%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG071+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 11:51:26 AM UTC 2026
% Result : Theorem 22.05s 3.66s
% Output : CNFRefutation 22.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 5
% Syntax : Number of formulae : 96 ( 4 unt; 0 def)
% Number of atoms : 307 ( 86 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 414 ( 203 ~; 161 |; 24 &)
% ( 0 <=>; 26 =>; 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 : 158 ( 0 sgn 38 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
( ( ! [X2] :
( sorti2(X2)
=> sorti1(j(X2)) )
& ! [X1] :
( sorti1(X1)
=> sorti2(h(X1)) ) )
=> ~ ( ! [X8] :
( sorti1(X8)
=> j(h(X8)) = X8 )
& ! [X7] :
( sorti2(X7)
=> h(j(X7)) = X7 )
& ! [X5] :
( sorti2(X5)
=> ! [X6] :
( sorti2(X6)
=> j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
& ! [X3] :
( sorti1(X3)
=> ! [X4] :
( sorti1(X4)
=> h(op1(X3,X4)) = op2(h(X3),h(X4)) ) ) ) ),
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] :
( op1(X1,op1(X2,X1)) = X2
& op1(X2,op1(X2,X1)) != X1
& sorti1(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] :
( op2(X1,op2(X2,X1)) = X2
& op2(X2,op2(X2,X1)) != X1
& sorti2(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(c_0_5,negated_conjecture,
~ ( ( ! [X2] :
( sorti2(X2)
=> sorti1(j(X2)) )
& ! [X1] :
( sorti1(X1)
=> sorti2(h(X1)) ) )
=> ~ ( ! [X8] :
( sorti1(X8)
=> j(h(X8)) = X8 )
& ! [X7] :
( sorti2(X7)
=> h(j(X7)) = X7 )
& ! [X5] :
( sorti2(X5)
=> ! [X6] :
( sorti2(X6)
=> j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
& ! [X3] :
( sorti1(X3)
=> ! [X4] :
( sorti1(X4)
=> h(op1(X3,X4)) = op2(h(X3),h(X4)) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_6,negated_conjecture,
! [X17,X18,X19,X20,X21,X22,X23,X24] :
( ( j(h(X24)) = X24
| ~ sorti1(X24) )
& ( h(j(X23)) = X23
| ~ sorti2(X23) )
& ( j(op2(X21,X22)) = op1(j(X21),j(X22))
| ~ sorti2(X22)
| ~ sorti2(X21) )
& ( h(op1(X19,X20)) = op2(h(X19),h(X20))
| ~ sorti1(X20)
| ~ sorti1(X19) )
& ( sorti1(j(X18))
| ~ sorti2(X18) )
& ( sorti2(h(X17))
| ~ sorti1(X17) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
cnf(c_0_7,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti1(X1)
| h(op1(X1,X2)) = op2(h(X1),h(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_8,negated_conjecture,
( ~ sorti2(X1)
| h(j(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
( ~ sorti2(X1)
| sorti1(j(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti2(X2)
| h(op1(X1,j(X2))) = op2(h(X1),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
cnf(c_0_11,negated_conjecture,
( ~ sorti2(X2)
| ~ sorti2(X1)
| j(op2(X1,X2)) = op1(j(X1),j(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_12,plain,
! [X11,X12] :
( sorti2(op2(X11,X12))
| ~ sorti2(X12)
| ~ sorti2(X11) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax2])])])]) ).
cnf(c_0_13,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti2(X1)
| h(op1(j(X1),X2)) = op2(X1,h(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( ~ sorti2(X1)
| ~ sorti2(X2)
| h(j(op2(X1,X2))) = op2(h(j(X1)),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_9]) ).
cnf(c_0_15,plain,
( ~ sorti2(X2)
| ~ sorti2(X1)
| sorti2(op2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
( ~ sorti2(X2)
| ~ sorti2(X1)
| h(j(op2(X1,X2))) = op2(X1,h(j(X2))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_11]),c_0_9]) ).
