%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : PUZ133+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 : n004.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 05:03:41 PM UTC 2026
% Result : Theorem 6.20s 4.42s
% Output : CNFRefutation 6.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 100 ( 42 unt; 0 def)
% Number of atoms : 263 ( 108 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 282 ( 119 ~; 121 |; 30 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 132 ( 0 sgn 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(queens_sym,conjecture,
( ( queens_p
& ! [X1] : q(X1) = p(perm(X1)) )
=> queens_q ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',queens_sym) ).
fof(queens_q,axiom,
( ! [X1,X2] :
( ( le(s(n0),X1)
& le(X1,n)
& le(s(X1),X2)
& le(X2,n)
& ( le(s(X1),X2)
<=> le(s(perm(X2)),perm(X1)) ) )
=> ( q(X1) != q(X2)
& plus(q(X1),X1) != plus(q(X2),X2)
& minus(q(X1),X1) != minus(q(X2),X2) ) )
=> queens_q ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',queens_q) ).
fof(le_trans,axiom,
! [X3,X4,X5] :
( ( le(X3,X4)
& le(X4,X5) )
=> le(X3,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',le_trans) ).
fof(succ_le,axiom,
! [X3] : le(X3,s(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_le) ).
fof(permutation_range,axiom,
! [X1] :
( ( le(s(n0),X1)
& le(X1,n) )
=> ( le(s(n0),perm(X1))
& le(perm(X1),n) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',permutation_range) ).
fof(permutation,axiom,
! [X1] :
( ( le(s(n0),X1)
& le(X1,n) )
=> perm(X1) = minus(s(n),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',permutation) ).
fof(queens_p,axiom,
( queens_p
=> ! [X1,X2] :
( ( le(s(n0),X1)
& le(X1,n)
& le(s(X1),X2)
& le(X2,n) )
=> ( p(X1) != p(X2)
& plus(p(X1),X1) != plus(p(X2),X2)
& minus(p(X1),X1) != minus(p(X2),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',queens_p) ).
fof(plus1,axiom,
! [X1,X2,X6,X7] :
( plus(X1,X2) = plus(X6,X7)
<=> minus(X1,X6) = minus(X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus1) ).
fof(minus1,axiom,
! [X1,X2,X6,X7] :
( minus(X1,X2) = minus(X6,X7)
<=> minus(X1,X6) = minus(X2,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minus1) ).
fof(permutation_another_one,axiom,
! [X2,X1] : minus(X1,X2) = minus(perm(X2),perm(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',permutation_another_one) ).
fof(c_0_10,negated_conjecture,
~ ( ( queens_p
& ! [X1] : q(X1) = p(perm(X1)) )
=> queens_q ),
inference(assume_negation,[status(cth)],[queens_sym]) ).
fof(c_0_11,plain,
( ( le(s(n0),esk1_0)
| queens_q )
& ( le(esk1_0,n)
| queens_q )
& ( le(s(esk1_0),esk2_0)
| queens_q )
& ( le(esk2_0,n)
| queens_q )
& ( ~ le(s(esk1_0),esk2_0)
| le(s(perm(esk2_0)),perm(esk1_0))
| queens_q )
& ( ~ le(s(perm(esk2_0)),perm(esk1_0))
| le(s(esk1_0),esk2_0)
| queens_q )
& ( q(esk1_0) = q(esk2_0)
| plus(q(esk1_0),esk1_0) = plus(q(esk2_0),esk2_0)
| minus(q(esk1_0),esk1_0) = minus(q(esk2_0),esk2_0)
| queens_q ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[queens_q])])])]) ).
fof(c_0_12,negated_conjecture,
! [X34] :
( queens_p
& q(X34) = p(perm(X34))
& ~ queens_q ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_13,plain,
! [X38,X39,X40] :
( ~ le(X38,X39)
| ~ le(X39,X40)
| le(X38,X40) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[le_trans])]) ).
cnf(c_0_14,plain,
( le(s(esk1_0),esk2_0)
| queens_q ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
~ queens_q,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( le(X1,X3)
| ~ le(X1,X2)
| ~ le(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
le(s(esk1_0),esk2_0),
inference(sr,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_18,plain,
! [X41] : le(X41,s(X41)),
inference(variable_rename,[status(thm)],[succ_le]) ).
