%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : PUZ133+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:01:58 PM UTC 2026
% Result : Theorem 20.84s 3.57s
% Output : CNFRefutation 20.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 10
% Syntax : Number of formulae : 121 ( 41 unt; 0 def)
% Number of atoms : 344 ( 159 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 367 ( 144 ~; 165 |; 41 &)
% ( 4 <=>; 13 =>; 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 : 144 ( 0 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(queens_q,axiom,
( ! [X1,X2] :
( ( ( le(s(X1),X2)
<=> le(s(perm(X2)),perm(X1)) )
& le(X2,n)
& le(s(X1),X2)
& le(X1,n)
& le(s(n0),X1) )
=> ( minus(q(X1),X1) != minus(q(X2),X2)
& plus(q(X1),X1) != plus(q(X2),X2)
& q(X1) != q(X2) ) )
=> queens_q ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',queens_q) ).
fof(queens_sym,conjecture,
( ( ! [X1] : q(X1) = p(perm(X1))
& queens_p )
=> queens_q ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',queens_sym) ).
fof(le_trans,axiom,
! [X3,X4,X5] :
( ( le(X4,X5)
& le(X3,X4) )
=> 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(X1,n)
& le(s(n0),X1) )
=> ( le(perm(X1),n)
& le(s(n0),perm(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',permutation_range) ).
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(queens_p,axiom,
( queens_p
=> ! [X1,X2] :
( ( le(X2,n)
& le(s(X1),X2)
& le(X1,n)
& le(s(n0),X1) )
=> ( minus(p(X1),X1) != minus(p(X2),X2)
& plus(p(X1),X1) != plus(p(X2),X2)
& p(X1) != p(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',queens_p) ).
fof(permutation,axiom,
! [X1] :
( ( le(X1,n)
& le(s(n0),X1) )
=> perm(X1) = minus(s(n),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',permutation) ).
fof(c_0_10,plain,
( ! [X1,X2] :
( ( ( le(s(X1),X2)
<=> le(s(perm(X2)),perm(X1)) )
& le(X2,n)
& le(s(X1),X2)
& le(X1,n)
& le(s(n0),X1) )
=> ( minus(q(X1),X1) != minus(q(X2),X2)
& plus(q(X1),X1) != plus(q(X2),X2)
& q(X1) != q(X2) ) )
=> queens_q ),
inference(fof_simplification,[status(thm)],[queens_q]) ).
fof(c_0_11,negated_conjecture,
~ ( ( ! [X1] : q(X1) = p(perm(X1))
& queens_p )
=> queens_q ),
inference(assume_negation,[status(cth)],[queens_sym]) ).
fof(c_0_12,plain,
( ( queens_q
| minus(q(esk1_0),esk1_0) = minus(q(esk2_0),esk2_0)
| plus(q(esk1_0),esk1_0) = plus(q(esk2_0),esk2_0)
| q(esk1_0) = q(esk2_0) )
& ( 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
| le(esk2_0,n) )
& ( queens_q
| le(s(esk1_0),esk2_0) )
& ( queens_q
| le(esk1_0,n) )
& ( queens_q
| le(s(n0),esk1_0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])]) ).
fof(c_0_13,negated_conjecture,
! [X13] :
( ~ queens_q
& q(X13) = p(perm(X13))
& queens_p ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
fof(c_0_14,plain,
! [X17,X18,X19] :
( le(X17,X19)
| ~ le(X18,X19)
| ~ le(X17,X18) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[le_trans])])]) ).
cnf(c_0_15,plain,
( queens_q
| le(s(esk1_0),esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
~ queens_q,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
( ~ le(X2,X3)
| ~ le(X1,X2)
| le(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
le(s(esk1_0),esk2_0),
inference(sr,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_19,plain,
! [X20] : le(X20,s(X20)),
inference(variable_rename,[status(thm)],[succ_le]) ).