fof(c_0_17,plain,
! [X1] :
( sorti1(X1)
=> ? [X2] :
( op1(X1,op1(X2,X1)) = X2
& op1(X2,op1(X2,X1)) != X1
& sorti1(X2) ) ),
inference(fof_simplification,[status(thm)],[ax3]) ).
cnf(c_0_18,negated_conjecture,
( ~ sorti1(X1)
| j(h(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
( ~ sorti1(X1)
| sorti2(h(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,negated_conjecture,
( ~ sorti2(X1)
| ~ sorti2(X2)
| op2(h(j(X1)),X2) = op2(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_14]),c_0_15]) ).
cnf(c_0_21,negated_conjecture,
( ~ sorti2(X1)
| ~ sorti2(X2)
| op2(h(j(X1)),X2) = op2(X1,h(j(X2))) ),
inference(spm,[status(thm)],[c_0_14,c_0_16]) ).
fof(c_0_22,plain,
! [X13] :
( ( ~ sorti1(X13)
| op1(X13,op1(esk1_1(X13),X13)) = esk1_1(X13) )
& ( ~ sorti1(X13)
| op1(esk1_1(X13),op1(esk1_1(X13),X13)) != X13 )
& ( ~ sorti1(X13)
| sorti1(esk1_1(X13)) ) ),
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_17])])])])]) ).
cnf(c_0_23,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti2(X2)
| j(op2(h(X1),X2)) = op1(X1,j(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_18]),c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( ~ sorti2(X1)
| ~ sorti2(X2)
| op2(X1,h(j(X2))) = op2(X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( ~ sorti1(X1)
| op1(esk1_1(X1),op1(esk1_1(X1),X1)) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti2(X2)
| ~ sorti2(h(j(X2)))
| op1(X1,j(h(j(X2)))) = j(op2(h(X1),X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_19]) ).
cnf(c_0_27,negated_conjecture,
( ~ sorti1(esk1_1(j(h(j(X1)))))
| ~ sorti2(X1)
| ~ sorti2(h(j(X1)))
| op1(esk1_1(j(h(j(X1)))),j(op2(h(esk1_1(j(h(j(X1))))),X1))) != j(h(j(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_9]) ).
cnf(c_0_28,negated_conjecture,
( ~ sorti1(esk1_1(j(X1)))
| ~ sorti2(X1)
| op1(esk1_1(j(X1)),j(op2(h(esk1_1(j(X1))),X1))) != j(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_8]) ).
cnf(c_0_29,plain,
( ~ sorti1(X1)
| sorti1(esk1_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,negated_conjecture,
( ~ sorti1(X1)
| op1(esk1_1(X1),j(op2(h(esk1_1(X1)),h(X1)))) != X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_18]),c_0_29]),c_0_19]) ).
cnf(c_0_31,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti1(X2)
| op2(h(X1),h(j(h(X2)))) = h(j(h(op1(X1,X2)))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_7]),c_0_19]),c_0_19]) ).
cnf(c_0_32,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti1(j(h(X1)))
| op1(esk1_1(j(h(X1))),j(h(j(h(op1(esk1_1(j(h(X1))),X1)))))) != j(h(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_29]) ).
cnf(c_0_33,negated_conjecture,
( ~ sorti1(X1)
| op1(esk1_1(X1),j(h(j(h(op1(esk1_1(X1),X1)))))) != X1 ),
inference(spm,[status(thm)],[c_0_32,c_0_18]) ).
cnf(c_0_34,negated_conjecture,
( ~ sorti1(esk1_1(j(X1)))
| ~ sorti2(X1)
| op1(esk1_1(j(X1)),j(h(j(op2(h(esk1_1(j(X1))),X1))))) != j(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_10]),c_0_9]) ).
