%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG074+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 : n016.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 11:51:27 AM UTC 2026
% Result : Theorem 61.15s 19.33s
% Output : CNFRefutation 61.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 5
% Syntax : Number of formulae : 90 ( 17 unt; 0 def)
% Number of atoms : 273 ( 76 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 312 ( 129 ~; 128 |; 33 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 130 ( 0 sgn 34 !; 8 ?)
% 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(ax1,axiom,
! [X1] :
( sorti1(X1)
=> ! [X2] :
( sorti1(X2)
=> sorti1(op1(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(ax4,axiom,
~ ? [X1] :
( ? [X2] :
( op2(op2(X1,X2),X1) != X2
& op2(op2(X1,X2),X2) = X1
& op2(X2,X1) != op2(X1,X2)
& sorti2(X2) )
& sorti2(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(ax3,axiom,
? [X1] :
( ? [X2] :
( op1(op1(X1,X2),X1) != X2
& op1(op1(X1,X2),X2) = X1
& op1(X2,X1) != op1(X1,X2)
& sorti1(X2) )
& sorti1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
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,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])])])]) ).
fof(c_0_7,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_8,plain,
( ~ sorti2(X2)
| ~ sorti2(X1)
| sorti2(op2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti1(X1)
| h(op1(X1,X2)) = op2(h(X1),h(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,negated_conjecture,
( ~ sorti1(X1)
| sorti2(h(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,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_12,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_8,c_0_9]),c_0_10]),c_0_10]) ).
cnf(c_0_13,negated_conjecture,
( ~ sorti2(X2)
| ~ sorti2(X1)
| j(op2(X1,X2)) = op1(j(X1),j(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
( ~ sorti2(X1)
| sorti1(j(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,plain,
( ~ sorti1(X2)
| ~ sorti1(X1)
| sorti1(op1(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,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_12,c_0_13]),c_0_14]),c_0_14]) ).
cnf(c_0_17,negated_conjecture,
( ~ sorti2(X1)
| h(j(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,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_15,c_0_13]),c_0_14]),c_0_14]) ).
fof(c_0_19,plain,
~ ? [X1] :
( ? [X2] :
( op2(op2(X1,X2),X1) != X2
& op2(op2(X1,X2),X2) = X1
& op2(X2,X1) != op2(X1,X2)
& sorti2(X2) )
& sorti2(X1) ),
inference(fof_simplification,[status(thm)],[ax4]) ).
cnf(c_0_20,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_16,c_0_9]),c_0_10]),c_0_10]) ).
cnf(c_0_21,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_9,c_0_17]),c_0_14]) ).
cnf(c_0_22,negated_conjecture,
( ~ sorti1(X1)
| j(h(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_23,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_18,c_0_9]),c_0_10]),c_0_10]) ).
cnf(c_0_24,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_9,c_0_17]),c_0_14]) ).
fof(c_0_25,plain,
! [X15,X16] :
( op2(op2(X15,X16),X15) = X16
| op2(op2(X15,X16),X16) != X15
| op2(X16,X15) = op2(X15,X16)
| ~ sorti2(X16)
| ~ sorti2(X15) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])]) ).
cnf(c_0_26,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti2(X1)
| sorti2(h(j(op2(X1,h(X2))))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_14]) ).
cnf(c_0_27,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_13,c_0_22]),c_0_10]) ).
cnf(c_0_28,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti2(X2)
| sorti1(j(op2(h(X1),X2))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_14]) ).
cnf(c_0_29,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_13,c_0_22]),c_0_10]) ).
cnf(c_0_30,plain,
( op2(op2(X1,X2),X2) != X1
| ~ sorti2(X2)
| ~ sorti2(X1)
| op2(op2(X1,X2),X1) = X2
| op2(X2,X1) = op2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_31,plain,
? [X1] :
( ? [X2] :
( op1(op1(X1,X2),X1) != X2
& op1(op1(X1,X2),X2) = X1
& op1(X2,X1) != op1(X1,X2)
& sorti1(X2) )
& sorti1(X1) ),
inference(fof_simplification,[status(thm)],[ax3]) ).