cnf(c_0_20,plain,
( ~ le(X1,s(esk1_0))
| le(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
le(X1,s(X1)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_22,plain,
le(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,plain,
( queens_q
| le(s(n0),esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_24,plain,
! [X14] :
( ( ~ le(X14,n)
| ~ le(s(n0),X14)
| le(perm(X14),n) )
& ( ~ le(X14,n)
| ~ le(s(n0),X14)
| le(s(n0),perm(X14)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[permutation_range])])])]) ).
cnf(c_0_25,plain,
( queens_q
| le(esk2_0,n) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_26,plain,
( ~ le(X1,esk1_0)
| le(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_22]) ).
cnf(c_0_27,plain,
le(s(n0),esk1_0),
inference(sr,[status(thm)],[c_0_23,c_0_16]) ).
cnf(c_0_28,plain,
( queens_q
| minus(q(esk1_0),esk1_0) = minus(q(esk2_0),esk2_0)
| plus(q(esk1_0),esk1_0) = plus(q(esk2_0),esk2_0)
| q(esk1_0) = q(esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_29,negated_conjecture,
q(X1) = p(perm(X1)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_30,plain,
! [X21,X22,X23,X24] :
( ( plus(X21,X22) = plus(X23,X24)
| minus(X21,X23) != minus(X24,X22) )
& ( minus(X21,X23) = minus(X24,X22)
| plus(X21,X22) != plus(X23,X24) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[plus1])])]) ).
cnf(c_0_31,plain,
( ~ le(X1,n)
| ~ le(s(n0),X1)
| le(perm(X1),n) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,plain,
le(esk2_0,n),
inference(sr,[status(thm)],[c_0_25,c_0_16]) ).
cnf(c_0_33,plain,
le(s(n0),esk2_0),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_34,plain,
! [X25,X26,X27,X28] :
( ( minus(X25,X26) = minus(X27,X28)
| minus(X25,X27) != minus(X26,X28) )
& ( minus(X25,X27) = minus(X26,X28)
| minus(X25,X26) != minus(X27,X28) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[minus1])])]) ).
fof(c_0_35,plain,
! [X15,X16] : minus(X16,X15) = minus(perm(X15),perm(X16)),
inference(variable_rename,[status(thm)],[permutation_another_one]) ).
cnf(c_0_36,negated_conjecture,
( queens_q
| 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(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_28,c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_29]) ).
cnf(c_0_37,plain,
( minus(X1,X2) != minus(X3,X4)
| plus(X1,X4) = plus(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_38,plain,
le(perm(esk2_0),n),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_39,plain,
( ~ le(X1,n)
| ~ le(s(n0),X1)
| le(s(n0),perm(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_40,plain,
( queens_q
| le(esk1_0,n) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_41,plain,
( minus(X1,X2) != minus(X3,X4)
| minus(X1,X3) = minus(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,plain,
minus(X1,X2) = minus(perm(X2),perm(X1)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
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) ),
inference(sr,[status(thm)],[c_0_36,c_0_16]) ).
cnf(c_0_44,plain,
plus(X1,X2) = plus(X2,X1),
inference(er,[status(thm)],[c_0_37]) ).
fof(c_0_45,plain,
( queens_p
=> ! [X1,X2] :
( ( le(X2,n)
& le(s(X1),X2)
& le(X1,n)
& le(s(n0),X1) )
=> ( minus(p(X1),X1) != minus(p(X2),X2)
& plus(p(X1),X1) != plus(p(X2),X2)
& p(X1) != p(X2) ) ) ),
inference(fof_simplification,[status(thm)],[queens_p]) ).
fof(c_0_46,plain,
! [X10] :
( perm(X10) = minus(s(n),X10)
| ~ le(X10,n)
| ~ le(s(n0),X10) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[permutation])])]) ).
cnf(c_0_47,plain,
( ~ le(s(n0),perm(esk2_0))
| le(perm(perm(esk2_0)),n) ),
inference(spm,[status(thm)],[c_0_31,c_0_38]) ).
cnf(c_0_48,plain,
le(s(n0),perm(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_32]),c_0_33])]) ).