cnf(c_0_19,plain,
( le(X1,esk2_0)
| ~ le(X1,s(esk1_0)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
le(X1,s(X1)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_21,plain,
! [X35] :
( ( le(s(n0),perm(X35))
| ~ le(s(n0),X35)
| ~ le(X35,n) )
& ( le(perm(X35),n)
| ~ le(s(n0),X35)
| ~ le(X35,n) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[permutation_range])])]) ).
cnf(c_0_22,plain,
( le(esk1_0,n)
| queens_q ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_23,plain,
( le(s(n0),esk1_0)
| queens_q ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_24,plain,
! [X31] :
( ~ le(s(n0),X31)
| ~ le(X31,n)
| perm(X31) = minus(s(n),X31) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[permutation])]) ).
cnf(c_0_25,plain,
le(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_26,plain,
! [X29,X30] :
( ( p(X29) != p(X30)
| ~ le(s(n0),X29)
| ~ le(X29,n)
| ~ le(s(X29),X30)
| ~ le(X30,n)
| ~ queens_p )
& ( plus(p(X29),X29) != plus(p(X30),X30)
| ~ le(s(n0),X29)
| ~ le(X29,n)
| ~ le(s(X29),X30)
| ~ le(X30,n)
| ~ queens_p )
& ( minus(p(X29),X29) != minus(p(X30),X30)
| ~ le(s(n0),X29)
| ~ le(X29,n)
| ~ le(s(X29),X30)
| ~ le(X30,n)
| ~ queens_p ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[queens_p])])])]) ).
cnf(c_0_27,plain,
( le(perm(X1),n)
| ~ le(s(n0),X1)
| ~ le(X1,n) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
le(esk1_0,n),
inference(sr,[status(thm)],[c_0_22,c_0_15]) ).
cnf(c_0_29,plain,
le(s(n0),esk1_0),
inference(sr,[status(thm)],[c_0_23,c_0_15]) ).
cnf(c_0_30,plain,
( perm(X1) = minus(s(n),X1)
| ~ le(s(n0),X1)
| ~ le(X1,n) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( le(esk2_0,n)
| queens_q ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_32,plain,
( le(X1,esk2_0)
| ~ le(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_25]) ).
cnf(c_0_33,plain,
( q(esk1_0) = q(esk2_0)
| plus(q(esk1_0),esk1_0) = plus(q(esk2_0),esk2_0)
| minus(q(esk1_0),esk1_0) = minus(q(esk2_0),esk2_0)
| queens_q ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_34,negated_conjecture,
q(X1) = p(perm(X1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_35,plain,
! [X42,X43,X44,X45] :
( ( plus(X42,X43) != plus(X44,X45)
| minus(X42,X44) = minus(X45,X43) )
& ( minus(X42,X44) != minus(X45,X43)
| plus(X42,X43) = plus(X44,X45) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[plus1])]) ).
cnf(c_0_36,plain,
( p(X1) != p(X2)
| ~ le(s(n0),X1)
| ~ le(X1,n)
| ~ le(s(X1),X2)
| ~ le(X2,n)
| ~ queens_p ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_37,negated_conjecture,
queens_p,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_38,plain,
le(perm(esk1_0),n),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_39,plain,
perm(esk1_0) = minus(s(n),esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_28]),c_0_29])]) ).
cnf(c_0_40,plain,
le(esk2_0,n),
inference(sr,[status(thm)],[c_0_31,c_0_15]) ).
cnf(c_0_41,plain,
le(s(n0),esk2_0),
inference(spm,[status(thm)],[c_0_32,c_0_29]) ).
cnf(c_0_42,plain,
( le(s(perm(esk2_0)),perm(esk1_0))
| queens_q
| ~ le(s(esk1_0),esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_43,negated_conjecture,
( p(perm(esk2_0)) = p(perm(esk1_0))
| plus(p(perm(esk2_0)),esk2_0) = plus(p(perm(esk1_0)),esk1_0)
| minus(p(perm(esk2_0)),esk2_0) = minus(p(perm(esk1_0)),esk1_0)
| queens_q ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_34]),c_0_34]),c_0_34]),c_0_34]),c_0_34]) ).
