%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM857+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 : n004.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 2.52s 2.05s
% Output : CNFRefutation 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 61 ( 34 unt; 0 def)
% Number of atoms : 108 ( 50 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 75 ( 28 ~; 37 |; 6 &)
% ( 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 105 ( 10 sgn 55 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof('def(cond(conseq(axiom(3)), 16), 1)',axiom,
! [X78,X79] :
( geq(X79,X78)
<=> ( greater(X79,X78)
| X79 = X78 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).
fof('ass(cond(73, 0), 0)',axiom,
! [X99,X100] : X100 != vplus(X99,X100),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
fof('ass(cond(33, 0), 0)',axiom,
! [X106,X107,X108] : vplus(vplus(X106,X107),X108) = vplus(X106,vplus(X107,X108)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof('ass(cond(140, 0), 0)',axiom,
! [X82,X83] :
( greater(X82,X83)
=> less(X83,X82) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
fof('holds(conjunct2(antec(323)), 531, 0)',axiom,
geq(vd529,vd530),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct2(antec(323)), 531, 0)') ).
fof('ass(cond(61, 0), 0)',axiom,
! [X101,X102] : vplus(X102,X101) = vplus(X101,X102),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof('def(cond(conseq(axiom(3)), 12), 1)',axiom,
! [X86,X87] :
( less(X87,X86)
<=> ? [X88] : X86 = vplus(X87,X88) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
fof('ass(cond(318, 0), 0)',axiom,
! [X1,X2,X3,X4] :
( ( ( greater(X3,X4)
& geq(X1,X2) )
| ( geq(X3,X4)
& greater(X1,X2) ) )
=> greater(vmul(X1,X3),vmul(X2,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(318, 0), 0)') ).
fof('holds(conjunct1(antec(323)), 528, 0)',axiom,
geq(vd526,vd527),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(antec(323)), 528, 0)') ).
fof('ass(cond(270, 0), 0)',axiom,
! [X31,X32] : vmul(X31,X32) = vmul(X32,X31),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
fof('ass(cond(189, 0), 0)',axiom,
! [X61,X62] : greater(vplus(X61,X62),X61),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
fof('holds(conseq(323), 532, 0)',conjecture,
geq(vmul(vd526,vd529),vmul(vd527,vd530)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq(323), 532, 0)') ).
fof('ass(cond(281, 0), 0)',axiom,
! [X28,X29,X30] : vmul(X28,vplus(X29,X30)) = vplus(vmul(X28,X29),vmul(X28,X30)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
fof('ass(cond(goal(88), 0), 0)',axiom,
! [X92,X93] :
( X92 = X93
| ? [X94] : X92 = vplus(X93,X94)
| ? [X95] : X93 = vplus(X92,X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
fof(c_0_14,plain,
! [X356,X357] :
( ( ~ geq(X357,X356)
| greater(X357,X356)
| X357 = X356 )
& ( ~ greater(X357,X356)
| geq(X357,X356) )
& ( X357 != X356
| geq(X357,X356) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['def(cond(conseq(axiom(3)), 16), 1)'])])]) ).
fof(c_0_15,plain,
! [X399,X400] : X400 != vplus(X399,X400),
inference(variable_rename,[status(thm)],['ass(cond(73, 0), 0)']) ).
fof(c_0_16,plain,
! [X406,X407,X408] : vplus(vplus(X406,X407),X408) = vplus(X406,vplus(X407,X408)),
inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).
fof(c_0_17,plain,
! [X360,X361] :
( ~ greater(X360,X361)
| less(X361,X360) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(140, 0), 0)'])]) ).
cnf(c_0_18,plain,
( greater(X1,X2)
| X1 = X2
| ~ geq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
geq(vd529,vd530),
inference(split_conjunct,[status(thm)],['holds(conjunct2(antec(323)), 531, 0)']) ).
cnf(c_0_20,plain,
X1 != vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_22,plain,
! [X401,X402] : vplus(X402,X401) = vplus(X401,X402),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
fof(c_0_23,plain,
! [X370,X371,X373,X374,X375] :
( ( ~ less(X371,X370)
| X370 = vplus(X371,esk1_2(X370,X371)) )
& ( X373 != vplus(X374,X375)
| less(X374,X373) ) ),
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)), 12), 1)'])])])])]) ).
cnf(c_0_24,plain,
( less(X2,X1)
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
( vd530 = vd529
| greater(vd529,vd530) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_26,plain,
! [X265,X266,X267,X268] :
( ( ~ greater(X267,X268)
| ~ geq(X265,X266)
| greater(vmul(X265,X267),vmul(X266,X268)) )
& ( ~ geq(X267,X268)
| ~ greater(X265,X266)
| greater(vmul(X265,X267),vmul(X266,X268)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(318, 0), 0)'])])]) ).