cnf(c_0_49,plain,
le(esk1_0,n),
inference(sr,[status(thm)],[c_0_40,c_0_16]) ).
cnf(c_0_50,plain,
( minus(X1,X3) != minus(X4,X2)
| minus(X1,perm(X2)) = minus(X3,perm(X4)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_51,plain,
( plus(X1,X2) != plus(X3,X4)
| minus(X1,X3) = minus(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_52,negated_conjecture,
( p(perm(esk2_0)) = p(perm(esk1_0))
| plus(esk2_0,p(perm(esk2_0))) = plus(esk1_0,p(perm(esk1_0)))
| minus(p(perm(esk2_0)),esk2_0) = minus(p(perm(esk1_0)),esk1_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44]),c_0_44]) ).
fof(c_0_53,plain,
! [X8,X9] :
( ( ~ queens_p
| ~ le(X9,n)
| ~ le(s(X8),X9)
| ~ le(X8,n)
| ~ le(s(n0),X8)
| minus(p(X8),X8) != minus(p(X9),X9) )
& ( ~ queens_p
| ~ le(X9,n)
| ~ le(s(X8),X9)
| ~ le(X8,n)
| ~ le(s(n0),X8)
| plus(p(X8),X8) != plus(p(X9),X9) )
& ( ~ queens_p
| ~ le(X9,n)
| ~ le(s(X8),X9)
| ~ le(X8,n)
| ~ le(s(n0),X8)
| p(X8) != p(X9) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])])]) ).
cnf(c_0_54,plain,
( ~ le(X1,n)
| ~ le(s(n0),X1)
| perm(X1) = minus(s(n),X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_55,plain,
le(perm(perm(esk2_0)),n),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]) ).
cnf(c_0_56,plain,
le(perm(esk1_0),n),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_49]),c_0_27])]) ).
cnf(c_0_57,plain,
( minus(X1,X3) != minus(X2,X4)
| plus(X1,perm(X2)) = plus(X3,perm(X4)) ),
inference(spm,[status(thm)],[c_0_37,c_0_42]) ).
cnf(c_0_58,plain,
minus(X1,perm(X2)) = minus(X2,perm(X1)),
inference(er,[status(thm)],[c_0_50]) ).
cnf(c_0_59,negated_conjecture,
( plus(X1,X2) != plus(esk1_0,p(perm(esk1_0)))
| p(perm(esk2_0)) = p(perm(esk1_0))
| minus(X1,esk2_0) = minus(p(perm(esk2_0)),X2)
| minus(p(perm(esk2_0)),esk2_0) = minus(p(perm(esk1_0)),esk1_0) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_60,plain,
( ~ queens_p
| ~ le(X2,n)
| ~ le(s(X1),X2)
| ~ le(X1,n)
| ~ le(s(n0),X1)
| minus(p(X1),X1) != minus(p(X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_61,negated_conjecture,
queens_p,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_62,plain,
( ~ le(s(n0),perm(perm(esk2_0)))
| minus(s(n),perm(perm(esk2_0))) = perm(perm(perm(esk2_0))) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_63,plain,
le(s(n0),perm(perm(esk2_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_38]),c_0_48])]) ).
cnf(c_0_64,plain,
( ~ le(s(n0),perm(esk1_0))
| le(perm(perm(esk1_0)),n) ),
inference(spm,[status(thm)],[c_0_31,c_0_56]) ).
cnf(c_0_65,plain,
le(s(n0),perm(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_49]),c_0_27])]) ).
cnf(c_0_66,plain,
( minus(X1,X3) != minus(X4,X2)
| plus(X1,perm(perm(X2))) = plus(X3,perm(perm(X4))) ),
inference(spm,[status(thm)],[c_0_57,c_0_42]) ).
cnf(c_0_67,plain,
minus(X1,perm(perm(X2))) = minus(X1,X2),
inference(spm,[status(thm)],[c_0_42,c_0_58]) ).