cnf(c_0_35,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti1(X1)
| j(h(op1(X1,X2))) = op1(X1,j(h(X2))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_7]),c_0_19]) ).
cnf(c_0_36,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti1(X2)
| sorti2(h(op1(X1,X2))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_7]),c_0_19]),c_0_19]) ).
cnf(c_0_37,negated_conjecture,
( ~ sorti1(X1)
| op1(esk1_1(X1),j(h(j(op2(h(esk1_1(X1)),h(X1)))))) != X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_18]),c_0_29]),c_0_19]) ).
cnf(c_0_38,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti2(X2)
| op1(X1,j(h(j(X2)))) = j(op2(h(X1),X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_10]),c_0_9]) ).
cnf(c_0_39,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti2(X1)
| j(op2(X1,h(X2))) = op1(j(X1),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_18]),c_0_19]) ).
cnf(c_0_40,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti2(X1)
| sorti2(op2(X1,h(X2))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_13]),c_0_9]) ).
cnf(c_0_41,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti2(op2(h(esk1_1(X1)),h(X1)))
| j(op2(h(esk1_1(X1)),op2(h(esk1_1(X1)),h(X1)))) != X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_29]) ).
cnf(c_0_42,negated_conjecture,
( ~ sorti1(X3)
| ~ sorti2(X2)
| ~ sorti2(X1)
| j(op2(X1,op2(X2,h(X3)))) = op1(j(X1),op1(j(X2),X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_39]),c_0_40]) ).
cnf(c_0_43,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti1(X2)
| j(h(op1(X1,X2))) = op1(j(h(X1)),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_7]),c_0_19]) ).
cnf(c_0_44,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti2(h(esk1_1(X1)))
| op1(j(h(esk1_1(X1))),op1(j(h(esk1_1(X1))),X1)) != X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_40]) ).
cnf(c_0_45,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti1(X3)
| ~ sorti2(X1)
| op1(j(X1),op1(j(h(X2)),X3)) = j(op2(X1,h(op1(X2,X3)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_43]),c_0_36]) ).
cnf(c_0_46,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti2(h(esk1_1(X1)))
| j(op2(h(esk1_1(X1)),h(op1(esk1_1(X1),X1)))) != X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_29]) ).
fof(c_0_47,plain,
! [X9,X10] :
( sorti1(op1(X9,X10))
| ~ sorti1(X10)
| ~ sorti1(X9) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax1])])])]) ).
cnf(c_0_48,negated_conjecture,
( ~ sorti1(esk1_1(j(X1)))
| ~ sorti2(X1)
| j(op2(h(esk1_1(j(X1))),op2(h(esk1_1(j(X1))),X1))) != j(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_10]),c_0_9]),c_0_19]) ).
cnf(c_0_49,plain,
( ~ sorti1(X2)
| ~ sorti1(X1)
| sorti1(op1(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_50,negated_conjecture,
( ~ sorti1(X1)
| j(op2(h(esk1_1(X1)),op2(h(esk1_1(X1)),h(X1)))) != X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_18]),c_0_29]),c_0_19]) ).
cnf(c_0_51,negated_conjecture,
( ~ sorti2(X1)
| ~ sorti2(X2)
| sorti1(j(op2(X1,X2))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_11]),c_0_9]),c_0_9]) ).
cnf(c_0_52,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti1(j(h(X1)))
| j(op2(h(esk1_1(j(h(X1)))),h(j(h(op1(esk1_1(j(h(X1))),X1)))))) != j(h(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_31]),c_0_29]) ).
cnf(c_0_53,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti1(X2)
| sorti1(j(h(op1(X1,X2)))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_7]),c_0_19]),c_0_19]) ).
cnf(c_0_54,negated_conjecture,
( ~ sorti1(X1)
| j(op2(h(esk1_1(X1)),h(j(h(op1(esk1_1(X1),X1)))))) != X1 ),
inference(spm,[status(thm)],[c_0_52,c_0_18]) ).
