TSTP Solution File: NUM856+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM856+1 : 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 : n008.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 0.20s 0.81s
% Output : CNFRefutation 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 32
% Syntax : Number of formulae : 89 ( 24 unt; 17 typ; 0 def)
% Number of atoms : 148 ( 38 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 133 ( 57 ~; 58 |; 10 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 130 ( 2 sgn; 72 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
vd517: $i ).
tff(decl_23,type,
vd519: $i ).
tff(decl_24,type,
vmul: ( $i * $i ) > $i ).
tff(decl_25,type,
vd518: $i ).
tff(decl_26,type,
vd520: $i ).
tff(decl_27,type,
greater: ( $i * $i ) > $o ).
tff(decl_28,type,
geq: ( $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('holds(conseq(scope(318)), 525, 0)',conjecture,
greater(vmul(vd517,vd519),vmul(vd518,vd520)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq(scope(318)), 525, 0)') ).
fof('ass(cond(312, 0), 0)',axiom,
! [X1,X2,X3,X4] :
( ( greater(X3,X4)
& greater(X1,X2) )
=> greater(vmul(X1,X3),vmul(X2,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(312, 0), 0)') ).
fof('def(cond(conseq(axiom(3)), 16), 1)',axiom,
! [X74,X75] :
( geq(X75,X74)
<=> ( greater(X75,X74)
| X75 = X74 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).
fof('dis(antec(scope(318)))',axiom,
( ( greater(vd519,vd520)
& geq(vd517,vd518) )
| ( geq(vd519,vd520)
& greater(vd517,vd518) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dis(antec(scope(318)))') ).
fof('ass(cond(conjunct1(307), 0), 0)',axiom,
! [X11,X12,X13] :
( greater(vmul(X11,X12),vmul(X13,X12))
=> greater(X11,X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conjunct1(307), 0), 0)') ).
fof('ass(cond(goal(88), 0), 1)',axiom,
! [X88,X89] :
( X88 != X89
| ~ ? [X91] : X89 = vplus(X88,X91) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
fof('ass(cond(281, 0), 0)',axiom,
! [X24,X25,X26] : vmul(X24,vplus(X25,X26)) = vplus(vmul(X24,X25),vmul(X24,X26)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
! [X85,X86] :
( greater(X86,X85)
<=> ? [X87] : X86 = vplus(X85,X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof('ass(cond(299, 0), 2)',axiom,
! [X14,X19,X20] :
( greater(X19,X20)
=> greater(vmul(X19,X14),vmul(X20,X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(299, 0), 2)') ).
fof('ass(cond(goal(130), 0), 1)',axiom,
! [X80,X81] :
( X80 != X81
| ~ less(X80,X81) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).
fof('ass(cond(168, 0), 0)',axiom,
! [X65,X66,X67] :
( ( less(X66,X67)
& less(X65,X66) )
=> less(X65,X67) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(168, 0), 0)') ).
fof('ass(cond(140, 0), 0)',axiom,
! [X78,X79] :
( greater(X78,X79)
=> less(X79,X78) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
fof('ass(cond(270, 0), 0)',axiom,
! [X27,X28] : vmul(X27,X28) = vmul(X28,X27),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
fof('ass(cond(conjunct2(conjunct2(307)), 0), 0)',axiom,
! [X5,X6,X7] :
( less(vmul(X5,X6),vmul(X7,X6))
=> less(X5,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conjunct2(conjunct2(307)), 0), 0)') ).
fof('ass(cond(goal(130), 0), 0)',axiom,
! [X80,X81] :
( X80 = X81
| greater(X80,X81)
| less(X80,X81) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
fof(c_0_15,negated_conjecture,
~ greater(vmul(vd517,vd519),vmul(vd518,vd520)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['holds(conseq(scope(318)), 525, 0)'])]) ).
fof(c_0_16,plain,
! [X114,X115,X116,X117] :
( ~ greater(X116,X117)
| ~ greater(X114,X115)
| greater(vmul(X114,X116),vmul(X115,X117)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(312, 0), 0)'])]) ).