cnf(c_0_68,negated_conjecture,
( plus(X2,X1) != plus(esk1_0,p(perm(esk1_0)))
| p(perm(esk2_0)) = p(perm(esk1_0))
| minus(X1,esk2_0) = minus(p(perm(esk2_0)),X2)
| minus(p(perm(esk2_0)),esk2_0) = minus(p(perm(esk1_0)),esk1_0) ),
inference(spm,[status(thm)],[c_0_59,c_0_44]) ).
cnf(c_0_69,plain,
( ~ le(X1,n)
| ~ le(X2,n)
| ~ le(s(X1),X2)
| ~ le(s(n0),X1)
| minus(p(X1),X1) != minus(p(X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61])]) ).
cnf(c_0_70,plain,
minus(s(n),perm(perm(esk2_0))) = perm(perm(perm(esk2_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63])]) ).
cnf(c_0_71,plain,
minus(s(n),esk2_0) = perm(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_32]),c_0_33])]) ).
cnf(c_0_72,plain,
le(perm(perm(esk1_0)),n),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65])]) ).
cnf(c_0_73,plain,
( ~ queens_p
| ~ le(X2,n)
| ~ le(s(X1),X2)
| ~ le(X1,n)
| ~ le(s(n0),X1)
| plus(p(X1),X1) != plus(p(X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_74,plain,
plus(X1,perm(perm(X2))) = plus(X2,perm(perm(X1))),
inference(er,[status(thm)],[c_0_66]) ).
cnf(c_0_75,plain,
( minus(X1,X3) != minus(X4,X2)
| plus(X1,perm(perm(X2))) = plus(X3,X4) ),
inference(spm,[status(thm)],[c_0_37,c_0_67]) ).
cnf(c_0_76,negated_conjecture,
( p(perm(esk2_0)) = p(perm(esk1_0))
| minus(p(perm(esk2_0)),esk2_0) = minus(p(perm(esk1_0)),esk1_0)
| minus(p(perm(esk2_0)),esk1_0) = minus(p(perm(esk1_0)),esk2_0) ),
inference(er,[status(thm)],[c_0_68]) ).
cnf(c_0_77,plain,
( ~ le(X2,n)
| ~ le(perm(X1),n)
| ~ le(s(perm(X1)),X2)
| ~ le(s(n0),perm(X1))
| minus(X1,perm(p(perm(X1)))) != minus(p(X2),X2) ),
inference(spm,[status(thm)],[c_0_69,c_0_58]) ).
cnf(c_0_78,plain,
perm(perm(perm(esk2_0))) = perm(esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_67]),c_0_71]) ).
cnf(c_0_79,plain,
( ~ le(s(n0),perm(perm(esk1_0)))
| minus(s(n),perm(perm(esk1_0))) = perm(perm(perm(esk1_0))) ),
inference(spm,[status(thm)],[c_0_54,c_0_72]) ).
cnf(c_0_80,plain,
le(s(n0),perm(perm(esk1_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_56]),c_0_65])]) ).
cnf(c_0_81,plain,
( ~ le(X1,n)
| ~ le(X2,n)
| ~ le(s(X1),X2)
| ~ le(s(n0),X1)
| plus(p(X1),X1) != plus(p(X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_61])]) ).
cnf(c_0_82,plain,
plus(perm(perm(X1)),X2) = plus(X1,perm(perm(X2))),
inference(spm,[status(thm)],[c_0_44,c_0_74]) ).
cnf(c_0_83,plain,
plus(X1,perm(perm(X2))) = plus(X2,X1),
inference(er,[status(thm)],[c_0_75]) ).
cnf(c_0_84,negated_conjecture,
( minus(p(perm(esk1_0)),esk1_0) != minus(X1,X2)
| p(perm(esk2_0)) = p(perm(esk1_0))
| minus(p(perm(esk2_0)),X1) = minus(esk2_0,X2)
| minus(p(perm(esk2_0)),esk1_0) = minus(p(perm(esk1_0)),esk2_0) ),
inference(spm,[status(thm)],[c_0_41,c_0_76]) ).
