%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG071+1 : TPTP v9.2.1. Released v2.7.0.
% 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 : n014.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 04:04:57 PM UTC 2026
% Result : Theorem 13.28s 8.50s
% Output : CNFRefutation 13.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 5
% Syntax : Number of formulae : 94 ( 4 unt; 0 def)
% Number of atoms : 299 ( 82 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 405 ( 200 ~; 161 |; 20 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 154 ( 0 sgn 36 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
( ( ! [X1] :
( sorti1(X1)
=> sorti2(h(X1)) )
& ! [X2] :
( sorti2(X2)
=> sorti1(j(X2)) ) )
=> ~ ( ! [X3] :
( sorti1(X3)
=> ! [X4] :
( sorti1(X4)
=> h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
& ! [X5] :
( sorti2(X5)
=> ! [X6] :
( sorti2(X6)
=> j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
& ! [X7] :
( sorti2(X7)
=> h(j(X7)) = X7 )
& ! [X8] :
( sorti1(X8)
=> j(h(X8)) = X8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax2,axiom,
! [X1] :
( sorti2(X1)
=> ! [X2] :
( sorti2(X2)
=> sorti2(op2(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(ax3,axiom,
! [X1] :
( sorti1(X1)
=> ? [X2] :
( sorti1(X2)
& op1(X2,op1(X2,X1)) != X1
& op1(X1,op1(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(ax1,axiom,
! [X1] :
( sorti1(X1)
=> ! [X2] :
( sorti1(X2)
=> sorti1(op1(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(ax4,axiom,
~ ! [X1] :
( sorti2(X1)
=> ? [X2] :
( sorti2(X2)
& op2(X2,op2(X2,X1)) != X1
& op2(X1,op2(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(c_0_5,negated_conjecture,
~ ( ( ! [X1] :
( sorti1(X1)
=> sorti2(h(X1)) )
& ! [X2] :
( sorti2(X2)
=> sorti1(j(X2)) ) )
=> ~ ( ! [X3] :
( sorti1(X3)
=> ! [X4] :
( sorti1(X4)
=> h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
& ! [X5] :
( sorti2(X5)
=> ! [X6] :
( sorti2(X6)
=> j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
& ! [X7] :
( sorti2(X7)
=> h(j(X7)) = X7 )
& ! [X8] :
( sorti1(X8)
=> j(h(X8)) = X8 ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_6,negated_conjecture,
! [X33,X34,X35,X36,X37,X38,X39,X40] :
( ( ~ sorti1(X33)
| sorti2(h(X33)) )
& ( ~ sorti2(X34)
| sorti1(j(X34)) )
& ( ~ sorti1(X35)
| ~ sorti1(X36)
| h(op1(X35,X36)) = op2(h(X35),h(X36)) )
& ( ~ sorti2(X37)
| ~ sorti2(X38)
| j(op2(X37,X38)) = op1(j(X37),j(X38)) )
& ( ~ sorti2(X39)
| h(j(X39)) = X39 )
& ( ~ sorti1(X40)
| j(h(X40)) = X40 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_7,negated_conjecture,
( h(op1(X1,X2)) = op2(h(X1),h(X2))
| ~ sorti1(X1)
| ~ sorti1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_8,negated_conjecture,
( h(j(X1)) = X1
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
( sorti1(j(X1))
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
( h(op1(X1,j(X2))) = op2(h(X1),X2)
| ~ sorti2(X2)
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
cnf(c_0_11,negated_conjecture,
( j(op2(X1,X2)) = op1(j(X1),j(X2))
| ~ sorti2(X1)
| ~ sorti2(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_12,plain,
! [X27,X28] :
( ~ sorti2(X27)
| ~ sorti2(X28)
| sorti2(op2(X27,X28)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax2])])]) ).
cnf(c_0_13,negated_conjecture,
( h(op1(j(X1),X2)) = op2(X1,h(X2))
| ~ sorti2(X1)
| ~ sorti1(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( h(j(op2(X1,X2))) = op2(h(j(X1)),X2)
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_9]) ).
