TSTP Solution File: NUM842+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM842+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n001.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 : Thu Aug 31 10:40:57 EDT 2023
% Result : Theorem 0.19s 0.78s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 31
% Syntax : Number of formulae : 95 ( 30 unt; 16 typ; 0 def)
% Number of atoms : 158 ( 45 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 138 ( 59 ~; 59 |; 11 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 11 >; 9 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 151 ( 10 sgn; 71 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
vd353: $i ).
tff(decl_23,type,
vd355: $i ).
tff(decl_24,type,
vplus: ( $i * $i ) > $i ).
tff(decl_25,type,
vd354: $i ).
tff(decl_26,type,
vd356: $i ).
tff(decl_27,type,
greater: ( $i * $i ) > $o ).
tff(decl_28,type,
geq: ( $i * $i ) > $o ).
tff(decl_29,type,
less: ( $i * $i ) > $o ).
tff(decl_30,type,
leq: ( $i * $i ) > $o ).
tff(decl_31,type,
vsucc: $i > $i ).
tff(decl_32,type,
v1: $i ).
tff(decl_33,type,
vskolem2: $i > $i ).
tff(decl_34,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_35,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_36,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_37,type,
esk4_2: ( $i * $i ) > $i ).
fof('holds(conseq(218), 361, 0)',conjecture,
greater(vplus(vd353,vd355),vplus(vd354,vd356)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq(218), 361, 0)') ).
fof('ass(cond(209, 0), 0)',axiom,
! [X1,X2,X3,X4] :
( ( greater(X3,X4)
& greater(X1,X2) )
=> greater(vplus(X1,X3),vplus(X2,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(209, 0), 0)') ).
fof('def(cond(conseq(axiom(3)), 16), 1)',axiom,
! [X28,X29] :
( geq(X29,X28)
<=> ( greater(X29,X28)
| X29 = X28 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).
fof('dis(antec(218))',axiom,
( ( greater(vd355,vd356)
& geq(vd353,vd354) )
| ( geq(vd355,vd356)
& greater(vd353,vd354) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dis(antec(218))') ).
fof('ass(cond(goal(202), 0), 2)',axiom,
! [X5,X6,X7] :
( greater(vplus(X5,X7),vplus(X6,X7))
=> greater(X5,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 2)') ).
fof('ass(cond(goal(193), 0), 2)',axiom,
! [X8,X9,X10] :
( greater(X8,X9)
=> greater(vplus(X8,X10),vplus(X9,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 2)') ).
fof('ass(cond(goal(88), 0), 1)',axiom,
! [X42,X43] :
( X42 != X43
| ~ ? [X45] : X43 = vplus(X42,X45) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
fof('ass(cond(168, 0), 0)',axiom,
! [X19,X20,X21] :
( ( less(X20,X21)
& less(X19,X20) )
=> less(X19,X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(168, 0), 0)') ).
fof('ass(cond(140, 0), 0)',axiom,
! [X32,X33] :
( greater(X32,X33)
=> less(X33,X32) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
fof('ass(cond(33, 0), 0)',axiom,
! [X56,X57,X58] : vplus(vplus(X56,X57),X58) = vplus(X56,vplus(X57,X58)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof('ass(cond(61, 0), 0)',axiom,
! [X51,X52] : vplus(X52,X51) = vplus(X51,X52),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof('ass(cond(147, 0), 0)',axiom,
! [X30,X31] :
( less(X30,X31)
=> greater(X31,X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
fof('def(cond(conseq(axiom(3)), 12), 1)',axiom,
! [X36,X37] :
( less(X37,X36)
<=> ? [X38] : X36 = vplus(X37,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
! [X39,X40] :
( greater(X40,X39)
<=> ? [X41] : X40 = vplus(X39,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof('ass(cond(goal(130), 0), 0)',axiom,
! [X34,X35] :
( X34 = X35
| greater(X34,X35)
| less(X34,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
fof(c_0_15,negated_conjecture,
~ greater(vplus(vd353,vd355),vplus(vd354,vd356)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['holds(conseq(218), 361, 0)'])]) ).
fof(c_0_16,plain,
! [X68,X69,X70,X71] :
( ~ greater(X70,X71)
| ~ greater(X68,X69)
| greater(vplus(X68,X70),vplus(X69,X71)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(209, 0), 0)'])]) ).
