%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM849+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 : n008.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 1.43s 1.78s
% Output : CNFRefutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 31 unt; 0 def)
% Number of atoms : 45 ( 44 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 : 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 : 52 ( 0 sgn 30 !; 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('qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))',axiom,
! [X84,X85] :
( vplus(X84,vsucc(X85)) = vsucc(vplus(X84,X85))
& vplus(X84,v1) = vsucc(X84) ),
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,
! [X80] : vplus(v1,X80) = vsucc(X80),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 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('ass(cond(61, 0), 0)',axiom,
! [X76,X77] : vplus(X77,X76) = vplus(X76,X77),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p','ass(cond(270, 0), 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('qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))',axiom,
! [X11,X12] :
( vmul(X11,vsucc(X12)) = vplus(vmul(X11,X12),X11)
& vmul(X11,v1) = X11 ),
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(c_0_8,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_9,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_8])])]) ).
fof(c_0_10,plain,
! [X336,X337] :
( vplus(X336,vsucc(X337)) = vsucc(vplus(X336,X337))
& vplus(X336,v1) = vsucc(X336) ),
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,
! [X332] : vplus(v1,X332) = vsucc(X332),
inference(variable_rename,[status(thm)],['ass(cond(43, 0), 0)']) ).
fof(c_0_12,plain,
! [X226,X227] : vmul(vsucc(X226),X227) = vplus(vmul(X226,X227),X227),
inference(variable_rename,[status(thm)],['ass(cond(261, 0), 0)']) ).
cnf(c_0_13,negated_conjecture,
vmul(vmul(vd448,vd449),vsucc(esk1_0)) != vmul(vd448,vmul(vd449,vsucc(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
vplus(X1,v1) = vsucc(X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
vplus(v1,X1) = vsucc(X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
vmul(vsucc(X1),X2) = vplus(vmul(X1,X2),X2),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X328,X329] : vplus(X329,X328) = vplus(X328,X329),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
fof(c_0_18,plain,
! [X224,X225] : vmul(X224,X225) = vmul(X225,X224),
inference(variable_rename,[status(thm)],['ass(cond(270, 0), 0)']) ).
cnf(c_0_19,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_13,c_0_14]),c_0_14]) ).
cnf(c_0_20,plain,
vplus(v1,X1) = vplus(X1,v1),
inference(rw,[status(thm)],[c_0_15,c_0_14]) ).
fof(c_0_21,plain,
! [X221,X222,X223] : vmul(X221,vplus(X222,X223)) = vplus(vmul(X221,X222),vmul(X221,X223)),
inference(variable_rename,[status(thm)],['ass(cond(281, 0), 0)']) ).
fof(c_0_22,plain,
! [X229,X230] :
( vmul(X229,vsucc(X230)) = vplus(vmul(X229,X230),X229)
& vmul(X229,v1) = X229 ),
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_23,plain,
vmul(vplus(X1,v1),X2) = vplus(vmul(X1,X2),X2),
inference(rw,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_24,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,negated_conjecture,
vmul(vmul(vd448,vd449),esk1_0) = vmul(vd448,vmul(vd449,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_26,plain,
vmul(X1,X2) = vmul(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,negated_conjecture,
vmul(vmul(vd448,vd449),vplus(v1,esk1_0)) != vmul(vd448,vmul(vd449,vplus(v1,esk1_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_20]) ).
cnf(c_0_28,plain,
vmul(X1,vplus(X2,X3)) = vplus(vmul(X1,X2),vmul(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
vmul(X1,v1) = X1,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
vmul(vplus(X1,v1),X2) = vplus(X2,vmul(X1,X2)),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,negated_conjecture,
vmul(esk1_0,vmul(vd449,vd448)) = vmul(vd448,vmul(vd449,esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_26]) ).
cnf(c_0_32,negated_conjecture,
vmul(vplus(v1,esk1_0),vmul(vd449,vd448)) != vmul(vd448,vmul(vd449,vplus(v1,esk1_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_26]),c_0_26]) ).
cnf(c_0_33,plain,
vplus(X1,vmul(X1,X2)) = vmul(X1,vplus(v1,X2)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
vplus(vmul(vd449,vd448),vmul(vd448,vmul(vd449,esk1_0))) = vmul(vplus(v1,esk1_0),vmul(vd449,vd448)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_20]) ).
cnf(c_0_35,plain,
vplus(vmul(X1,X2),vmul(X2,X3)) = vmul(X2,vplus(X1,X3)),
inference(spm,[status(thm)],[c_0_28,c_0_26]) ).
cnf(c_0_36,negated_conjecture,
vmul(vplus(v1,esk1_0),vmul(vd449,vd448)) != vmul(vd448,vplus(vd449,vmul(vd449,esk1_0))),
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM849+1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n008.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 01:15:58 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.43/1.78 % Version : CSE_E---1.7
% 1.43/1.78 % Problem : theBenchmark.p
% 1.43/1.78 % SZS status Theorem for theBenchmark.p
% 1.43/1.78 % SZS output start CNFRefutation
% See solution above
% 1.43/1.78 % Total time : 1.374s
%------------------------------------------------------------------------------