cnf(c_0_85,negated_conjecture,
( p(perm(esk2_0)) = p(perm(esk1_0))
| minus(p(perm(esk2_0)),esk2_0) = minus(p(perm(esk1_0)),esk1_0)
| minus(p(perm(esk2_0)),p(perm(esk1_0))) = minus(esk1_0,esk2_0) ),
inference(er,[status(thm)],[c_0_59]) ).
cnf(c_0_86,plain,
( ~ le(X1,n)
| ~ le(s(perm(esk2_0)),X1)
| minus(esk2_0,perm(p(perm(esk2_0)))) != minus(p(X1),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_42]),c_0_58]),c_0_48]),c_0_38])]) ).
cnf(c_0_87,plain,
minus(s(n),perm(perm(esk1_0))) = perm(perm(perm(esk1_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80])]) ).
cnf(c_0_88,plain,
minus(s(n),esk1_0) = perm(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_49]),c_0_27])]) ).
cnf(c_0_89,plain,
( ~ le(s(esk1_0),esk2_0)
| queens_q
| le(s(perm(esk2_0)),perm(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_90,plain,
( ~ le(X1,n)
| ~ le(X2,n)
| ~ le(s(X1),X2)
| ~ le(s(n0),X1)
| plus(X1,p(X1)) != plus(X2,p(X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_44]),c_0_44]) ).
cnf(c_0_91,plain,
plus(perm(perm(X1)),X2) = plus(X2,X1),
inference(rw,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_92,plain,
( minus(X3,X1) != minus(X4,X2)
| plus(perm(X1),X2) = plus(perm(X3),X4) ),
inference(spm,[status(thm)],[c_0_37,c_0_42]) ).
cnf(c_0_93,negated_conjecture,
( p(perm(esk2_0)) = p(perm(esk1_0))
| minus(p(perm(esk2_0)),esk1_0) = minus(p(perm(esk1_0)),esk2_0)
| minus(p(perm(esk2_0)),p(perm(esk1_0))) = minus(esk2_0,esk1_0) ),
inference(er,[status(thm)],[c_0_84]) ).
cnf(c_0_94,negated_conjecture,
( minus(X1,X2) != minus(esk1_0,esk2_0)
| p(perm(esk2_0)) = p(perm(esk1_0))
| minus(p(perm(esk2_0)),esk2_0) = minus(p(perm(esk1_0)),esk1_0)
| minus(X1,perm(p(perm(esk1_0)))) = minus(X2,perm(p(perm(esk2_0)))) ),
inference(spm,[status(thm)],[c_0_50,c_0_85]) ).
cnf(c_0_95,plain,
( ~ le(perm(perm(X1)),n)
| ~ le(s(perm(esk2_0)),perm(perm(X1)))
| minus(p(perm(perm(X1))),X1) != minus(esk2_0,perm(p(perm(esk2_0)))) ),
inference(spm,[status(thm)],[c_0_86,c_0_67]) ).
cnf(c_0_96,plain,
perm(perm(perm(esk1_0))) = perm(esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_67]),c_0_88]) ).
cnf(c_0_97,plain,
le(s(perm(esk2_0)),perm(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_18])]),c_0_16]) ).
cnf(c_0_98,plain,
( ~ le(X1,n)
| ~ le(s(n0),X1)
| ~ le(perm(perm(X2)),n)
| ~ le(s(X1),perm(perm(X2)))
| plus(X1,p(X1)) != plus(X2,p(perm(perm(X2)))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_44]) ).
