TSTP Solution File: NUM855+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM855+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 : n023.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 10:41:04 EDT 2023
% Result : Theorem 0.56s 0.72s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 34
% Syntax : Number of formulae : 91 ( 51 unt; 17 typ; 0 def)
% Number of atoms : 108 ( 60 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 79 ( 45 ~; 29 |; 2 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 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 : 127 ( 23 sgn; 61 !; 5 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
vd508: $i ).
tff(decl_23,type,
vd511: $i ).
tff(decl_24,type,
vmul: ( $i * $i ) > $i ).
tff(decl_25,type,
vd509: $i ).
tff(decl_26,type,
vd512: $i ).
tff(decl_27,type,
greater: ( $i * $i ) > $o ).
tff(decl_28,type,
less: ( $i * $i ) > $o ).
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(goal(130), 0), 2)',axiom,
! [X76,X77] :
( ~ greater(X76,X77)
| ~ less(X76,X77) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
fof('def(cond(conseq(axiom(3)), 12), 1)',axiom,
! [X78,X79] :
( less(X79,X78)
<=> ? [X80] : X78 = vplus(X79,X80) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
fof('ass(cond(61, 0), 0)',axiom,
! [X93,X94] : vplus(X94,X93) = vplus(X93,X94),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof('ass(cond(33, 0), 0)',axiom,
! [X98,X99,X100] : vplus(vplus(X98,X99),X100) = vplus(X98,vplus(X99,X100)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof('ass(cond(73, 0), 0)',axiom,
! [X91,X92] : X92 != vplus(X91,X92),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
! [X81,X82] :
( greater(X82,X81)
<=> ? [X83] : X82 = vplus(X81,X83) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof('holds(conjunct2(315), 515, 1)',axiom,
greater(vmul(vd511,vd509),vmul(vd512,vd509)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(315), 515, 1)') ).
fof('holds(conjunct2(315), 515, 0)',axiom,
vmul(vd509,vd511) = vmul(vd511,vd509),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(315), 515, 0)') ).
fof('holds(conjunct2(315), 515, 2)',axiom,
vmul(vd512,vd509) = vmul(vd509,vd512),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(315), 515, 2)') ).
fof('ass(cond(281, 0), 0)',axiom,
! [X20,X21,X22] : vmul(X20,vplus(X21,X22)) = vplus(vmul(X20,X21),vmul(X20,X22)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
fof('ass(cond(270, 0), 0)',axiom,
! [X23,X24] : vmul(X23,X24) = vmul(X24,X23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
fof('holds(conjunct1(314), 510, 0)',axiom,
greater(vd508,vd509),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(314), 510, 0)') ).
fof('ass(cond(goal(88), 0), 1)',axiom,
! [X84,X85] :
( X84 != X85
| ~ ? [X87] : X85 = vplus(X84,X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
fof('ass(cond(goal(88), 0), 0)',axiom,
! [X84,X85] :
( X84 = X85
| ? [X86] : X84 = vplus(X85,X86)
| ? [X87] : X85 = vplus(X84,X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
fof('ass(cond(147, 0), 0)',axiom,
! [X72,X73] :
( less(X72,X73)
=> greater(X73,X72) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
fof('ass(cond(goal(130), 0), 0)',axiom,
! [X76,X77] :
( X76 = X77
| greater(X76,X77)
| less(X76,X77) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
fof('holds(conseq_conjunct2(315), 516, 0)',conjecture,
greater(vmul(vd508,vd511),vmul(vd509,vd512)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq_conjunct2(315), 516, 0)') ).
fof(c_0_17,plain,
! [X76,X77] :
( ~ greater(X76,X77)
| ~ less(X76,X77) ),
inference(fof_simplification,[status(thm)],['ass(cond(goal(130), 0), 2)']) ).
fof(c_0_18,plain,
! [X207,X208,X210,X211,X212] :
( ( ~ less(X208,X207)
| X207 = vplus(X208,esk1_2(X207,X208)) )
& ( X210 != vplus(X211,X212)
| less(X211,X210) ) ),
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)'])])])])]) ).
