%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : PUZ133+1 : 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 : n007.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 02:01:57 PM UTC 2026
% Result : Theorem 23.88s 4.54s
% Output : CNFRefutation 23.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 86 ( 29 unt; 0 def)
% Number of atoms : 267 ( 102 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 299 ( 118 ~; 125 |; 40 &)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 6 ( 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 : 110 ( 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(permutation,axiom,
! [X1] : perm(X1) = minus(s(n),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',permutation) ).
fof(succ_le,axiom,
! [X3] : le(X3,s(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_le) ).
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(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_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(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(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(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]) ).
fof(c_0_17,plain,
! [X10] : perm(X10) = minus(s(n),X10),
inference(variable_rename,[status(thm)],[permutation]) ).
cnf(c_0_18,plain,
( ~ le(X2,X3)
| ~ le(X1,X2)
| le(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
le(s(esk1_0),esk2_0),
inference(sr,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_20,plain,
! [X20] : le(X20,s(X20)),
inference(variable_rename,[status(thm)],[succ_le]) ).
cnf(c_0_21,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_22,negated_conjecture,
q(X1) = p(perm(X1)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_23,plain,
perm(X1) = minus(s(n),X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_24,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])])]) ).
fof(c_0_25,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_26,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_27,plain,
( ~ le(X1,s(esk1_0))
| le(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_28,plain,
le(X1,s(X1)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,negated_conjecture,
( queens_q
| minus(p(minus(s(n),esk2_0)),esk2_0) = minus(p(minus(s(n),esk1_0)),esk1_0)
| plus(p(minus(s(n),esk2_0)),esk2_0) = plus(p(minus(s(n),esk1_0)),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_22]),c_0_22]),c_0_22]),c_0_22]),c_0_22]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]) ).
cnf(c_0_30,plain,
( minus(X1,X2) != minus(X3,X4)
| plus(X1,X4) = plus(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_31,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_25])])])])]) ).
cnf(c_0_32,plain,
( ~ le(X1,n)
| ~ le(s(n0),X1)
| le(perm(X1),n) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
( queens_q
| le(esk1_0,n) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_34,plain,
( queens_q
| le(s(n0),esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_35,plain,
le(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_36,plain,
! [X15,X16] : minus(X16,X15) = minus(perm(X15),perm(X16)),
inference(variable_rename,[status(thm)],[permutation_another_one]) ).
cnf(c_0_37,negated_conjecture,
( p(minus(s(n),esk2_0)) = p(minus(s(n),esk1_0))
| plus(p(minus(s(n),esk2_0)),esk2_0) = plus(p(minus(s(n),esk1_0)),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_29,c_0_16]) ).
cnf(c_0_38,plain,
plus(X1,X2) = plus(X2,X1),
inference(er,[status(thm)],[c_0_30]) ).
cnf(c_0_39,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_31]) ).
cnf(c_0_40,negated_conjecture,
queens_p,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_41,plain,
( ~ le(s(n0),X1)
| ~ le(X1,n)
| le(minus(s(n),X1),n) ),
inference(rw,[status(thm)],[c_0_32,c_0_23]) ).
cnf(c_0_42,plain,
le(esk1_0,n),
inference(sr,[status(thm)],[c_0_33,c_0_16]) ).
cnf(c_0_43,plain,
le(s(n0),esk1_0),
inference(sr,[status(thm)],[c_0_34,c_0_16]) ).
cnf(c_0_44,plain,
( queens_q
| le(esk2_0,n) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_45,plain,
( ~ le(X1,esk1_0)
| le(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_35]) ).
cnf(c_0_46,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_47,plain,
( ~ le(X1,n)
| ~ le(s(n0),X1)
| le(s(n0),perm(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_48,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])])]) ).
cnf(c_0_49,plain,
minus(X1,X2) = minus(perm(X2),perm(X1)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_50,plain,
( plus(X1,X2) != plus(X3,X4)
| minus(X1,X3) = minus(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_51,negated_conjecture,
( p(minus(s(n),esk2_0)) = p(minus(s(n),esk1_0))
| 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(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38]),c_0_38]) ).
cnf(c_0_52,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_39,c_0_40])]) ).