cnf(c_0_15,plain,
( sorti2(op2(X1,X2))
| ~ sorti2(X1)
| ~ sorti2(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
( h(j(op2(X1,X2))) = op2(X1,h(j(X2)))
| ~ sorti2(X1)
| ~ sorti2(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_11]),c_0_9]) ).
cnf(c_0_17,negated_conjecture,
( j(h(X1)) = X1
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_18,negated_conjecture,
( sorti2(h(X1))
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
( op2(h(j(X1)),X2) = op2(X1,X2)
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_14]),c_0_15]) ).
cnf(c_0_20,negated_conjecture,
( op2(h(j(X1)),X2) = op2(X1,h(j(X2)))
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_16]) ).
fof(c_0_21,plain,
! [X29] :
( ( sorti1(esk1_1(X29))
| ~ sorti1(X29) )
& ( op1(esk1_1(X29),op1(esk1_1(X29),X29)) != X29
| ~ sorti1(X29) )
& ( op1(X29,op1(esk1_1(X29),X29)) = esk1_1(X29)
| ~ sorti1(X29) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])]) ).
cnf(c_0_22,negated_conjecture,
( j(op2(h(X1),X2)) = op1(X1,j(X2))
| ~ sorti2(X2)
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_17]),c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( op2(X1,h(j(X2))) = op2(X1,X2)
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( op1(esk1_1(X1),op1(esk1_1(X1),X1)) != X1
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,negated_conjecture,
( op1(X1,j(h(j(X2)))) = j(op2(h(X1),X2))
| ~ sorti2(h(j(X2)))
| ~ sorti2(X2)
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_18]) ).
cnf(c_0_26,negated_conjecture,
( op1(esk1_1(j(h(j(X1)))),j(op2(h(esk1_1(j(h(j(X1))))),X1))) != j(h(j(X1)))
| ~ sorti2(h(j(X1)))
| ~ sorti2(X1)
| ~ sorti1(esk1_1(j(h(j(X1))))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_9]) ).
cnf(c_0_27,negated_conjecture,
( op1(esk1_1(j(X1)),j(op2(h(esk1_1(j(X1))),X1))) != j(X1)
| ~ sorti2(X1)
| ~ sorti1(esk1_1(j(X1))) ),
inference(spm,[status(thm)],[c_0_26,c_0_8]) ).
cnf(c_0_28,plain,
( sorti1(esk1_1(X1))
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,negated_conjecture,
( op1(esk1_1(X1),j(op2(h(esk1_1(X1)),h(X1)))) != X1
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_17]),c_0_28]),c_0_18]) ).
cnf(c_0_30,negated_conjecture,
( op2(h(X1),h(j(h(X2)))) = h(j(h(op1(X1,X2))))
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_7]),c_0_18]),c_0_18]) ).
cnf(c_0_31,negated_conjecture,
( op1(esk1_1(j(h(X1))),j(h(j(h(op1(esk1_1(j(h(X1))),X1)))))) != j(h(X1))
| ~ sorti1(j(h(X1)))
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( op1(esk1_1(X1),j(h(j(h(op1(esk1_1(X1),X1)))))) != X1
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_17]) ).
cnf(c_0_33,negated_conjecture,
( op1(esk1_1(j(X1)),j(h(j(op2(h(esk1_1(j(X1))),X1))))) != j(X1)
| ~ sorti2(X1)
| ~ sorti1(esk1_1(j(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_10]),c_0_9]) ).
cnf(c_0_34,negated_conjecture,
( j(h(op1(X1,X2))) = op1(X1,j(h(X2)))
| ~ sorti1(X1)
| ~ sorti1(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_7]),c_0_18]) ).
cnf(c_0_35,negated_conjecture,
( sorti2(h(op1(X1,X2)))
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_7]),c_0_18]),c_0_18]) ).
cnf(c_0_36,negated_conjecture,
( op1(esk1_1(X1),j(h(j(op2(h(esk1_1(X1)),h(X1)))))) != X1
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_17]),c_0_28]),c_0_18]) ).
cnf(c_0_37,negated_conjecture,
( op1(X1,j(h(j(X2)))) = j(op2(h(X1),X2))
| ~ sorti2(X2)
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_10]),c_0_9]) ).