fof(c_0_19,plain,
! [X203,X204] :
( ~ greater(X203,X204)
| ~ less(X203,X204) ),
inference(variable_rename,[status(thm)],[c_0_17]) ).
cnf(c_0_20,plain,
( less(X2,X1)
| X1 != vplus(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,plain,
( ~ greater(X1,X2)
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_22,plain,
less(X1,vplus(X1,X2)),
inference(er,[status(thm)],[c_0_20]) ).
fof(c_0_23,plain,
! [X238,X239] : vplus(X239,X238) = vplus(X238,X239),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
cnf(c_0_24,plain,
~ greater(X1,vplus(X1,X2)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_26,plain,
! [X243,X244,X245] : vplus(vplus(X243,X244),X245) = vplus(X243,vplus(X244,X245)),
inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).
fof(c_0_27,plain,
! [X236,X237] : X237 != vplus(X236,X237),
inference(variable_rename,[status(thm)],['ass(cond(73, 0), 0)']) ).
cnf(c_0_28,plain,
~ greater(X1,vplus(X2,X1)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_30,plain,
! [X213,X214,X216,X217,X218] :
( ( ~ greater(X214,X213)
| X214 = vplus(X213,esk2_2(X213,X214)) )
& ( X217 != vplus(X216,X218)
| greater(X217,X216) ) ),
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_31,plain,
greater(vmul(vd511,vd509),vmul(vd512,vd509)),
inference(split_conjunct,[status(thm)],['holds(conjunct2(315), 515, 1)']) ).
cnf(c_0_32,plain,
vmul(vd509,vd511) = vmul(vd511,vd509),
inference(split_conjunct,[status(thm)],['holds(conjunct2(315), 515, 0)']) ).
cnf(c_0_33,plain,
vmul(vd512,vd509) = vmul(vd509,vd512),
inference(split_conjunct,[status(thm)],['holds(conjunct2(315), 515, 2)']) ).
cnf(c_0_34,plain,
X1 != vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,plain,
~ greater(X1,vplus(X2,vplus(X3,X1))),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,plain,
( X1 = vplus(X2,esk2_2(X2,X1))
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,plain,
greater(vmul(vd509,vd511),vmul(vd509,vd512)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
fof(c_0_38,plain,
! [X131,X132,X133] : vmul(X131,vplus(X132,X133)) = vplus(vmul(X131,X132),vmul(X131,X133)),
inference(variable_rename,[status(thm)],['ass(cond(281, 0), 0)']) ).
fof(c_0_39,plain,
! [X134,X135] : vmul(X134,X135) = vmul(X135,X134),
inference(variable_rename,[status(thm)],['ass(cond(270, 0), 0)']) ).
cnf(c_0_40,plain,
vplus(X1,vplus(X2,X3)) != X3,
inference(spm,[status(thm)],[c_0_34,c_0_29]) ).
cnf(c_0_41,plain,
greater(vd508,vd509),
inference(split_conjunct,[status(thm)],['holds(conjunct1(314), 510, 0)']) ).
fof(c_0_42,plain,
! [X223,X224,X225] :
( X223 != X224
| X224 != vplus(X223,X225) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(goal(88), 0), 1)'])])]) ).
cnf(c_0_43,plain,
~ greater(X1,vplus(X2,vplus(X1,X3))),
inference(spm,[status(thm)],[c_0_35,c_0_25]) ).
cnf(c_0_44,plain,
vplus(vmul(vd509,vd512),esk2_2(vmul(vd509,vd512),vmul(vd509,vd511))) = vmul(vd509,vd511),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_45,plain,
vmul(X1,vplus(X2,X3)) = vplus(vmul(X1,X2),vmul(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,plain,
vmul(X1,X2) = vmul(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_47,plain,
vplus(X1,vplus(X2,X3)) != X2,
inference(spm,[status(thm)],[c_0_40,c_0_25]) ).
cnf(c_0_48,plain,
vplus(vd509,esk2_2(vd509,vd508)) = vd508,
inference(spm,[status(thm)],[c_0_36,c_0_41]) ).