cnf(c_0_99,negated_conjecture,
( minus(X2,X1) != minus(esk2_0,esk1_0)
| p(perm(esk2_0)) = p(perm(esk1_0))
| minus(p(perm(esk2_0)),esk1_0) = minus(p(perm(esk1_0)),esk2_0)
| plus(perm(X1),p(perm(esk1_0))) = plus(perm(X2),p(perm(esk2_0))) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_100,negated_conjecture,
( p(perm(esk2_0)) = p(perm(esk1_0))
| minus(p(perm(esk2_0)),esk2_0) = minus(p(perm(esk1_0)),esk1_0)
| minus(esk2_0,perm(p(perm(esk2_0)))) = minus(esk1_0,perm(p(perm(esk1_0)))) ),
inference(er,[status(thm)],[c_0_94]) ).
cnf(c_0_101,plain,
minus(esk2_0,perm(p(perm(esk2_0)))) != minus(esk1_0,perm(p(perm(esk1_0)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_58]),c_0_97]),c_0_56])]) ).
cnf(c_0_102,plain,
( ~ le(X1,n)
| ~ le(s(n0),X1)
| ~ le(s(X1),perm(esk1_0))
| plus(X1,p(X1)) != plus(perm(esk1_0),p(perm(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_96]),c_0_56])]) ).
cnf(c_0_103,negated_conjecture,
( p(perm(esk2_0)) = p(perm(esk1_0))
| minus(p(perm(esk2_0)),esk1_0) = minus(p(perm(esk1_0)),esk2_0)
| plus(perm(esk2_0),p(perm(esk2_0))) = plus(perm(esk1_0),p(perm(esk1_0))) ),
inference(er,[status(thm)],[c_0_99]) ).
cnf(c_0_104,negated_conjecture,
( p(perm(esk2_0)) = p(perm(esk1_0))
| minus(p(perm(esk2_0)),esk2_0) = minus(p(perm(esk1_0)),esk1_0) ),
inference(sr,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_105,negated_conjecture,
( p(perm(esk2_0)) = p(perm(esk1_0))
| minus(p(perm(esk2_0)),esk1_0) = minus(p(perm(esk1_0)),esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_97]),c_0_48]),c_0_38])]) ).
cnf(c_0_106,negated_conjecture,
( minus(p(perm(esk1_0)),esk1_0) != minus(X1,X2)
| p(perm(esk2_0)) = p(perm(esk1_0))
| minus(p(perm(esk2_0)),X1) = minus(esk2_0,X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_104]) ).
cnf(c_0_107,negated_conjecture,
( minus(p(perm(esk1_0)),esk2_0) != minus(X1,X2)
| p(perm(esk2_0)) = p(perm(esk1_0))
| minus(p(perm(esk2_0)),X1) = minus(esk1_0,X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_105]) ).
cnf(c_0_108,plain,
( ~ queens_p
| ~ le(X2,n)
| ~ le(s(X1),X2)
| ~ le(X1,n)
| ~ le(s(n0),X1)
| p(X1) != p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_109,negated_conjecture,
( p(perm(esk2_0)) = p(perm(esk1_0))
| minus(p(perm(esk2_0)),p(perm(esk1_0))) = minus(esk2_0,esk1_0) ),
inference(er,[status(thm)],[c_0_106]) ).
cnf(c_0_110,negated_conjecture,
( p(perm(esk2_0)) = p(perm(esk1_0))
| minus(p(perm(esk2_0)),p(perm(esk1_0))) = minus(esk1_0,esk2_0) ),
inference(er,[status(thm)],[c_0_107]) ).
cnf(c_0_111,plain,
( ~ le(X1,n)
| ~ le(X2,n)
| ~ le(s(X1),X2)
| ~ le(s(n0),X1)
| p(X1) != p(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_61])]) ).
cnf(c_0_112,negated_conjecture,
( minus(esk2_0,esk1_0) = minus(esk1_0,esk2_0)
| p(perm(esk2_0)) = p(perm(esk1_0)) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_113,negated_conjecture,
( ~ le(X1,n)
| ~ le(s(perm(esk2_0)),X1)
| p(perm(esk1_0)) != p(X1)
| minus(esk2_0,esk1_0) = minus(esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_48]),c_0_38])]) ).
cnf(c_0_114,negated_conjecture,
minus(esk2_0,esk1_0) = minus(esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_113]),c_0_97]),c_0_56])]) ).
