TSTP Solution File: NUM853+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM853+2 : 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 : n006.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 0.19s 0.76s
% Output : CNFRefutation 0.19s
% 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,
! [X49,X50] : X50 != vplus(X49,X50),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
fof('ass(cond(33, 0), 0)',axiom,
! [X56,X57,X58] : vplus(vplus(X56,X57),X58) = vplus(X56,vplus(X57,X58)),
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,
! [X51,X52] : vplus(X52,X51) = vplus(X51,X52),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
! [X39,X40] :
( greater(X40,X39)
<=> ? [X41] : X40 = vplus(X39,X41) ),
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,
! [X36,X37] :
( less(X37,X36)
<=> ? [X38] : X36 = vplus(X37,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
fof('ass(cond(goal(130), 0), 0)',axiom,
! [X34,X35] :
( X34 = X35
| greater(X34,X35)
| less(X34,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
fof('ass(cond(goal(88), 0), 1)',axiom,
! [X42,X43] :
( X42 != X43
| ~ ? [X45] : X43 = vplus(X42,X45) ),
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,
! [X137,X138] : X138 != vplus(X137,X138),
inference(variable_rename,[status(thm)],['ass(cond(73, 0), 0)']) ).
fof(c_0_12,plain,
! [X144,X145,X146] : vplus(vplus(X144,X145),X146) = vplus(X144,vplus(X145,X146)),
inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).
fof(c_0_13,plain,
! [X80,X81] : vmul(X80,X81) = vmul(X81,X80),
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,
! [X139,X140] : vplus(X140,X139) = vplus(X139,X140),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
fof(c_0_17,plain,
! [X114,X115,X117,X118,X119] :
( ( ~ greater(X115,X114)
| X115 = vplus(X114,esk2_2(X114,X115)) )
& ( X118 != vplus(X117,X119)
| greater(X118,X117) ) ),
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,
! [X77,X78,X79] : vmul(X77,vplus(X78,X79)) = vplus(vmul(X77,X78),vmul(X77,X79)),
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,
! [X108,X109,X111,X112,X113] :
( ( ~ less(X109,X108)
| X108 = vplus(X109,esk1_2(X108,X109)) )
& ( X111 != vplus(X112,X113)
| less(X112,X111) ) ),
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,
! [X100,X101] :
( X100 = X101
| greater(X100,X101)
| less(X100,X101) ),
inference(variable_rename,[status(thm)],['ass(cond(goal(130), 0), 0)']) ).
fof(c_0_32,plain,
! [X124,X125,X126] :
( X124 != X125
| X125 != vplus(X124,X126) ),
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+2 : 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
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 16:49:38 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.59 start to proof: theBenchmark
% 0.19/0.76 % Version : CSE_E---1.5
% 0.19/0.76 % Problem : theBenchmark.p
% 0.19/0.76 % Proof found
% 0.19/0.76 % SZS status Theorem for theBenchmark.p
% 0.19/0.76 % SZS output start Proof
% See solution above
% 0.19/0.76 % Total time : 0.157000 s
% 0.19/0.76 % SZS output end Proof
% 0.19/0.76 % Total time : 0.159000 s
%------------------------------------------------------------------------------