cnf(c_0_32,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti2(X1)
| sorti2(h(op1(j(X1),X2))) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti2(X1)
| sorti2(op2(X1,h(X2))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_21]),c_0_14]) ).
cnf(c_0_34,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti2(X2)
| sorti2(op2(h(X1),X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_24]),c_0_14]) ).
cnf(c_0_35,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti2(X2)
| sorti1(op1(X1,j(X2))) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti1(X2)
| op2(h(op1(X1,X2)),h(X2)) != h(X1)
| op2(h(X2),h(X1)) = h(op1(X1,X2))
| op2(h(op1(X1,X2)),h(X1)) = h(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_9]),c_0_10]),c_0_10]) ).
fof(c_0_37,plain,
( op1(op1(esk1_0,esk2_0),esk1_0) != esk2_0
& op1(op1(esk1_0,esk2_0),esk2_0) = esk1_0
& op1(esk2_0,esk1_0) != op1(esk1_0,esk2_0)
& sorti1(esk2_0)
& sorti1(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_31])])]) ).
cnf(c_0_38,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti1(X3)
| ~ sorti2(X1)
| sorti2(h(op1(op1(j(X1),X2),X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_27]),c_0_33]) ).
cnf(c_0_39,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti2(X2)
| ~ sorti2(X3)
| sorti2(op2(op2(h(X1),X2),X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_24]),c_0_35]) ).
cnf(c_0_40,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti1(X1)
| h(op1(op1(X2,X1),X1)) != h(X2)
| op2(h(op1(X2,X1)),h(X2)) = h(X1)
| op2(h(X1),h(X2)) = h(op1(X2,X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_9]),c_0_15]) ).
cnf(c_0_41,plain,
op1(op1(esk1_0,esk2_0),esk2_0) = esk1_0,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,plain,
sorti1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,plain,
sorti1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_44,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti1(X2)
| ~ sorti1(X3)
| sorti2(h(op1(op1(X1,X2),X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_22]),c_0_10]) ).
cnf(c_0_45,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti1(X1)
| ~ sorti2(X3)
| sorti2(op2(h(op1(X1,X2)),X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_9]),c_0_10]) ).
cnf(c_0_46,negated_conjecture,
( op2(h(esk2_0),h(esk1_0)) = h(op1(esk1_0,esk2_0))
| op2(h(op1(esk1_0,esk2_0)),h(esk1_0)) = h(esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_43])]) ).
cnf(c_0_47,negated_conjecture,
sorti2(h(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_41]),c_0_42]),c_0_43])]) ).
cnf(c_0_48,negated_conjecture,
( ~ sorti2(X1)
| ~ sorti2(X2)
| sorti1(j(h(j(op2(X1,X2))))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_13]),c_0_14]),c_0_14]) ).
cnf(c_0_49,negated_conjecture,
( sorti2(h(esk2_0))
| op2(h(esk2_0),h(esk1_0)) = h(op1(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_45,c_0_46]),c_0_47]),c_0_43]),c_0_42])]) ).
cnf(c_0_50,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti1(X2)
| sorti1(j(h(j(h(op1(X1,X2)))))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_9]),c_0_10]),c_0_10]) ).
cnf(c_0_51,negated_conjecture,
( sorti2(h(esk2_0))
| h(op1(esk1_0,esk2_0)) = h(op1(esk2_0,esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_49]),c_0_43]),c_0_42])]) ).
cnf(c_0_52,negated_conjecture,
( sorti1(j(h(j(h(op1(esk2_0,esk1_0))))))
| sorti2(h(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_42]),c_0_43])]) ).
cnf(c_0_53,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_29,c_0_9]),c_0_10]) ).
cnf(c_0_54,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti2(X1)
| sorti1(j(op2(X1,h(X2)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_21]),c_0_14]) ).
cnf(c_0_55,negated_conjecture,
( sorti1(j(h(op1(esk2_0,j(h(esk1_0))))))
| sorti2(h(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_42]),c_0_43])]) ).
cnf(c_0_56,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_27,c_0_9]),c_0_10]) ).
cnf(c_0_57,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti2(X1)
| sorti1(op1(j(X1),X2)) ),
inference(spm,[status(thm)],[c_0_54,c_0_27]) ).
