%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV487+1 : TPTP v9.2.1. Released v4.0.0.
% 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 : n005.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 05:23:31 PM UTC 2026
% Result : Theorem 2.19s 1.98s
% Output : CNFRefutation 2.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 11 unt; 0 def)
% Number of atoms : 169 ( 39 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 184 ( 62 ~; 64 |; 36 &)
% ( 4 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn 51 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ut,conjecture,
! [X1,X2] :
( ( int_leq(int_one,X2)
& int_less(X2,X1)
& int_leq(X1,n) )
=> a(X1,X2) = real_zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ut) ).
fof(int_leq,axiom,
! [X1,X2] :
( int_leq(X1,X2)
<=> ( int_less(X1,X2)
| X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_leq) ).
fof(plus_and_inverse,axiom,
! [X1,X2] :
( int_less(X1,X2)
<=> ? [X3] :
( plus(X1,X3) = X2
& int_less(int_zero,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_and_inverse) ).
fof(int_less_transitive,axiom,
! [X1,X2,X3] :
( ( int_less(X1,X2)
& int_less(X2,X3) )
=> int_less(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_less_transitive) ).
fof(one_successor_of_zero,axiom,
! [X1] :
( int_less(int_zero,X1)
<=> int_leq(int_one,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_successor_of_zero) ).
fof(qiu,hypothesis,
! [X1,X2] :
( ( int_leq(int_one,X1)
& int_leq(X1,n)
& int_leq(int_one,X2)
& int_leq(X2,n) )
=> ( ! [X8] :
( ( int_less(int_zero,X8)
& X1 = plus(X2,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X2) )
=> a(plus(X3,X8),X3) = real_zero ) )
& ! [X8] :
( ( int_leq(int_zero,X8)
& X2 = plus(X1,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(X3,plus(X3,X8)) = lu(X3,plus(X3,X8)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qiu) ).
fof(c_0_6,plain,
! [X2,X1] :
( epred1_2(X1,X2)
<=> ( ! [X8] :
( ( int_less(int_zero,X8)
& X1 = plus(X2,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X2) )
=> a(plus(X3,X8),X3) = real_zero ) )
& ! [X8] :
( ( int_leq(int_zero,X8)
& X2 = plus(X1,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(X3,plus(X3,X8)) = lu(X3,plus(X3,X8)) ) ) ) ),
introduced(definition) ).
fof(c_0_7,plain,
! [X2,X1] :
( epred1_2(X1,X2)
=> ( ! [X8] :
( ( int_less(int_zero,X8)
& X1 = plus(X2,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X2) )
=> a(plus(X3,X8),X3) = real_zero ) )
& ! [X8] :
( ( int_leq(int_zero,X8)
& X2 = plus(X1,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(X3,plus(X3,X8)) = lu(X3,plus(X3,X8)) ) ) ) ),
inference(split_equiv,[status(thm)],[c_0_6]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2] :
( ( int_leq(int_one,X2)
& int_less(X2,X1)
& int_leq(X1,n) )
=> a(X1,X2) = real_zero ),
inference(assume_negation,[status(cth)],[ut]) ).
fof(c_0_9,plain,
! [X64,X65,X66,X67,X68,X69] :
( ( ~ int_less(int_zero,X66)
| X65 != plus(X64,X66)
| ~ int_leq(int_one,X67)
| ~ int_leq(X67,X64)
| a(plus(X67,X66),X67) = real_zero
| ~ epred1_2(X65,X64) )
& ( ~ int_leq(int_zero,X68)
| X64 != plus(X65,X68)
| ~ int_leq(int_one,X69)
| ~ int_leq(X69,X65)
| a(X69,plus(X69,X68)) = lu(X69,plus(X69,X68))
| ~ epred1_2(X65,X64) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_10,plain,
! [X37,X38] :
( ( ~ int_leq(X37,X38)
| int_less(X37,X38)
| X37 = X38 )
& ( ~ int_less(X37,X38)
| int_leq(X37,X38) )
& ( X37 != X38
| int_leq(X37,X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[int_leq])])]) ).
fof(c_0_11,negated_conjecture,
( int_leq(int_one,esk3_0)
& int_less(esk3_0,esk2_0)
& int_leq(esk2_0,n)
& a(esk2_0,esk3_0) != real_zero ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_12,plain,
( a(plus(X4,X1),X4) = real_zero
| ~ int_less(int_zero,X1)
| X2 != plus(X3,X1)
| ~ int_leq(int_one,X4)
| ~ int_leq(X4,X3)
| ~ epred1_2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X53,X54,X56,X57,X58] :
( ( plus(X53,esk1_2(X53,X54)) = X54
| ~ int_less(X53,X54) )
& ( int_less(int_zero,esk1_2(X53,X54))
| ~ int_less(X53,X54) )
& ( plus(X56,X58) != X57
| ~ int_less(int_zero,X58)
| int_less(X56,X57) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[plus_and_inverse])])])])])]) ).
