TSTP Solution File: NUM848+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM848+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 : n002.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 10:41:00 EDT 2023
% Result : Theorem 0.10s 0.43s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 17
% Syntax : Number of formulae : 39 ( 25 unt; 10 typ; 0 def)
% Number of atoms : 33 ( 32 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 0 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 6 >; 4 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn; 18 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
vd436: $i ).
tff(decl_23,type,
vd437: $i ).
tff(decl_24,type,
vmul: ( $i * $i ) > $i ).
tff(decl_25,type,
vd439: $i ).
tff(decl_26,type,
vplus: ( $i * $i ) > $i ).
tff(decl_27,type,
vsucc: $i > $i ).
tff(decl_28,type,
v1: $i ).
tff(decl_29,type,
less: ( $i * $i ) > $o ).
tff(decl_30,type,
leq: ( $i * $i ) > $o ).
tff(decl_31,type,
vskolem2: $i > $i ).
fof('holds(286, 441, 4)',conjecture,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(286, 441, 4)') ).
fof('qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))',axiom,
! [X13,X14] :
( vplus(X13,vsucc(X14)) = vsucc(vplus(X13,X14))
& vplus(X13,v1) = vsucc(X13) ),
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('qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))',axiom,
! [X1,X2] :
( vmul(X1,vsucc(X2)) = vplus(vmul(X1,X2),X1)
& vmul(X1,v1) = X1 ),
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('ass(cond(61, 0), 0)',axiom,
! [X5,X6] : vplus(X6,X5) = vplus(X5,X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof('ass(cond(33, 0), 0)',axiom,
! [X10,X11,X12] : vplus(vplus(X10,X11),X12) = vplus(X10,vplus(X11,X12)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof('holds(286, 441, 3)',axiom,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(286, 441, 3)') ).
fof('holds(285, 440, 0)',axiom,
vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd436,vd437),vmul(vd436,vd439)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(285, 440, 0)') ).
fof(c_0_7,negated_conjecture,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['holds(286, 441, 4)'])]) ).
fof(c_0_8,plain,
! [X28,X29] :
( vplus(X28,vsucc(X29)) = vsucc(vplus(X28,X29))
& vplus(X28,v1) = vsucc(X28) ),
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,plain,
! [X16,X17] :
( vmul(X16,vsucc(X17)) = vplus(vmul(X16,X17),X16)
& vmul(X16,v1) = X16 ),
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_10,negated_conjecture,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
vplus(X1,v1) = vsucc(X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X20,X21] : vplus(X21,X20) = vplus(X20,X21),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
cnf(c_0_13,plain,
vmul(X1,vsucc(X2)) = vplus(vmul(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,plain,
! [X25,X26,X27] : vplus(vplus(X25,X26),X27) = vplus(X25,vplus(X26,X27)),
inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).
cnf(c_0_15,negated_conjecture,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vplus(vd439,v1))),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(split_conjunct,[status(thm)],['holds(286, 441, 3)']) ).
cnf(c_0_18,plain,
vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd436,vd437),vmul(vd436,vd439)),
inference(split_conjunct,[status(thm)],['holds(285, 440, 0)']) ).
cnf(c_0_19,plain,
vmul(X1,vplus(X2,v1)) = vplus(vmul(X1,X2),X1),
inference(rw,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_20,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,negated_conjecture,
vplus(vmul(vd436,vd437),vmul(vd436,vplus(v1,vd439))) != vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]) ).
cnf(c_0_22,plain,
vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) = vplus(vd436,vmul(vd436,vplus(vd437,vd439))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_16]),c_0_16]) ).
cnf(c_0_23,plain,
vmul(X1,vplus(X2,v1)) = vplus(X1,vmul(X1,X2)),
inference(rw,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_24,plain,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),X1)) = vplus(vmul(vd436,vplus(vd437,vd439)),X1),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_25,negated_conjecture,
vplus(vmul(vd436,vd437),vmul(vd436,vplus(v1,vd439))) != vplus(vd436,vmul(vd436,vplus(vd437,vd439))),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
vmul(X1,vplus(v1,X2)) = vplus(X1,vmul(X1,X2)),
inference(spm,[status(thm)],[c_0_23,c_0_16]) ).
cnf(c_0_27,plain,
vplus(vmul(vd436,vd437),vplus(X1,vmul(vd436,vd439))) = vplus(vmul(vd436,vplus(vd437,vd439)),X1),
inference(spm,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.07 % Problem : NUM848+2 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.07 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.06/0.26 % Computer : n002.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 300
% 0.06/0.26 % DateTime : Fri Aug 25 13:08:02 EDT 2023
% 0.06/0.26 % CPUTime :
% 0.10/0.40 start to proof: theBenchmark
% 0.10/0.43 % Version : CSE_E---1.5
% 0.10/0.43 % Problem : theBenchmark.p
% 0.10/0.43 % Proof found
% 0.10/0.43 % SZS status Theorem for theBenchmark.p
% 0.10/0.43 % SZS output start Proof
% See solution above
% 0.10/0.44 % Total time : 0.024000 s
% 0.10/0.44 % SZS output end Proof
% 0.10/0.44 % Total time : 0.027000 s
%------------------------------------------------------------------------------