fof(c_0_17,plain,
! [X107,X108] :
( ( ~ geq(X108,X107)
| greater(X108,X107)
| X108 = X107 )
& ( ~ greater(X108,X107)
| geq(X108,X107) )
& ( X108 != X107
| geq(X108,X107) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['def(cond(conseq(axiom(3)), 16), 1)'])])]) ).
fof(c_0_18,plain,
( ( geq(vd355,vd356)
| greater(vd355,vd356) )
& ( greater(vd353,vd354)
| greater(vd355,vd356) )
& ( geq(vd355,vd356)
| geq(vd353,vd354) )
& ( greater(vd353,vd354)
| geq(vd353,vd354) ) ),
inference(distribute,[status(thm)],['dis(antec(218))']) ).
cnf(c_0_19,negated_conjecture,
~ greater(vplus(vd353,vd355),vplus(vd354,vd356)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( greater(vplus(X3,X1),vplus(X4,X2))
| ~ greater(X1,X2)
| ~ greater(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( greater(X1,X2)
| X1 = X2
| ~ geq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
( geq(vd355,vd356)
| greater(vd355,vd356) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( ~ greater(vd353,vd354)
| ~ greater(vd355,vd356) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( vd356 = vd355
| greater(vd355,vd356) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_25,plain,
! [X78,X79,X80] :
( ~ greater(vplus(X78,X80),vplus(X79,X80))
| greater(X78,X79) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(goal(202), 0), 2)'])]) ).
cnf(c_0_26,negated_conjecture,
( vd356 = vd355
| ~ greater(vd353,vd354) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,plain,
( greater(X1,X3)
| ~ greater(vplus(X1,X2),vplus(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_28,plain,
! [X87,X88,X89] :
( ~ greater(X87,X88)
| greater(vplus(X87,X89),vplus(X88,X89)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(goal(193), 0), 2)'])]) ).
fof(c_0_29,plain,
! [X137,X138,X139] :
( X137 != X138
| X138 != vplus(X137,X139) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(goal(88), 0), 1)'])])]) ).
fof(c_0_30,plain,
! [X98,X99,X100] :
( ~ less(X99,X100)
| ~ less(X98,X99)
| less(X98,X100) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(168, 0), 0)'])]) ).
fof(c_0_31,plain,
! [X111,X112] :
( ~ greater(X111,X112)
| less(X112,X111) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(140, 0), 0)'])]) ).
cnf(c_0_32,negated_conjecture,
~ greater(vplus(vd353,vd355),vplus(vd354,vd355)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_26]),c_0_27]) ).
cnf(c_0_33,plain,
( greater(vplus(X1,X3),vplus(X2,X3))
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
( X1 != X2
| X2 != vplus(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_35,plain,
! [X157,X158,X159] : vplus(vplus(X157,X158),X159) = vplus(X157,vplus(X158,X159)),
inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).
cnf(c_0_36,plain,
( less(X3,X2)
| ~ less(X1,X2)
| ~ less(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,plain,
( less(X2,X1)
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,plain,
( greater(vd353,vd354)
| greater(vd355,vd356) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_39,negated_conjecture,
~ greater(vd353,vd354),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,plain,
vplus(X1,X2) != X1,
inference(er,[status(thm)],[c_0_34]) ).
cnf(c_0_41,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_42,plain,
! [X152,X153] : vplus(X153,X152) = vplus(X152,X153),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
fof(c_0_43,plain,
! [X109,X110] :
( ~ less(X109,X110)
| greater(X110,X109) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(147, 0), 0)'])]) ).
cnf(c_0_44,plain,
( less(X1,X2)
| ~ less(X3,X2)
| ~ greater(X3,X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_45,plain,
greater(vd355,vd356),
inference(sr,[status(thm)],[c_0_38,c_0_39]) ).
fof(c_0_46,plain,
! [X121,X122,X124,X125,X126] :
( ( ~ less(X122,X121)
| X121 = vplus(X122,esk1_2(X121,X122)) )
& ( X124 != vplus(X125,X126)
| less(X125,X124) ) ),
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_47,plain,
vplus(X1,vplus(X2,X3)) != vplus(X1,X2),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_49,plain,
! [X127,X128,X130,X131,X132] :
( ( ~ greater(X128,X127)
| X128 = vplus(X127,esk2_2(X127,X128)) )
& ( X131 != vplus(X130,X132)
| greater(X131,X130) ) ),
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_50,plain,
( greater(X2,X1)
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_51,plain,
( less(vd356,X1)
| ~ less(vd355,X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_52,plain,
( less(X2,X1)
| X1 != vplus(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_53,plain,
vplus(X1,vplus(X2,X3)) != vplus(X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_41]) ).
