theorem 1.35s 1.74s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 66 ( 37 unt; 0 def)
% Number of atoms : 108 ( 30 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 89 ( 47 ~; 35 |; 3 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 105 ( 16 sgn 47 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof('ass(cond(goal(130), 0), 2)',axiom,
! [X76,X77] :
( ~ greater(X76,X77)
| ~ less(X76,X77) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
fof('ass(cond(189, 0), 0)',axiom,
! [X53,X54] : greater(vplus(X53,X54),X53),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
fof('ass(cond(61, 0), 0)',axiom,
! [X93,X94] : vplus(X94,X93) = vplus(X93,X94),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof('ass(cond(33, 0), 0)',axiom,
! [X98,X99,X100] : vplus(vplus(X98,X99),X100) = vplus(X98,vplus(X99,X100)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof('ass(cond(73, 0), 0)',axiom,
! [X91,X92] : X92 != vplus(X91,X92),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
! [X81,X82] :
( greater(X82,X81)
<=> ? [X83] : X82 = vplus(X81,X83) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof('def(cond(conseq(axiom(3)), 16), 1)',axiom,
! [X70,X71] :
( geq(X71,X70)
<=> ( greater(X71,X70)
| X71 = X70 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).
fof('ass(cond(147, 0), 0)',axiom,
! [X72,X73] :
( less(X72,X73)
=> greater(X73,X72) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
fof('holds(conseq_conjunct2(315), 516, 0)',conjecture,
greater(vmul(vd508,vd511),vmul(vd509,vd512)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq_conjunct2(315), 516, 0)') ).
fof('ass(cond(goal(130), 0), 0)',axiom,
! [X76,X77] :
( X76 = X77
| greater(X76,X77)
| less(X76,X77) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
fof('ass(cond(140, 0), 0)',axiom,
! [X74,X75] :
( greater(X74,X75)
=> less(X75,X74) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
fof('holds(conjunct2(315), 515, 1)',axiom,
greater(vmul(vd511,vd509),vmul(vd512,vd509)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct2(315), 515, 1)') ).
fof('holds(conjunct2(315), 515, 0)',axiom,
vmul(vd509,vd511) = vmul(vd511,vd509),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct2(315), 515, 0)') ).
fof('holds(conjunct2(315), 515, 2)',axiom,
vmul(vd512,vd509) = vmul(vd509,vd512),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct2(315), 515, 2)') ).
fof('holds(conjunct1(315), 514, 0)',axiom,
greater(vmul(vd508,vd511),vmul(vd509,vd511)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(315), 514, 0)') ).
fof(c_0_15,plain,
! [X76,X77] :
( ~ greater(X76,X77)
| ~ less(X76,X77) ),
inference(fof_simplification,[status(thm)],['ass(cond(goal(130), 0), 2)']) ).
fof(c_0_16,plain,
! [X342,X343] :
( ~ greater(X342,X343)
| ~ less(X342,X343) ),
inference(variable_rename,[status(thm)],[c_0_15]) ).
fof(c_0_17,plain,
! [X315,X316] : greater(vplus(X315,X316),X315),
inference(variable_rename,[status(thm)],['ass(cond(189, 0), 0)']) ).
cnf(c_0_18,plain,
( ~ greater(X1,X2)
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,plain,
greater(vplus(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_20,plain,
! [X377,X378] : vplus(X378,X377) = vplus(X377,X378),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
cnf(c_0_21,plain,
~ less(vplus(X1,X2),X1),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_23,plain,
! [X382,X383,X384] : vplus(vplus(X382,X383),X384) = vplus(X382,vplus(X383,X384)),
inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).
cnf(c_0_24,plain,
~ less(vplus(X1,X2),X2),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_26,plain,
! [X375,X376] : X376 != vplus(X375,X376),
inference(variable_rename,[status(thm)],['ass(cond(73, 0), 0)']) ).
cnf(c_0_27,plain,
~ less(vplus(X1,vplus(X2,X3)),X3),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_28,plain,
! [X352,X353,X355,X356,X357] :
( ( ~ greater(X353,X352)
| X353 = vplus(X352,esk2_2(X352,X353)) )
& ( X356 != vplus(X355,X357)
| greater(X356,X355) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],['def(cond(conseq(axiom(3)), 11), 1)'])])])])]) ).
cnf(c_0_29,plain,
X1 != vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,plain,
~ less(vplus(X1,vplus(X2,X3)),X2),
inference(spm,[status(thm)],[c_0_27,c_0_22]) ).
cnf(c_0_31,plain,
( X1 = vplus(X2,esk2_2(X2,X1))
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_32,plain,
vplus(X1,vplus(X2,X3)) != X3,
inference(spm,[status(thm)],[c_0_29,c_0_25]) ).
fof(c_0_33,plain,
! [X332,X333] :
( ( ~ geq(X333,X332)
| greater(X333,X332)
| X333 = X332 )
& ( ~ greater(X333,X332)
| geq(X333,X332) )
& ( X333 != X332
| geq(X333,X332) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['def(cond(conseq(axiom(3)), 16), 1)'])])]) ).
