%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG073+1 : TPTP v9.2.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n001.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 1.34s 1.75s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 62 ( 16 unt; 0 def)
% Number of atoms : 176 ( 65 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 191 ( 77 ~; 69 |; 25 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 12 ( 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 : 74 ( 0 sgn 30 !; 4 ?)
% 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/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax3,axiom,
? [X1] :
( sorti1(X1)
& ? [X2] :
( sorti1(X2)
& op1(X1,X1) = X2
& op1(X2,X2) = X1
& op1(X1,X2) != X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(ax2,axiom,
! [X1] :
( sorti2(X1)
=> ! [X2] :
( sorti2(X2)
=> sorti2(op2(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(ax4,axiom,
~ ? [X1] :
( sorti2(X1)
& ? [X2] :
( sorti2(X2)
& op2(X1,X1) = X2
& op2(X2,X2) = X1
& op2(X1,X2) != X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(c_0_4,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_5,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_4])])]) ).
cnf(c_0_6,negated_conjecture,
( h(j(X1)) = X1
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_7,negated_conjecture,
( sorti2(h(X1))
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
( h(j(h(X1))) = h(X1)
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,negated_conjecture,
( sorti1(j(X1))
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
( h(j(h(j(X1)))) = h(j(X1))
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,negated_conjecture,
( h(j(h(j(h(X1))))) = h(j(h(X1)))
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_7]) ).
cnf(c_0_12,negated_conjecture,
( h(j(h(j(h(j(X1)))))) = h(j(h(j(X1))))
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_9]) ).
fof(c_0_13,plain,
( sorti1(esk1_0)
& sorti1(esk2_0)
& op1(esk1_0,esk1_0) = esk2_0
& op1(esk2_0,esk2_0) = esk1_0
& op1(esk1_0,esk2_0) != esk1_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[ax3])]) ).
cnf(c_0_14,negated_conjecture,
( h(j(h(j(h(j(h(X1))))))) = h(j(h(j(h(X1)))))
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_7]) ).
cnf(c_0_15,negated_conjecture,
( j(h(X1)) = X1
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,plain,
sorti1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
( h(j(h(j(h(j(h(j(X1)))))))) = h(j(h(j(h(j(X1))))))
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_9]) ).
fof(c_0_18,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_19,negated_conjecture,
( h(op1(X1,X2)) = op2(h(X1),h(X2))
| ~ sorti1(X1)
| ~ sorti1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_20,negated_conjecture,
( j(op2(X1,X2)) = op1(j(X1),j(X2))
| ~ sorti2(X1)
| ~ sorti2(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_21,negated_conjecture,
j(h(esk2_0)) = esk2_0,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( h(j(h(j(h(j(h(j(h(X1))))))))) = h(j(h(j(h(j(h(X1)))))))
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_7]) ).
cnf(c_0_23,plain,
( sorti2(op2(X1,X2))
| ~ sorti2(X1)
| ~ sorti2(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,negated_conjecture,
( op2(h(X1),h(esk2_0)) = h(op1(X1,esk2_0))
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_25,negated_conjecture,
( j(op2(X1,h(esk2_0))) = op1(j(X1),esk2_0)
| ~ sorti2(h(esk2_0))
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
( h(j(h(j(h(j(h(j(h(j(X1)))))))))) = h(j(h(j(h(j(h(j(X1))))))))
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_9]) ).
cnf(c_0_27,plain,
sorti1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_28,negated_conjecture,
( sorti2(h(op1(X1,esk2_0)))
| ~ sorti2(h(esk2_0))
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_7]) ).
cnf(c_0_29,plain,
op1(esk2_0,esk2_0) = esk1_0,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_30,negated_conjecture,
( j(op2(X1,h(esk2_0))) = op1(j(X1),esk2_0)
| ~ sorti2(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_7]),c_0_16])]) ).
cnf(c_0_31,negated_conjecture,
( j(op2(h(esk2_0),X1)) = op1(esk2_0,j(X1))
| ~ sorti2(h(esk2_0))
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_32,negated_conjecture,
( h(j(h(j(h(j(h(j(h(j(h(X1))))))))))) = h(j(h(j(h(j(h(j(h(X1)))))))))
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_7]) ).
cnf(c_0_33,negated_conjecture,
j(h(esk1_0)) = esk1_0,
inference(spm,[status(thm)],[c_0_15,c_0_27]) ).
cnf(c_0_34,negated_conjecture,
( sorti2(h(esk1_0))
| ~ sorti2(h(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_16])]) ).
cnf(c_0_35,negated_conjecture,
( sorti1(op1(j(X1),esk2_0))
| ~ sorti2(op2(X1,h(esk2_0)))
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
( h(j(op2(X1,X2))) = op2(X1,X2)
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_23]) ).
