TSTP Solution File: NUM857+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM857+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 : n031.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 10:41:05 EDT 2023
% Result : Theorem 0.70s 0.83s
% Output : CNFRefutation 0.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 31
% Syntax : Number of formulae : 78 ( 34 unt; 17 typ; 0 def)
% Number of atoms : 108 ( 50 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 75 ( 28 ~; 37 |; 6 &)
% ( 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 : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 105 ( 10 sgn; 55 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
vd526: $i ).
tff(decl_23,type,
vd529: $i ).
tff(decl_24,type,
vmul: ( $i * $i ) > $i ).
tff(decl_25,type,
vd527: $i ).
tff(decl_26,type,
vd530: $i ).
tff(decl_27,type,
geq: ( $i * $i ) > $o ).
tff(decl_28,type,
greater: ( $i * $i ) > $o ).
tff(decl_29,type,
less: ( $i * $i ) > $o ).
tff(decl_30,type,
vplus: ( $i * $i ) > $i ).
tff(decl_31,type,
vsucc: $i > $i ).
tff(decl_32,type,
v1: $i ).
tff(decl_33,type,
leq: ( $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('def(cond(conseq(axiom(3)), 16), 1)',axiom,
! [X78,X79] :
( geq(X79,X78)
<=> ( greater(X79,X78)
| X79 = X78 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).
fof('ass(cond(73, 0), 0)',axiom,
! [X99,X100] : X100 != vplus(X99,X100),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
fof('ass(cond(33, 0), 0)',axiom,
! [X106,X107,X108] : vplus(vplus(X106,X107),X108) = vplus(X106,vplus(X107,X108)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof('ass(cond(140, 0), 0)',axiom,
! [X82,X83] :
( greater(X82,X83)
=> less(X83,X82) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
fof('holds(conjunct2(antec(323)), 531, 0)',axiom,
geq(vd529,vd530),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(antec(323)), 531, 0)') ).
fof('ass(cond(61, 0), 0)',axiom,
! [X101,X102] : vplus(X102,X101) = vplus(X101,X102),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof('def(cond(conseq(axiom(3)), 12), 1)',axiom,
! [X86,X87] :
( less(X87,X86)
<=> ? [X88] : X86 = vplus(X87,X88) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
fof('ass(cond(318, 0), 0)',axiom,
! [X1,X2,X3,X4] :
( ( ( greater(X3,X4)
& geq(X1,X2) )
| ( geq(X3,X4)
& greater(X1,X2) ) )
=> greater(vmul(X1,X3),vmul(X2,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(318, 0), 0)') ).
fof('holds(conjunct1(antec(323)), 528, 0)',axiom,
geq(vd526,vd527),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(antec(323)), 528, 0)') ).
fof('ass(cond(270, 0), 0)',axiom,
! [X31,X32] : vmul(X31,X32) = vmul(X32,X31),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
fof('ass(cond(189, 0), 0)',axiom,
! [X61,X62] : greater(vplus(X61,X62),X61),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
fof('holds(conseq(323), 532, 0)',conjecture,
geq(vmul(vd526,vd529),vmul(vd527,vd530)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq(323), 532, 0)') ).
fof('ass(cond(281, 0), 0)',axiom,
! [X28,X29,X30] : vmul(X28,vplus(X29,X30)) = vplus(vmul(X28,X29),vmul(X28,X30)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
fof('ass(cond(goal(88), 0), 0)',axiom,
! [X92,X93] :
( X92 = X93
| ? [X94] : X92 = vplus(X93,X94)
| ? [X95] : X93 = vplus(X92,X95) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
fof(c_0_14,plain,
! [X209,X210] :
( ( ~ geq(X210,X209)
| greater(X210,X209)
| X210 = X209 )
& ( ~ greater(X210,X209)
| geq(X210,X209) )
& ( X210 != X209
| geq(X210,X209) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['def(cond(conseq(axiom(3)), 16), 1)'])])]) ).
fof(c_0_15,plain,
! [X252,X253] : X253 != vplus(X252,X253),
inference(variable_rename,[status(thm)],['ass(cond(73, 0), 0)']) ).
fof(c_0_16,plain,
! [X259,X260,X261] : vplus(vplus(X259,X260),X261) = vplus(X259,vplus(X260,X261)),
inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).
fof(c_0_17,plain,
! [X213,X214] :
( ~ greater(X213,X214)
| less(X214,X213) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(140, 0), 0)'])]) ).
cnf(c_0_18,plain,
( greater(X1,X2)
| X1 = X2
| ~ geq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
geq(vd529,vd530),
inference(split_conjunct,[status(thm)],['holds(conjunct2(antec(323)), 531, 0)']) ).
cnf(c_0_20,plain,
X1 != vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_22,plain,
! [X254,X255] : vplus(X255,X254) = vplus(X254,X255),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
fof(c_0_23,plain,
! [X223,X224,X226,X227,X228] :
( ( ~ less(X224,X223)
| X223 = vplus(X224,esk1_2(X223,X224)) )
& ( X226 != vplus(X227,X228)
| less(X227,X226) ) ),
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_17]) ).
