TSTP Solution File: NUM853+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM853+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 : n025.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 10:41:03 EDT 2023
% Result : Theorem 0.20s 0.77s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 27
% Syntax : Number of formulae : 62 ( 32 unt; 16 typ; 0 def)
% Number of atoms : 69 ( 46 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 48 ( 25 ~; 19 |; 2 &)
% ( 2 <=>; 0 =>; 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 : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 88 ( 10 sgn; 47 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
vd486: $i ).
tff(decl_23,type,
vd488: $i ).
tff(decl_24,type,
greater: ( $i * $i ) > $o ).
tff(decl_25,type,
vd487: $i ).
tff(decl_26,type,
vmul: ( $i * $i ) > $i ).
tff(decl_27,type,
less: ( $i * $i ) > $o ).
tff(decl_28,type,
vplus: ( $i * $i ) > $i ).
tff(decl_29,type,
vsucc: $i > $i ).
tff(decl_30,type,
v1: $i ).
tff(decl_31,type,
leq: ( $i * $i ) > $o ).
tff(decl_32,type,
geq: ( $i * $i ) > $o ).
tff(decl_33,type,
vskolem2: $i > $i ).
tff(decl_34,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_35,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_36,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_37,type,
esk4_2: ( $i * $i ) > $i ).
fof('ass(cond(73, 0), 0)',axiom,
! [X82,X83] : X83 != vplus(X82,X83),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
fof('ass(cond(33, 0), 0)',axiom,
! [X89,X90,X91] : vplus(vplus(X89,X90),X91) = vplus(X89,vplus(X90,X91)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof('ass(cond(270, 0), 0)',axiom,
! [X14,X15] : vmul(X14,X15) = vmul(X15,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
fof('ass(cond(61, 0), 0)',axiom,
! [X84,X85] : vplus(X85,X84) = vplus(X84,X85),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
! [X72,X73] :
( greater(X73,X72)
<=> ? [X74] : X73 = vplus(X72,X74) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof('holds(antec(307), 489, 0)',axiom,
greater(vmul(vd486,vd487),vmul(vd488,vd487)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(antec(307), 489, 0)') ).
fof('ass(cond(281, 0), 0)',axiom,
! [X11,X12,X13] : vmul(X11,vplus(X12,X13)) = vplus(vmul(X11,X12),vmul(X11,X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
fof('def(cond(conseq(axiom(3)), 12), 1)',axiom,
! [X69,X70] :
( less(X70,X69)
<=> ? [X71] : X69 = vplus(X70,X71) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
fof('ass(cond(goal(130), 0), 0)',axiom,
! [X67,X68] :
( X67 = X68
| greater(X67,X68)
| less(X67,X68) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
fof('ass(cond(goal(88), 0), 1)',axiom,
! [X75,X76] :
( X75 != X76
| ~ ? [X78] : X76 = vplus(X75,X78) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
fof('holds(conseq(307), 490, 0)',conjecture,
greater(vd486,vd488),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq(307), 490, 0)') ).
fof(c_0_11,plain,
! [X218,X219] : X219 != vplus(X218,X219),
inference(variable_rename,[status(thm)],['ass(cond(73, 0), 0)']) ).
fof(c_0_12,plain,
! [X225,X226,X227] : vplus(vplus(X225,X226),X227) = vplus(X225,vplus(X226,X227)),
inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).
fof(c_0_13,plain,
! [X116,X117] : vmul(X116,X117) = vmul(X117,X116),
inference(variable_rename,[status(thm)],['ass(cond(270, 0), 0)']) ).
cnf(c_0_14,plain,
X1 != vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X220,X221] : vplus(X221,X220) = vplus(X220,X221),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
fof(c_0_17,plain,
! [X195,X196,X198,X199,X200] :
( ( ~ greater(X196,X195)
| X196 = vplus(X195,esk2_2(X195,X196)) )
& ( X199 != vplus(X198,X200)
| greater(X199,X198) ) ),
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_18,plain,
greater(vmul(vd486,vd487),vmul(vd488,vd487)),
inference(split_conjunct,[status(thm)],['holds(antec(307), 489, 0)']) ).