cnf(c_0_53,plain,
le(minus(s(n),esk1_0),n),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).
cnf(c_0_54,plain,
le(esk2_0,n),
inference(sr,[status(thm)],[c_0_44,c_0_16]) ).
cnf(c_0_55,plain,
le(s(n0),esk2_0),
inference(spm,[status(thm)],[c_0_45,c_0_43]) ).
cnf(c_0_56,plain,
( ~ le(s(esk1_0),esk2_0)
| le(s(minus(s(n),esk2_0)),minus(s(n),esk1_0))
| queens_q ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_23]),c_0_23]) ).
cnf(c_0_57,plain,
( ~ le(s(n0),X1)
| ~ le(X1,n)
| le(s(n0),minus(s(n),X1)) ),
inference(rw,[status(thm)],[c_0_47,c_0_23]) ).
cnf(c_0_58,plain,
( minus(X1,X2) != minus(X3,X4)
| minus(X1,X3) = minus(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_59,plain,
minus(X1,X2) = minus(minus(s(n),X2),minus(s(n),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_23]),c_0_23]) ).
cnf(c_0_60,negated_conjecture,
( plus(X1,X2) != plus(esk1_0,p(minus(s(n),esk1_0)))
| minus(X1,esk2_0) = minus(p(minus(s(n),esk2_0)),X2)
| p(minus(s(n),esk2_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(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_61,plain,
( ~ le(X1,n)
| ~ le(s(n0),X1)
| ~ le(s(X1),minus(s(n),esk1_0))
| minus(p(X1),X1) != minus(p(minus(s(n),esk1_0)),minus(s(n),esk1_0)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_62,plain,
le(minus(s(n),esk2_0),n),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_54]),c_0_55])]) ).
cnf(c_0_63,plain,
le(s(minus(s(n),esk2_0)),minus(s(n),esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_19])]),c_0_16]) ).
cnf(c_0_64,plain,
le(s(n0),minus(s(n),esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_54]),c_0_55])]) ).
cnf(c_0_65,plain,
( minus(X1,X3) != minus(X4,X2)
| minus(X1,minus(s(n),X2)) = minus(X3,minus(s(n),X4)) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_66,negated_conjecture,
( p(minus(s(n),esk2_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)
| minus(p(minus(s(n),esk2_0)),p(minus(s(n),esk1_0))) = minus(esk1_0,esk2_0) ),
inference(er,[status(thm)],[c_0_60]) ).
cnf(c_0_67,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_61,c_0_62]),c_0_63]),c_0_64])]) ).
cnf(c_0_68,plain,
minus(X1,minus(s(n),X2)) = minus(X2,minus(s(n),X1)),
inference(er,[status(thm)],[c_0_65]) ).
cnf(c_0_69,negated_conjecture,
( minus(esk1_0,esk2_0) != minus(X2,X1)
| p(minus(s(n),esk2_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)
| minus(p(minus(s(n),esk2_0)),minus(s(n),X1)) = minus(p(minus(s(n),esk1_0)),minus(s(n),X2)) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_70,plain,
minus(esk2_0,minus(s(n),p(minus(s(n),esk2_0)))) != minus(esk1_0,minus(s(n),p(minus(s(n),esk1_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68]),c_0_68]) ).
cnf(c_0_71,negated_conjecture,
( p(minus(s(n),esk2_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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_69]),c_0_68]),c_0_68]),c_0_70]) ).
cnf(c_0_72,negated_conjecture,
( minus(p(minus(s(n),esk1_0)),esk1_0) != minus(X1,X2)
| minus(p(minus(s(n),esk2_0)),X1) = minus(esk2_0,X2)
| p(minus(s(n),esk2_0)) = p(minus(s(n),esk1_0)) ),
inference(spm,[status(thm)],[c_0_58,c_0_71]) ).
