%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KRS167+1 : TPTP v9.2.1. Released v3.1.0.
% 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 : n004.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 04:36:46 PM UTC 2026
% Result : Theorem 1.25s 1.72s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 64 ( 6 unt; 0 def)
% Number of atoms : 249 ( 16 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 296 ( 111 ~; 150 |; 25 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-1 aty)
% Number of variables : 72 ( 10 sgn 28 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(the_axiom,conjecture,
( ! [X4] :
( cowlThing(X4)
& ~ cowlNothing(X4) )
& ! [X4] :
( xsd_string(X4)
<=> ~ xsd_integer(X4) )
& ! [X4] :
( cc1(X4)
<=> cc2(X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_axiom) ).
fof(axiom_0,axiom,
! [X4] :
( cowlThing(X4)
& ~ cowlNothing(X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
fof(axiom_3,axiom,
! [X4] :
( cc2(X4)
<=> ( ? [X5] : rp(X4,X5)
& ! [X5,X6] :
( ( rp(X4,X5)
& rp(X4,X6) )
=> X5 = X6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(axiom_2,axiom,
! [X4] :
( cc1(X4)
<=> ( ? [X5] : rp(X4,X5)
& ! [X5,X6] :
( ( rp(X4,X5)
& rp(X4,X6) )
=> X5 = X6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(axiom_1,axiom,
! [X4] :
( xsd_string(X4)
<=> ~ xsd_integer(X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(c_0_5,negated_conjecture,
~ ( ! [X4] :
( cowlThing(X4)
& ~ cowlNothing(X4) )
& ! [X4] :
( xsd_string(X4)
<=> ~ xsd_integer(X4) )
& ! [X4] :
( cc1(X4)
<=> cc2(X4) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[the_axiom])]) ).
fof(c_0_6,plain,
! [X4] :
( cowlThing(X4)
& ~ cowlNothing(X4) ),
inference(fof_simplification,[status(thm)],[axiom_0]) ).
fof(c_0_7,plain,
! [X66,X68,X69,X70,X71] :
( ( rp(X66,esk4_1(X66))
| ~ cc2(X66) )
& ( ~ rp(X66,X68)
| ~ rp(X66,X69)
| X68 = X69
| ~ cc2(X66) )
& ( rp(X70,esk5_1(X70))
| ~ rp(X70,X71)
| cc2(X70) )
& ( rp(X70,esk6_1(X70))
| ~ rp(X70,X71)
| cc2(X70) )
& ( esk5_1(X70) != esk6_1(X70)
| ~ rp(X70,X71)
| cc2(X70) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_3])])])])])]) ).
fof(c_0_8,plain,
! [X58,X60,X61,X62,X63] :
( ( rp(X58,esk1_1(X58))
| ~ cc1(X58) )
& ( ~ rp(X58,X60)
| ~ rp(X58,X61)
| X60 = X61
| ~ cc1(X58) )
& ( rp(X62,esk2_1(X62))
| ~ rp(X62,X63)
| cc1(X62) )
& ( rp(X62,esk3_1(X62))
| ~ rp(X62,X63)
| cc1(X62) )
& ( esk2_1(X62) != esk3_1(X62)
| ~ rp(X62,X63)
| cc1(X62) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_2])])])])])]) ).