cnf(c_0_25,plain,
( vd530 = vd529
| greater(vd529,vd530) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_26,plain,
! [X118,X119,X120,X121] :
( ( ~ greater(X120,X121)
| ~ geq(X118,X119)
| greater(vmul(X118,X120),vmul(X119,X121)) )
& ( ~ geq(X120,X121)
| ~ greater(X118,X119)
| greater(vmul(X118,X120),vmul(X119,X121)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(318, 0), 0)'])])]) ).
cnf(c_0_27,plain,
vplus(X1,vplus(X2,X3)) != X3,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
( X2 = vplus(X1,esk1_2(X2,X1))
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( vd530 = vd529
| less(vd530,vd529) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
( greater(vmul(X3,X1),vmul(X4,X2))
| ~ greater(X1,X2)
| ~ geq(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
geq(vd526,vd527),
inference(split_conjunct,[status(thm)],['holds(conjunct1(antec(323)), 528, 0)']) ).
fof(c_0_33,plain,
! [X150,X151] : vmul(X150,X151) = vmul(X151,X150),
inference(variable_rename,[status(thm)],['ass(cond(270, 0), 0)']) ).
fof(c_0_34,plain,
! [X192,X193] : greater(vplus(X192,X193),X192),
inference(variable_rename,[status(thm)],['ass(cond(189, 0), 0)']) ).
cnf(c_0_35,plain,
vplus(X1,vplus(X2,X3)) != X2,
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_36,plain,
( vplus(vd530,esk1_2(vd529,vd530)) = vd529
| vd530 = vd529 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,plain,
( greater(vmul(vd529,X1),vmul(vd530,X2))
| ~ greater(X1,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_19]) ).
cnf(c_0_38,plain,
( vd527 = vd526
| greater(vd526,vd527) ),
inference(spm,[status(thm)],[c_0_18,c_0_32]) ).
cnf(c_0_39,plain,
vmul(X1,X2) = vmul(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_40,negated_conjecture,
~ geq(vmul(vd526,vd529),vmul(vd527,vd530)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['holds(conseq(323), 532, 0)'])]) ).
cnf(c_0_41,plain,
( geq(X1,X2)
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_42,plain,
greater(vplus(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_43,plain,
! [X147,X148,X149] : vmul(X147,vplus(X148,X149)) = vplus(vmul(X147,X148),vmul(X147,X149)),
inference(variable_rename,[status(thm)],['ass(cond(281, 0), 0)']) ).
cnf(c_0_44,plain,
( vd530 = vd529
| vplus(X1,vd529) != vd530 ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_45,plain,
! [X235,X236] :
( X235 = X236
| X235 = vplus(X236,esk3_2(X235,X236))
| X236 = vplus(X235,esk4_2(X235,X236)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],['ass(cond(goal(88), 0), 0)'])]) ).
cnf(c_0_46,plain,
( vd527 = vd526
| greater(vmul(vd526,vd529),vmul(vd527,vd530)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_39]) ).
cnf(c_0_47,negated_conjecture,
~ geq(vmul(vd526,vd529),vmul(vd527,vd530)),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_48,plain,
geq(vplus(X1,X2),X1),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_49,plain,
vmul(X1,vplus(X2,X3)) = vplus(vmul(X1,X2),vmul(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_50,plain,
( vd530 = vd529
| vplus(vd529,X1) != vd530 ),
inference(spm,[status(thm)],[c_0_44,c_0_28]) ).
cnf(c_0_51,plain,
( X1 = X2
| X1 = vplus(X2,esk3_2(X1,X2))
| X2 = vplus(X1,esk4_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_52,plain,
vd527 = vd526,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_46]),c_0_47]) ).
cnf(c_0_53,plain,
geq(vmul(X1,vplus(X2,X3)),vmul(X1,X2)),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,plain,
( vplus(vd530,esk4_2(vd530,vd529)) = vd529
| vd530 = vd529 ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51])]) ).
cnf(c_0_55,negated_conjecture,
~ geq(vmul(vd526,vd529),vmul(vd526,vd530)),
inference(spm,[status(thm)],[c_0_47,c_0_52]) ).
cnf(c_0_56,plain,
( vd530 = vd529
| geq(vmul(X1,vd529),vmul(X1,vd530)) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_57,plain,
( geq(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_58,negated_conjecture,
vd530 = vd529,
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_59,plain,
geq(X1,X1),
inference(er,[status(thm)],[c_0_57]) ).
cnf(c_0_60,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_58]),c_0_52]),c_0_59])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : NUM857+2 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.35 % Computer : n031.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8042.1875MB
% 0.11/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Fri Aug 25 13:15:36 EDT 2023
% 0.11/0.35 % CPUTime :
% 0.17/0.56 start to proof: theBenchmark
% 0.70/0.83 % Version : CSE_E---1.5
% 0.70/0.83 % Problem : theBenchmark.p
% 0.70/0.83 % Proof found
% 0.70/0.83 % SZS status Theorem for theBenchmark.p
% 0.70/0.83 % SZS output start Proof
% See solution above
% 0.70/0.84 % Total time : 0.270000 s
% 0.70/0.84 % SZS output end Proof
% 0.70/0.84 % Total time : 0.273000 s
%------------------------------------------------------------------------------