TSTP Solution File: NUM840+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM840+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 : n005.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 10:40:56 EDT 2023
% Result : Theorem 0.66s 0.77s
% Output : CNFRefutation 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 26
% Syntax : Number of formulae : 63 ( 28 unt; 15 typ; 0 def)
% Number of atoms : 80 ( 57 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 62 ( 30 ~; 27 |; 2 &)
% ( 2 <=>; 1 =>; 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 : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 97 ( 12 sgn; 47 !; 5 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
vd328: $i ).
tff(decl_23,type,
vd329: $i ).
tff(decl_24,type,
less: ( $i * $i ) > $o ).
tff(decl_25,type,
vd330: $i ).
tff(decl_26,type,
vplus: ( $i * $i ) > $i ).
tff(decl_27,type,
greater: ( $i * $i ) > $o ).
tff(decl_28,type,
leq: ( $i * $i ) > $o ).
tff(decl_29,type,
geq: ( $i * $i ) > $o ).
tff(decl_30,type,
vsucc: $i > $i ).
tff(decl_31,type,
v1: $i ).
tff(decl_32,type,
vskolem2: $i > $i ).
tff(decl_33,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_34,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_35,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_36,type,
esk4_2: ( $i * $i ) > $i ).
fof('ass(cond(73, 0), 0)',axiom,
! [X42,X43] : X43 != vplus(X42,X43),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
fof('ass(cond(33, 0), 0)',axiom,
! [X49,X50,X51] : vplus(vplus(X49,X50),X51) = vplus(X49,vplus(X50,X51)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof('ass(cond(61, 0), 0)',axiom,
! [X44,X45] : vplus(X45,X44) = vplus(X44,X45),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof('def(cond(conseq(axiom(3)), 12), 1)',axiom,
! [X29,X30] :
( less(X30,X29)
<=> ? [X31] : X29 = vplus(X30,X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
fof('holds(antec(conjunct2(conjunct2(204))), 335, 0)',axiom,
less(vplus(vd328,vd330),vplus(vd329,vd330)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(antec(conjunct2(conjunct2(204))), 335, 0)') ).
fof('ass(cond(goal(88), 0), 1)',axiom,
! [X35,X36] :
( X35 != X36
| ~ ? [X38] : X36 = vplus(X35,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
! [X32,X33] :
( greater(X33,X32)
<=> ? [X34] : X33 = vplus(X32,X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof('ass(cond(goal(130), 0), 0)',axiom,
! [X27,X28] :
( X27 = X28
| greater(X27,X28)
| less(X27,X28) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
fof('ass(cond(81, 0), 0)',axiom,
! [X39,X40] :
( X39 != X40
=> ! [X41] : vplus(X41,X39) != vplus(X41,X40) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
fof('ass(cond(goal(88), 0), 0)',axiom,
! [X35,X36] :
( X35 = X36
| ? [X37] : X35 = vplus(X36,X37)
| ? [X38] : X36 = vplus(X35,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
fof('holds(conseq(conjunct2(conjunct2(204))), 336, 0)',conjecture,
less(vd328,vd329),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq(conjunct2(conjunct2(204))), 336, 0)') ).
fof(c_0_11,plain,
! [X130,X131] : X131 != vplus(X130,X131),
inference(variable_rename,[status(thm)],['ass(cond(73, 0), 0)']) ).
fof(c_0_12,plain,
! [X137,X138,X139] : vplus(vplus(X137,X138),X139) = vplus(X137,vplus(X138,X139)),
inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).
cnf(c_0_13,plain,
X1 != vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,plain,
! [X132,X133] : vplus(X133,X132) = vplus(X132,X133),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
cnf(c_0_16,plain,
vplus(X1,vplus(X2,X3)) != X3,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_18,plain,
! [X101,X102,X104,X105,X106] :
( ( ~ less(X102,X101)
| X101 = vplus(X102,esk1_2(X101,X102)) )
& ( X104 != vplus(X105,X106)
| less(X105,X104) ) ),
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_19,plain,
less(vplus(vd328,vd330),vplus(vd329,vd330)),
inference(split_conjunct,[status(thm)],['holds(antec(conjunct2(conjunct2(204))), 335, 0)']) ).
