TSTP Solution File: NUM852+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM852+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n022.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 10:41:02 EDT 2023
% Result : Theorem 0.19s 0.59s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 23
% Syntax : Number of formulae : 38 ( 14 unt; 17 typ; 0 def)
% Number of atoms : 28 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 13 >; 11 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 1 sgn; 16 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
vd481: $i ).
tff(decl_23,type,
vd469: $i ).
tff(decl_24,type,
vmul: ( $i * $i ) > $i ).
tff(decl_25,type,
vd480: $i ).
tff(decl_26,type,
greater: ( $i * $i ) > $o ).
tff(decl_27,type,
less: ( $i * $i ) > $o ).
tff(decl_28,type,
vskolem9: ( $i * $i ) > $i ).
tff(decl_29,type,
vplus: ( $i * $i ) > $i ).
tff(decl_30,type,
vsucc: $i > $i ).
tff(decl_31,type,
v1: $i ).
tff(decl_32,type,
leq: ( $i * $i ) > $o ).
tff(decl_33,type,
geq: ( $i * $i ) > $o ).
tff(decl_34,type,
vskolem2: $i > $i ).
tff(decl_35,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_36,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_37,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk4_2: ( $i * $i ) > $i ).
fof('ass(cond(302, 0), 1)',axiom,
! [X3,X4] :
( greater(X3,X4)
=> vmul(vplus(X4,vskolem9(X3,X4)),vd469) = vplus(vmul(X4,vd469),vmul(vskolem9(X3,X4),vd469)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(302, 0), 1)') ).
fof('ass(cond(270, 0), 0)',axiom,
! [X11,X12] : vmul(X11,X12) = vmul(X12,X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
fof('ass(cond(302, 0), 3)',axiom,
! [X3,X4] :
( greater(X3,X4)
=> X3 = vplus(X4,vskolem9(X3,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(302, 0), 3)') ).
fof('holds(conseq_conjunct1(conseq(304)), 483, 0)',axiom,
greater(vd481,vd480),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq_conjunct1(conseq(304)), 483, 0)') ).
fof('ass(cond(189, 0), 0)',axiom,
! [X41,X42] : greater(vplus(X41,X42),X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
fof('holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)',conjecture,
greater(vmul(vd481,vd469),vmul(vd480,vd469)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)') ).
fof(c_0_6,plain,
! [X102,X103] :
( ~ greater(X102,X103)
| vmul(vplus(X103,vskolem9(X102,X103)),vd469) = vplus(vmul(X103,vd469),vmul(vskolem9(X102,X103),vd469)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(302, 0), 1)'])]) ).
fof(c_0_7,plain,
! [X114,X115] : vmul(X114,X115) = vmul(X115,X114),
inference(variable_rename,[status(thm)],['ass(cond(270, 0), 0)']) ).
fof(c_0_8,plain,
! [X106,X107] :
( ~ greater(X106,X107)
| X106 = vplus(X107,vskolem9(X106,X107)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(302, 0), 3)'])]) ).
cnf(c_0_9,plain,
( vmul(vplus(X2,vskolem9(X1,X2)),vd469) = vplus(vmul(X2,vd469),vmul(vskolem9(X1,X2),vd469))
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
vmul(X1,X2) = vmul(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( X1 = vplus(X2,vskolem9(X1,X2))
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
greater(vd481,vd480),
inference(split_conjunct,[status(thm)],['holds(conseq_conjunct1(conseq(304)), 483, 0)']) ).
fof(c_0_13,plain,
! [X156,X157] : greater(vplus(X156,X157),X156),
inference(variable_rename,[status(thm)],['ass(cond(189, 0), 0)']) ).
cnf(c_0_14,plain,
( vplus(vmul(X1,vd469),vmul(vd469,vskolem9(X2,X1))) = vmul(vd469,vplus(X1,vskolem9(X2,X1)))
| ~ greater(X2,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_10]) ).
cnf(c_0_15,plain,
vplus(vd480,vskolem9(vd481,vd480)) = vd481,
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_16,negated_conjecture,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)'])]) ).
cnf(c_0_17,plain,
greater(vplus(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
vplus(vmul(vd480,vd469),vmul(vd469,vskolem9(vd481,vd480))) = vmul(vd481,vd469),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_12]),c_0_15]),c_0_10]) ).
cnf(c_0_19,negated_conjecture,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM852+1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n022.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 17:21:25 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.54 start to proof: theBenchmark
% 0.19/0.59 % Version : CSE_E---1.5
% 0.19/0.59 % Problem : theBenchmark.p
% 0.19/0.59 % Proof found
% 0.19/0.59 % SZS status Theorem for theBenchmark.p
% 0.19/0.59 % SZS output start Proof
% See solution above
% 0.19/0.60 % Total time : 0.039000 s
% 0.19/0.60 % SZS output end Proof
% 0.19/0.60 % Total time : 0.043000 s
%------------------------------------------------------------------------------