cnf(c_0_37,negated_conjecture,
( j(op2(h(esk2_0),X1)) = op1(esk2_0,j(X1))
| ~ sorti2(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_7]),c_0_16])]) ).
cnf(c_0_38,negated_conjecture,
( sorti2(h(j(h(j(h(j(h(j(h(X1))))))))))
| ~ sorti1(j(h(j(h(j(h(j(h(j(h(X1)))))))))))
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_32]) ).
cnf(c_0_39,negated_conjecture,
( j(op2(h(esk1_0),X1)) = op1(esk1_0,j(X1))
| ~ sorti2(h(esk1_0))
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_33]) ).
cnf(c_0_40,negated_conjecture,
sorti2(h(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_7]),c_0_16])]) ).
cnf(c_0_41,negated_conjecture,
( sorti1(op1(j(X1),esk2_0))
| ~ sorti2(h(esk2_0))
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_23]) ).
fof(c_0_42,plain,
! [X31,X32] :
( ~ sorti2(X31)
| ~ sorti2(X32)
| op2(X31,X31) != X32
| op2(X32,X32) != X31
| op2(X31,X32) = X31 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])]) ).
cnf(c_0_43,negated_conjecture,
( h(op1(esk2_0,j(X1))) = op2(h(esk2_0),X1)
| ~ sorti2(h(esk2_0))
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,negated_conjecture,
sorti2(h(esk2_0)),
inference(cn,[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(spm,[status(thm)],[c_0_38,c_0_21]),c_0_21]),c_0_21]),c_0_21]),c_0_21]),c_0_21]),c_0_21]),c_0_21]),c_0_16]),c_0_16])]) ).
cnf(c_0_45,negated_conjecture,
( h(op1(j(X1),esk2_0)) = op2(X1,h(esk2_0))
| ~ sorti2(h(esk2_0))
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_30]) ).
cnf(c_0_46,negated_conjecture,
( j(op2(h(esk1_0),X1)) = op1(esk1_0,j(X1))
| ~ sorti2(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40])]) ).
cnf(c_0_47,negated_conjecture,
( sorti1(op1(esk1_0,esk2_0))
| ~ sorti2(h(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_33]),c_0_40])]) ).
cnf(c_0_48,plain,
( op2(X1,X2) = X1
| ~ sorti2(X1)
| ~ sorti2(X2)
| op2(X1,X1) != X2
| op2(X2,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,negated_conjecture,
( h(op1(esk2_0,j(X1))) = op2(h(esk2_0),X1)
| ~ sorti2(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]) ).
cnf(c_0_50,negated_conjecture,
( h(op1(j(X1),esk2_0)) = op2(X1,h(esk2_0))
| ~ sorti2(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_44])]) ).
cnf(c_0_51,negated_conjecture,
( h(op1(esk1_0,j(X1))) = op2(h(esk1_0),X1)
| ~ sorti2(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_46]),c_0_40])]) ).
cnf(c_0_52,plain,
op1(esk1_0,esk1_0) = esk2_0,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_53,negated_conjecture,
sorti1(op1(esk1_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_44])]) ).
cnf(c_0_54,plain,
( op2(op2(X1,X1),X1) = op2(X1,X1)
| op2(op2(X1,X1),op2(X1,X1)) != X1
| ~ sorti2(op2(X1,X1))
| ~ sorti2(X1) ),
inference(er,[status(thm)],[c_0_48]) ).
cnf(c_0_55,negated_conjecture,
op2(h(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_49,c_0_21]),c_0_29]),c_0_44])]) ).
cnf(c_0_56,negated_conjecture,
op2(h(esk1_0),h(esk2_0)) = h(op1(esk1_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_33]),c_0_40])]) ).
cnf(c_0_57,negated_conjecture,
op2(h(esk1_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_51,c_0_33]),c_0_52]),c_0_40])]) ).
cnf(c_0_58,negated_conjecture,
j(h(op1(esk1_0,esk2_0))) = op1(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_15,c_0_53]) ).
cnf(c_0_59,negated_conjecture,
h(op1(esk1_0,esk2_0)) = h(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_40]),c_0_44])]),c_0_56]),c_0_57])]) ).
cnf(c_0_60,plain,
op1(esk1_0,esk2_0) != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_61,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59]),c_0_33]),c_0_60]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG073+1 : TPTP v9.2.1. Released v2.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n001.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 10:21:03 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.34/1.75 % Version : CSE_E---1.7
% 1.34/1.75 % Problem : theBenchmark.p
% 1.34/1.75 % SZS status Theorem for theBenchmark.p
% 1.34/1.75 % SZS output start CNFRefutation
% See solution above
% 1.34/1.75 % Total time : 1.372s
%------------------------------------------------------------------------------