fof(c_0_14,plain,
! [X39,X40,X41] :
( ~ int_less(X39,X40)
| ~ int_less(X40,X41)
| int_less(X39,X41) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[int_less_transitive])]) ).
cnf(c_0_15,plain,
( int_less(X1,X2)
| X1 = X2
| ~ int_leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
int_leq(esk2_0,n),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( a(plus(X1,X2),X1) = real_zero
| ~ epred1_2(plus(X3,X2),X3)
| ~ int_less(int_zero,X2)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X3) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( plus(X1,esk1_2(X1,X2)) = X2
| ~ int_less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( int_less(int_zero,esk1_2(X1,X2))
| ~ int_less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( int_leq(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_21,plain,
! [X59] :
( ( ~ int_less(int_zero,X59)
| int_leq(int_one,X59) )
& ( ~ int_leq(int_one,X59)
| int_less(int_zero,X59) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[one_successor_of_zero])]) ).
cnf(c_0_22,plain,
( int_less(X1,X3)
| ~ int_less(X1,X2)
| ~ int_less(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,negated_conjecture,
int_less(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_24,negated_conjecture,
( esk2_0 = n
| int_less(esk2_0,n) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_25,plain,
( a(plus(X1,esk1_2(X2,X3)),X1) = real_zero
| ~ epred1_2(X3,X2)
| ~ int_less(X2,X3)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_26,plain,
int_leq(X1,X1),
inference(er,[status(thm)],[c_0_20]) ).
fof(c_0_27,hypothesis,
! [X1,X2] :
( ( int_leq(int_one,X1)
& int_leq(X1,n)
& int_leq(int_one,X2)
& int_leq(X2,n) )
=> epred1_2(X1,X2) ),
inference(apply_def,[status(thm)],[qiu,c_0_6]) ).
cnf(c_0_28,plain,
( int_leq(int_one,X1)
| ~ int_less(int_zero,X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,negated_conjecture,
( int_less(X1,esk2_0)
| ~ int_less(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,negated_conjecture,
( esk2_0 = n
| int_less(X1,n)
| ~ int_less(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_24]) ).
cnf(c_0_31,negated_conjecture,
a(esk2_0,esk3_0) != real_zero,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_32,plain,
( a(X1,X2) = real_zero
| ~ epred1_2(X1,X2)
| ~ int_less(X2,X1)
| ~ int_leq(int_one,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_18]),c_0_26])]) ).
cnf(c_0_33,negated_conjecture,
int_leq(int_one,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_34,hypothesis,
! [X60,X61] :
( ~ int_leq(int_one,X60)
| ~ int_leq(X60,n)
| ~ int_leq(int_one,X61)
| ~ int_leq(X61,n)
| epred1_2(X60,X61) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])]) ).
cnf(c_0_35,negated_conjecture,
( int_leq(int_one,esk2_0)
| ~ int_less(int_zero,esk3_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,plain,
( int_less(int_zero,X1)
| ~ int_leq(int_one,X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_37,plain,
( int_leq(X1,X2)
| ~ int_less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_38,negated_conjecture,
( esk2_0 = n
| int_less(esk3_0,n) ),
inference(spm,[status(thm)],[c_0_30,c_0_23]) ).
cnf(c_0_39,negated_conjecture,
~ epred1_2(esk2_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_23]),c_0_33])]) ).
cnf(c_0_40,hypothesis,
( epred1_2(X1,X2)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X2)
| ~ int_leq(X2,n) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,negated_conjecture,
int_leq(int_one,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_33])]) ).
cnf(c_0_42,negated_conjecture,
( esk2_0 = n
| int_leq(esk3_0,n) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,hypothesis,
~ int_leq(esk3_0,n),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_16]),c_0_33]),c_0_41])]) ).
cnf(c_0_44,negated_conjecture,
int_leq(esk3_0,esk2_0),
inference(spm,[status(thm)],[c_0_37,c_0_23]) ).
cnf(c_0_45,negated_conjecture,
esk2_0 = n,
inference(sr,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV487+1 : TPTP v9.2.1. Released v4.0.0.
% 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
% 0.15/0.33 % Computer : n005.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 05:19:00 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 2.19/1.98 % Version : CSE_E---1.7
% 2.19/1.98 % Problem : theBenchmark.p
% 2.19/1.98 % SZS status Theorem for theBenchmark.p
% 2.19/1.98 % SZS output start CNFRefutation
% See solution above
% 2.19/1.99 % Total time : 1.370s
%------------------------------------------------------------------------------