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_31]) ).
cnf(c_0_74,plain,
( minus(X1,X3) != minus(X2,X4)
| plus(X1,minus(s(n),X2)) = plus(X3,minus(s(n),X4)) ),
inference(spm,[status(thm)],[c_0_30,c_0_59]) ).
cnf(c_0_75,negated_conjecture,
( p(minus(s(n),esk2_0)) = p(minus(s(n),esk1_0))
| minus(p(minus(s(n),esk2_0)),p(minus(s(n),esk1_0))) = minus(esk2_0,esk1_0) ),
inference(er,[status(thm)],[c_0_72]) ).
cnf(c_0_76,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_40])]) ).
cnf(c_0_77,negated_conjecture,
( minus(esk2_0,esk1_0) != minus(X1,X2)
| p(minus(s(n),esk2_0)) = p(minus(s(n),esk1_0))
| plus(p(minus(s(n),esk2_0)),minus(s(n),X1)) = plus(p(minus(s(n),esk1_0)),minus(s(n),X2)) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_78,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_76,c_0_38]),c_0_38]) ).
cnf(c_0_79,negated_conjecture,
( p(minus(s(n),esk2_0)) = p(minus(s(n),esk1_0))
| 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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_77]),c_0_38]),c_0_38]) ).
cnf(c_0_80,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_31]) ).
cnf(c_0_81,negated_conjecture,
( ~ le(X1,n)
| ~ le(s(minus(s(n),esk2_0)),X1)
| plus(minus(s(n),esk1_0),p(minus(s(n),esk1_0))) != plus(X1,p(X1))
| 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_78,c_0_79]),c_0_64]),c_0_62])]) ).
cnf(c_0_82,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_80,c_0_40])]) ).
cnf(c_0_83,negated_conjecture,
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(er,[status(thm)],[c_0_81]),c_0_63]),c_0_53])]) ).
cnf(c_0_84,negated_conjecture,
( ~ le(X1,n)
| ~ le(s(minus(s(n),esk2_0)),X1)
| p(minus(s(n),esk1_0)) != p(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_64]),c_0_62])]) ).
cnf(c_0_85,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_84]),c_0_63]),c_0_53])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : PUZ133+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.43 % Computer : n007.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 03:50:05 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.51 Running first-order theorem proving
% 0.26/0.51 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
% 23.88/4.54 % Version: 3.5.1
% 23.88/4.54 % Preprocessing class: FSMSSLSSSSSNFFN.
% 23.88/4.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 23.88/4.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 23.88/4.54 % Starting new_bool_3 with 300s (1) cores
% 23.88/4.54 % Starting new_bool_1 with 300s (1) cores
% 23.88/4.54 % Starting sh5l with 300s (1) cores
% 23.88/4.54 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 108628 completed with status 0
% 23.88/4.54 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 23.88/4.54 % Preprocessing class: FSMSSLSSSSSNFFN.
% 23.88/4.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 23.88/4.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 23.88/4.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 23.88/4.54 % No SInE strategy applied
% 23.88/4.54 % Search class: FGHSS-FFMM21-MFFFFFNN
% 23.88/4.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 23.88/4.54 % Starting SubtermCWHack with 136s (1) cores
% 23.88/4.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 151s (1) cores
% 23.88/4.54 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 23.88/4.54 % Starting new_bool_3 with 136s (1) cores
% 23.88/4.54 % Starting new_bool_1 with 136s (1) cores
% 23.88/4.54 % new_bool_3 with pid 108637 completed with status 0
% 23.88/4.54 % Result found by new_bool_3
% 23.88/4.54 % Preprocessing class: FSMSSLSSSSSNFFN.
% 23.88/4.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 23.88/4.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 23.88/4.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 23.88/4.54 % No SInE strategy applied
% 23.88/4.54 % Search class: FGHSS-FFMM21-MFFFFFNN
% 23.88/4.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 23.88/4.54 % Starting SubtermCWHack with 136s (1) cores
% 23.88/4.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 151s (1) cores
% 23.88/4.54 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 23.88/4.54 % Starting new_bool_3 with 136s (1) cores
% 23.88/4.54 % Preprocessing time : 0.002 s
% 23.88/4.54 % Presaturation interreduction done
% 23.88/4.54
% 23.88/4.54 % Proof found!