cnf(c_0_44,plain,
( plus(X1,X4) = plus(X2,X3)
| minus(X1,X2) != minus(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_45,plain,
( p(X1) != p(X2)
| ~ le(s(n0),X1)
| ~ le(s(X1),X2)
| ~ le(X2,n)
| ~ le(X1,n) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]) ).
cnf(c_0_46,plain,
le(minus(s(n),esk1_0),n),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_47,plain,
le(perm(esk2_0),n),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_40]),c_0_41])]) ).
cnf(c_0_48,plain,
perm(esk2_0) = minus(s(n),esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_40]),c_0_41])]) ).
cnf(c_0_49,plain,
le(s(perm(esk2_0)),perm(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_17])]),c_0_15]) ).
cnf(c_0_50,plain,
( le(s(n0),perm(X1))
| ~ le(s(n0),X1)
| ~ le(X1,n) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_51,plain,
! [X46,X47,X48,X49] :
( ( minus(X46,X47) != minus(X48,X49)
| minus(X46,X48) = minus(X47,X49) )
& ( minus(X46,X48) != minus(X47,X49)
| minus(X46,X47) = minus(X48,X49) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[minus1])]) ).
fof(c_0_52,plain,
! [X36,X37] : minus(X37,X36) = minus(perm(X36),perm(X37)),
inference(variable_rename,[status(thm)],[permutation_another_one]) ).
cnf(c_0_53,negated_conjecture,
( minus(p(perm(esk2_0)),esk2_0) = minus(p(perm(esk1_0)),esk1_0)
| plus(p(perm(esk2_0)),esk2_0) = plus(p(perm(esk1_0)),esk1_0)
| p(perm(esk2_0)) = p(perm(esk1_0)) ),
inference(sr,[status(thm)],[c_0_43,c_0_15]) ).
cnf(c_0_54,plain,
plus(X1,X2) = plus(X2,X1),
inference(er,[status(thm)],[c_0_44]) ).
cnf(c_0_55,plain,
( p(X1) != p(minus(s(n),esk1_0))
| ~ le(s(X1),minus(s(n),esk1_0))
| ~ le(s(n0),X1)
| ~ le(X1,n) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_56,plain,
le(minus(s(n),esk2_0),n),
inference(rw,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_57,plain,
le(s(minus(s(n),esk2_0)),minus(s(n),esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_48]),c_0_39]) ).
cnf(c_0_58,plain,
le(s(n0),minus(s(n),esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_40]),c_0_48]),c_0_41])]) ).
cnf(c_0_59,plain,
( minus(X1,X3) = minus(X2,X4)
| minus(X1,X2) != minus(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_60,plain,
minus(X1,X2) = minus(perm(X2),perm(X1)),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_61,negated_conjecture,
( minus(p(minus(s(n),esk2_0)),esk2_0) = minus(p(minus(s(n),esk1_0)),esk1_0)
| plus(esk2_0,p(minus(s(n),esk2_0))) = plus(esk1_0,p(minus(s(n),esk1_0)))
| p(minus(s(n),esk2_0)) = p(minus(s(n),esk1_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_48]),c_0_48]),c_0_48]),c_0_39]),c_0_54]),c_0_54]),c_0_39]),c_0_39]) ).
cnf(c_0_62,plain,
p(minus(s(n),esk2_0)) != p(minus(s(n),esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]),c_0_58])]) ).
cnf(c_0_63,plain,
( minus(p(X1),X1) != minus(p(X2),X2)
| ~ le(s(n0),X1)
| ~ le(X1,n)
| ~ le(s(X1),X2)
| ~ le(X2,n)
| ~ queens_p ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_64,plain,
( minus(X1,perm(X2)) = minus(X3,perm(X4))
| minus(X1,X3) != minus(X4,X2) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_65,plain,
( minus(X1,X3) = minus(X4,X2)
| plus(X1,X2) != plus(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_66,plain,
( plus(X1,perm(X2)) = plus(X3,perm(X4))
| minus(X1,X3) != minus(X2,X4) ),
inference(spm,[status(thm)],[c_0_44,c_0_60]) ).
