TSTP Solution File: NUM841+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM841+2 : 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 : n017.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 0.20s 0.63s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 26
% Syntax : Number of formulae : 72 ( 41 unt; 11 typ; 0 def)
% Number of atoms : 87 ( 35 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 59 ( 33 ~; 22 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 6 >; 4 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 89 ( 11 sgn; 44 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
vd344: $i ).
tff(decl_23,type,
vd347: $i ).
tff(decl_24,type,
vplus: ( $i * $i ) > $i ).
tff(decl_25,type,
vd345: $i ).
tff(decl_26,type,
vd348: $i ).
tff(decl_27,type,
greater: ( $i * $i ) > $o ).
tff(decl_28,type,
less: ( $i * $i ) > $o ).
tff(decl_29,type,
vsucc: $i > $i ).
tff(decl_30,type,
v1: $i ).
tff(decl_31,type,
vskolem2: $i > $i ).
tff(decl_32,type,
esk1_2: ( $i * $i ) > $i ).
fof('ass(cond(goal(130), 0), 2)',axiom,
! [X13,X14] :
( ~ greater(X13,X14)
| ~ less(X13,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
fof('ass(cond(140, 0), 0)',axiom,
! [X11,X12] :
( greater(X11,X12)
=> less(X12,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
fof('ass(cond(189, 0), 0)',axiom,
! [X7,X8] : greater(vplus(X7,X8),X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
! [X15,X16] :
( greater(X16,X15)
<=> ? [X17] : X16 = vplus(X15,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof('holds(213, 351, 1)',axiom,
greater(vplus(vd347,vd345),vplus(vd348,vd345)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(213, 351, 1)') ).
fof('holds(213, 351, 0)',axiom,
vplus(vd345,vd347) = vplus(vd347,vd345),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(213, 351, 0)') ).
fof('holds(213, 351, 2)',axiom,
vplus(vd348,vd345) = vplus(vd345,vd348),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(213, 351, 2)') ).
fof('ass(cond(33, 0), 0)',axiom,
! [X26,X27,X28] : vplus(vplus(X26,X27),X28) = vplus(X26,vplus(X27,X28)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof('ass(cond(goal(88), 0), 3)',axiom,
! [X18,X19] :
( X18 != X19
| ~ ? [X20] : X18 = vplus(X19,X20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
fof('holds(conjunct2(211), 349, 0)',axiom,
greater(vd347,vd348),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct2(211), 349, 0)') ).
fof('ass(cond(61, 0), 0)',axiom,
! [X21,X22] : vplus(X22,X21) = vplus(X21,X22),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof('holds(conjunct1(211), 346, 0)',axiom,
greater(vd344,vd345),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(211), 346, 0)') ).
fof('ass(cond(147, 0), 0)',axiom,
! [X9,X10] :
( less(X9,X10)
=> greater(X10,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
fof('ass(cond(goal(130), 0), 0)',axiom,
! [X13,X14] :
( X13 = X14
| greater(X13,X14)
| less(X13,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
fof('holds(214, 352, 0)',conjecture,
greater(vplus(vd344,vd347),vplus(vd345,vd348)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(214, 352, 0)') ).
fof(c_0_15,plain,
! [X13,X14] :
( ~ greater(X13,X14)
| ~ less(X13,X14) ),
inference(fof_simplification,[status(thm)],['ass(cond(goal(130), 0), 2)']) ).
fof(c_0_16,plain,
! [X54,X55] :
( ~ greater(X54,X55)
| less(X55,X54) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(140, 0), 0)'])]) ).
fof(c_0_17,plain,
! [X50,X51] : greater(vplus(X50,X51),X50),
inference(variable_rename,[status(thm)],['ass(cond(189, 0), 0)']) ).
fof(c_0_18,plain,
! [X58,X59] :
( ~ greater(X58,X59)
| ~ less(X58,X59) ),
inference(variable_rename,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( less(X2,X1)
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
greater(vplus(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_21,plain,
! [X60,X61,X63,X64,X65] :
( ( ~ greater(X61,X60)
| X61 = vplus(X60,esk1_2(X60,X61)) )
& ( X64 != vplus(X63,X65)
| greater(X64,X63) ) ),
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_22,plain,
greater(vplus(vd347,vd345),vplus(vd348,vd345)),
inference(split_conjunct,[status(thm)],['holds(213, 351, 1)']) ).
cnf(c_0_23,plain,
vplus(vd345,vd347) = vplus(vd347,vd345),
inference(split_conjunct,[status(thm)],['holds(213, 351, 0)']) ).
cnf(c_0_24,plain,
vplus(vd348,vd345) = vplus(vd345,vd348),
inference(split_conjunct,[status(thm)],['holds(213, 351, 2)']) ).
fof(c_0_25,plain,
! [X74,X75,X76] : vplus(vplus(X74,X75),X76) = vplus(X74,vplus(X75,X76)),
inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).