fof(c_0_17,plain,
! [X201,X202] :
( ( ~ geq(X202,X201)
| greater(X202,X201)
| X202 = X201 )
& ( ~ greater(X202,X201)
| geq(X202,X201) )
& ( X202 != X201
| geq(X202,X201) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['def(cond(conseq(axiom(3)), 16), 1)'])])]) ).
fof(c_0_18,plain,
( ( geq(vd519,vd520)
| greater(vd519,vd520) )
& ( greater(vd517,vd518)
| greater(vd519,vd520) )
& ( geq(vd519,vd520)
| geq(vd517,vd518) )
& ( greater(vd517,vd518)
| geq(vd517,vd518) ) ),
inference(distribute,[status(thm)],['dis(antec(scope(318)))']) ).
cnf(c_0_19,negated_conjecture,
~ greater(vmul(vd517,vd519),vmul(vd518,vd520)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( greater(vmul(X3,X1),vmul(X4,X2))
| ~ greater(X1,X2)
| ~ greater(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( greater(X1,X2)
| X1 = X2
| ~ geq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
( geq(vd519,vd520)
| greater(vd519,vd520) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( ~ greater(vd517,vd518)
| ~ greater(vd519,vd520) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( vd520 = vd519
| greater(vd519,vd520) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_25,plain,
! [X124,X125,X126] :
( ~ greater(vmul(X124,X125),vmul(X126,X125))
| greater(X124,X126) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conjunct1(307), 0), 0)'])]) ).
fof(c_0_26,plain,
! [X231,X232,X233] :
( X231 != X232
| X232 != vplus(X231,X233) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(goal(88), 0), 1)'])])]) ).
fof(c_0_27,plain,
! [X139,X140,X141] : vmul(X139,vplus(X140,X141)) = vplus(vmul(X139,X140),vmul(X139,X141)),
inference(variable_rename,[status(thm)],['ass(cond(281, 0), 0)']) ).
fof(c_0_28,plain,
! [X221,X222,X224,X225,X226] :
( ( ~ greater(X222,X221)
| X222 = vplus(X221,esk2_2(X221,X222)) )
& ( X225 != vplus(X224,X226)
| greater(X225,X224) ) ),
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_29,negated_conjecture,
( vd520 = vd519
| ~ greater(vd517,vd518) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,plain,
( greater(X1,X3)
| ~ greater(vmul(X1,X2),vmul(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_31,plain,
! [X133,X134,X135] :
( ~ greater(X134,X135)
| greater(vmul(X134,X133),vmul(X135,X133)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(299, 0), 2)'])]) ).
cnf(c_0_32,plain,
( X1 != X2
| X2 != vplus(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
vmul(X1,vplus(X2,X3)) = vplus(vmul(X1,X2),vmul(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,plain,
( X1 = vplus(X2,esk2_2(X2,X1))
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,negated_conjecture,
~ greater(vmul(vd517,vd519),vmul(vd518,vd519)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_29]),c_0_30]) ).
cnf(c_0_36,plain,
( greater(vmul(X1,X3),vmul(X2,X3))
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_37,plain,
! [X80,X81] :
( X80 != X81
| ~ less(X80,X81) ),
inference(fof_simplification,[status(thm)],['ass(cond(goal(130), 0), 1)']) ).
fof(c_0_38,plain,
! [X192,X193,X194] :
( ~ less(X193,X194)
| ~ less(X192,X193)
| less(X192,X194) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(168, 0), 0)'])]) ).
fof(c_0_39,plain,
! [X205,X206] :
( ~ greater(X205,X206)
| less(X206,X205) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(140, 0), 0)'])]) ).
cnf(c_0_40,plain,
vplus(X1,X2) != X1,
inference(er,[status(thm)],[c_0_32]) ).
cnf(c_0_41,plain,
( vplus(vmul(X1,X2),vmul(X1,esk2_2(X2,X3))) = vmul(X1,X3)
| ~ greater(X3,X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_42,plain,
( greater(vd517,vd518)
| greater(vd519,vd520) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_43,negated_conjecture,
~ greater(vd517,vd518),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_44,plain,
! [X209,X210] :
( X209 != X210
| ~ less(X209,X210) ),
inference(variable_rename,[status(thm)],[c_0_37]) ).