cnf(c_0_38,negated_conjecture,
( j(op2(X1,h(X2))) = op1(j(X1),X2)
| ~ sorti2(X1)
| ~ sorti1(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_17]),c_0_18]) ).
cnf(c_0_39,negated_conjecture,
( sorti2(op2(X1,h(X2)))
| ~ sorti2(X1)
| ~ sorti1(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_13]),c_0_9]) ).
cnf(c_0_40,negated_conjecture,
( j(op2(h(esk1_1(X1)),op2(h(esk1_1(X1)),h(X1)))) != X1
| ~ sorti2(op2(h(esk1_1(X1)),h(X1)))
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_28]) ).
cnf(c_0_41,negated_conjecture,
( j(op2(X1,op2(X2,h(X3)))) = op1(j(X1),op1(j(X2),X3))
| ~ sorti2(X1)
| ~ sorti2(X2)
| ~ sorti1(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_38]),c_0_39]) ).
cnf(c_0_42,negated_conjecture,
( j(h(op1(X1,X2))) = op1(j(h(X1)),X2)
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_7]),c_0_18]) ).
cnf(c_0_43,negated_conjecture,
( op1(j(h(esk1_1(X1))),op1(j(h(esk1_1(X1))),X1)) != X1
| ~ sorti2(h(esk1_1(X1)))
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_39]) ).
cnf(c_0_44,negated_conjecture,
( op1(j(X1),op1(j(h(X2)),X3)) = j(op2(X1,h(op1(X2,X3))))
| ~ sorti2(X1)
| ~ sorti1(X3)
| ~ sorti1(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_42]),c_0_35]) ).
cnf(c_0_45,negated_conjecture,
( j(op2(h(esk1_1(X1)),h(op1(esk1_1(X1),X1)))) != X1
| ~ sorti2(h(esk1_1(X1)))
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_28]) ).
fof(c_0_46,plain,
! [X25,X26] :
( ~ sorti1(X25)
| ~ sorti1(X26)
| sorti1(op1(X25,X26)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax1])])]) ).
cnf(c_0_47,negated_conjecture,
( j(op2(h(esk1_1(j(X1))),op2(h(esk1_1(j(X1))),X1))) != j(X1)
| ~ sorti2(X1)
| ~ sorti1(esk1_1(j(X1))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_10]),c_0_9]),c_0_18]) ).
cnf(c_0_48,plain,
( sorti1(op1(X1,X2))
| ~ sorti1(X1)
| ~ sorti1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_49,negated_conjecture,
( j(op2(h(esk1_1(X1)),op2(h(esk1_1(X1)),h(X1)))) != X1
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_17]),c_0_28]),c_0_18]) ).
cnf(c_0_50,negated_conjecture,
( sorti1(j(op2(X1,X2)))
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_11]),c_0_9]),c_0_9]) ).
cnf(c_0_51,negated_conjecture,
( j(op2(h(esk1_1(j(h(X1)))),h(j(h(op1(esk1_1(j(h(X1))),X1)))))) != j(h(X1))
| ~ sorti1(j(h(X1)))
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_30]),c_0_28]) ).
cnf(c_0_52,negated_conjecture,
( sorti1(j(h(op1(X1,X2))))
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_7]),c_0_18]),c_0_18]) ).
cnf(c_0_53,negated_conjecture,
( j(op2(h(esk1_1(X1)),h(j(h(op1(esk1_1(X1),X1)))))) != X1
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_17]) ).
cnf(c_0_54,plain,
( op1(X1,op1(esk1_1(X1),X1)) = esk1_1(X1)
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_55,negated_conjecture,
( sorti1(j(op2(X1,h(X2))))
| ~ sorti2(X1)
| ~ sorti1(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_13]),c_0_9]) ).
cnf(c_0_56,negated_conjecture,
( sorti2(h(j(op2(X1,X2))))
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_11]),c_0_9]),c_0_9]) ).
cnf(c_0_57,negated_conjecture,
( j(op2(h(esk1_1(X1)),h(op1(j(h(esk1_1(X1))),X1)))) != X1
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_42]),c_0_28]) ).
cnf(c_0_58,negated_conjecture,
( sorti1(j(h(esk1_1(X1))))
| ~ sorti1(op1(esk1_1(X1),X1))
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_54]) ).