cnf(c_0_27,plain,
vplus(X1,vplus(X2,X3)) != X3,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
( X2 = vplus(X1,esk1_2(X2,X1))
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( vd530 = vd529
| less(vd530,vd529) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
( greater(vmul(X3,X1),vmul(X4,X2))
| ~ greater(X1,X2)
| ~ geq(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
geq(vd526,vd527),
inference(split_conjunct,[status(thm)],['holds(conjunct1(antec(323)), 528, 0)']) ).
fof(c_0_33,plain,
! [X297,X298] : vmul(X297,X298) = vmul(X298,X297),
inference(variable_rename,[status(thm)],['ass(cond(270, 0), 0)']) ).
fof(c_0_34,plain,
! [X339,X340] : greater(vplus(X339,X340),X339),
inference(variable_rename,[status(thm)],['ass(cond(189, 0), 0)']) ).
cnf(c_0_35,plain,
vplus(X1,vplus(X2,X3)) != X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_21]) ).
cnf(c_0_36,plain,
( vplus(vd530,esk1_2(vd529,vd530)) = vd529
| vd530 = vd529 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,plain,
( greater(vmul(vd529,X1),vmul(vd530,X2))
| ~ greater(X1,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_19]) ).
cnf(c_0_38,plain,
( vd527 = vd526
| greater(vd526,vd527) ),
inference(spm,[status(thm)],[c_0_18,c_0_32]) ).
cnf(c_0_39,plain,
vmul(X1,X2) = vmul(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_40,negated_conjecture,
~ geq(vmul(vd526,vd529),vmul(vd527,vd530)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['holds(conseq(323), 532, 0)'])]) ).
cnf(c_0_41,plain,
( geq(X1,X2)
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_42,plain,
greater(vplus(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_43,plain,
! [X294,X295,X296] : vmul(X294,vplus(X295,X296)) = vplus(vmul(X294,X295),vmul(X294,X296)),
inference(variable_rename,[status(thm)],['ass(cond(281, 0), 0)']) ).
cnf(c_0_44,plain,
( vd530 = vd529
| vplus(X1,vd529) != vd530 ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_45,plain,
! [X382,X383] :
( X382 = X383
| X382 = vplus(X383,esk3_2(X382,X383))
| X383 = vplus(X382,esk4_2(X382,X383)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],['ass(cond(goal(88), 0), 0)'])]) ).
cnf(c_0_46,plain,
( vd527 = vd526
| greater(vmul(vd526,vd529),vmul(vd527,vd530)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_39]) ).
cnf(c_0_47,negated_conjecture,
~ geq(vmul(vd526,vd529),vmul(vd527,vd530)),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_48,plain,
geq(vplus(X1,X2),X1),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_49,plain,
vmul(X1,vplus(X2,X3)) = vplus(vmul(X1,X2),vmul(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_50,plain,
( vd530 = vd529
| vplus(vd529,X1) != vd530 ),
inference(spm,[status(thm)],[c_0_44,c_0_28]) ).
cnf(c_0_51,plain,
( X1 = X2
| X1 = vplus(X2,esk3_2(X1,X2))
| X2 = vplus(X1,esk4_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_52,plain,
vd527 = vd526,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_46]),c_0_47]) ).
cnf(c_0_53,plain,
geq(vmul(X1,vplus(X2,X3)),vmul(X1,X2)),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,plain,
( vplus(vd530,esk4_2(vd530,vd529)) = vd529
| vd530 = vd529 ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51])]) ).
cnf(c_0_55,negated_conjecture,
~ geq(vmul(vd526,vd529),vmul(vd526,vd530)),
inference(rw,[status(thm)],[c_0_47,c_0_52]) ).
cnf(c_0_56,plain,
( vd530 = vd529
| geq(vmul(X1,vd529),vmul(X1,vd530)) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_57,plain,
( geq(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_58,negated_conjecture,
vd530 = vd529,
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_59,plain,
geq(X1,X1),
inference(er,[status(thm)],[c_0_57]) ).
cnf(c_0_60,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_58]),c_0_59])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM857+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
% 0.15/0.33 % Computer : n004.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 : Tue May 5 01:15:47 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 2.52/2.05 % Version : CSE_E---1.7
% 2.52/2.05 % Problem : theBenchmark.p
% 2.52/2.05 % SZS status Theorem for theBenchmark.p
% 2.52/2.05 % SZS output start CNFRefutation
% See solution above
% 2.52/2.06 % Total time : 1.374s
%------------------------------------------------------------------------------