cnf(c_0_19,plain,
vmul(X1,X2) = vmul(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
vplus(X1,vplus(X2,X3)) != X3,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( X1 = vplus(X2,esk2_2(X2,X1))
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
greater(vmul(vd486,vd487),vmul(vd487,vd488)),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_24,plain,
! [X113,X114,X115] : vmul(X113,vplus(X114,X115)) = vplus(vmul(X113,X114),vmul(X113,X115)),
inference(variable_rename,[status(thm)],['ass(cond(281, 0), 0)']) ).
cnf(c_0_25,plain,
vplus(X1,vplus(X2,X3)) != X2,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
vplus(vmul(vd487,vd488),esk2_2(vmul(vd487,vd488),vmul(vd486,vd487))) = vmul(vd486,vd487),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
vmul(X1,vplus(X2,X3)) = vplus(vmul(X1,X2),vmul(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,plain,
vplus(X1,vmul(vd486,vd487)) != vmul(vd487,vd488),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,plain,
vplus(vmul(X1,X2),vmul(X3,X1)) = vmul(X1,vplus(X2,X3)),
inference(spm,[status(thm)],[c_0_27,c_0_19]) ).
fof(c_0_30,plain,
! [X189,X190,X192,X193,X194] :
( ( ~ less(X190,X189)
| X189 = vplus(X190,esk1_2(X189,X190)) )
& ( X192 != vplus(X193,X194)
| less(X193,X192) ) ),
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_31,plain,
! [X181,X182] :
( X181 = X182
| greater(X181,X182)
| less(X181,X182) ),
inference(variable_rename,[status(thm)],['ass(cond(goal(130), 0), 0)']) ).
fof(c_0_32,plain,
! [X205,X206,X207] :
( X205 != X206
| X206 != vplus(X205,X207) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(goal(88), 0), 1)'])])]) ).
cnf(c_0_33,plain,
vmul(vd487,vplus(X1,vd486)) != vmul(vd487,vd488),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
( X2 = vplus(X1,esk1_2(X2,X1))
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,plain,
( X1 = X2
| greater(X1,X2)
| less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,plain,
( X1 != X2
| X2 != vplus(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,plain,
vmul(vd487,vplus(vd486,X1)) != vmul(vd487,vd488),
inference(spm,[status(thm)],[c_0_33,c_0_21]) ).
cnf(c_0_38,plain,
( vplus(X1,esk1_2(X2,X1)) = X2
| X1 = X2
| greater(X1,X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
fof(c_0_39,negated_conjecture,
~ greater(vd486,vd488),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['holds(conseq(307), 490, 0)'])]) ).
cnf(c_0_40,plain,
vplus(X1,X2) != X1,
inference(er,[status(thm)],[c_0_36]) ).
cnf(c_0_41,plain,
( vd486 = X1
| greater(vd486,X1)
| vmul(vd487,X1) != vmul(vd487,vd488) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
~ greater(vd486,vd488),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_43,plain,
vmul(vd487,vd488) != vmul(vd486,vd487),
inference(spm,[status(thm)],[c_0_40,c_0_26]) ).
cnf(c_0_44,plain,
vd488 = vd486,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_41]),c_0_42]) ).
cnf(c_0_45,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM853+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
% 0.14/0.34 % Computer : n025.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 16:36:52 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.77 % Version : CSE_E---1.5
% 0.20/0.77 % Problem : theBenchmark.p
% 0.20/0.77 % Proof found
% 0.20/0.77 % SZS status Theorem for theBenchmark.p
% 0.20/0.77 % SZS output start Proof
% See solution above
% 0.20/0.78 % Total time : 0.206000 s
% 0.20/0.78 % SZS output end Proof
% 0.20/0.78 % Total time : 0.210000 s
%------------------------------------------------------------------------------