cnf(c_0_58,negated_conjecture,
( ~ sorti1(j(h(esk1_0)))
| sorti1(op1(j(h(esk2_0)),j(h(esk1_0)))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_42])]),c_0_57]) ).
cnf(c_0_59,negated_conjecture,
sorti1(op1(j(h(esk2_0)),esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_22]),c_0_43])]) ).
cnf(c_0_60,negated_conjecture,
( sorti2(h(esk2_0))
| j(h(op1(esk2_0,esk1_0))) = op1(j(h(esk1_0)),esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_51]),c_0_42]),c_0_43])]) ).
cnf(c_0_61,negated_conjecture,
sorti1(op1(esk2_0,esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_22]),c_0_42])]) ).
cnf(c_0_62,negated_conjecture,
( ~ sorti1(op1(esk1_0,esk2_0))
| op1(j(h(op1(esk1_0,esk2_0))),esk2_0) = j(h(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_41]),c_0_42])]) ).
cnf(c_0_63,negated_conjecture,
( ~ sorti1(op1(esk1_0,esk2_0))
| sorti1(j(h(esk2_0)))
| op2(h(esk2_0),h(esk1_0)) = h(op1(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_46]),c_0_47])]) ).
cnf(c_0_64,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti1(X2)
| op1(j(h(X1)),X2) = op1(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_56]),c_0_15]) ).
cnf(c_0_65,negated_conjecture,
( sorti2(h(esk2_0))
| op1(j(h(esk1_0)),esk2_0) = op1(esk2_0,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_60]),c_0_61])]) ).
cnf(c_0_66,plain,
op1(esk2_0,esk1_0) != op1(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_67,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti1(X2)
| sorti1(op1(j(h(X1)),X2)) ),
inference(spm,[status(thm)],[c_0_23,c_0_56]) ).
cnf(c_0_68,negated_conjecture,
( ~ sorti1(op1(esk1_0,esk2_0))
| j(h(esk1_0)) = esk1_0 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_22]),c_0_41]) ).
cnf(c_0_69,negated_conjecture,
( sorti1(j(h(esk2_0)))
| op2(h(esk2_0),h(esk1_0)) = h(op1(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_15]),c_0_42]),c_0_43])]) ).
cnf(c_0_70,negated_conjecture,
sorti2(h(esk2_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_42]),c_0_43])]),c_0_66]) ).
cnf(c_0_71,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti1(op1(esk1_0,esk2_0))
| sorti1(op1(esk1_0,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_43])]) ).
cnf(c_0_72,negated_conjecture,
( sorti1(j(h(esk2_0)))
| sorti1(j(h(op1(esk1_0,esk2_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_69]),c_0_47]),c_0_70])]) ).
cnf(c_0_73,negated_conjecture,
( ~ sorti1(X1)
| sorti1(op1(esk1_0,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_15]),c_0_42]),c_0_43])]) ).
cnf(c_0_74,negated_conjecture,
sorti1(op1(esk1_0,j(h(esk2_0)))),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_53]),c_0_43]),c_0_42])]),c_0_73]) ).
cnf(c_0_75,negated_conjecture,
sorti1(op1(esk1_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_22]),c_0_42])]) ).
cnf(c_0_76,negated_conjecture,
( ~ sorti1(op1(esk1_0,esk2_0))
| op1(op1(esk1_0,esk2_0),j(h(esk2_0))) = j(h(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_41]),c_0_42])]) ).
cnf(c_0_77,negated_conjecture,
j(h(esk1_0)) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_75])]) ).
cnf(c_0_78,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti1(X1)
| ~ sorti2(X3)
| h(op1(X1,op1(X2,j(X3)))) = op2(h(X1),op2(h(X2),X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_24]),c_0_35]) ).
cnf(c_0_79,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti1(X1)
| ~ sorti2(X3)
| sorti1(op1(X1,op1(X2,j(X3)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_29]),c_0_34]) ).
cnf(c_0_80,negated_conjecture,
op1(op1(esk1_0,esk2_0),j(h(esk2_0))) = esk1_0,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_75])]),c_0_77]) ).
