%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM845+2 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n029.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 1.24s 1.71s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 26 unt; 0 def)
% Number of atoms : 50 ( 49 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 11 ~; 4 |; 5 &)
% ( 0 <=>; 3 =>; 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 : 46 ( 0 sgn 24 !; 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/sandbox/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,
! [X11,X12] :
( vplus(X11,vsucc(X12)) = vsucc(vplus(X11,X12))
& vplus(X11,v1) = vsucc(X11) ),
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('ass(cond(43, 0), 0)',axiom,
! [X7] : vplus(v1,X7) = vsucc(X7),
file('/export/starexec/sandbox/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,
! [X3,X4] :
( vmul(X3,vsucc(X4)) = vplus(vmul(X3,X4),X3)
& vmul(X3,v1) = X3 ),
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,
! [X5,X6] : vplus(X6,X5) = vplus(X5,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof('ass(cond(conseq(263), 1), 7)',axiom,
! [X2] :
( vmul(vsucc(vd411),X2) = vplus(vmul(vd411,X2),X2)
=> vmul(vsucc(vd411),vsucc(X2)) = vplus(vmul(vsucc(vd411),X2),vsucc(vd411)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 7)') ).
fof('ass(cond(33, 0), 0)',axiom,
! [X8,X9,X10] : vplus(vplus(X8,X9),X10) = vplus(X8,vplus(X9,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof(c_0_7,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_8,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_7])])]) ).
fof(c_0_9,plain,
! [X49,X50] :
( vplus(X49,vsucc(X50)) = vsucc(vplus(X49,X50))
& vplus(X49,v1) = vsucc(X49) ),
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_10,plain,
! [X45] : vplus(v1,X45) = vsucc(X45),
inference(variable_rename,[status(thm)],['ass(cond(43, 0), 0)']) ).
fof(c_0_11,plain,
! [X41,X42] :
( vmul(X41,vsucc(X42)) = vplus(vmul(X41,X42),X41)
& vmul(X41,v1) = X41 ),
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_12,negated_conjecture,
vmul(vsucc(vd411),vsucc(esk1_0)) != vplus(vmul(vd411,vsucc(esk1_0)),vsucc(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
vplus(X1,v1) = vsucc(X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
vplus(v1,X1) = vsucc(X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
vmul(X1,vsucc(X2)) = vplus(vmul(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,plain,
! [X43,X44] : vplus(X44,X43) = vplus(X43,X44),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
fof(c_0_17,plain,
! [X40] :
( vmul(vsucc(vd411),X40) != vplus(vmul(vd411,X40),X40)
| vmul(vsucc(vd411),vsucc(X40)) = vplus(vmul(vsucc(vd411),X40),vsucc(vd411)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conseq(263), 1), 7)'])]) ).
cnf(c_0_18,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_12,c_0_13]),c_0_13]),c_0_13]),c_0_13]) ).
cnf(c_0_19,plain,
vplus(v1,X1) = vplus(X1,v1),
inference(rw,[status(thm)],[c_0_14,c_0_13]) ).
fof(c_0_20,plain,
! [X46,X47,X48] : vplus(vplus(X46,X47),X48) = vplus(X46,vplus(X47,X48)),
inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).
cnf(c_0_21,plain,
vmul(X1,vplus(X2,v1)) = vplus(vmul(X1,X2),X1),
inference(rw,[status(thm)],[c_0_15,c_0_13]) ).
cnf(c_0_22,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
( vmul(vsucc(vd411),vsucc(X1)) = vplus(vmul(vsucc(vd411),X1),vsucc(vd411))
| vmul(vsucc(vd411),X1) != vplus(vmul(vd411,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,negated_conjecture,
vmul(vsucc(vd411),esk1_0) = vplus(vmul(vd411,esk1_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,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_18,c_0_19]),c_0_19]),c_0_19]) ).
cnf(c_0_26,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
vmul(X1,vplus(X2,v1)) = vplus(X1,vmul(X1,X2)),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
( vmul(vplus(vd411,v1),vplus(X1,v1)) = vplus(vmul(vplus(vd411,v1),X1),vplus(vd411,v1))
| vmul(vplus(vd411,v1),X1) != vplus(vmul(vd411,X1),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_13]),c_0_13]),c_0_13]),c_0_13]),c_0_13]) ).
cnf(c_0_29,negated_conjecture,
vplus(vmul(vd411,esk1_0),esk1_0) = vmul(vplus(vd411,v1),esk1_0),
inference(rw,[status(thm)],[c_0_24,c_0_13]) ).
cnf(c_0_30,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)],[inference(rw,[status(thm)],[c_0_25,c_0_22]),c_0_26]) ).
cnf(c_0_31,plain,
vmul(X1,vplus(v1,X2)) = vplus(X1,vmul(X1,X2)),
inference(spm,[status(thm)],[c_0_27,c_0_22]) ).
cnf(c_0_32,plain,
( vplus(vd411,vplus(v1,vmul(vplus(vd411,v1),X1))) = vmul(vplus(vd411,v1),vplus(X1,v1))
| vmul(vplus(vd411,v1),X1) != vplus(X1,vmul(vd411,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_22]),c_0_26]),c_0_22]) ).
cnf(c_0_33,negated_conjecture,
vmul(vplus(vd411,v1),esk1_0) = vplus(esk1_0,vmul(vd411,esk1_0)),
inference(rw,[status(thm)],[c_0_29,c_0_22]) ).
cnf(c_0_34,negated_conjecture,
vplus(v1,vplus(esk1_0,vplus(vd411,vmul(vd411,esk1_0)))) != vmul(vplus(vd411,v1),vplus(v1,esk1_0)),
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
vplus(X1,vplus(X2,X3)) = vplus(X3,vplus(X1,X2)),
inference(spm,[status(thm)],[c_0_22,c_0_26]) ).
cnf(c_0_36,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(spm,[status(thm)],[c_0_32,c_0_33]),c_0_19]) ).
cnf(c_0_37,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)],[c_0_34,c_0_35]),c_0_22]),c_0_35]),c_0_26]),c_0_22]),c_0_35]),c_0_22]),c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM845+2 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n029.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 01:15:44 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.24/1.71 % Version : CSE_E---1.7
% 1.24/1.71 % Problem : theBenchmark.p
% 1.24/1.71 % SZS status Theorem for theBenchmark.p
% 1.24/1.71 % SZS output start CNFRefutation
% See solution above
% 1.24/1.71 % Total time : 1.369s
%------------------------------------------------------------------------------