%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM841+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 : n016.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 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 48 ( 31 unt; 0 def)
% Number of atoms : 71 ( 28 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 58 ( 35 ~; 20 |; 1 &)
% ( 1 <=>; 1 =>; 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 78 ( 15 sgn 30 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof('ass(cond(goal(88), 0), 3)',axiom,
! [X18,X19] :
( X18 != X19
| ~ ? [X20] : X18 = vplus(X19,X20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
fof('ass(cond(61, 0), 0)',axiom,
! [X21,X22] : vplus(X22,X21) = vplus(X21,X22),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof('ass(cond(33, 0), 0)',axiom,
! [X26,X27,X28] : vplus(vplus(X26,X27),X28) = vplus(X26,vplus(X27,X28)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
! [X15,X16] :
( greater(X16,X15)
<=> ? [X17] : X16 = vplus(X15,X17) ),
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,
! [X9,X10] :
( less(X9,X10)
=> greater(X10,X9) ),
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,
! [X13,X14] :
( X13 = X14
| greater(X13,X14)
| less(X13,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
fof(c_0_11,plain,
! [X111,X112,X113] :
( X111 != X112
| X111 != vplus(X112,X113) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(goal(88), 0), 3)'])])]) ).
cnf(c_0_12,plain,
( X1 != X2
| X1 != vplus(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_13,plain,
! [X114,X115] : vplus(X115,X114) = vplus(X114,X115),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
cnf(c_0_14,plain,
vplus(X1,X2) != X1,
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_15,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_16,plain,
! [X119,X120,X121] : vplus(vplus(X119,X120),X121) = vplus(X119,vplus(X120,X121)),
inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).
cnf(c_0_17,plain,
vplus(X1,X2) != X2,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,plain,
vplus(X1,vplus(X2,X3)) != X3,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_20,plain,
! [X105,X106,X108,X109,X110] :
( ( ~ greater(X106,X105)
| X106 = vplus(X105,esk1_2(X105,X106)) )
& ( X109 != vplus(X108,X110)
| greater(X109,X108) ) ),
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_21,plain,
vplus(X1,vplus(X2,X3)) != X2,
inference(spm,[status(thm)],[c_0_19,c_0_15]) ).
cnf(c_0_22,plain,
( X1 = vplus(X2,esk1_2(X2,X1))
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,plain,
~ greater(X1,vplus(X2,X1)),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22])]) ).
cnf(c_0_24,plain,
~ greater(X1,vplus(X2,vplus(X3,X1))),
inference(spm,[status(thm)],[c_0_23,c_0_18]) ).
cnf(c_0_25,plain,
~ greater(X1,vplus(X2,vplus(X1,X3))),
inference(spm,[status(thm)],[c_0_24,c_0_15]) ).
cnf(c_0_26,plain,
( ~ greater(X1,vplus(X2,X3))
| ~ greater(X3,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_22]) ).
cnf(c_0_27,plain,
( ~ greater(X1,vplus(X2,X3))
| ~ greater(X2,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_15]) ).
cnf(c_0_28,plain,
greater(vplus(vd347,vd345),vplus(vd348,vd345)),
inference(split_conjunct,[status(thm)],['holds(213, 351, 1)']) ).
cnf(c_0_29,plain,
vplus(vd345,vd347) = vplus(vd347,vd345),
inference(split_conjunct,[status(thm)],['holds(213, 351, 0)']) ).
cnf(c_0_30,plain,
vplus(vd348,vd345) = vplus(vd345,vd348),
inference(split_conjunct,[status(thm)],['holds(213, 351, 2)']) ).
cnf(c_0_31,plain,
( ~ greater(X1,X2)
| ~ greater(X3,X1)
| ~ greater(X2,X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_22]) ).
cnf(c_0_32,plain,
greater(vplus(vd345,vd347),vplus(vd345,vd348)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
fof(c_0_33,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_34,plain,
! [X97,X98] :
( ~ less(X97,X98)
| greater(X98,X97) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(147, 0), 0)'])]) ).
cnf(c_0_35,plain,
~ greater(X1,vplus(X1,X2)),
inference(spm,[status(thm)],[c_0_23,c_0_15]) ).
cnf(c_0_36,plain,
( ~ greater(X1,vplus(vd345,vd347))
| ~ greater(vplus(vd345,vd348),X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
greater(vplus(vd344,vd347),vplus(vd345,vd347)),
inference(split_conjunct,[status(thm)],['holds(212, 350, 0)']) ).
fof(c_0_38,plain,
! [X101,X102] :
( X101 = X102
| greater(X101,X102)
| less(X101,X102) ),
inference(variable_rename,[status(thm)],['ass(cond(goal(130), 0), 0)']) ).
cnf(c_0_39,negated_conjecture,
~ greater(vplus(vd344,vd347),vplus(vd345,vd348)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,plain,
( greater(X2,X1)
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,plain,
( ~ greater(X1,X2)
| ~ greater(X2,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_22]) ).
cnf(c_0_42,plain,
~ greater(vplus(vd345,vd348),vplus(vd344,vd347)),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_43,plain,
( X1 = X2
| greater(X1,X2)
| less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,negated_conjecture,
~ less(vplus(vd345,vd348),vplus(vd344,vd347)),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,plain,
~ greater(vplus(vd345,vd348),vplus(vd345,vd347)),
inference(spm,[status(thm)],[c_0_41,c_0_32]) ).
cnf(c_0_46,plain,
vplus(vd345,vd348) = vplus(vd344,vd347),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_47,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_37])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM841+2 : 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
% 0.14/0.32 % Computer : n016.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
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------