cnf(c_0_67,plain,
minus(perm(X1),minus(s(n),esk2_0)) = minus(esk2_0,X1),
inference(spm,[status(thm)],[c_0_60,c_0_48]) ).
cnf(c_0_68,negated_conjecture,
( plus(esk2_0,p(minus(s(n),esk2_0))) = plus(esk1_0,p(minus(s(n),esk1_0)))
| minus(p(minus(s(n),esk2_0)),esk2_0) = minus(p(minus(s(n),esk1_0)),esk1_0) ),
inference(sr,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_69,plain,
( minus(p(X1),X1) != minus(p(X2),X2)
| ~ le(s(n0),X1)
| ~ le(s(X1),X2)
| ~ le(X2,n)
| ~ le(X1,n) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_37])]) ).
cnf(c_0_70,plain,
minus(minus(s(n),esk2_0),perm(X1)) = minus(X1,esk2_0),
inference(spm,[status(thm)],[c_0_60,c_0_48]) ).
cnf(c_0_71,plain,
minus(X1,perm(X2)) = minus(X2,perm(X1)),
inference(er,[status(thm)],[c_0_64]) ).
cnf(c_0_72,plain,
minus(X1,X1) = minus(X2,X2),
inference(er,[status(thm)],[c_0_65]) ).
cnf(c_0_73,plain,
( plus(X1,perm(perm(X2))) = plus(X3,perm(perm(X4)))
| minus(X1,X3) != minus(X4,X2) ),
inference(spm,[status(thm)],[c_0_66,c_0_60]) ).
cnf(c_0_74,plain,
minus(minus(s(n),esk1_0),minus(s(n),esk2_0)) = minus(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_67,c_0_39]) ).
cnf(c_0_75,negated_conjecture,
( minus(p(minus(s(n),esk2_0)),esk2_0) = minus(p(minus(s(n),esk1_0)),esk1_0)
| minus(esk2_0,X1) = minus(X2,p(minus(s(n),esk2_0)))
| plus(esk1_0,p(minus(s(n),esk1_0))) != plus(X1,X2) ),
inference(spm,[status(thm)],[c_0_65,c_0_68]) ).
cnf(c_0_76,plain,
( minus(p(X1),X1) != minus(p(minus(s(n),esk1_0)),minus(s(n),esk1_0))
| ~ le(s(X1),minus(s(n),esk1_0))
| ~ le(s(n0),X1)
| ~ le(X1,n) ),
inference(spm,[status(thm)],[c_0_69,c_0_46]) ).
cnf(c_0_77,plain,
( plus(p(X1),X1) != plus(p(X2),X2)
| ~ le(s(n0),X1)
| ~ le(X1,n)
| ~ le(s(X1),X2)
| ~ le(X2,n)
| ~ queens_p ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_78,plain,
minus(minus(s(n),esk2_0),minus(s(n),esk1_0)) = minus(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_70,c_0_39]) ).
cnf(c_0_79,plain,
minus(X1,perm(perm(X2))) = minus(X1,X2),
inference(spm,[status(thm)],[c_0_60,c_0_71]) ).
cnf(c_0_80,plain,
( plus(X1,X2) = plus(X3,X2)
| minus(X1,X3) != minus(X4,X4) ),
inference(spm,[status(thm)],[c_0_44,c_0_72]) ).
cnf(c_0_81,plain,
plus(X1,perm(perm(X2))) = plus(X2,perm(perm(X1))),
inference(er,[status(thm)],[c_0_73]) ).
cnf(c_0_82,plain,
( minus(X1,minus(s(n),esk1_0)) = minus(X2,minus(s(n),esk2_0))
| minus(X1,X2) != minus(esk2_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_59,c_0_74]) ).
cnf(c_0_83,negated_conjecture,
( minus(p(minus(s(n),esk1_0)),p(minus(s(n),esk2_0))) = minus(esk2_0,esk1_0)
| minus(p(minus(s(n),esk2_0)),esk2_0) = minus(p(minus(s(n),esk1_0)),esk1_0) ),
inference(er,[status(thm)],[c_0_75]) ).