fof(c_0_9,negated_conjecture,
( ( ~ cc1(esk9_0)
| ~ cc2(esk9_0)
| ~ xsd_string(esk8_0)
| xsd_integer(esk8_0)
| ~ cowlThing(esk7_0)
| cowlNothing(esk7_0) )
& ( cc1(esk9_0)
| cc2(esk9_0)
| ~ xsd_string(esk8_0)
| xsd_integer(esk8_0)
| ~ cowlThing(esk7_0)
| cowlNothing(esk7_0) )
& ( ~ cc1(esk9_0)
| ~ cc2(esk9_0)
| xsd_string(esk8_0)
| ~ xsd_integer(esk8_0)
| ~ cowlThing(esk7_0)
| cowlNothing(esk7_0) )
& ( cc1(esk9_0)
| cc2(esk9_0)
| xsd_string(esk8_0)
| ~ xsd_integer(esk8_0)
| ~ cowlThing(esk7_0)
| cowlNothing(esk7_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_10,plain,
! [X56] :
( cowlThing(X56)
& ~ cowlNothing(X56) ),
inference(variable_rename,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( X2 = X3
| ~ rp(X1,X2)
| ~ rp(X1,X3)
| ~ cc2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( rp(X1,esk4_1(X1))
| ~ cc2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( rp(X1,esk2_1(X1))
| cc1(X1)
| ~ rp(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( rp(X1,esk3_1(X1))
| cc1(X1)
| ~ rp(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
( cc1(esk9_0)
| cc2(esk9_0)
| xsd_integer(esk8_0)
| cowlNothing(esk7_0)
| ~ xsd_string(esk8_0)
| ~ cowlThing(esk7_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
cowlThing(X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_17,plain,
! [X4] :
( xsd_string(X4)
<=> ~ xsd_integer(X4) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
cnf(c_0_18,plain,
( X1 = esk4_1(X2)
| ~ rp(X2,X1)
| ~ cc2(X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_19,plain,
( rp(X1,esk2_1(X1))
| cc1(X1)
| ~ cc2(X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_20,plain,
( rp(X1,esk3_1(X1))
| cc1(X1)
| ~ cc2(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_21,negated_conjecture,
( cc1(esk9_0)
| cc2(esk9_0)
| xsd_string(esk8_0)
| cowlNothing(esk7_0)
| ~ xsd_integer(esk8_0)
| ~ cowlThing(esk7_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_22,negated_conjecture,
( cc1(esk9_0)
| cc2(esk9_0)
| cowlNothing(esk7_0)
| xsd_integer(esk8_0)
| ~ xsd_string(esk8_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]) ).
cnf(c_0_23,plain,
~ cowlNothing(X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_24,plain,
! [X57] :
( ( ~ xsd_string(X57)
| ~ xsd_integer(X57) )
& ( xsd_integer(X57)
| xsd_string(X57) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])]) ).
cnf(c_0_25,negated_conjecture,
( xsd_integer(esk8_0)
| cowlNothing(esk7_0)
| ~ cc1(esk9_0)
| ~ cc2(esk9_0)
| ~ xsd_string(esk8_0)
| ~ cowlThing(esk7_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_26,plain,
( esk4_1(X1) = esk2_1(X1)
| cc1(X1)
| ~ cc2(X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_27,plain,
( esk4_1(X1) = esk3_1(X1)
| cc1(X1)
| ~ cc2(X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_28,negated_conjecture,
( cc1(esk9_0)
| cc2(esk9_0)
| cowlNothing(esk7_0)
| xsd_string(esk8_0)
| ~ xsd_integer(esk8_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_16])]) ).
cnf(c_0_29,negated_conjecture,
( xsd_integer(esk8_0)
| cc2(esk9_0)
| cc1(esk9_0)
| ~ xsd_string(esk8_0) ),
inference(sr,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
( xsd_integer(X1)
| xsd_string(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( rp(X1,esk5_1(X1))
| cc2(X1)
| ~ rp(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_32,plain,
( rp(X1,esk1_1(X1))
| ~ cc1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_33,negated_conjecture,
( xsd_string(esk8_0)
| cowlNothing(esk7_0)
| ~ cc1(esk9_0)
| ~ cc2(esk9_0)
| ~ xsd_integer(esk8_0)
| ~ cowlThing(esk7_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_34,negated_conjecture,
( cowlNothing(esk7_0)
| xsd_integer(esk8_0)
| ~ cc1(esk9_0)
| ~ cc2(esk9_0)
| ~ xsd_string(esk8_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_16])]) ).
cnf(c_0_35,plain,
( cc1(X1)
| esk2_1(X1) != esk3_1(X1)
| ~ rp(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_36,plain,
( esk3_1(X1) = esk2_1(X1)
| cc1(X1)
| ~ cc2(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_37,negated_conjecture,
( xsd_string(esk8_0)
| cc2(esk9_0)
| cc1(esk9_0)
| ~ xsd_integer(esk8_0) ),
inference(sr,[status(thm)],[c_0_28,c_0_23]) ).