cnf(c_0_55,plain,
( ~ sorti1(X1)
| op1(X1,op1(esk1_1(X1),X1)) = esk1_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_56,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti2(X1)
| sorti1(j(op2(X1,h(X2)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_13]),c_0_9]) ).
cnf(c_0_57,negated_conjecture,
( ~ sorti2(X1)
| ~ sorti2(X2)
| sorti2(h(j(op2(X1,X2)))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_11]),c_0_9]),c_0_9]) ).
cnf(c_0_58,negated_conjecture,
( ~ sorti1(X1)
| j(op2(h(esk1_1(X1)),h(op1(j(h(esk1_1(X1))),X1)))) != X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_43]),c_0_29]) ).
cnf(c_0_59,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti1(op1(esk1_1(X1),X1))
| sorti1(j(h(esk1_1(X1)))) ),
inference(spm,[status(thm)],[c_0_53,c_0_55]) ).
cnf(c_0_60,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti2(X1)
| sorti1(op1(j(X1),X2)) ),
inference(spm,[status(thm)],[c_0_56,c_0_39]) ).
cnf(c_0_61,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti1(X2)
| sorti2(h(j(h(op1(X1,X2))))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_7]),c_0_19]),c_0_19]) ).
cnf(c_0_62,negated_conjecture,
( ~ sorti1(j(h(esk1_1(j(X1)))))
| ~ sorti2(X1)
| j(op2(h(esk1_1(j(X1))),op2(h(j(h(esk1_1(j(X1))))),X1))) != j(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_10]),c_0_9]) ).
cnf(c_0_63,negated_conjecture,
( ~ sorti1(X1)
| sorti1(j(h(esk1_1(X1)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_49]),c_0_29]) ).
cnf(c_0_64,negated_conjecture,
( ~ sorti1(X3)
| ~ sorti1(X1)
| ~ sorti2(X2)
| h(op1(X1,op1(j(X2),X3))) = op2(h(X1),op2(X2,h(X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_13]),c_0_60]) ).
cnf(c_0_65,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti1(op1(esk1_1(X1),X1))
| sorti2(h(j(h(esk1_1(X1))))) ),
inference(spm,[status(thm)],[c_0_61,c_0_55]) ).
cnf(c_0_66,negated_conjecture,
( ~ sorti1(X1)
| j(op2(h(esk1_1(X1)),op2(h(j(h(esk1_1(X1)))),h(X1)))) != X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_18]),c_0_63]),c_0_19]) ).
cnf(c_0_67,negated_conjecture,
( ~ sorti1(X3)
| ~ sorti1(X1)
| ~ sorti2(X2)
| j(op2(h(X1),op2(X2,h(X3)))) = op1(j(h(X1)),op1(j(X2),X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_64]),c_0_60]) ).
cnf(c_0_68,negated_conjecture,
( ~ sorti1(X1)
| sorti2(h(j(h(esk1_1(X1))))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_49]),c_0_29]) ).
cnf(c_0_69,negated_conjecture,
( ~ sorti1(X1)
| op1(j(h(esk1_1(X1))),op1(j(h(j(h(esk1_1(X1))))),X1)) != X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_29]),c_0_68]) ).
cnf(c_0_70,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti2(X2)
| op1(j(h(X1)),j(X2)) = j(op2(h(X1),X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_10]),c_0_9]) ).
cnf(c_0_71,negated_conjecture,
( ~ sorti1(j(h(esk1_1(j(X1)))))
| ~ sorti2(X1)
| op1(j(h(esk1_1(j(X1)))),j(op2(h(j(h(esk1_1(j(X1))))),X1))) != j(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_9]) ).
cnf(c_0_72,negated_conjecture,
( ~ sorti1(X1)
| op1(j(h(esk1_1(X1))),j(op2(h(j(h(esk1_1(X1)))),h(X1)))) != X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_18]),c_0_63]),c_0_19]) ).