cnf(c_0_84,plain,
minus(p(minus(s(n),esk2_0)),minus(s(n),esk2_0)) != minus(p(minus(s(n),esk1_0)),minus(s(n),esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_56]),c_0_57]),c_0_58])]) ).
cnf(c_0_85,plain,
( plus(p(X1),X1) != plus(p(X2),X2)
| ~ le(s(n0),X1)
| ~ le(s(X1),X2)
| ~ le(X2,n)
| ~ le(X1,n) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_37])]) ).
cnf(c_0_86,plain,
( plus(X1,minus(s(n),esk1_0)) = plus(X2,minus(s(n),esk2_0))
| minus(X1,X2) != minus(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_78]) ).
cnf(c_0_87,plain,
minus(perm(X1),X2) = minus(perm(X2),X1),
inference(spm,[status(thm)],[c_0_60,c_0_79]) ).
cnf(c_0_88,plain,
( plus(X1,X2) = plus(perm(X3),X2)
| minus(X3,perm(X1)) != minus(X4,X4) ),
inference(spm,[status(thm)],[c_0_80,c_0_71]) ).
cnf(c_0_89,plain,
plus(perm(perm(X1)),X2) = plus(X1,perm(perm(X2))),
inference(spm,[status(thm)],[c_0_54,c_0_81]) ).
cnf(c_0_90,negated_conjecture,
minus(p(minus(s(n),esk2_0)),esk2_0) = minus(p(minus(s(n),esk1_0)),esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84]) ).
cnf(c_0_91,plain,
( plus(X1,p(X1)) != plus(X2,p(X2))
| ~ le(s(n0),X1)
| ~ le(s(X1),X2)
| ~ le(X2,n)
| ~ le(X1,n) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_54]),c_0_54]) ).
cnf(c_0_92,plain,
( plus(minus(s(n),esk1_0),perm(X1)) = plus(X2,minus(s(n),esk2_0))
| minus(perm(X2),X1) != minus(esk1_0,esk2_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_54]) ).
cnf(c_0_93,plain,
plus(X1,perm(perm(X2))) = plus(X1,X2),
inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_88]),c_0_89]) ).
cnf(c_0_94,negated_conjecture,
( minus(X1,p(minus(s(n),esk2_0))) = minus(X2,esk2_0)
| minus(X1,X2) != minus(p(minus(s(n),esk1_0)),esk1_0) ),
inference(spm,[status(thm)],[c_0_59,c_0_90]) ).
cnf(c_0_95,plain,
( plus(X1,p(X1)) != plus(minus(s(n),esk1_0),p(minus(s(n),esk1_0)))
| ~ le(s(X1),minus(s(n),esk1_0))
| ~ le(s(n0),X1)
| ~ le(X1,n) ),
inference(spm,[status(thm)],[c_0_91,c_0_46]) ).
cnf(c_0_96,plain,
( plus(minus(s(n),esk1_0),X1) = plus(X2,minus(s(n),esk2_0))
| minus(X1,X2) != minus(esk1_0,esk2_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_71]),c_0_93]),c_0_79]) ).
cnf(c_0_97,negated_conjecture,
minus(p(minus(s(n),esk1_0)),p(minus(s(n),esk2_0))) = minus(esk1_0,esk2_0),
inference(er,[status(thm)],[c_0_94]) ).
cnf(c_0_98,plain,
plus(minus(s(n),esk2_0),p(minus(s(n),esk2_0))) != plus(minus(s(n),esk1_0),p(minus(s(n),esk1_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_56]),c_0_57]),c_0_58])]) ).
cnf(c_0_99,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_54]),c_0_98]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ133+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
% 0.14/0.33 % Computer : n004.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 01:36:33 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 6.20/4.42 % Version : CSE_E---1.7
% 6.20/4.42 % Problem : theBenchmark.p
% 6.20/4.42 % SZS status Theorem for theBenchmark.p
% 6.20/4.42 % SZS output start CNFRefutation
% See solution above
% 6.20/4.43 % Total time : 3.372s
%------------------------------------------------------------------------------