%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV488+3 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/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 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 10 unt; 0 def)
% Number of atoms : 126 ( 36 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 141 ( 42 ~; 36 |; 39 &)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 53 ( 2 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(uti,conjecture,
! [X1,X2] :
( ( int_leq(int_one,X2)
& int_leq(X2,X1)
& int_leq(X1,n) )
=> ( X1 = X2
=> a(X1,X2) != real_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uti) ).
fof(qii,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 ) )
& ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X2) )
=> a(X3,X3) = real_one )
& ! [X8] :
( ( int_less(int_zero,X8)
& X2 = plus(X1,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(X3,plus(X3,X8)) = real_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qii) ).
fof(real_constants,axiom,
real_zero != real_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',real_constants) ).
fof(int_leq,axiom,
! [X1,X2] :
( int_leq(X1,X2)
<=> ( int_less(X1,X2)
| X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_leq) ).
fof(c_0_4,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 ) )
& ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X2) )
=> a(X3,X3) = real_one )
& ! [X8] :
( ( int_less(int_zero,X8)
& X2 = plus(X1,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(X3,plus(X3,X8)) = real_zero ) ) ) ),
introduced(definition) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( ( int_leq(int_one,X2)
& int_leq(X2,X1)
& int_leq(X1,n) )
=> ( X1 = X2
=> a(X1,X2) != real_zero ) ),
inference(assume_negation,[status(cth)],[uti]) ).
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 ) )
& ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X2) )
=> a(X3,X3) = real_one )
& ! [X8] :
( ( int_less(int_zero,X8)
& X2 = plus(X1,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(X3,plus(X3,X8)) = real_zero ) ) ) ),
inference(split_equiv,[status(thm)],[c_0_4]) ).
fof(c_0_7,negated_conjecture,
( int_leq(int_one,esk3_0)
& int_leq(esk3_0,esk2_0)
& int_leq(esk2_0,n)
& esk2_0 = esk3_0
& a(esk2_0,esk3_0) = real_zero ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_8,plain,
! [X65,X66,X67,X68,X69,X70,X71] :
( ( ~ int_less(int_zero,X67)
| X66 != plus(X65,X67)
| ~ int_leq(int_one,X68)
| ~ int_leq(X68,X65)
| a(plus(X68,X67),X68) = real_zero
| ~ epred1_2(X66,X65) )
& ( ~ int_leq(int_one,X69)
| ~ int_leq(X69,X65)
| a(X69,X69) = real_one
| ~ epred1_2(X66,X65) )
& ( ~ int_less(int_zero,X70)
| X65 != plus(X66,X70)
| ~ int_leq(int_one,X71)
| ~ int_leq(X71,X66)
| a(X71,plus(X71,X70)) = real_zero
| ~ epred1_2(X66,X65) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
cnf(c_0_9,negated_conjecture,
int_leq(int_one,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,negated_conjecture,
esk2_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
a(esk2_0,esk3_0) = real_zero,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,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)],[qii,c_0_4]) ).
cnf(c_0_13,plain,
( a(X1,X1) = real_one
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X2)
| ~ epred1_2(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
int_leq(int_one,esk2_0),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
a(esk2_0,esk2_0) = real_zero,
inference(rw,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_16,plain,
real_zero != real_one,
inference(split_conjunct,[status(thm)],[real_constants]) ).
fof(c_0_17,hypothesis,
! [X61,X62] :
( ~ int_leq(int_one,X61)
| ~ int_leq(X61,n)
| ~ int_leq(int_one,X62)
| ~ int_leq(X62,n)
| epred1_2(X61,X62) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).
fof(c_0_18,plain,
! [X38,X39] :
( ( ~ int_leq(X38,X39)
| int_less(X38,X39)
| X38 = X39 )
& ( ~ int_less(X38,X39)
| int_leq(X38,X39) )
& ( X38 != X39
| int_leq(X38,X39) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[int_leq])])]) ).
cnf(c_0_19,negated_conjecture,
( ~ epred1_2(X1,X2)
| ~ int_leq(esk2_0,X2) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16]) ).
cnf(c_0_20,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_17]) ).
cnf(c_0_21,plain,
( int_leq(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,hypothesis,
( ~ int_leq(esk2_0,X1)
| ~ int_leq(X1,n)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_one,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
int_leq(X1,X1),
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_24,negated_conjecture,
int_leq(esk2_0,n),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_25,hypothesis,
( ~ int_leq(X1,n)
| ~ int_leq(int_one,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_14])]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_24]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV488+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n005.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 05:19:00 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Theorem for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.369s
%------------------------------------------------------------------------------