cnf(c_0_49,plain,
( X1 != X2
| X2 != vplus(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_50,plain,
~ greater(vmul(vd509,vd512),vplus(X1,vmul(vd509,vd511))),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_51,plain,
vplus(vmul(X1,X2),vmul(X3,X1)) = vmul(X1,vplus(X2,X3)),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,plain,
vplus(X1,vd508) != vd509,
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
fof(c_0_53,plain,
! [X219,X220] :
( X219 = X220
| X219 = vplus(X220,esk3_2(X219,X220))
| X220 = vplus(X219,esk4_2(X219,X220)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],['ass(cond(goal(88), 0), 0)'])]) ).
cnf(c_0_54,plain,
vplus(X1,X2) != X1,
inference(er,[status(thm)],[c_0_49]) ).
cnf(c_0_55,plain,
vplus(X1,vmul(vd509,vd511)) != vmul(vd509,vd512),
inference(spm,[status(thm)],[c_0_47,c_0_44]) ).
cnf(c_0_56,plain,
~ greater(vmul(vd509,vd512),vmul(vd511,vplus(X1,vd509))),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_57,plain,
vplus(vd508,X1) != vd509,
inference(spm,[status(thm)],[c_0_52,c_0_25]) ).
cnf(c_0_58,plain,
( X1 = X2
| X1 = vplus(X2,esk3_2(X1,X2))
| X2 = vplus(X1,esk4_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_59,plain,
vd509 != vd508,
inference(spm,[status(thm)],[c_0_54,c_0_48]) ).
fof(c_0_60,plain,
! [X195,X196] :
( ~ less(X195,X196)
| greater(X196,X195) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(147, 0), 0)'])]) ).
fof(c_0_61,plain,
! [X199,X200] :
( X199 = X200
| greater(X199,X200)
| less(X199,X200) ),
inference(variable_rename,[status(thm)],['ass(cond(goal(130), 0), 0)']) ).
cnf(c_0_62,plain,
vmul(vd511,vplus(X1,vd509)) != vmul(vd509,vd512),
inference(spm,[status(thm)],[c_0_55,c_0_51]) ).
cnf(c_0_63,plain,
~ greater(vmul(vd509,vd512),vmul(vd511,vplus(vd509,X1))),
inference(spm,[status(thm)],[c_0_56,c_0_25]) ).
cnf(c_0_64,plain,
vplus(vd509,esk4_2(vd509,vd508)) = vd508,
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58])]),c_0_59]) ).
cnf(c_0_65,plain,
( greater(X2,X1)
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_66,plain,
( X1 = X2
| greater(X1,X2)
| less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_67,plain,
vmul(vd511,vplus(vd509,X1)) != vmul(vd509,vd512),
inference(spm,[status(thm)],[c_0_62,c_0_25]) ).
fof(c_0_68,negated_conjecture,
~ greater(vmul(vd508,vd511),vmul(vd509,vd512)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['holds(conseq_conjunct2(315), 516, 0)'])]) ).
cnf(c_0_69,plain,
~ greater(vmul(vd509,vd512),vmul(vd508,vd511)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_46]) ).
cnf(c_0_70,plain,
( X1 = X2
| greater(X1,X2)
| greater(X2,X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_71,plain,
vmul(vd509,vd512) != vmul(vd508,vd511),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_64]),c_0_46]) ).
cnf(c_0_72,negated_conjecture,
~ greater(vmul(vd508,vd511),vmul(vd509,vd512)),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_73,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]),c_0_72]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM855+1 : TPTP v8.1.2. Released v4.1.0.
% 0.14/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 14:52:57 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.54/0.57 start to proof: theBenchmark
% 0.56/0.72 % Version : CSE_E---1.5
% 0.56/0.72 % Problem : theBenchmark.p
% 0.56/0.72 % Proof found
% 0.56/0.72 % SZS status Theorem for theBenchmark.p
% 0.56/0.72 % SZS output start Proof
% See solution above
% 0.56/0.73 % Total time : 0.138000 s
% 0.56/0.73 % SZS output end Proof
% 0.56/0.73 % Total time : 0.142000 s
%------------------------------------------------------------------------------