%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG072+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 : n005.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 11.58s 7.47s
% Output : CNFRefutation 11.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 66 ( 17 unt; 0 def)
% Number of atoms : 210 ( 88 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 237 ( 93 ~; 84 |; 34 &)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 87 ( 0 sgn 39 !; 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(ax6,axiom,
! [X1] :
( sorti2(X1)
=> ! [X2] :
( sorti2(X2)
=> sorti2(op2(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
fof(ax7,axiom,
? [X1] :
( sorti1(X1)
& ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> ( op1(X2,X3) != X1
| ( op1(X2,X1) = X3
& X1 != unit1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7) ).
fof(ax2,axiom,
( ! [X1] :
( sorti1(X1)
=> ( op1(unit1,X1) = X1
& op1(X1,unit1) = X1 ) )
& ? [X2] :
( sorti1(X2)
& unit1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(ax1,axiom,
sorti1(unit1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
fof(ax4,axiom,
( ! [X1] :
( sorti2(X1)
=> ( op2(unit2,X1) = X1
& op2(X1,unit2) = X1 ) )
& ? [X2] :
( sorti2(X2)
& unit2 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(ax3,axiom,
sorti2(unit2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(ax8,axiom,
~ ? [X1] :
( sorti2(X1)
& ! [X2] :
( sorti2(X2)
=> ! [X3] :
( sorti2(X3)
=> ( op2(X2,X3) != X1
| ( op2(X2,X1) = X3
& X1 != unit2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8) ).
fof(c_0_8,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_9,negated_conjecture,
! [X45,X46,X47,X48,X49,X50,X51,X52] :
( ( ~ sorti1(X45)
| sorti2(h(X45)) )
& ( ~ sorti2(X46)
| sorti1(j(X46)) )
& ( ~ sorti1(X47)
| ~ sorti1(X48)
| h(op1(X47,X48)) = op2(h(X47),h(X48)) )
& ( ~ sorti2(X49)
| ~ sorti2(X50)
| j(op2(X49,X50)) = op1(j(X49),j(X50)) )
& ( ~ sorti2(X51)
| h(j(X51)) = X51 )
& ( ~ sorti1(X52)
| j(h(X52)) = X52 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_10,plain,
! [X37,X38] :
( ~ sorti2(X37)
| ~ sorti2(X38)
| sorti2(op2(X37,X38)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])])]) ).
fof(c_0_11,plain,
! [X40,X41] :
( sorti1(esk3_0)
& ( op1(X40,esk3_0) = X41
| op1(X40,X41) != esk3_0
| ~ sorti1(X41)
| ~ sorti1(X40) )
& ( esk3_0 != unit1
| op1(X40,X41) != esk3_0
| ~ sorti1(X41)
| ~ sorti1(X40) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax7])])])])]) ).
fof(c_0_12,plain,
! [X31] :
( ( op1(unit1,X31) = X31
| ~ sorti1(X31) )
& ( op1(X31,unit1) = X31
| ~ sorti1(X31) )
& sorti1(esk1_0)
& unit1 = esk1_0 ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax2])])])])]) ).
cnf(c_0_13,negated_conjecture,
( h(op1(X1,X2)) = op2(h(X1),h(X2))
| ~ sorti1(X1)
| ~ sorti1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( h(j(X1)) = X1
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
( sorti1(j(X1))
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( sorti2(op2(X1,X2))
| ~ sorti2(X1)
| ~ sorti2(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
( sorti2(h(X1))
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,plain,
( op1(X1,esk3_0) = X2
| op1(X1,X2) != esk3_0
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( op1(X1,unit1) = X1
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
sorti1(unit1),
inference(split_conjunct,[status(thm)],[ax1]) ).
cnf(c_0_21,plain,
sorti1(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_22,plain,
! [X33] :
( ( op2(unit2,X33) = X33
| ~ sorti2(X33) )
& ( op2(X33,unit2) = X33
| ~ sorti2(X33) )
& sorti2(esk2_0)
& unit2 = esk2_0 ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])])])]) ).
cnf(c_0_23,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_13,c_0_14]),c_0_15]) ).
cnf(c_0_24,plain,
( op1(unit1,X1) = X1
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_25,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_16,c_0_13]),c_0_17]),c_0_17]) ).
cnf(c_0_26,plain,
op1(esk3_0,esk3_0) = unit1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])])]),c_0_21])]) ).
cnf(c_0_27,plain,
( op2(X1,unit2) = X1
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
( op2(h(unit1),X1) = h(j(X1))
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_20])]),c_0_15]) ).
cnf(c_0_29,negated_conjecture,
sorti2(h(unit1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_21])]) ).
cnf(c_0_30,plain,
sorti2(unit2),
inference(split_conjunct,[status(thm)],[ax3]) ).
cnf(c_0_31,negated_conjecture,
h(j(unit2)) = h(unit1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30])]) ).
cnf(c_0_32,negated_conjecture,
h(unit1) = unit2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_31]),c_0_30])]) ).
cnf(c_0_33,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_13,c_0_14]),c_0_15]) ).
