%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KRS169+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 : n013.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 1.24s 1.71s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 8 unt; 0 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 110 ( 48 ~; 41 |; 16 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 20 ( 2 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(the_axiom,conjecture,
( ! [X1] :
( cowlThing(X1)
& ~ cowlNothing(X1) )
& ! [X1] :
( xsd_string(X1)
<=> ~ xsd_integer(X1) )
& cowlThing(iX)
& rhasHead(iX,iY)
& cowlThing(iY) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_axiom) ).
fof(axiom_0,axiom,
! [X1] :
( cowlThing(X1)
& ~ cowlNothing(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
fof(axiom_5,axiom,
! [X1,X2] :
( rhasLeader(X1,X2)
<=> rhasHead(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(axiom_1,axiom,
! [X1] :
( xsd_string(X1)
<=> ~ xsd_integer(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(axiom_3,axiom,
rhasLeader(iX,iY),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(c_0_5,negated_conjecture,
~ ( ! [X1] :
( cowlThing(X1)
& ~ cowlNothing(X1) )
& ! [X1] :
( xsd_string(X1)
<=> ~ xsd_integer(X1) )
& cowlThing(iX)
& rhasHead(iX,iY)
& cowlThing(iY) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[the_axiom])]) ).
fof(c_0_6,plain,
! [X1] :
( cowlThing(X1)
& ~ cowlNothing(X1) ),
inference(fof_simplification,[status(thm)],[axiom_0]) ).
fof(c_0_7,negated_conjecture,
( ( ~ xsd_string(esk2_0)
| xsd_integer(esk2_0)
| ~ cowlThing(esk1_0)
| cowlNothing(esk1_0)
| ~ cowlThing(iX)
| ~ rhasHead(iX,iY)
| ~ cowlThing(iY) )
& ( xsd_string(esk2_0)
| ~ xsd_integer(esk2_0)
| ~ cowlThing(esk1_0)
| cowlNothing(esk1_0)
| ~ cowlThing(iX)
| ~ rhasHead(iX,iY)
| ~ cowlThing(iY) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_8,plain,
! [X9] :
( cowlThing(X9)
& ~ cowlNothing(X9) ),
inference(variable_rename,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
( xsd_string(esk2_0)
| cowlNothing(esk1_0)
| ~ xsd_integer(esk2_0)
| ~ cowlThing(esk1_0)
| ~ cowlThing(iX)
| ~ rhasHead(iX,iY)
| ~ cowlThing(iY) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
cowlThing(X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X11,X12] :
( ( ~ rhasLeader(X11,X12)
| rhasHead(X11,X12) )
& ( ~ rhasHead(X11,X12)
| rhasLeader(X11,X12) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_5])]) ).
fof(c_0_12,plain,
! [X1] :
( xsd_string(X1)
<=> ~ xsd_integer(X1) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
cnf(c_0_13,negated_conjecture,
( xsd_integer(esk2_0)
| cowlNothing(esk1_0)
| ~ xsd_string(esk2_0)
| ~ cowlThing(esk1_0)
| ~ cowlThing(iX)
| ~ rhasHead(iX,iY)
| ~ cowlThing(iY) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
( cowlNothing(esk1_0)
| xsd_string(esk2_0)
| ~ xsd_integer(esk2_0)
| ~ rhasHead(iX,iY) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_10]),c_0_10])]) ).
cnf(c_0_15,plain,
~ cowlNothing(X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,plain,
( rhasHead(X1,X2)
| ~ rhasLeader(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
rhasLeader(iX,iY),
inference(split_conjunct,[status(thm)],[axiom_3]) ).
fof(c_0_18,plain,
! [X10] :
( ( ~ xsd_string(X10)
| ~ xsd_integer(X10) )
& ( xsd_integer(X10)
| xsd_string(X10) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).
cnf(c_0_19,negated_conjecture,
( cowlNothing(esk1_0)
| xsd_integer(esk2_0)
| ~ xsd_string(esk2_0)
| ~ rhasHead(iX,iY) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_10]),c_0_10]),c_0_10])]) ).
cnf(c_0_20,negated_conjecture,
( xsd_string(esk2_0)
| ~ rhasHead(iX,iY)
| ~ xsd_integer(esk2_0) ),
inference(sr,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
rhasHead(iX,iY),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( ~ xsd_string(X1)
| ~ xsd_integer(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( xsd_integer(esk2_0)
| ~ rhasHead(iX,iY)
| ~ xsd_string(esk2_0) ),
inference(sr,[status(thm)],[c_0_19,c_0_15]) ).
cnf(c_0_24,negated_conjecture,
~ xsd_integer(esk2_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]),c_0_22]) ).
cnf(c_0_25,plain,
( xsd_integer(X1)
| xsd_string(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,negated_conjecture,
~ xsd_string(esk2_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_21])]),c_0_24]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS169+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
% 0.15/0.32 % Computer : n013.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 20:40:11 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.24/1.71 % Version : CSE_E---1.7
% 1.24/1.71 % Problem : theBenchmark.p
% 1.24/1.71 % SZS status Theorem for theBenchmark.p
% 1.24/1.71 % SZS output start CNFRefutation
% See solution above
% 1.24/1.71 % Total time : 1.372s
%------------------------------------------------------------------------------