cnf(c_0_81,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti1(X1)
| ~ sorti2(X3)
| j(op2(h(X1),op2(h(X2),X3))) = op1(X1,op1(X2,j(X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_78]),c_0_79]) ).
cnf(c_0_82,negated_conjecture,
op2(h(op1(esk1_0,esk2_0)),h(esk2_0)) = h(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_80]),c_0_70]),c_0_75])]) ).
cnf(c_0_83,negated_conjecture,
( ~ sorti1(X1)
| j(op2(h(X1),h(esk1_0))) = op1(X1,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_80]),c_0_70]),c_0_75])]) ).
cnf(c_0_84,negated_conjecture,
( j(h(esk2_0)) = op1(op1(esk1_0,esk2_0),esk1_0)
| op2(h(esk2_0),h(esk1_0)) = h(op1(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_46]),c_0_75])]) ).
cnf(c_0_85,negated_conjecture,
( h(op1(esk1_0,esk2_0)) = h(op1(esk2_0,esk1_0))
| j(h(esk2_0)) = op1(op1(esk1_0,esk2_0),esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_84]),c_0_43]),c_0_42])]) ).
cnf(c_0_86,plain,
op1(op1(esk1_0,esk2_0),esk1_0) != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_87,negated_conjecture,
h(op1(esk1_0,esk2_0)) = h(op1(esk2_0,esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_85]),c_0_42])]),c_0_86]) ).
cnf(c_0_88,negated_conjecture,
j(h(op1(esk2_0,esk1_0))) = op1(esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_87]),c_0_75])]) ).
cnf(c_0_89,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_88]),c_0_61])]),c_0_66]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG074+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/10.39 % Computer : n016.cluster.edu
% 0.12/10.39 % Model : x86_64 x86_64
% 0.12/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.39 % Memory : 8046.5625MB
% 0.12/10.39 % OS : Linux 6.8.0-71-generic
% 0.12/10.39 % CPULimit : 300
% 0.12/10.39 % WCLimit : 300
% 0.12/10.39 % DateTime : Mon Sep 21 13:00:19 UTC 2026
% 0.12/10.39 % CPUTime :
% 0.12/10.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/10.43 Running first-order theorem proving
% 0.15/10.43 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
% 61.15/19.33 % Version: 3.5.1
% 61.15/19.33 % Preprocessing class: FSMSSMSSSSSNFFN.
% 61.15/19.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 61.15/19.33 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 61.15/19.33 % Starting new_bool_3 with 300s (1) cores
% 61.15/19.33 % Starting new_bool_1 with 300s (1) cores
% 61.15/19.33 % Starting sh5l with 300s (1) cores
% 61.15/19.33 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2463634 completed with status 0
% 61.15/19.33 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 61.15/19.33 % Preprocessing class: FSMSSMSSSSSNFFN.
% 61.15/19.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 61.15/19.33 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 61.15/19.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 61.15/19.33 % No SInE strategy applied
% 61.15/19.33 % Search class: FGUSF-FFSS21-SFFFFFNN
% 61.15/19.33 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 61.15/19.33 % Starting SubtermCWHack with 136s (1) cores
% 61.15/19.33 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 61.15/19.33 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 61.15/19.33 % Starting new_bool_3 with 136s (1) cores
% 61.15/19.33 % Starting new_bool_1 with 136s (1) cores
% 61.15/19.33 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2463639 completed with status 0
% 61.15/19.33 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 61.15/19.33 % Preprocessing class: FSMSSMSSSSSNFFN.
% 61.15/19.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 61.15/19.33 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 61.15/19.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 61.15/19.33 % No SInE strategy applied
% 61.15/19.33 % Search class: FGUSF-FFSS21-SFFFFFNN
% 61.15/19.33 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 61.15/19.33 % Starting SubtermCWHack with 136s (1) cores
% 61.15/19.33 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 61.15/19.33 % Preprocessing time : 0.001 s
% 61.15/19.33 % Presaturation interreduction done
% 61.15/19.33
% 61.15/19.33 % Proof found!
