TSTP Solution File: NUM849+1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM849+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 : n022.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 10:41:01 EDT 2023
% Result : Theorem 0.19s 0.65s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 24
% Syntax : Number of formulae : 54 ( 31 unt; 16 typ; 0 def)
% Number of atoms : 45 ( 44 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 7 ~; 0 |; 5 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 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 : 52 ( 0 sgn; 30 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
vd448: $i ).
tff(decl_23,type,
vd449: $i ).
tff(decl_24,type,
vmul: ( $i * $i ) > $i ).
tff(decl_25,type,
vsucc: $i > $i ).
tff(decl_26,type,
vplus: ( $i * $i ) > $i ).
tff(decl_27,type,
v1: $i ).
tff(decl_28,type,
less: ( $i * $i ) > $o ).
tff(decl_29,type,
leq: ( $i * $i ) > $o ).
tff(decl_30,type,
greater: ( $i * $i ) > $o ).
tff(decl_31,type,
geq: ( $i * $i ) > $o ).
tff(decl_32,type,
vskolem2: $i > $i ).
tff(decl_33,type,
esk1_0: $i ).
tff(decl_34,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_35,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_36,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_37,type,
esk5_2: ( $i * $i ) > $i ).
fof('qu(ind(296), imp(296))',conjecture,
! [X1] :
( vmul(vmul(vd448,vd449),X1) = vmul(vd448,vmul(vd449,X1))
=> vmul(vmul(vd448,vd449),vsucc(X1)) = vmul(vd448,vmul(vd449,vsucc(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(ind(296), imp(296))') ).
fof('qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))',axiom,
! [X84,X85] :
( vplus(X84,vsucc(X85)) = vsucc(vplus(X84,X85))
& vplus(X84,v1) = vsucc(X84) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
fof('ass(cond(43, 0), 0)',axiom,
! [X80] : vplus(v1,X80) = vsucc(X80),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
fof('ass(cond(261, 0), 0)',axiom,
! [X8,X9] : vmul(vsucc(X8),X9) = vplus(vmul(X8,X9),X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(261, 0), 0)') ).
fof('ass(cond(61, 0), 0)',axiom,
! [X76,X77] : vplus(X77,X76) = vplus(X76,X77),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof('ass(cond(270, 0), 0)',axiom,
! [X6,X7] : vmul(X6,X7) = vmul(X7,X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
fof('ass(cond(281, 0), 0)',axiom,
! [X3,X4,X5] : vmul(X3,vplus(X4,X5)) = vplus(vmul(X3,X4),vmul(X3,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
fof('qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))',axiom,
! [X11,X12] :
( vmul(X11,vsucc(X12)) = vplus(vmul(X11,X12),X11)
& vmul(X11,v1) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).
fof(c_0_8,negated_conjecture,
~ ! [X1] :
( vmul(vmul(vd448,vd449),X1) = vmul(vd448,vmul(vd449,X1))
=> vmul(vmul(vd448,vd449),vsucc(X1)) = vmul(vd448,vmul(vd449,vsucc(X1))) ),
inference(assume_negation,[status(cth)],['qu(ind(296), imp(296))']) ).
fof(c_0_9,negated_conjecture,
( vmul(vmul(vd448,vd449),esk1_0) = vmul(vd448,vmul(vd449,esk1_0))
& vmul(vmul(vd448,vd449),vsucc(esk1_0)) != vmul(vd448,vmul(vd449,vsucc(esk1_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_10,plain,
! [X213,X214] :
( vplus(X213,vsucc(X214)) = vsucc(vplus(X213,X214))
& vplus(X213,v1) = vsucc(X213) ),
inference(variable_rename,[status(thm)],['qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))']) ).
fof(c_0_11,plain,
! [X209] : vplus(v1,X209) = vsucc(X209),
inference(variable_rename,[status(thm)],['ass(cond(43, 0), 0)']) ).
fof(c_0_12,plain,
! [X103,X104] : vmul(vsucc(X103),X104) = vplus(vmul(X103,X104),X104),
inference(variable_rename,[status(thm)],['ass(cond(261, 0), 0)']) ).