cnf(c_0_38,negated_conjecture,
( xsd_integer(esk8_0)
| cc2(esk9_0)
| cc1(esk9_0) ),
inference(csr,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_39,plain,
( X2 = X3
| ~ rp(X1,X2)
| ~ rp(X1,X3)
| ~ cc1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_40,plain,
( rp(X1,esk5_1(X1))
| cc2(X1)
| ~ cc1(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_41,plain,
( rp(X1,esk6_1(X1))
| cc2(X1)
| ~ rp(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_42,negated_conjecture,
( cowlNothing(esk7_0)
| xsd_string(esk8_0)
| ~ cc1(esk9_0)
| ~ cc2(esk9_0)
| ~ xsd_integer(esk8_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_16])]) ).
cnf(c_0_43,negated_conjecture,
( xsd_integer(esk8_0)
| ~ xsd_string(esk8_0)
| ~ cc2(esk9_0)
| ~ cc1(esk9_0) ),
inference(sr,[status(thm)],[c_0_34,c_0_23]) ).
cnf(c_0_44,plain,
( cc1(X1)
| ~ rp(X1,X2)
| ~ cc2(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_45,plain,
( ~ xsd_string(X1)
| ~ xsd_integer(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_46,negated_conjecture,
( xsd_string(esk8_0)
| cc2(esk9_0)
| cc1(esk9_0) ),
inference(csr,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_47,plain,
( X1 = esk5_1(X2)
| cc2(X2)
| ~ rp(X2,X1)
| ~ cc1(X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,plain,
( rp(X1,esk6_1(X1))
| cc2(X1)
| ~ cc1(X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_32]) ).
cnf(c_0_49,negated_conjecture,
( xsd_string(esk8_0)
| ~ xsd_integer(esk8_0)
| ~ cc2(esk9_0)
| ~ cc1(esk9_0) ),
inference(sr,[status(thm)],[c_0_42,c_0_23]) ).
cnf(c_0_50,negated_conjecture,
( xsd_integer(esk8_0)
| ~ cc2(esk9_0)
| ~ cc1(esk9_0) ),
inference(csr,[status(thm)],[c_0_43,c_0_30]) ).
cnf(c_0_51,plain,
( cc1(X1)
| ~ cc2(X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_12]) ).
cnf(c_0_52,negated_conjecture,
( cc2(esk9_0)
| cc1(esk9_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_38]) ).
cnf(c_0_53,plain,
( cc2(X1)
| esk5_1(X1) != esk6_1(X1)
| ~ rp(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_54,plain,
( esk6_1(X1) = esk5_1(X1)
| cc2(X1)
| ~ cc1(X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_55,negated_conjecture,
( xsd_string(esk8_0)
| ~ cc2(esk9_0)
| ~ cc1(esk9_0) ),
inference(csr,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_56,negated_conjecture,
cc1(esk9_0),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_57,plain,
( cc2(X1)
| ~ rp(X1,X2)
| ~ cc1(X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_58,negated_conjecture,
( xsd_string(esk8_0)
| ~ cc2(esk9_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56])]) ).
cnf(c_0_59,plain,
( cc2(X1)
| ~ cc1(X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_48]) ).
cnf(c_0_60,negated_conjecture,
( xsd_integer(esk8_0)
| ~ cc2(esk9_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_56])]) ).
cnf(c_0_61,negated_conjecture,
xsd_string(esk8_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_56])]) ).
cnf(c_0_62,negated_conjecture,
xsd_integer(esk8_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_59]),c_0_56])]) ).
cnf(c_0_63,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_61]),c_0_62])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS167+1 : TPTP v9.2.1. Released v3.1.0.
% 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 : n004.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 : Mon May 4 20:41:17 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.25/1.72 % Version : CSE_E---1.7
% 1.25/1.72 % Problem : theBenchmark.p
% 1.25/1.72 % SZS status Theorem for theBenchmark.p
% 1.25/1.72 % SZS output start CNFRefutation
% See solution above
% 1.25/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------