cnf(c_0_54,plain,
( X1 = vplus(X2,esk2_2(X2,X1))
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_55,plain,
( greater(X1,vd356)
| ~ less(vd355,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_56,plain,
less(X1,vplus(X1,X2)),
inference(er,[status(thm)],[c_0_52]) ).
cnf(c_0_57,plain,
vplus(X1,vplus(X2,X3)) != vplus(X2,X1),
inference(spm,[status(thm)],[c_0_53,c_0_48]) ).
cnf(c_0_58,plain,
( vplus(X1,X2) != vplus(X1,X3)
| ~ greater(X2,X3) ),
inference(spm,[status(thm)],[c_0_47,c_0_54]) ).
cnf(c_0_59,plain,
greater(vplus(vd355,X1),vd356),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_60,plain,
( vplus(X1,X2) != vplus(X3,X1)
| ~ greater(X2,X3) ),
inference(spm,[status(thm)],[c_0_57,c_0_54]) ).
cnf(c_0_61,plain,
vplus(X1,vplus(vd355,X2)) != vplus(X1,vd356),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_62,plain,
vplus(X1,vplus(X2,X3)) = vplus(X2,vplus(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_48]),c_0_41]) ).
fof(c_0_63,plain,
! [X113,X114] :
( X113 = X114
| greater(X113,X114)
| less(X113,X114) ),
inference(variable_rename,[status(thm)],['ass(cond(goal(130), 0), 0)']) ).
cnf(c_0_64,plain,
vplus(X1,vd355) != vplus(vd356,X1),
inference(spm,[status(thm)],[c_0_60,c_0_45]) ).
cnf(c_0_65,plain,
( greater(vd353,vd354)
| geq(vd353,vd354) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_66,plain,
vplus(vd355,vplus(X1,X2)) != vplus(X1,vd356),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_67,plain,
( vplus(X1,vplus(X2,esk2_2(vplus(X1,X2),X3))) = X3
| ~ greater(X3,vplus(X1,X2)) ),
inference(spm,[status(thm)],[c_0_41,c_0_54]) ).
cnf(c_0_68,plain,
( X1 = X2
| greater(X1,X2)
| less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_69,plain,
vplus(vd356,X1) != vplus(vd355,X1),
inference(spm,[status(thm)],[c_0_64,c_0_48]) ).
cnf(c_0_70,plain,
( vd354 = vd353
| greater(vd353,vd354) ),
inference(spm,[status(thm)],[c_0_21,c_0_65]) ).
cnf(c_0_71,plain,
~ greater(vplus(X1,vd356),vplus(vd355,X1)),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67])]) ).
cnf(c_0_72,plain,
( X1 = X2
| greater(X1,X2)
| greater(X2,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_68]) ).
cnf(c_0_73,plain,
vplus(X1,vd356) != vplus(vd355,X1),
inference(spm,[status(thm)],[c_0_69,c_0_48]) ).
cnf(c_0_74,plain,
vd354 = vd353,
inference(sr,[status(thm)],[c_0_70,c_0_39]) ).
cnf(c_0_75,plain,
greater(vplus(vd355,X1),vplus(X1,vd356)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_76,negated_conjecture,
~ greater(vplus(vd353,vd355),vplus(vd353,vd356)),
inference(spm,[status(thm)],[c_0_19,c_0_74]) ).
cnf(c_0_77,plain,
greater(vplus(X1,vd355),vplus(X1,vd356)),
inference(spm,[status(thm)],[c_0_75,c_0_48]) ).
cnf(c_0_78,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM842+1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 08:26:13 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.66 start to proof: theBenchmark
% 0.19/0.78 % Version : CSE_E---1.5
% 0.19/0.78 % Problem : theBenchmark.p
% 0.19/0.78 % Proof found
% 0.19/0.78 % SZS status Theorem for theBenchmark.p
% 0.19/0.78 % SZS output start Proof
% See solution above
% 0.19/0.78 % Total time : 0.110000 s
% 0.19/0.78 % SZS output end Proof
% 0.19/0.78 % Total time : 0.114000 s
%------------------------------------------------------------------------------