cnf(c_0_45,plain,
( less(X3,X2)
| ~ less(X1,X2)
| ~ less(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,plain,
( less(X2,X1)
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_47,plain,
( vmul(X1,X2) != vmul(X1,X3)
| ~ greater(X2,X3) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,plain,
greater(vd519,vd520),
inference(sr,[status(thm)],[c_0_42,c_0_43]) ).
fof(c_0_49,plain,
! [X142,X143] : vmul(X142,X143) = vmul(X143,X142),
inference(variable_rename,[status(thm)],['ass(cond(270, 0), 0)']) ).
cnf(c_0_50,plain,
( X1 != X2
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_51,plain,
( less(X1,X2)
| ~ less(X3,X2)
| ~ greater(X3,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
fof(c_0_52,plain,
! [X118,X119,X120] :
( ~ less(vmul(X118,X119),vmul(X120,X119))
| less(X118,X120) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conjunct2(conjunct2(307)), 0), 0)'])]) ).
fof(c_0_53,plain,
! [X207,X208] :
( X207 = X208
| greater(X207,X208)
| less(X207,X208) ),
inference(variable_rename,[status(thm)],['ass(cond(goal(130), 0), 0)']) ).
cnf(c_0_54,plain,
vmul(X1,vd520) != vmul(X1,vd519),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_55,plain,
vmul(X1,X2) = vmul(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_56,plain,
~ less(X1,X1),
inference(er,[status(thm)],[c_0_50]) ).
cnf(c_0_57,plain,
( less(vd520,X1)
| ~ less(vd519,X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_48]) ).
cnf(c_0_58,plain,
( less(X1,X3)
| ~ less(vmul(X1,X2),vmul(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_59,plain,
( X1 = X2
| greater(X1,X2)
| less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_60,plain,
vmul(vd520,X1) != vmul(X1,vd519),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_61,plain,
( greater(vd517,vd518)
| geq(vd517,vd518) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_62,plain,
~ less(vd519,vd520),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_63,plain,
( vmul(X1,X2) = vmul(X3,X2)
| less(X1,X3)
| greater(vmul(X1,X2),vmul(X3,X2)) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_64,plain,
vmul(vd520,X1) != vmul(vd519,X1),
inference(spm,[status(thm)],[c_0_60,c_0_55]) ).
cnf(c_0_65,plain,
( vd518 = vd517
| greater(vd517,vd518) ),
inference(spm,[status(thm)],[c_0_21,c_0_61]) ).
cnf(c_0_66,plain,
greater(vmul(vd519,X1),vmul(vd520,X1)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]) ).
cnf(c_0_67,plain,
vd518 = vd517,
inference(sr,[status(thm)],[c_0_65,c_0_43]) ).
cnf(c_0_68,plain,
greater(vmul(vd519,X1),vmul(X1,vd520)),
inference(spm,[status(thm)],[c_0_66,c_0_55]) ).
cnf(c_0_69,negated_conjecture,
~ greater(vmul(vd517,vd519),vmul(vd517,vd520)),
inference(spm,[status(thm)],[c_0_19,c_0_67]) ).
cnf(c_0_70,plain,
greater(vmul(X1,vd519),vmul(X1,vd520)),
inference(spm,[status(thm)],[c_0_68,c_0_55]) ).
cnf(c_0_71,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM856+1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 16:03:17 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.60 start to proof: theBenchmark
% 0.20/0.81 % Version : CSE_E---1.5
% 0.20/0.81 % Problem : theBenchmark.p
% 0.20/0.81 % Proof found
% 0.20/0.81 % SZS status Theorem for theBenchmark.p
% 0.20/0.81 % SZS output start Proof
% See solution above
% 0.73/0.82 % Total time : 0.206000 s
% 0.73/0.82 % SZS output end Proof
% 0.73/0.82 % Total time : 0.210000 s
%------------------------------------------------------------------------------