%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM845+1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 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 : Tue May 5 04:58:42 PM UTC 2026
% Result : Theorem 1.41s 1.78s
% Output : CNFRefutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 26 unt; 0 def)
% Number of atoms : 40 ( 39 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 : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('qu(ind(267), imp(267))',conjecture,
! [X1] :
( vmul(vsucc(vd411),X1) = vplus(vmul(vd411,X1),X1)
=> vmul(vsucc(vd411),vsucc(X1)) = vplus(vmul(vd411,vsucc(X1)),vsucc(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(ind(267), imp(267))') ).
fof('qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))',axiom,
! [X77,X78] :
( vplus(X77,vsucc(X78)) = vsucc(vplus(X77,X78))
& vplus(X77,v1) = vsucc(X77) ),
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,
! [X73] : vplus(v1,X73) = vsucc(X73),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
fof('qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))',axiom,
! [X4,X5] :
( vmul(X4,vsucc(X5)) = vplus(vmul(X4,X5),X4)
& vmul(X4,v1) = X4 ),
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,
! [X69,X70] : vplus(X70,X69) = vplus(X69,X70),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof('ass(cond(33, 0), 0)',axiom,
! [X74,X75,X76] : vplus(vplus(X74,X75),X76) = vplus(X74,vplus(X75,X76)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( vmul(vsucc(vd411),X1) = vplus(vmul(vd411,X1),X1)
=> vmul(vsucc(vd411),vsucc(X1)) = vplus(vmul(vd411,vsucc(X1)),vsucc(X1)) ),
inference(assume_negation,[status(cth)],['qu(ind(267), imp(267))']) ).
fof(c_0_7,negated_conjecture,
( vmul(vsucc(vd411),esk1_0) = vplus(vmul(vd411,esk1_0),esk1_0)
& vmul(vsucc(vd411),vsucc(esk1_0)) != vplus(vmul(vd411,vsucc(esk1_0)),vsucc(esk1_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_8,plain,
! [X323,X324] :
( vplus(X323,vsucc(X324)) = vsucc(vplus(X323,X324))
& vplus(X323,v1) = vsucc(X323) ),
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,
! [X319] : vplus(v1,X319) = vsucc(X319),
inference(variable_rename,[status(thm)],['ass(cond(43, 0), 0)']) ).
cnf(c_0_10,negated_conjecture,
vmul(vsucc(vd411),vsucc(esk1_0)) != vplus(vmul(vd411,vsucc(esk1_0)),vsucc(esk1_0)),
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]) ).
cnf(c_0_12,plain,
vplus(v1,X1) = vsucc(X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X216,X217] :
( vmul(X216,vsucc(X217)) = vplus(vmul(X216,X217),X216)
& vmul(X216,v1) = X216 ),
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_14,negated_conjecture,
vmul(vplus(vd411,v1),vplus(esk1_0,v1)) != vplus(vmul(vd411,vplus(esk1_0,v1)),vplus(esk1_0,v1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_11]),c_0_11]),c_0_11]) ).
cnf(c_0_15,plain,
vplus(v1,X1) = vplus(X1,v1),
inference(rw,[status(thm)],[c_0_12,c_0_11]) ).
fof(c_0_16,plain,
! [X315,X316] : vplus(X316,X315) = vplus(X315,X316),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
cnf(c_0_17,plain,
vmul(X1,vsucc(X2)) = vplus(vmul(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
vmul(vsucc(vd411),esk1_0) = vplus(vmul(vd411,esk1_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,negated_conjecture,
vplus(vmul(vd411,vplus(v1,esk1_0)),vplus(v1,esk1_0)) != vmul(vplus(vd411,v1),vplus(v1,esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_15]),c_0_15]) ).
cnf(c_0_20,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_21,plain,
! [X320,X321,X322] : vplus(vplus(X320,X321),X322) = vplus(X320,vplus(X321,X322)),
inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).
cnf(c_0_22,plain,
vmul(X1,vplus(X2,v1)) = vplus(vmul(X1,X2),X1),
inference(rw,[status(thm)],[c_0_17,c_0_11]) ).
cnf(c_0_23,negated_conjecture,
vplus(vmul(vd411,esk1_0),esk1_0) = vmul(vplus(vd411,v1),esk1_0),
inference(rw,[status(thm)],[c_0_18,c_0_11]) ).
cnf(c_0_24,negated_conjecture,
vplus(vplus(v1,esk1_0),vmul(vd411,vplus(v1,esk1_0))) != vmul(vplus(vd411,v1),vplus(v1,esk1_0)),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,plain,
vmul(X1,vplus(X2,v1)) = vplus(X1,vmul(X1,X2)),
inference(rw,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_27,negated_conjecture,
vmul(vplus(vd411,v1),esk1_0) = vplus(esk1_0,vmul(vd411,esk1_0)),
inference(rw,[status(thm)],[c_0_23,c_0_20]) ).
cnf(c_0_28,negated_conjecture,
vplus(v1,vplus(esk1_0,vmul(vd411,vplus(v1,esk1_0)))) != vmul(vplus(vd411,v1),vplus(v1,esk1_0)),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
vmul(X1,vplus(v1,X2)) = vplus(X1,vmul(X1,X2)),
inference(spm,[status(thm)],[c_0_26,c_0_20]) ).
cnf(c_0_30,plain,
vplus(X1,vplus(X2,X3)) = vplus(X2,vplus(X3,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_31,negated_conjecture,
vplus(vd411,vplus(v1,vplus(esk1_0,vmul(vd411,esk1_0)))) = vmul(vplus(vd411,v1),vplus(v1,esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_15]),c_0_25]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_20]),c_0_30]),c_0_25]),c_0_20]),c_0_30]),c_0_20]),c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM845+1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n006.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 01:15:16 EDT 2026
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % start to proof: theBenchmark
% 1.41/1.78 % Version : CSE_E---1.7
% 1.41/1.78 % Problem : theBenchmark.p
% 1.41/1.78 % SZS status Theorem for theBenchmark.p
% 1.41/1.78 % SZS output start CNFRefutation
% See solution above
% 1.41/1.78 % Total time : 1.372s
%------------------------------------------------------------------------------