cnf(c_0_34,negated_conjecture,
( j(op2(X1,X2)) = op1(j(X1),j(X2))
| ~ sorti2(X1)
| ~ sorti2(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_35,negated_conjecture,
( h(j(X1)) = op2(unit2,X1)
| ~ sorti2(X1) ),
inference(rw,[status(thm)],[c_0_28,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( h(j(X1)) = op2(X1,unit2)
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_19]),c_0_32]),c_0_20])]),c_0_15]) ).
cnf(c_0_37,negated_conjecture,
( j(h(X1)) = X1
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_38,negated_conjecture,
( op1(j(X1),esk3_0) = j(X2)
| j(op2(X1,X2)) != esk3_0
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_34]),c_0_15]),c_0_15]) ).
cnf(c_0_39,negated_conjecture,
( op2(X1,unit2) = op2(unit2,X1)
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
j(unit2) = unit1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_32]),c_0_20])]) ).
cnf(c_0_41,plain,
op1(unit1,esk3_0) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_24]),c_0_20])])]),c_0_21])]) ).
cnf(c_0_42,negated_conjecture,
( j(X1) = esk3_0
| j(op2(X1,unit2)) != esk3_0
| ~ sorti2(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_41]),c_0_30])]) ).
cnf(c_0_43,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_34,c_0_37]),c_0_17]) ).
cnf(c_0_44,negated_conjecture,
( j(op2(X1,unit2)) = op1(j(X1),unit1)
| ~ sorti2(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_40]),c_0_30])]) ).
fof(c_0_45,plain,
! [X42] :
( ( sorti2(esk4_1(X42))
| ~ sorti2(X42) )
& ( sorti2(esk5_1(X42))
| ~ sorti2(X42) )
& ( op2(esk4_1(X42),esk5_1(X42)) = X42
| ~ sorti2(X42) )
& ( op2(esk4_1(X42),X42) != esk5_1(X42)
| X42 = unit2
| ~ sorti2(X42) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax8])])])]) ).
cnf(c_0_46,negated_conjecture,
( j(h(X1)) = esk3_0
| op1(X1,unit1) != esk3_0
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_40]),c_0_30])]),c_0_17]) ).
cnf(c_0_47,negated_conjecture,
( op1(j(X1),unit1) = j(X1)
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_27]) ).
cnf(c_0_48,plain,
( op2(esk4_1(X1),esk5_1(X1)) = X1
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_49,plain,
( sorti2(esk4_1(X1))
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_50,plain,
( sorti2(esk5_1(X1))
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_51,negated_conjecture,
( h(esk3_0) = h(X1)
| op1(X1,unit1) != esk3_0
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_46]),c_0_17]) ).
cnf(c_0_52,negated_conjecture,
( op1(esk3_0,unit1) = esk3_0
| op1(X1,unit1) != esk3_0
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_46]),c_0_17]) ).
cnf(c_0_53,negated_conjecture,
( op1(j(esk4_1(X1)),esk3_0) = j(esk5_1(X1))
| j(X1) != esk3_0
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_48]),c_0_49]),c_0_50]) ).
cnf(c_0_54,negated_conjecture,
( j(h(esk3_0)) = esk3_0
| op1(X1,unit1) != esk3_0
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_51]) ).
cnf(c_0_55,negated_conjecture,
op1(esk3_0,unit1) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_19])]),c_0_21])]) ).
cnf(c_0_56,plain,
( X1 = unit2
| op2(esk4_1(X1),X1) != esk5_1(X1)
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_57,negated_conjecture,
( op2(esk4_1(X1),h(esk3_0)) = h(j(esk5_1(X1)))
| j(X1) != esk3_0
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_53]),c_0_21])]),c_0_49]) ).
cnf(c_0_58,negated_conjecture,
sorti2(h(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_41]),c_0_21]),c_0_20])]) ).
cnf(c_0_59,negated_conjecture,
j(h(esk3_0)) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_21])]) ).
cnf(c_0_60,negated_conjecture,
( h(esk3_0) = unit2
| h(j(esk5_1(h(esk3_0)))) != esk5_1(h(esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_59])]) ).
cnf(c_0_61,negated_conjecture,
( h(esk3_0) = unit2
| ~ sorti2(esk5_1(h(esk3_0))) ),
inference(spm,[status(thm)],[c_0_60,c_0_14]) ).
cnf(c_0_62,plain,
( esk3_0 != unit1
| op1(X1,X2) != esk3_0
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_63,negated_conjecture,
h(esk3_0) = unit2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_50]),c_0_58])]) ).
cnf(c_0_64,plain,
esk3_0 != unit1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_24]),c_0_20])])]),c_0_21])]) ).
cnf(c_0_65,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_63]),c_0_40]),c_0_64]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG072+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
% 0.16/0.33 % Computer : n005.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 10:20:00 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 11.58/7.47 % Version : CSE_E---1.7
% 11.58/7.47 % Problem : theBenchmark.p
% 11.58/7.47 % SZS status Theorem for theBenchmark.p
% 11.58/7.47 % SZS output start CNFRefutation
% See solution above
% 11.69/7.52 % Total time : 5.371s
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