cnf(c_0_115,negated_conjecture,
( minus(X1,X2) != minus(p(perm(esk1_0)),esk1_0)
| p(perm(esk2_0)) = p(perm(esk1_0))
| minus(X1,p(perm(esk2_0))) = minus(X2,esk2_0) ),
inference(spm,[status(thm)],[c_0_41,c_0_104]) ).
cnf(c_0_116,negated_conjecture,
( minus(X1,X2) != minus(esk1_0,esk2_0)
| minus(X1,perm(esk1_0)) = minus(X2,perm(esk2_0)) ),
inference(spm,[status(thm)],[c_0_50,c_0_114]) ).
cnf(c_0_117,negated_conjecture,
( p(perm(esk2_0)) = p(perm(esk1_0))
| minus(p(perm(esk1_0)),p(perm(esk2_0))) = minus(esk1_0,esk2_0) ),
inference(er,[status(thm)],[c_0_115]) ).
cnf(c_0_118,negated_conjecture,
p(perm(esk2_0)) = p(perm(esk1_0)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_58]),c_0_58]),c_0_101]) ).
cnf(c_0_119,negated_conjecture,
( ~ le(X1,n)
| ~ le(s(perm(esk2_0)),X1)
| p(perm(esk1_0)) != p(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_118]),c_0_48]),c_0_38])]) ).
cnf(c_0_120,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_119]),c_0_97]),c_0_56])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ133+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 03:53:45 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.84/3.57 % Version: 3.5.1
% 20.84/3.57 % Preprocessing class: FSMSSLSSSSSNFFN.
% 20.84/3.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 20.84/3.57 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 20.84/3.57 % Starting new_bool_3 with 300s (1) cores
% 20.84/3.57 % Starting new_bool_1 with 300s (1) cores
% 20.84/3.57 % Starting sh5l with 300s (1) cores
% 20.84/3.57 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 3348270 completed with status 0
% 20.84/3.57 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 20.84/3.57 % Preprocessing class: FSMSSLSSSSSNFFN.
% 20.84/3.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 20.84/3.57 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 20.84/3.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 20.84/3.57 % No SInE strategy applied
% 20.84/3.57 % Search class: FGHSS-FFMM21-MFFFFFNN
% 20.84/3.57 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 20.84/3.57 % Starting SubtermCWHack with 136s (1) cores
% 20.84/3.57 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 151s (1) cores
% 20.84/3.57 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 20.84/3.57 % Starting new_bool_3 with 136s (1) cores
% 20.84/3.57 % Starting new_bool_1 with 136s (1) cores
% 20.84/3.57 % new_bool_1 with pid 3348280 completed with status 0
% 20.84/3.57 % Result found by new_bool_1
% 20.84/3.57 % Preprocessing class: FSMSSLSSSSSNFFN.
% 20.84/3.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 20.84/3.57 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 20.84/3.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 20.84/3.57 % No SInE strategy applied
% 20.84/3.57 % Search class: FGHSS-FFMM21-MFFFFFNN
% 20.84/3.57 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 20.84/3.57 % Starting SubtermCWHack with 136s (1) cores
% 20.84/3.57 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 151s (1) cores
% 20.84/3.57 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 20.84/3.57 % Starting new_bool_3 with 136s (1) cores
% 20.84/3.57 % Starting new_bool_1 with 136s (1) cores
% 20.84/3.57 % Preprocessing time : 0.001 s
% 20.84/3.57 % Presaturation interreduction done
% 20.84/3.57
% 20.84/3.57 % Proof found!
