%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM852+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 : n024.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 04:58:44 PM UTC 2026
% Result : Theorem 1.15s 1.64s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 15 unt; 0 def)
% Number of atoms : 35 ( 14 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 11 ~; 8 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 3 sgn 21 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
! [X24,X25] :
( greater(X25,X24)
<=> ? [X26] : X25 = vplus(X24,X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof('ass(cond(281, 0), 0)',axiom,
! [X8,X9,X10] : vmul(X8,vplus(X9,X10)) = vplus(vmul(X8,X9),vmul(X8,X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
fof('ass(cond(302, 0), 2)',axiom,
! [X3,X4] :
( greater(X3,X4)
=> vmul(X3,vd469) = vmul(vplus(X4,vskolem9(X3,X4)),vd469) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(302, 0), 2)') ).
fof('ass(cond(270, 0), 0)',axiom,
! [X11,X12] : vmul(X11,X12) = vmul(X12,X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
fof('holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)',conjecture,
greater(vmul(vd481,vd469),vmul(vd480,vd469)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)') ).
fof('holds(conseq_conjunct1(conseq(304)), 483, 0)',axiom,
greater(vd481,vd480),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq_conjunct1(conseq(304)), 483, 0)') ).
fof(c_0_6,plain,
! [X103,X104,X106,X107,X108] :
( ( ~ greater(X104,X103)
| X104 = vplus(X103,esk2_2(X103,X104)) )
& ( X107 != vplus(X106,X108)
| greater(X107,X106) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],['def(cond(conseq(axiom(3)), 11), 1)'])])])])]) ).
cnf(c_0_7,plain,
( greater(X1,X2)
| X1 != vplus(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_8,plain,
! [X78,X79,X80] : vmul(X78,vplus(X79,X80)) = vplus(vmul(X78,X79),vmul(X78,X80)),
inference(variable_rename,[status(thm)],['ass(cond(281, 0), 0)']) ).
fof(c_0_9,plain,
! [X71,X72] :
( ~ greater(X71,X72)
| vmul(X71,vd469) = vmul(vplus(X72,vskolem9(X71,X72)),vd469) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(302, 0), 2)'])]) ).
fof(c_0_10,plain,
! [X81,X82] : vmul(X81,X82) = vmul(X82,X81),
inference(variable_rename,[status(thm)],['ass(cond(270, 0), 0)']) ).
cnf(c_0_11,plain,
greater(vplus(X1,X2),X1),
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
vmul(X1,vplus(X2,X3)) = vplus(vmul(X1,X2),vmul(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( vmul(X1,vd469) = vmul(vplus(X2,vskolem9(X1,X2)),vd469)
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
vmul(X1,X2) = vmul(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,negated_conjecture,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)'])]) ).
cnf(c_0_16,plain,
greater(vmul(X1,vplus(X2,X3)),vmul(X1,X2)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( vmul(vd469,vplus(X1,vskolem9(X2,X1))) = vmul(X2,vd469)
| ~ greater(X2,X1) ),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( greater(vmul(X1,vd469),vmul(vd469,X2))
| ~ greater(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
~ greater(vmul(vd469,vd481),vmul(vd469,vd480)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_14]),c_0_14]) ).
cnf(c_0_21,plain,
( greater(vmul(vd469,X1),vmul(vd469,X2))
| ~ greater(X1,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_22,plain,
greater(vd481,vd480),
inference(split_conjunct,[status(thm)],['holds(conseq_conjunct1(conseq(304)), 483, 0)']) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : NUM852+2 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.07 % 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
% 0.05/0.26 % Computer : n024.cluster.edu
% 0.05/0.26 % Model : x86_64 x86_64
% 0.05/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.26 % Memory : 8042.1875MB
% 0.05/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.05/0.26 % CPULimit : 300
% 0.05/0.26 % WCLimit : 300
% 0.05/0.26 % DateTime : Mon May 4 20:15:57 EDT 2026
% 0.05/0.26 % CPUTime :
% 0.05/0.26 % start to proof: theBenchmark
% 1.15/1.64 % Version : CSE_E---1.7
% 1.15/1.64 % Problem : theBenchmark.p
% 1.15/1.64 % SZS status Theorem for theBenchmark.p
% 1.15/1.64 % SZS output start CNFRefutation
% See solution above
% 1.15/1.64 % Total time : 1.361s
%------------------------------------------------------------------------------