TSTP Solution File: NUM849+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM849+2 : 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 : n027.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 0.20s 0.59s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of formulae : 40 ( 22 unt; 7 typ; 0 def)
% Number of atoms : 44 ( 43 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 8 ~; 3 |; 5 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn; 24 !; 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,
esk1_0: $i ).
fof('ass(cond(261, 0), 0)',axiom,
! [X8,X9] : vmul(vsucc(X8),X9) = vplus(vmul(X8,X9),X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(261, 0), 0)') ).
fof('qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))',axiom,
! [X14,X15] :
( vplus(X14,vsucc(X15)) = vsucc(vplus(X14,X15))
& vplus(X14,v1) = vsucc(X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
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/sandbox/benchmark/theBenchmark.p','qu(ind(296), imp(296))') ).
fof('qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))',axiom,
! [X10,X11] :
( vmul(X10,vsucc(X11)) = vplus(vmul(X10,X11),X10)
& vmul(X10,v1) = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).
fof('ass(cond(61, 0), 0)',axiom,
! [X12,X13] : vplus(X13,X12) = vplus(X12,X13),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
fof('ass(cond(conseq(292), 1), 1)',axiom,
! [X2] :
( vmul(vmul(vd448,vd449),X2) = vmul(vd448,vmul(vd449,X2))
=> vplus(vmul(vd448,vmul(vd449,X2)),vmul(vd448,vd449)) = vmul(vd448,vplus(vmul(vd449,X2),vd449)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(292), 1), 1)') ).
fof(c_0_7,plain,
! [X26,X27] : vmul(vsucc(X26),X27) = vplus(vmul(X26,X27),X27),
inference(variable_rename,[status(thm)],['ass(cond(261, 0), 0)']) ).
fof(c_0_8,plain,
! [X32,X33] :
( vplus(X32,vsucc(X33)) = vsucc(vplus(X32,X33))
& vplus(X32,v1) = vsucc(X32) ),
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_9,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_10,plain,
! [X28,X29] :
( vmul(X28,vsucc(X29)) = vplus(vmul(X28,X29),X28)
& vmul(X28,v1) = X28 ),
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_11,plain,
vmul(vsucc(X1),X2) = vplus(vmul(X1,X2),X2),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
vplus(X1,v1) = vsucc(X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X30,X31] : vplus(X31,X30) = vplus(X30,X31),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
fof(c_0_14,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_9])])]) ).
fof(c_0_15,plain,
! [X24,X25] : vmul(X24,X25) = vmul(X25,X24),
inference(variable_rename,[status(thm)],['ass(cond(270, 0), 0)']) ).
cnf(c_0_16,plain,
vmul(X1,vsucc(X2)) = vplus(vmul(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
vmul(vplus(X1,v1),X2) = vplus(vmul(X1,X2),X2),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_18,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
vmul(vmul(vd448,vd449),esk1_0) = vmul(vd448,vmul(vd449,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
vmul(X1,X2) = vmul(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_21,plain,
! [X18] :
( vmul(vmul(vd448,vd449),X18) != vmul(vd448,vmul(vd449,X18))
| vplus(vmul(vd448,vmul(vd449,X18)),vmul(vd448,vd449)) = vmul(vd448,vplus(vmul(vd449,X18),vd449)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conseq(292), 1), 1)'])]) ).
cnf(c_0_22,plain,
vmul(X1,vplus(X2,v1)) = vplus(vmul(X1,X2),X1),
inference(rw,[status(thm)],[c_0_16,c_0_12]) ).
cnf(c_0_23,negated_conjecture,
vmul(vmul(vd448,vd449),vsucc(esk1_0)) != vmul(vd448,vmul(vd449,vsucc(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,plain,
vplus(X1,vmul(X2,X1)) = vmul(vplus(X2,v1),X1),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,negated_conjecture,
vmul(esk1_0,vmul(vd449,vd448)) = vmul(vd448,vmul(vd449,esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_20]) ).
cnf(c_0_26,plain,
( vplus(vmul(vd448,vmul(vd449,X1)),vmul(vd448,vd449)) = vmul(vd448,vplus(vmul(vd449,X1),vd449))
| vmul(vmul(vd448,vd449),X1) != vmul(vd448,vmul(vd449,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
vplus(X1,vmul(X1,X2)) = vmul(X1,vplus(X2,v1)),
inference(rw,[status(thm)],[c_0_22,c_0_18]) ).
cnf(c_0_28,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_23,c_0_12]),c_0_12]) ).
cnf(c_0_29,negated_conjecture,
vplus(vmul(vd449,vd448),vmul(vd448,vmul(vd449,esk1_0))) = vmul(vmul(vd449,vd448),vplus(v1,esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_18]),c_0_20]) ).
cnf(c_0_30,plain,
( vplus(vmul(vd449,vd448),vmul(vd448,vmul(vd449,X1))) = vmul(vd448,vmul(vd449,vplus(X1,v1)))
| vmul(vmul(vd449,vd448),X1) != vmul(vd448,vmul(vd449,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_20]),c_0_18]),c_0_18]),c_0_27]),c_0_20]) ).
cnf(c_0_31,negated_conjecture,
vmul(vmul(vd449,vd448),vplus(v1,esk1_0)) != vmul(vd448,vmul(vd449,vplus(v1,esk1_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_20]),c_0_18]),c_0_18]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_18]),c_0_31]),c_0_20]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM849+2 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n027.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 17:51:48 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.59 % Version : CSE_E---1.5
% 0.20/0.59 % Problem : theBenchmark.p
% 0.20/0.59 % Proof found
% 0.20/0.59 % SZS status Theorem for theBenchmark.p
% 0.20/0.59 % SZS output start Proof
% See solution above
% 0.20/0.59 % Total time : 0.008000 s
% 0.20/0.59 % SZS output end Proof
% 0.20/0.59 % Total time : 0.010000 s
%------------------------------------------------------------------------------