fof(c_0_26,plain,
! [X66,X67,X68] :
( X66 != X67
| X66 != vplus(X67,X68) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(goal(88), 0), 3)'])])]) ).
cnf(c_0_27,plain,
( ~ greater(X1,X2)
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,plain,
less(X1,vplus(X1,X2)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_29,plain,
( X1 = vplus(X2,esk1_2(X2,X1))
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,plain,
greater(vplus(vd345,vd347),vplus(vd345,vd348)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_31,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
( X1 != X2
| X1 != vplus(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
greater(vd347,vd348),
inference(split_conjunct,[status(thm)],['holds(conjunct2(211), 349, 0)']) ).
cnf(c_0_34,plain,
~ greater(X1,vplus(X1,X2)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,plain,
vplus(vd345,vplus(vd348,esk1_2(vplus(vd345,vd348),vplus(vd345,vd347)))) = vplus(vd345,vd347),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_36,plain,
vplus(X1,X2) != X1,
inference(er,[status(thm)],[c_0_32]) ).
cnf(c_0_37,plain,
vplus(vd348,esk1_2(vd348,vd347)) = vd347,
inference(spm,[status(thm)],[c_0_29,c_0_33]) ).
cnf(c_0_38,plain,
~ greater(vplus(X1,X2),vplus(X1,vplus(X2,X3))),
inference(spm,[status(thm)],[c_0_34,c_0_31]) ).
cnf(c_0_39,plain,
vplus(vd345,vplus(vd348,vplus(esk1_2(vplus(vd345,vd348),vplus(vd345,vd347)),X1))) = vplus(vd345,vplus(vd347,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_35]),c_0_31]),c_0_31]) ).
fof(c_0_40,plain,
! [X69,X70] : vplus(X70,X69) = vplus(X69,X70),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
cnf(c_0_41,plain,
greater(vd344,vd345),
inference(split_conjunct,[status(thm)],['holds(conjunct1(211), 346, 0)']) ).
cnf(c_0_42,plain,
vplus(X1,vplus(X2,X3)) != vplus(X1,X2),
inference(spm,[status(thm)],[c_0_36,c_0_31]) ).
cnf(c_0_43,plain,
vplus(vd348,vplus(esk1_2(vd348,vd347),X1)) = vplus(vd347,X1),
inference(spm,[status(thm)],[c_0_31,c_0_37]) ).
cnf(c_0_44,plain,
~ greater(vplus(vd345,vd348),vplus(vd345,vplus(vd347,X1))),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_46,plain,
vplus(vd345,esk1_2(vd345,vd344)) = vd344,
inference(spm,[status(thm)],[c_0_29,c_0_41]) ).
fof(c_0_47,plain,
! [X52,X53] :
( ~ less(X52,X53)
| greater(X53,X52) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(147, 0), 0)'])]) ).
fof(c_0_48,plain,
! [X56,X57] :
( X56 = X57
| greater(X56,X57)
| less(X56,X57) ),
inference(variable_rename,[status(thm)],['ass(cond(goal(130), 0), 0)']) ).
cnf(c_0_49,plain,
vplus(X1,vplus(vd347,X2)) != vplus(X1,vd348),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,plain,
~ greater(vplus(vd345,vd348),vplus(vd345,vplus(X1,vd347))),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,plain,
vplus(vd345,vplus(esk1_2(vd345,vd344),X1)) = vplus(vd344,X1),
inference(spm,[status(thm)],[c_0_31,c_0_46]) ).
cnf(c_0_52,plain,
( greater(X2,X1)
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_53,plain,
( X1 = X2
| greater(X1,X2)
| less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_54,plain,
vplus(X1,vplus(X2,vd347)) != vplus(X1,vd348),
inference(spm,[status(thm)],[c_0_49,c_0_45]) ).
fof(c_0_55,negated_conjecture,
~ greater(vplus(vd344,vd347),vplus(vd345,vd348)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['holds(214, 352, 0)'])]) ).
cnf(c_0_56,plain,
~ greater(vplus(vd345,vd348),vplus(vd344,vd347)),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_57,plain,
( X1 = X2
| greater(X1,X2)
| greater(X2,X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,plain,
vplus(vd345,vd348) != vplus(vd344,vd347),
inference(spm,[status(thm)],[c_0_54,c_0_51]) ).
cnf(c_0_59,negated_conjecture,
~ greater(vplus(vd344,vd347),vplus(vd345,vd348)),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_60,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_59]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM841+2 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 15:15:55 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.20/0.54 start to proof: theBenchmark
% 0.20/0.63 % Version : CSE_E---1.5
% 0.20/0.63 % Problem : theBenchmark.p
% 0.20/0.63 % Proof found
% 0.20/0.63 % SZS status Theorem for theBenchmark.p
% 0.20/0.63 % SZS output start Proof
% See solution above
% 0.20/0.63 % Total time : 0.077000 s
% 0.20/0.63 % SZS output end Proof
% 0.20/0.63 % Total time : 0.080000 s
%------------------------------------------------------------------------------