cnf(c_0_73,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti1(X2)
| op2(h(j(h(X1))),h(X2)) = h(j(h(op1(X1,X2)))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_7]),c_0_19]),c_0_19]) ).
cnf(c_0_74,negated_conjecture,
( ~ sorti1(X1)
| op1(j(h(esk1_1(X1))),j(h(j(h(op1(esk1_1(X1),X1)))))) != X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_29]) ).
cnf(c_0_75,negated_conjecture,
( ~ sorti1(esk1_1(j(X1)))
| ~ sorti2(X1)
| op1(j(h(esk1_1(j(X1)))),j(h(j(op2(h(esk1_1(j(X1))),X1))))) != j(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_10]),c_0_9]) ).
cnf(c_0_76,negated_conjecture,
( ~ sorti1(X1)
| op1(j(h(esk1_1(X1))),j(h(j(op2(h(esk1_1(X1)),h(X1)))))) != X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_18]),c_0_29]),c_0_19]) ).
cnf(c_0_77,negated_conjecture,
( ~ sorti2(X1)
| ~ sorti2(X2)
| op1(j(X1),j(h(j(X2)))) = j(h(j(op2(X1,X2)))) ),
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_78,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti2(h(esk1_1(X1)))
| j(h(j(op2(h(esk1_1(X1)),op2(h(esk1_1(X1)),h(X1)))))) != X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_40]) ).
fof(c_0_79,plain,
~ ! [X1] :
( sorti2(X1)
=> ? [X2] :
( op2(X1,op2(X2,X1)) = X2
& op2(X2,op2(X2,X1)) != X1
& sorti2(X2) ) ),
inference(fof_simplification,[status(thm)],[ax4]) ).
cnf(c_0_80,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti2(h(esk1_1(X1)))
| j(h(op1(j(h(esk1_1(X1))),op1(j(h(esk1_1(X1))),X1)))) != X1 ),
inference(spm,[status(thm)],[c_0_78,c_0_42]) ).
fof(c_0_81,plain,
! [X16] :
( ( op2(esk2_0,op2(X16,esk2_0)) != X16
| op2(X16,op2(X16,esk2_0)) = esk2_0
| ~ sorti2(X16) )
& sorti2(esk2_0) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_79])])])])]) ).
cnf(c_0_82,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti2(h(esk1_1(X1)))
| j(op2(h(j(h(esk1_1(X1)))),op2(h(esk1_1(X1)),h(X1)))) != X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_64]),c_0_9]) ).
cnf(c_0_83,plain,
( op2(esk2_0,op2(X1,esk2_0)) != X1
| ~ sorti2(X1)
| op2(X1,op2(X1,esk2_0)) = esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_84,plain,
sorti2(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_85,negated_conjecture,
( ~ sorti2(X1)
| ~ sorti2(h(esk1_1(j(X1))))
| j(op2(h(j(h(esk1_1(j(X1))))),op2(h(esk1_1(j(X1))),X1))) != j(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_8]),c_0_9]) ).
cnf(c_0_86,negated_conjecture,
( ~ sorti2(X1)
| ~ sorti2(h(j(X1)))
| h(j(X1)) != op2(esk2_0,op2(X1,esk2_0))
| op2(h(j(X1)),op2(X1,esk2_0)) = esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_20]),c_0_84])]) ).
cnf(c_0_87,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti2(X2)
| sorti1(j(op2(h(X1),X2))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_10]),c_0_9]) ).
cnf(c_0_88,negated_conjecture,
( ~ sorti2(h(esk1_1(j(esk2_0))))
| ~ sorti2(h(j(h(esk1_1(j(esk2_0))))))
| h(j(h(esk1_1(j(esk2_0))))) != op2(esk2_0,op2(h(esk1_1(j(esk2_0))),esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_84])]) ).