cnf(c_0_20,plain,
vplus(X1,vplus(X2,X3)) != X2,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
( X2 = vplus(X1,esk1_2(X2,X1))
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
less(vplus(vd328,vd330),vplus(vd330,vd329)),
inference(rw,[status(thm)],[c_0_19,c_0_17]) ).
fof(c_0_23,plain,
! [X117,X118,X119] :
( X117 != X118
| X118 != vplus(X117,X119) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(goal(88), 0), 1)'])])]) ).
cnf(c_0_24,plain,
vplus(X1,vplus(X2,vplus(X3,X4))) != vplus(X2,X3),
inference(spm,[status(thm)],[c_0_20,c_0_14]) ).
cnf(c_0_25,plain,
vplus(vd328,vplus(vd330,esk1_2(vplus(vd330,vd329),vplus(vd328,vd330)))) = vplus(vd330,vd329),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_14]) ).
fof(c_0_26,plain,
! [X107,X108,X110,X111,X112] :
( ( ~ greater(X108,X107)
| X108 = vplus(X107,esk2_2(X107,X108)) )
& ( X111 != vplus(X110,X112)
| greater(X111,X110) ) ),
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)'])])])])]) ).
fof(c_0_27,plain,
! [X93,X94] :
( X93 = X94
| greater(X93,X94)
| less(X93,X94) ),
inference(variable_rename,[status(thm)],['ass(cond(goal(130), 0), 0)']) ).
fof(c_0_28,plain,
! [X127,X128,X129] :
( X127 = X128
| vplus(X129,X127) != vplus(X129,X128) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(81, 0), 0)'])])]) ).
fof(c_0_29,plain,
! [X113,X114] :
( X113 = X114
| X113 = vplus(X114,esk3_2(X113,X114))
| X114 = vplus(X113,esk4_2(X113,X114)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],['ass(cond(goal(88), 0), 0)'])]) ).
cnf(c_0_30,plain,
( X1 != X2
| X2 != vplus(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,plain,
vplus(X1,vplus(vd330,vd329)) != vplus(vd328,vd330),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
( X1 = vplus(X2,esk2_2(X2,X1))
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
( X1 = X2
| greater(X1,X2)
| less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,plain,
( X1 = X2
| vplus(X3,X1) != vplus(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
( X1 = X2
| X1 = vplus(X2,esk3_2(X1,X2))
| X2 = vplus(X1,esk4_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
vplus(X1,X2) != X1,
inference(er,[status(thm)],[c_0_30]) ).
cnf(c_0_37,plain,
vplus(vd330,vplus(vd329,X1)) != vplus(vd328,vd330),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_17]),c_0_14]) ).
cnf(c_0_38,plain,
( vplus(X1,esk2_2(X1,X2)) = X2
| X2 = X1
| less(X2,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,plain,
esk4_2(X1,vplus(X1,X2)) = X2,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35])]),c_0_14]),c_0_36]),c_0_36]) ).
fof(c_0_40,negated_conjecture,
~ less(vd328,vd329),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['holds(conseq(conjunct2(conjunct2(204))), 336, 0)'])]) ).
cnf(c_0_41,plain,
vplus(X1,vplus(X2,X3)) != vplus(X1,X2),
inference(spm,[status(thm)],[c_0_36,c_0_14]) ).
cnf(c_0_42,plain,
( X1 = vd329
| less(X1,vd329)
| vplus(vd330,X1) != vplus(vd328,vd330) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,plain,
esk4_2(X1,vplus(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_39,c_0_17]) ).
cnf(c_0_44,negated_conjecture,
~ less(vd328,vd329),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_45,plain,
vplus(vd330,vd329) != vplus(vd328,vd330),
inference(spm,[status(thm)],[c_0_41,c_0_25]) ).
cnf(c_0_46,plain,
vd329 = vd328,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_35])]),c_0_43]),c_0_43]),c_0_14]),c_0_44]),c_0_20]),c_0_13]) ).
cnf(c_0_47,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM840+1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n005.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 14:11:08 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.66/0.77 % Version : CSE_E---1.5
% 0.66/0.77 % Problem : theBenchmark.p
% 0.66/0.77 % Proof found
% 0.66/0.77 % SZS status Theorem for theBenchmark.p
% 0.66/0.77 % SZS output start Proof
% See solution above
% 0.66/0.77 % Total time : 0.200000 s
% 0.66/0.77 % SZS output end Proof
% 0.66/0.77 % Total time : 0.203000 s
%------------------------------------------------------------------------------