% 20.84/3.57 % SZS status Theorem
% 20.84/3.57 % SZS output start CNFRefutation
% See solution above
% 20.84/3.57 % Parsed axioms : 10
% 20.84/3.57 % Removed by relevancy pruning/SinE : 0
% 20.84/3.57 % Initial clauses : 23
% 20.84/3.57 % Removed in clause preprocessing : 1
% 20.84/3.57 % Initial clauses in saturation : 22
% 20.84/3.57 % Processed clauses : 22250
% 20.84/3.57 % ...of these trivial : 448
% 20.84/3.57 % ...subsumed : 17559
% 20.84/3.57 % ...remaining for further processing : 4243
% 20.84/3.57 % Other redundant clauses eliminated : 0
% 20.84/3.57 % Clauses deleted for lack of memory : 0
% 20.84/3.57 % Backward-subsumed : 1584
% 20.84/3.57 % Backward-rewritten : 782
% 20.84/3.57 % Generated clauses : 33198
% 20.84/3.57 % ...of the previous two non-redundant : 32456
% 20.84/3.57 % ...aggressively subsumed : 0
% 20.84/3.57 % Contextual simplify-reflections : 0
% 20.84/3.57 % Paramodulations : 32724
% 20.84/3.57 % Factorizations : 0
% 20.84/3.57 % NegExts : 0
% 20.84/3.57 % Equation resolutions : 473
% 20.84/3.57 % Disequality decompositions : 0
% 20.84/3.57 % Total rewrite steps : 28977
% 20.84/3.57 % ...of those cached : 27620
% 20.84/3.57 % Propositional unsat checks : 0
% 20.84/3.57 % Propositional check models : 0
% 20.84/3.57 % Propositional check unsatisfiable : 0
% 20.84/3.57 % Propositional clauses : 0
% 20.84/3.57 % Propositional clauses after purity: 0
% 20.84/3.57 % Propositional unsat core size : 0
% 20.84/3.57 % Propositional preprocessing time : 0.000
% 20.84/3.57 % Propositional encoding time : 0.000
% 20.84/3.57 % Propositional solver time : 0.000
% 20.84/3.57 % Success case prop preproc time : 0.000
% 20.84/3.57 % Success case prop encoding time : 0.000
% 20.84/3.57 % Success case prop solver time : 0.000
% 20.84/3.57 % Current number of processed clauses : 1856
% 20.84/3.57 % Positive orientable unit clauses : 304
% 20.84/3.57 % Positive unorientable unit clauses: 5
% 20.84/3.57 % Negative unit clauses : 17
% 20.84/3.57 % Non-unit-clauses : 1530
% 20.84/3.57 % Current number of unprocessed clauses: 7031
% 20.84/3.57 % ...number of literals in the above : 21902
% 20.84/3.57 % Current number of archived formulas : 0
% 20.84/3.57 % Current number of archived clauses : 2388
% 20.84/3.57 % Clause-clause subsumption calls (NU) : 2895832
% 20.84/3.57 % Rec. Clause-clause subsumption calls : 1613860
% 20.84/3.57 % Non-unit clause-clause subsumptions : 18562
% 20.84/3.57 % Unit Clause-clause subsumption calls : 11228
% 20.84/3.57 % Rewrite failures with RHS unbound : 135
% 20.84/3.57 % BW rewrite match attempts : 4498
% 20.84/3.57 % BW rewrite match successes : 143
% 20.84/3.57 % Condensation attempts : 0
% 20.84/3.57 % Condensation successes : 0
% 20.84/3.57 % Termbank termtop insertions : 687610
% 20.84/3.57 % Search garbage collected termcells : 362
% 20.84/3.57
% 20.84/3.57 % -------------------------------------------------
% 20.84/3.57 % User time : 2.534 s
% 20.84/3.57 % System time : 0.023 s
% 20.84/3.57 % Total time : 2.557 s
% 20.84/3.57 % Maximum resident set size: 3644 pages
% 20.84/3.57
% 20.84/3.57 % -------------------------------------------------
% 20.84/3.57 % User time : 14.022 s
% 20.84/3.57 % System time : 0.329 s
% 20.84/3.57 % Total time : 14.351 s
% 20.84/3.57 % Maximum resident set size: 4608 pages
% 20.84/3.57 % E exiting
%------------------------------------------------------------------------------