cnf(c_0_89,negated_conjecture,
( ~ sorti1(op1(esk1_1(j(X1)),j(X1)))
| ~ sorti2(X1)
| op2(X1,h(op1(esk1_1(j(X1)),j(X1)))) = h(esk1_1(j(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_55]),c_0_9]) ).
cnf(c_0_90,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti2(X2)
| sorti1(op1(X1,j(X2))) ),
inference(spm,[status(thm)],[c_0_87,c_0_23]) ).
cnf(c_0_91,negated_conjecture,
( ~ sorti2(h(esk1_1(j(esk2_0))))
| op2(esk2_0,op2(h(esk1_1(j(esk2_0))),esk2_0)) != h(esk1_1(j(esk2_0))) ),
inference(spm,[status(thm)],[c_0_88,c_0_8]) ).
cnf(c_0_92,negated_conjecture,
( ~ sorti1(esk1_1(j(X1)))
| ~ sorti2(X1)
| op2(X1,op2(h(esk1_1(j(X1))),X1)) = h(esk1_1(j(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_10]),c_0_90]) ).
cnf(c_0_93,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_91,c_0_92]),c_0_84])]),c_0_19]) ).
cnf(c_0_94,negated_conjecture,
~ sorti1(j(esk2_0)),
inference(spm,[status(thm)],[c_0_93,c_0_29]) ).
cnf(c_0_95,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_9]),c_0_84])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG071+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 12:55:41 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 22.05/3.66 % Version: 3.5.1
% 22.05/3.66 % Preprocessing class: FSMSSMSSSSSNFFN.
% 22.05/3.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 22.05/3.66 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 22.05/3.66 % Starting new_bool_3 with 300s (1) cores
% 22.05/3.66 % Starting new_bool_1 with 300s (1) cores
% 22.05/3.66 % Starting sh5l with 300s (1) cores
% 22.05/3.66 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 918586 completed with status 0
% 22.05/3.66 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 22.05/3.66 % Preprocessing class: FSMSSMSSSSSNFFN.
% 22.05/3.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 22.05/3.66 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 22.05/3.66 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 22.05/3.66 % No SInE strategy applied
% 22.05/3.66 % Search class: FHHSF-FFSF21-MFFFFFNN
% 22.05/3.66 % partial match(1): FHHSM-FFSF21-MFFFFFNN
% 22.05/3.66 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 22.05/3.66 % Starting SubtermCWHack with 136s (1) cores
% 22.05/3.66 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 22.05/3.66 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 22.05/3.66 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 22.05/3.66 % Starting new_bool_3 with 136s (1) cores
% 22.05/3.66 % SAT001_MinMin_p005000_rr_RG with pid 918592 completed with status 0
% 22.05/3.66 % Result found by SAT001_MinMin_p005000_rr_RG
% 22.05/3.66 % Preprocessing class: FSMSSMSSSSSNFFN.
% 22.05/3.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 22.05/3.66 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 22.05/3.66 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 22.05/3.66 % No SInE strategy applied
% 22.05/3.66 % Search class: FHHSF-FFSF21-MFFFFFNN
% 22.05/3.66 % partial match(1): FHHSM-FFSF21-MFFFFFNN
% 22.05/3.66 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 22.05/3.66 % Starting SubtermCWHack with 136s (1) cores
% 22.05/3.66 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 22.05/3.66 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 22.05/3.66 % Preprocessing time : 0.001 s
% 22.05/3.66 % Presaturation interreduction done
% 22.05/3.66
% 22.05/3.66 % Proof found!