cnf(c_0_59,negated_conjecture,
( sorti1(op1(j(X1),X2))
| ~ sorti2(X1)
| ~ sorti1(X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_38]) ).
cnf(c_0_60,negated_conjecture,
( sorti2(h(j(h(op1(X1,X2)))))
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_7]),c_0_18]),c_0_18]) ).
cnf(c_0_61,negated_conjecture,
( j(op2(h(esk1_1(j(X1))),op2(h(j(h(esk1_1(j(X1))))),X1))) != j(X1)
| ~ sorti2(X1)
| ~ sorti1(j(h(esk1_1(j(X1))))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_10]),c_0_9]) ).
cnf(c_0_62,negated_conjecture,
( sorti1(j(h(esk1_1(X1))))
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_48]),c_0_28]) ).
cnf(c_0_63,negated_conjecture,
( h(op1(X1,op1(j(X2),X3))) = op2(h(X1),op2(X2,h(X3)))
| ~ sorti2(X2)
| ~ sorti1(X1)
| ~ sorti1(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_13]),c_0_59]) ).
cnf(c_0_64,negated_conjecture,
( sorti2(h(j(h(esk1_1(X1)))))
| ~ sorti1(op1(esk1_1(X1),X1))
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_54]) ).
cnf(c_0_65,negated_conjecture,
( j(op2(h(esk1_1(X1)),op2(h(j(h(esk1_1(X1)))),h(X1)))) != X1
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_17]),c_0_62]),c_0_18]) ).
cnf(c_0_66,negated_conjecture,
( j(op2(h(X1),op2(X2,h(X3)))) = op1(j(h(X1)),op1(j(X2),X3))
| ~ sorti2(X2)
| ~ sorti1(X1)
| ~ sorti1(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_63]),c_0_59]) ).
cnf(c_0_67,negated_conjecture,
( sorti2(h(j(h(esk1_1(X1)))))
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_48]),c_0_28]) ).
cnf(c_0_68,negated_conjecture,
( op1(j(h(esk1_1(X1))),op1(j(h(j(h(esk1_1(X1))))),X1)) != X1
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_28]),c_0_67]) ).
cnf(c_0_69,negated_conjecture,
( op1(j(h(X1)),j(X2)) = j(op2(h(X1),X2))
| ~ sorti2(X2)
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_10]),c_0_9]) ).
cnf(c_0_70,negated_conjecture,
( op1(j(h(esk1_1(j(X1)))),j(op2(h(j(h(esk1_1(j(X1))))),X1))) != j(X1)
| ~ sorti2(X1)
| ~ sorti1(j(h(esk1_1(j(X1))))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_9]) ).
cnf(c_0_71,negated_conjecture,
( op1(j(h(esk1_1(X1))),j(op2(h(j(h(esk1_1(X1)))),h(X1)))) != X1
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_17]),c_0_62]),c_0_18]) ).
cnf(c_0_72,negated_conjecture,
( op2(h(j(h(X1))),h(X2)) = h(j(h(op1(X1,X2))))
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_7]),c_0_18]),c_0_18]) ).
cnf(c_0_73,negated_conjecture,
( op1(j(h(esk1_1(X1))),j(h(j(h(op1(esk1_1(X1),X1)))))) != X1
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_28]) ).
cnf(c_0_74,negated_conjecture,
( op1(j(h(esk1_1(j(X1)))),j(h(j(op2(h(esk1_1(j(X1))),X1))))) != j(X1)
| ~ sorti2(X1)
| ~ sorti1(esk1_1(j(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_10]),c_0_9]) ).
cnf(c_0_75,negated_conjecture,
( op1(j(h(esk1_1(X1))),j(h(j(op2(h(esk1_1(X1)),h(X1)))))) != X1
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_17]),c_0_28]),c_0_18]) ).
cnf(c_0_76,negated_conjecture,
( op1(j(X1),j(h(j(X2)))) = j(h(j(op2(X1,X2))))
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_11]),c_0_9]),c_0_9]) ).