cnf(c_0_13,negated_conjecture,
vmul(vmul(vd448,vd449),vsucc(esk1_0)) != vmul(vd448,vmul(vd449,vsucc(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
vplus(X1,v1) = vsucc(X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
vplus(v1,X1) = vsucc(X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
vmul(vsucc(X1),X2) = vplus(vmul(X1,X2),X2),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X205,X206] : vplus(X206,X205) = vplus(X205,X206),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
fof(c_0_18,plain,
! [X101,X102] : vmul(X101,X102) = vmul(X102,X101),
inference(variable_rename,[status(thm)],['ass(cond(270, 0), 0)']) ).
cnf(c_0_19,negated_conjecture,
vmul(vmul(vd448,vd449),vplus(esk1_0,v1)) != vmul(vd448,vmul(vd449,vplus(esk1_0,v1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_14]) ).
cnf(c_0_20,plain,
vplus(v1,X1) = vplus(X1,v1),
inference(rw,[status(thm)],[c_0_15,c_0_14]) ).
fof(c_0_21,plain,
! [X98,X99,X100] : vmul(X98,vplus(X99,X100)) = vplus(vmul(X98,X99),vmul(X98,X100)),
inference(variable_rename,[status(thm)],['ass(cond(281, 0), 0)']) ).
fof(c_0_22,plain,
! [X106,X107] :
( vmul(X106,vsucc(X107)) = vplus(vmul(X106,X107),X106)
& vmul(X106,v1) = X106 ),
inference(variable_rename,[status(thm)],['qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))']) ).
cnf(c_0_23,plain,
vmul(vplus(X1,v1),X2) = vplus(vmul(X1,X2),X2),
inference(rw,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_24,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,negated_conjecture,
vmul(vmul(vd448,vd449),esk1_0) = vmul(vd448,vmul(vd449,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_26,plain,
vmul(X1,X2) = vmul(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,negated_conjecture,
vmul(vmul(vd448,vd449),vplus(v1,esk1_0)) != vmul(vd448,vmul(vd449,vplus(v1,esk1_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_20]) ).
cnf(c_0_28,plain,
vmul(X1,vplus(X2,X3)) = vplus(vmul(X1,X2),vmul(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
vmul(X1,v1) = X1,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
vmul(vplus(X1,v1),X2) = vplus(X2,vmul(X1,X2)),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,negated_conjecture,
vmul(esk1_0,vmul(vd449,vd448)) = vmul(vd448,vmul(vd449,esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_26]) ).
cnf(c_0_32,negated_conjecture,
vmul(vplus(v1,esk1_0),vmul(vd449,vd448)) != vmul(vd448,vmul(vd449,vplus(v1,esk1_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_26]),c_0_26]) ).
cnf(c_0_33,plain,
vplus(X1,vmul(X1,X2)) = vmul(X1,vplus(v1,X2)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
vplus(vmul(vd449,vd448),vmul(vd448,vmul(vd449,esk1_0))) = vmul(vplus(v1,esk1_0),vmul(vd449,vd448)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_20]) ).
cnf(c_0_35,plain,
vplus(vmul(X1,X2),vmul(X2,X3)) = vmul(X2,vplus(X1,X3)),
inference(spm,[status(thm)],[c_0_28,c_0_26]) ).
cnf(c_0_36,negated_conjecture,
vmul(vplus(v1,esk1_0),vmul(vd449,vd448)) != vmul(vd448,vplus(vd449,vmul(vd449,esk1_0))),
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM849+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
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 14:06:25 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.65 % Version : CSE_E---1.5
% 0.19/0.65 % Problem : theBenchmark.p
% 0.19/0.65 % Proof found
% 0.19/0.65 % SZS status Theorem for theBenchmark.p
% 0.19/0.65 % SZS output start Proof
% See solution above
% 0.19/0.66 % Total time : 0.071000 s
% 0.19/0.66 % SZS output end Proof
% 0.19/0.66 % Total time : 0.075000 s
%------------------------------------------------------------------------------