TSTP Solution File: NUM850+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM850+2 : 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 : 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 10:41:01 EDT 2023
% Result : Theorem 0.20s 0.60s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 23
% Syntax : Number of formulae : 46 ( 19 unt; 15 typ; 0 def)
% Number of atoms : 52 ( 21 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 38 ( 17 ~; 14 |; 3 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 12 >; 10 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 6 sgn; 30 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
vd470: $i ).
tff(decl_23,type,
vd471: $i ).
tff(decl_24,type,
vplus: ( $i * $i ) > $i ).
tff(decl_25,type,
greater: ( $i * $i ) > $o ).
tff(decl_26,type,
vmul: ( $i * $i ) > $i ).
tff(decl_27,type,
vsucc: $i > $i ).
tff(decl_28,type,
v1: $i ).
tff(decl_29,type,
less: ( $i * $i ) > $o ).
tff(decl_30,type,
leq: ( $i * $i ) > $o ).
tff(decl_31,type,
geq: ( $i * $i ) > $o ).
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('qe(conseq_conjunct1(conseq(302)))',conjecture,
? [X1] : vd470 = vplus(vd471,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qe(conseq_conjunct1(conseq(302)))') ).
fof('ass(cond(234, 0), 0)',axiom,
! [X17,X18] :
( greater(X17,X18)
=> geq(X17,vplus(X18,v1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(234, 0), 0)') ).
fof('ass(cond(61, 0), 0)',axiom,
! [X76,X77] : vplus(X77,X76) = vplus(X76,X77),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof('def(cond(conseq(axiom(3)), 16), 1)',axiom,
! [X53,X54] :
( geq(X54,X53)
<=> ( greater(X54,X53)
| X54 = X53 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).
fof('holds(antec(302), 472, 0)',axiom,
greater(vd470,vd471),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(antec(302), 472, 0)') ).
fof('ass(cond(33, 0), 0)',axiom,
! [X81,X82,X83] : vplus(vplus(X81,X82),X83) = vplus(X81,vplus(X82,X83)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof('ass(cond(140, 0), 0)',axiom,
! [X57,X58] :
( greater(X57,X58)
=> less(X58,X57) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
fof('def(cond(conseq(axiom(3)), 12), 1)',axiom,
! [X61,X62] :
( less(X62,X61)
<=> ? [X63] : X61 = vplus(X62,X63) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
fof(c_0_8,negated_conjecture,
~ ? [X1] : vd470 = vplus(vd471,X1),
inference(assume_negation,[status(cth)],['qe(conseq_conjunct1(conseq(302)))']) ).
fof(c_0_9,plain,
! [X109,X110] :
( ~ greater(X109,X110)
| geq(X109,vplus(X110,v1)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(234, 0), 0)'])]) ).
fof(c_0_10,plain,
! [X202,X203] : vplus(X203,X202) = vplus(X202,X203),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
fof(c_0_11,negated_conjecture,
! [X93] : vd470 != vplus(vd471,X93),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])]) ).
fof(c_0_12,plain,
! [X157,X158] :
( ( ~ geq(X158,X157)
| greater(X158,X157)
| X158 = X157 )
& ( ~ greater(X158,X157)
| geq(X158,X157) )
& ( X158 != X157
| geq(X158,X157) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['def(cond(conseq(axiom(3)), 16), 1)'])])]) ).
cnf(c_0_13,plain,
( geq(X1,vplus(X2,v1))
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
greater(vd470,vd471),
inference(split_conjunct,[status(thm)],['holds(antec(302), 472, 0)']) ).
cnf(c_0_15,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
vd470 != vplus(vd471,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,plain,
! [X207,X208,X209] : vplus(vplus(X207,X208),X209) = vplus(X207,vplus(X208,X209)),
inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).
fof(c_0_18,plain,
! [X161,X162] :
( ~ greater(X161,X162)
| less(X162,X161) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(140, 0), 0)'])]) ).
cnf(c_0_19,plain,
( greater(X1,X2)
| X1 = X2
| ~ geq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
geq(vd470,vplus(v1,vd471)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_21,negated_conjecture,
vplus(X1,vd471) != vd470,
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_22,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_23,plain,
! [X171,X172,X174,X175,X176] :
( ( ~ less(X172,X171)
| X171 = vplus(X172,esk1_2(X171,X172)) )
& ( X174 != vplus(X175,X176)
| less(X175,X174) ) ),
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_18]) ).
cnf(c_0_25,plain,
greater(vd470,vplus(v1,vd471)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_26,negated_conjecture,
vplus(X1,vplus(X2,vd471)) != vd470,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( X2 = vplus(X1,esk1_2(X2,X1))
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
less(vplus(v1,vd471),vd470),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
vplus(X1,vplus(vd471,X2)) != vd470,
inference(spm,[status(thm)],[c_0_26,c_0_15]) ).
cnf(c_0_30,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_22]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM850+2 : 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
% 0.14/0.34 % Computer : n001.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 11:21:58 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.60 % Version : CSE_E---1.5
% 0.20/0.60 % Problem : theBenchmark.p
% 0.20/0.60 % Proof found
% 0.20/0.60 % SZS status Theorem for theBenchmark.p
% 0.20/0.60 % SZS output start Proof
% See solution above
% 0.20/0.60 % Total time : 0.018000 s
% 0.20/0.60 % SZS output end Proof
% 0.20/0.60 % Total time : 0.021000 s
%------------------------------------------------------------------------------