% 61.15/19.33 % SZS status Theorem
% 61.15/19.33 % SZS output start CNFRefutation
% See solution above
% 61.15/19.33 % Parsed axioms : 5
% 61.15/19.33 % Removed by relevancy pruning/SinE : 0
% 61.15/19.33 % Initial clauses : 14
% 61.15/19.33 % Removed in clause preprocessing : 0
% 61.15/19.33 % Initial clauses in saturation : 14
% 61.15/19.33 % Processed clauses : 14054
% 61.15/19.33 % ...of these trivial : 152
% 61.15/19.33 % ...subsumed : 12150
% 61.15/19.33 % ...remaining for further processing : 1752
% 61.15/19.33 % Other redundant clauses eliminated : 0
% 61.15/19.33 % Clauses deleted for lack of memory : 0
% 61.15/19.33 % Backward-subsumed : 70
% 61.15/19.33 % Backward-rewritten : 164
% 61.15/19.33 % Generated clauses : 350240
% 61.15/19.33 % ...of the previous two non-redundant : 344703
% 61.15/19.33 % ...aggressively subsumed : 0
% 61.15/19.33 % Contextual simplify-reflections : 976
% 61.15/19.33 % Paramodulations : 350240
% 61.15/19.33 % Factorizations : 0
% 61.15/19.33 % NegExts : 0
% 61.15/19.33 % Equation resolutions : 0
% 61.15/19.33 % Disequality decompositions : 0
% 61.15/19.33 % Total rewrite steps : 89450
% 61.15/19.33 % ...of those cached : 89301
% 61.15/19.33 % Propositional unsat checks : 0
% 61.15/19.33 % Propositional check models : 0
% 61.15/19.33 % Propositional check unsatisfiable : 0
% 61.15/19.33 % Propositional clauses : 0
% 61.15/19.33 % Propositional clauses after purity: 0
% 61.15/19.33 % Propositional unsat core size : 0
% 61.15/19.33 % Propositional preprocessing time : 0.000
% 61.15/19.33 % Propositional encoding time : 0.000
% 61.15/19.33 % Propositional solver time : 0.000
% 61.15/19.33 % Success case prop preproc time : 0.000
% 61.15/19.33 % Success case prop encoding time : 0.000
% 61.15/19.33 % Success case prop solver time : 0.000
% 61.15/19.33 % Current number of processed clauses : 1504
% 61.15/19.33 % Positive orientable unit clauses : 158
% 61.15/19.33 % Positive unorientable unit clauses: 0
% 61.15/19.33 % Negative unit clauses : 2
% 61.15/19.33 % Non-unit-clauses : 1344
% 61.15/19.33 % Current number of unprocessed clauses: 328859
% 61.15/19.33 % ...number of literals in the above : 2383212
% 61.15/19.33 % Current number of archived formulas : 0
% 61.15/19.33 % Current number of archived clauses : 248
% 61.15/19.33 % Clause-clause subsumption calls (NU) : 466452
% 61.15/19.33 % Rec. Clause-clause subsumption calls : 131740
% 61.15/19.33 % Non-unit clause-clause subsumptions : 13181
% 61.15/19.33 % Unit Clause-clause subsumption calls : 334
% 61.15/19.33 % Rewrite failures with RHS unbound : 0
% 61.15/19.33 % BW rewrite match attempts : 5065
% 61.15/19.33 % BW rewrite match successes : 29
% 61.15/19.33 % Condensation attempts : 0
% 61.15/19.33 % Condensation successes : 0
% 61.15/19.33 % Termbank termtop insertions : 10230788
% 61.15/19.33 % Search garbage collected termcells : 362
% 61.15/19.33
% 61.15/19.33 % -------------------------------------------------
% 61.15/19.33 % User time : 8.245 s
% 61.15/19.33 % System time : 0.359 s
% 61.15/19.33 % Total time : 8.604 s
% 61.15/19.33 % Maximum resident set size: 3384 pages
% 61.15/19.33
% 61.15/19.33 % -------------------------------------------------
% 61.15/19.33 % User time : 41.684 s
% 61.15/19.33 % System time : 1.707 s
% 61.15/19.33 % Total time : 43.392 s
% 61.15/19.33 % Maximum resident set size: 4864 pages
% 61.15/19.33 % E exiting
%------------------------------------------------------------------------------