%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM836+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 : n006.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 04:58:40 PM UTC 2026
% Result : Theorem 1.26s 1.71s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 9 unt; 0 def)
% Number of atoms : 60 ( 37 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 57 ( 28 ~; 23 |; 3 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 70 ( 3 sgn 35 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof('ass(cond(goal(88), 0), 1)',axiom,
! [X7,X8] :
( X7 != X8
| ~ ? [X10] : X8 = vplus(X7,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
fof('ass(cond(81, 0), 0)',axiom,
! [X11,X12] :
( X11 != X12
=> ! [X13] : vplus(X13,X11) != vplus(X13,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
fof('ass(cond(goal(88), 0), 0)',axiom,
! [X7,X8] :
( X7 = X8
| ? [X9] : X7 = vplus(X8,X9)
| ? [X10] : X8 = vplus(X7,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
fof('ass(cond(33, 0), 0)',axiom,
! [X14,X15,X16] : vplus(vplus(X14,X15),X16) = vplus(X14,vplus(X15,X16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof('def(cond(conseq(axiom(3)), 12), 1)',axiom,
! [X1,X2] :
( less(X2,X1)
<=> ? [X3] : X1 = vplus(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
! [X4,X5] :
( greater(X5,X4)
<=> ? [X6] : X5 = vplus(X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof('dis(ex(cond(conseq(131), 0), 1))',conjecture,
( ~ greater(vd203,vd204)
| ~ less(vd203,vd204) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dis(ex(cond(conseq(131), 0), 1))') ).
fof(c_0_7,plain,
! [X63,X64,X65] :
( X63 != X64
| X64 != vplus(X63,X65) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(goal(88), 0), 1)'])])]) ).
fof(c_0_8,plain,
! [X73,X74,X75] :
( X73 = X74
| vplus(X75,X73) != vplus(X75,X74) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(81, 0), 0)'])])]) ).
fof(c_0_9,plain,
! [X59,X60] :
( X59 = X60
| X59 = vplus(X60,esk3_2(X59,X60))
| X60 = vplus(X59,esk4_2(X59,X60)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],['ass(cond(goal(88), 0), 0)'])]) ).
fof(c_0_10,plain,
! [X76,X77,X78] : vplus(vplus(X76,X77),X78) = vplus(X76,vplus(X77,X78)),
inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).
cnf(c_0_11,plain,
( X1 != X2
| X2 != vplus(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,plain,
! [X47,X48,X50,X51,X52] :
( ( ~ less(X48,X47)
| X47 = vplus(X48,esk1_2(X47,X48)) )
& ( X50 != vplus(X51,X52)
| less(X51,X50) ) ),
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_13,plain,
( X1 = X2
| vplus(X3,X1) != vplus(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( X1 = X2
| X1 = vplus(X2,esk3_2(X1,X2))
| X2 = vplus(X1,esk4_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
vplus(X1,X2) != X1,
inference(er,[status(thm)],[c_0_11]) ).
fof(c_0_17,plain,
! [X53,X54,X56,X57,X58] :
( ( ~ greater(X54,X53)
| X54 = vplus(X53,esk2_2(X53,X54)) )
& ( X57 != vplus(X56,X58)
| greater(X57,X56) ) ),
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_18,plain,
( X2 = vplus(X1,esk1_2(X2,X1))
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
esk3_2(vplus(X1,X2),X1) = X2,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14])]),c_0_15]),c_0_16]),c_0_16]) ).
cnf(c_0_20,plain,
( X1 = vplus(X2,esk2_2(X2,X1))
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
( vplus(X1,vplus(X2,esk1_2(X3,vplus(X1,X2)))) = X3
| ~ less(vplus(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_22,plain,
( esk2_2(X1,X2) = esk3_2(X2,X1)
| ~ greater(X2,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_23,negated_conjecture,
~ ( ~ greater(vd203,vd204)
| ~ less(vd203,vd204) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['dis(ex(cond(conseq(131), 0), 1))'])]) ).
cnf(c_0_24,plain,
~ less(vplus(X1,X2),X1),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_21])]) ).
cnf(c_0_25,plain,
( vplus(X1,esk3_2(X2,X1)) = X2
| ~ greater(X2,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_22]) ).
fof(c_0_26,negated_conjecture,
( greater(vd203,vd204)
& less(vd203,vd204) ),
inference(fof_nnf,[status(thm)],[c_0_23]) ).
cnf(c_0_27,plain,
( ~ less(X1,X2)
| ~ greater(X1,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
less(vd203,vd204),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_29,negated_conjecture,
greater(vd203,vd204),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM836+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 : n006.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 01:14:46 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.26/1.71 % Version : CSE_E---1.7
% 1.26/1.71 % Problem : theBenchmark.p
% 1.26/1.71 % SZS status Theorem for theBenchmark.p
% 1.26/1.71 % SZS output start CNFRefutation
% See solution above
% 1.26/1.71 % Total time : 1.371s
%------------------------------------------------------------------------------