%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM841+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 : n031.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 04:58:41 PM UTC 2026
% Result : Theorem 1.34s 1.74s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 53 ( 28 unt; 0 def)
% Number of atoms : 86 ( 22 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 73 ( 40 ~; 27 |; 2 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 92 ( 10 sgn 44 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof('ass(cond(goal(130), 0), 2)',axiom,
! [X30,X31] :
( ~ greater(X30,X31)
| ~ less(X30,X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
fof('ass(cond(goal(193), 0), 2)',axiom,
! [X4,X5,X6] :
( greater(X4,X5)
=> greater(vplus(X4,X6),vplus(X5,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 2)') ).
fof('def(cond(conseq(axiom(3)), 12), 1)',axiom,
! [X32,X33] :
( less(X33,X32)
<=> ? [X34] : X32 = vplus(X33,X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
fof('ass(cond(61, 0), 0)',axiom,
! [X47,X48] : vplus(X48,X47) = vplus(X47,X48),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof('ass(cond(33, 0), 0)',axiom,
! [X52,X53,X54] : vplus(vplus(X52,X53),X54) = vplus(X52,vplus(X53,X54)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
! [X35,X36] :
( greater(X36,X35)
<=> ? [X37] : X36 = vplus(X35,X37) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof('holds(213, 351, 1)',axiom,
greater(vplus(vd347,vd345),vplus(vd348,vd345)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(213, 351, 1)') ).
fof('holds(213, 351, 0)',axiom,
vplus(vd345,vd347) = vplus(vd347,vd345),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(213, 351, 0)') ).
fof('holds(213, 351, 2)',axiom,
vplus(vd348,vd345) = vplus(vd345,vd348),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(213, 351, 2)') ).
fof('holds(214, 352, 0)',conjecture,
greater(vplus(vd344,vd347),vplus(vd345,vd348)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(214, 352, 0)') ).
fof('ass(cond(147, 0), 0)',axiom,
! [X26,X27] :
( less(X26,X27)
=> greater(X27,X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
fof('holds(212, 350, 0)',axiom,
greater(vplus(vd344,vd347),vplus(vd345,vd347)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(212, 350, 0)') ).
fof('ass(cond(goal(130), 0), 0)',axiom,
! [X30,X31] :
( X30 = X31
| greater(X30,X31)
| less(X30,X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
fof(c_0_13,plain,
! [X30,X31] :
( ~ greater(X30,X31)
| ~ less(X30,X31) ),
inference(fof_simplification,[status(thm)],['ass(cond(goal(130), 0), 2)']) ).
fof(c_0_14,plain,
! [X200,X201] :
( ~ greater(X200,X201)
| ~ less(X200,X201) ),
inference(variable_rename,[status(thm)],[c_0_13]) ).
fof(c_0_15,plain,
! [X170,X171,X172] :
( ~ greater(X170,X171)
| greater(vplus(X170,X172),vplus(X171,X172)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(goal(193), 0), 2)'])]) ).
fof(c_0_16,plain,
! [X204,X205,X207,X208,X209] :
( ( ~ less(X205,X204)
| X204 = vplus(X205,esk1_2(X204,X205)) )
& ( X207 != vplus(X208,X209)
| less(X208,X207) ) ),
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)), 12), 1)'])])])])]) ).
cnf(c_0_17,plain,
( ~ greater(X1,X2)
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( greater(vplus(X1,X3),vplus(X2,X3))
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( less(X2,X1)
| X1 != vplus(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
( ~ less(vplus(X1,X2),vplus(X3,X2))
| ~ greater(X1,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
less(X1,vplus(X1,X2)),
inference(er,[status(thm)],[c_0_19]) ).
fof(c_0_22,plain,
! [X235,X236] : vplus(X236,X235) = vplus(X235,X236),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
cnf(c_0_23,plain,
~ greater(X1,vplus(X1,X2)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_25,plain,
! [X240,X241,X242] : vplus(vplus(X240,X241),X242) = vplus(X240,vplus(X241,X242)),
inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).