% 23.88/4.54 % SZS status Theorem
% 23.88/4.54 % SZS output start CNFRefutation
% See solution above
% 23.88/4.54 % Parsed axioms : 10
% 23.88/4.54 % Removed by relevancy pruning/SinE : 0
% 23.88/4.54 % Initial clauses : 23
% 23.88/4.54 % Removed in clause preprocessing : 2
% 23.88/4.54 % Initial clauses in saturation : 21
% 23.88/4.54 % Processed clauses : 29314
% 23.88/4.54 % ...of these trivial : 6021
% 23.88/4.54 % ...subsumed : 19342
% 23.88/4.54 % ...remaining for further processing : 3951
% 23.88/4.54 % Other redundant clauses eliminated : 0
% 23.88/4.54 % Clauses deleted for lack of memory : 0
% 23.88/4.54 % Backward-subsumed : 302
% 23.88/4.54 % Backward-rewritten : 946
% 23.88/4.54 % Generated clauses : 61034
% 23.88/4.54 % ...of the previous two non-redundant : 52910
% 23.88/4.54 % ...aggressively subsumed : 0
% 23.88/4.54 % Contextual simplify-reflections : 0
% 23.88/4.54 % Paramodulations : 60534
% 23.88/4.54 % Factorizations : 0
% 23.88/4.54 % NegExts : 0
% 23.88/4.54 % Equation resolutions : 500
% 23.88/4.54 % Disequality decompositions : 0
% 23.88/4.54 % Total rewrite steps : 44174
% 23.88/4.54 % ...of those cached : 41867
% 23.88/4.54 % Propositional unsat checks : 0
% 23.88/4.54 % Propositional check models : 0
% 23.88/4.54 % Propositional check unsatisfiable : 0
% 23.88/4.54 % Propositional clauses : 0
% 23.88/4.54 % Propositional clauses after purity: 0
% 23.88/4.54 % Propositional unsat core size : 0
% 23.88/4.54 % Propositional preprocessing time : 0.000
% 23.88/4.54 % Propositional encoding time : 0.000
% 23.88/4.54 % Propositional solver time : 0.000
% 23.88/4.54 % Success case prop preproc time : 0.000
% 23.88/4.54 % Success case prop encoding time : 0.000
% 23.88/4.54 % Success case prop solver time : 0.000
% 23.88/4.54 % Current number of processed clauses : 2684
% 23.88/4.54 % Positive orientable unit clauses : 1043
% 23.88/4.54 % Positive unorientable unit clauses: 11
% 23.88/4.54 % Negative unit clauses : 22
% 23.88/4.54 % Non-unit-clauses : 1608
% 23.88/4.54 % Current number of unprocessed clauses: 20105
% 23.88/4.54 % ...number of literals in the above : 37451
% 23.88/4.54 % Current number of archived formulas : 0
% 23.88/4.54 % Current number of archived clauses : 1269
% 23.88/4.54 % Clause-clause subsumption calls (NU) : 1957810
% 23.88/4.54 % Rec. Clause-clause subsumption calls : 1878152
% 23.88/4.54 % Non-unit clause-clause subsumptions : 18191
% 23.88/4.54 % Unit Clause-clause subsumption calls : 4611
% 23.88/4.54 % Rewrite failures with RHS unbound : 595
% 23.88/4.54 % BW rewrite match attempts : 76498
% 23.88/4.54 % BW rewrite match successes : 277
% 23.88/4.54 % Condensation attempts : 0
% 23.88/4.54 % Condensation successes : 0
% 23.88/4.54 % Termbank termtop insertions : 1556394
% 23.88/4.54 % Search garbage collected termcells : 352
% 23.88/4.54
% 23.88/4.54 % -------------------------------------------------
% 23.88/4.54 % User time : 3.880 s
% 23.88/4.54 % System time : 0.046 s
% 23.88/4.54 % Total time : 3.926 s
% 23.88/4.54 % Maximum resident set size: 3644 pages
% 23.88/4.54
% 23.88/4.54 % -------------------------------------------------
% 23.88/4.54 % User time : 18.992 s
% 23.88/4.54 % System time : 0.383 s
% 23.88/4.54 % Total time : 19.374 s
% 23.88/4.54 % Maximum resident set size: 4608 pages
% 23.88/4.54 % E exiting
%------------------------------------------------------------------------------