% 22.05/3.66 % SZS status Theorem
% 22.05/3.66 % SZS output start CNFRefutation
% See solution above
% 22.05/3.66 % Parsed axioms : 5
% 22.05/3.66 % Removed by relevancy pruning/SinE : 0
% 22.05/3.66 % Initial clauses : 13
% 22.05/3.66 % Removed in clause preprocessing : 0
% 22.05/3.66 % Initial clauses in saturation : 13
% 22.05/3.66 % Processed clauses : 7294
% 22.05/3.66 % ...of these trivial : 0
% 22.05/3.66 % ...subsumed : 6074
% 22.05/3.66 % ...remaining for further processing : 1220
% 22.05/3.66 % Other redundant clauses eliminated : 0
% 22.05/3.66 % Clauses deleted for lack of memory : 0
% 22.05/3.66 % Backward-subsumed : 157
% 22.05/3.66 % Backward-rewritten : 0
% 22.05/3.66 % Generated clauses : 138491
% 22.05/3.66 % ...of the previous two non-redundant : 137947
% 22.05/3.66 % ...aggressively subsumed : 0
% 22.05/3.66 % Contextual simplify-reflections : 791
% 22.05/3.66 % Paramodulations : 138491
% 22.05/3.66 % Factorizations : 0
% 22.05/3.66 % NegExts : 0
% 22.05/3.66 % Equation resolutions : 0
% 22.05/3.66 % Disequality decompositions : 0
% 22.05/3.66 % Total rewrite steps : 532
% 22.05/3.66 % ...of those cached : 531
% 22.05/3.66 % Propositional unsat checks : 0
% 22.05/3.66 % Propositional check models : 0
% 22.05/3.66 % Propositional check unsatisfiable : 0
% 22.05/3.66 % Propositional clauses : 0
% 22.05/3.66 % Propositional clauses after purity: 0
% 22.05/3.66 % Propositional unsat core size : 0
% 22.05/3.66 % Propositional preprocessing time : 0.000
% 22.05/3.66 % Propositional encoding time : 0.000
% 22.05/3.66 % Propositional solver time : 0.000
% 22.05/3.66 % Success case prop preproc time : 0.000
% 22.05/3.66 % Success case prop encoding time : 0.000
% 22.05/3.66 % Success case prop solver time : 0.000
% 22.05/3.66 % Current number of processed clauses : 1050
% 22.05/3.66 % Positive orientable unit clauses : 1
% 22.05/3.66 % Positive unorientable unit clauses: 0
% 22.05/3.66 % Negative unit clauses : 2
% 22.05/3.66 % Non-unit-clauses : 1047
% 22.05/3.66 % Current number of unprocessed clauses: 130529
% 22.05/3.66 % ...number of literals in the above : 854724
% 22.05/3.66 % Current number of archived formulas : 0
% 22.05/3.66 % Current number of archived clauses : 170
% 22.05/3.66 % Clause-clause subsumption calls (NU) : 229320
% 22.05/3.66 % Rec. Clause-clause subsumption calls : 36360
% 22.05/3.66 % Non-unit clause-clause subsumptions : 7019
% 22.05/3.66 % Unit Clause-clause subsumption calls : 16
% 22.05/3.66 % Rewrite failures with RHS unbound : 0
% 22.05/3.66 % BW rewrite match attempts : 0
% 22.05/3.66 % BW rewrite match successes : 0
% 22.05/3.66 % Condensation attempts : 0
% 22.05/3.66 % Condensation successes : 0
% 22.05/3.66 % Termbank termtop insertions : 3910292
% 22.05/3.66 % Search garbage collected termcells : 368
% 22.05/3.66
% 22.05/3.66 % -------------------------------------------------
% 22.05/3.66 % User time : 3.035 s
% 22.05/3.66 % System time : 0.105 s
% 22.05/3.66 % Total time : 3.140 s
% 22.05/3.66 % Maximum resident set size: 3640 pages
% 22.05/3.66
% 22.05/3.66 % -------------------------------------------------
% 22.05/3.66 % User time : 14.978 s
% 22.05/3.66 % System time : 0.614 s
% 22.05/3.66 % Total time : 15.592 s
% 22.05/3.66 % Maximum resident set size: 4864 pages
% 22.05/3.66 % E exiting
%------------------------------------------------------------------------------