cnf(c_0_26,plain,
~ greater(X1,vplus(X2,X1)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_28,plain,
~ greater(X1,vplus(X2,vplus(X3,X1))),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_29,plain,
! [X210,X211,X213,X214,X215] :
( ( ~ greater(X211,X210)
| X211 = vplus(X210,esk2_2(X210,X211)) )
& ( X214 != vplus(X213,X215)
| greater(X214,X213) ) ),
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_30,plain,
~ greater(X1,vplus(X2,vplus(X1,X3))),
inference(spm,[status(thm)],[c_0_28,c_0_24]) ).
cnf(c_0_31,plain,
( X1 = vplus(X2,esk2_2(X2,X1))
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_32,plain,
( ~ greater(X1,vplus(X2,X3))
| ~ greater(X3,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,plain,
( ~ greater(X1,vplus(X2,X3))
| ~ greater(X2,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_24]) ).
cnf(c_0_34,plain,
greater(vplus(vd347,vd345),vplus(vd348,vd345)),
inference(split_conjunct,[status(thm)],['holds(213, 351, 1)']) ).
cnf(c_0_35,plain,
vplus(vd345,vd347) = vplus(vd347,vd345),
inference(split_conjunct,[status(thm)],['holds(213, 351, 0)']) ).
cnf(c_0_36,plain,
vplus(vd348,vd345) = vplus(vd345,vd348),
inference(split_conjunct,[status(thm)],['holds(213, 351, 2)']) ).
cnf(c_0_37,plain,
( ~ greater(X1,X2)
| ~ greater(X3,X1)
| ~ greater(X2,X3) ),
inference(spm,[status(thm)],[c_0_33,c_0_31]) ).
cnf(c_0_38,plain,
greater(vplus(vd345,vd347),vplus(vd345,vd348)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
fof(c_0_39,negated_conjecture,
~ greater(vplus(vd344,vd347),vplus(vd345,vd348)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['holds(214, 352, 0)'])]) ).
fof(c_0_40,plain,
! [X192,X193] :
( ~ less(X192,X193)
| greater(X193,X192) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(147, 0), 0)'])]) ).
cnf(c_0_41,plain,
( ~ greater(X1,vplus(vd345,vd347))
| ~ greater(vplus(vd345,vd348),X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,plain,
greater(vplus(vd344,vd347),vplus(vd345,vd347)),
inference(split_conjunct,[status(thm)],['holds(212, 350, 0)']) ).
fof(c_0_43,plain,
! [X196,X197] :
( X196 = X197
| greater(X196,X197)
| less(X196,X197) ),
inference(variable_rename,[status(thm)],['ass(cond(goal(130), 0), 0)']) ).
cnf(c_0_44,negated_conjecture,
~ greater(vplus(vd344,vd347),vplus(vd345,vd348)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_45,plain,
( greater(X2,X1)
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_46,plain,
( ~ greater(X1,X2)
| ~ greater(X2,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_31]) ).
cnf(c_0_47,plain,
~ greater(vplus(vd345,vd348),vplus(vd344,vd347)),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,plain,
( X1 = X2
| greater(X1,X2)
| less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_49,negated_conjecture,
~ less(vplus(vd345,vd348),vplus(vd344,vd347)),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,plain,
~ greater(vplus(vd345,vd348),vplus(vd345,vd347)),
inference(spm,[status(thm)],[c_0_46,c_0_38]) ).
cnf(c_0_51,plain,
vplus(vd345,vd348) = vplus(vd344,vd347),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_52,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM841+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 : n031.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 01:17:38 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.34/1.74 % Version : CSE_E---1.7
% 1.34/1.74 % Problem : theBenchmark.p
% 1.34/1.74 % SZS status Theorem for theBenchmark.p
% 1.34/1.74 % SZS output start CNFRefutation
% See solution above
% 1.34/1.74 % Total time : 1.370s
%------------------------------------------------------------------------------