fof(c_0_34,plain,
! [X334,X335] :
( ~ less(X334,X335)
| greater(X335,X334) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(147, 0), 0)'])]) ).
fof(c_0_35,negated_conjecture,
~ greater(vmul(vd508,vd511),vmul(vd509,vd512)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['holds(conseq_conjunct2(315), 516, 0)'])]) ).
fof(c_0_36,plain,
! [X338,X339] :
( X338 = X339
| greater(X338,X339)
| less(X338,X339) ),
inference(variable_rename,[status(thm)],['ass(cond(goal(130), 0), 0)']) ).
cnf(c_0_37,plain,
( ~ less(vplus(X1,X2),X3)
| ~ greater(X2,X3) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
fof(c_0_38,plain,
! [X336,X337] :
( ~ greater(X336,X337)
| less(X337,X336) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(140, 0), 0)'])]) ).
cnf(c_0_39,plain,
greater(vmul(vd511,vd509),vmul(vd512,vd509)),
inference(split_conjunct,[status(thm)],['holds(conjunct2(315), 515, 1)']) ).
cnf(c_0_40,plain,
vmul(vd509,vd511) = vmul(vd511,vd509),
inference(split_conjunct,[status(thm)],['holds(conjunct2(315), 515, 0)']) ).
cnf(c_0_41,plain,
vmul(vd512,vd509) = vmul(vd509,vd512),
inference(split_conjunct,[status(thm)],['holds(conjunct2(315), 515, 2)']) ).
cnf(c_0_42,plain,
vplus(X1,vplus(X2,X3)) != X2,
inference(spm,[status(thm)],[c_0_32,c_0_22]) ).
cnf(c_0_43,plain,
( geq(X1,X2)
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_44,plain,
( greater(X2,X1)
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_45,negated_conjecture,
~ greater(vmul(vd508,vd511),vmul(vd509,vd512)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_46,plain,
( X1 = X2
| greater(X1,X2)
| less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_47,plain,
( ~ less(vplus(X1,X2),X3)
| ~ greater(X1,X3) ),
inference(spm,[status(thm)],[c_0_37,c_0_22]) ).
cnf(c_0_48,plain,
( less(X2,X1)
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_49,plain,
greater(vmul(vd509,vd511),vmul(vd509,vd512)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_50,plain,
~ greater(X1,vplus(X2,X1)),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_31])]) ).
cnf(c_0_51,plain,
( geq(X1,X2)
| ~ less(X2,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_52,negated_conjecture,
( vmul(vd509,vd512) = vmul(vd508,vd511)
| less(vmul(vd508,vd511),vmul(vd509,vd512)) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_53,plain,
( ~ less(X1,X2)
| ~ greater(X3,X2)
| ~ greater(X1,X3) ),
inference(spm,[status(thm)],[c_0_47,c_0_31]) ).
cnf(c_0_54,plain,
less(vmul(vd509,vd512),vmul(vd509,vd511)),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_55,plain,
~ greater(X1,vplus(X1,X2)),
inference(spm,[status(thm)],[c_0_50,c_0_22]) ).
cnf(c_0_56,plain,
( greater(X1,X2)
| X1 = X2
| ~ geq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_57,negated_conjecture,
( vmul(vd509,vd512) = vmul(vd508,vd511)
| geq(vmul(vd509,vd512),vmul(vd508,vd511)) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_58,plain,
( ~ greater(X1,vmul(vd509,vd511))
| ~ greater(vmul(vd509,vd512),X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,plain,
greater(vmul(vd508,vd511),vmul(vd509,vd511)),
inference(split_conjunct,[status(thm)],['holds(conjunct1(315), 514, 0)']) ).
cnf(c_0_60,plain,
( ~ greater(X1,X2)
| ~ greater(X2,X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_31]) ).
cnf(c_0_61,negated_conjecture,
( vmul(vd509,vd512) = vmul(vd508,vd511)
| greater(vmul(vd509,vd512),vmul(vd508,vd511)) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_62,plain,
~ greater(vmul(vd509,vd512),vmul(vd508,vd511)),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_63,plain,
~ greater(vmul(vd509,vd512),vmul(vd509,vd511)),
inference(spm,[status(thm)],[c_0_60,c_0_49]) ).
cnf(c_0_64,negated_conjecture,
vmul(vd509,vd512) = vmul(vd508,vd511),
inference(sr,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_65,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64]),c_0_59])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM855+2 : TPTP v9.2.1. Released v4.1.0.
% 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
% 0.16/0.33 % Computer : n008.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 01:16:13 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.35/1.74 % Version : CSE_E---1.7
% 1.35/1.74 % Problem : theBenchmark.p
% 1.35/1.74 % SZS status Theorem for theBenchmark.p
% 1.35/1.74 % SZS output start CNFRefutation
% See solution above
% 1.35/1.75 % Total time : 1.374s
%------------------------------------------------------------------------------