%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM849+2 : 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 : n014.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 04:58:43 PM UTC 2026
% Result : Theorem 1.30s 1.73s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 23 unt; 0 def)
% Number of atoms : 33 ( 32 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 5 ~; 0 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% 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 : 40 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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('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(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('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/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 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('ass(cond(61, 0), 0)',axiom,
! [X12,X13] : vplus(X13,X12) = vplus(X12,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(c_0_6,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_7,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_6])])]) ).
fof(c_0_8,plain,
! [X42,X43] : vmul(X42,X43) = vmul(X43,X42),
inference(variable_rename,[status(thm)],['ass(cond(270, 0), 0)']) ).
fof(c_0_9,plain,
! [X44,X45] : vmul(vsucc(X44),X45) = vplus(vmul(X44,X45),X45),
inference(variable_rename,[status(thm)],['ass(cond(261, 0), 0)']) ).
fof(c_0_10,plain,
! [X50,X51] :
( vplus(X50,vsucc(X51)) = vsucc(vplus(X50,X51))
& vplus(X50,v1) = vsucc(X50) ),
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,
! [X39,X40,X41] : vmul(X39,vplus(X40,X41)) = vplus(vmul(X39,X40),vmul(X39,X41)),
inference(variable_rename,[status(thm)],['ass(cond(281, 0), 0)']) ).
cnf(c_0_12,negated_conjecture,
vmul(vmul(vd448,vd449),esk1_0) = vmul(vd448,vmul(vd449,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
vmul(X1,X2) = vmul(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
vmul(vsucc(X1),X2) = vplus(vmul(X1,X2),X2),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
vplus(X1,v1) = vsucc(X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X48,X49] : vplus(X49,X48) = vplus(X48,X49),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
cnf(c_0_17,plain,
vmul(X1,vplus(X2,X3)) = vplus(vmul(X1,X2),vmul(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
vmul(vd448,vmul(esk1_0,vd449)) = vmul(esk1_0,vmul(vd449,vd448)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_13]),c_0_13]) ).
cnf(c_0_19,negated_conjecture,
vmul(vmul(vd448,vd449),vsucc(esk1_0)) != vmul(vd448,vmul(vd449,vsucc(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,plain,
vmul(vplus(X1,v1),X2) = vplus(vmul(X1,X2),X2),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
vplus(vmul(vd448,X1),vmul(esk1_0,vmul(vd449,vd448))) = vmul(vd448,vplus(X1,vmul(esk1_0,vd449))),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,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_19,c_0_15]),c_0_15]) ).
cnf(c_0_24,plain,
vmul(vplus(X1,v1),X2) = vplus(X2,vmul(X1,X2)),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
vplus(vmul(X1,vd448),vmul(esk1_0,vmul(vd449,vd448))) = vmul(vd448,vplus(X1,vmul(esk1_0,vd449))),
inference(spm,[status(thm)],[c_0_22,c_0_13]) ).
cnf(c_0_26,negated_conjecture,
vmul(vplus(esk1_0,v1),vmul(vd449,vd448)) != vmul(vd448,vmul(vd449,vplus(esk1_0,v1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_13]),c_0_13]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_24]),c_0_13]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM849+2 : 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 : n014.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 01:16:06 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.30/1.73 % Version : CSE_E---1.7
% 1.30/1.73 % Problem : theBenchmark.p
% 1.30/1.73 % SZS status Theorem for theBenchmark.p
% 1.30/1.73 % SZS output start CNFRefutation
% See solution above
% 1.30/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------