cnf(c_0_77,negated_conjecture,
( j(h(j(op2(h(esk1_1(X1)),op2(h(esk1_1(X1)),h(X1)))))) != X1
| ~ sorti2(h(esk1_1(X1)))
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_39]) ).
cnf(c_0_78,negated_conjecture,
( j(h(op1(j(h(esk1_1(X1))),op1(j(h(esk1_1(X1))),X1)))) != X1
| ~ sorti2(h(esk1_1(X1)))
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_41]) ).
fof(c_0_79,plain,
! [X32] :
( sorti2(esk2_0)
& ( ~ sorti2(X32)
| op2(X32,op2(X32,esk2_0)) = esk2_0
| op2(esk2_0,op2(X32,esk2_0)) != X32 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])])]) ).
cnf(c_0_80,negated_conjecture,
( j(op2(h(j(h(esk1_1(X1)))),op2(h(esk1_1(X1)),h(X1)))) != X1
| ~ sorti2(h(esk1_1(X1)))
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_63]),c_0_9]) ).
cnf(c_0_81,plain,
( op2(X1,op2(X1,esk2_0)) = esk2_0
| ~ sorti2(X1)
| op2(esk2_0,op2(X1,esk2_0)) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_82,plain,
sorti2(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_83,negated_conjecture,
( j(op2(h(j(h(esk1_1(j(X1))))),op2(h(esk1_1(j(X1))),X1))) != j(X1)
| ~ sorti2(h(esk1_1(j(X1))))
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_8]),c_0_9]) ).
cnf(c_0_84,negated_conjecture,
( op2(h(j(X1)),op2(X1,esk2_0)) = esk2_0
| h(j(X1)) != op2(esk2_0,op2(X1,esk2_0))
| ~ sorti2(h(j(X1)))
| ~ sorti2(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_19]),c_0_82])]) ).
cnf(c_0_85,negated_conjecture,
( sorti1(j(op2(h(X1),X2)))
| ~ sorti2(X2)
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_10]),c_0_9]) ).
cnf(c_0_86,negated_conjecture,
( h(j(h(esk1_1(j(esk2_0))))) != op2(esk2_0,op2(h(esk1_1(j(esk2_0))),esk2_0))
| ~ sorti2(h(j(h(esk1_1(j(esk2_0))))))
| ~ sorti2(h(esk1_1(j(esk2_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_82])]) ).
cnf(c_0_87,negated_conjecture,
( op2(X1,h(op1(esk1_1(j(X1)),j(X1)))) = h(esk1_1(j(X1)))
| ~ sorti2(X1)
| ~ sorti1(op1(esk1_1(j(X1)),j(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_54]),c_0_9]) ).
cnf(c_0_88,negated_conjecture,
( sorti1(op1(X1,j(X2)))
| ~ sorti2(X2)
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_85,c_0_22]) ).
cnf(c_0_89,negated_conjecture,
( op2(esk2_0,op2(h(esk1_1(j(esk2_0))),esk2_0)) != h(esk1_1(j(esk2_0)))
| ~ sorti2(h(esk1_1(j(esk2_0)))) ),
inference(spm,[status(thm)],[c_0_86,c_0_8]) ).
cnf(c_0_90,negated_conjecture,
( op2(X1,op2(h(esk1_1(j(X1))),X1)) = h(esk1_1(j(X1)))
| ~ sorti2(X1)
| ~ sorti1(esk1_1(j(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_10]),c_0_88]) ).
cnf(c_0_91,negated_conjecture,
~ sorti1(esk1_1(j(esk2_0))),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_82])]),c_0_18]) ).
cnf(c_0_92,negated_conjecture,
~ sorti1(j(esk2_0)),
inference(spm,[status(thm)],[c_0_91,c_0_28]) ).
cnf(c_0_93,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_9]),c_0_82])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG071+1 : TPTP v9.2.1. Released v2.7.0.
% 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 : n014.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 10:19:51 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 13.28/8.50 % Version : CSE_E---1.7
% 13.28/8.50 % Problem : theBenchmark.p
% 13.28/8.50 % SZS status Theorem for theBenchmark.p
% 13.28/8.50 % SZS output start CNFRefutation
% See solution above
% 13.28/8.55 % Total time : 6.385s
%------------------------------------------------------------------------------