%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL636+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n002.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 : Mon Sep 7 11:12:14 AM UTC 2026
% Result : Theorem 3.72s 2.23s
% Output : CNFRefutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 87 ( 0 equ)
% Maximal formula atoms : 69 ( 7 avg)
% Number of connectives : 146 ( 71 ~; 48 |; 27 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 16 ( 15 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ r1 > p2 > p102 > p101 > p100 > p1 > #nlpp > #skF_2 > #skF_5 > #skF_1 > #skF_4 > #skF_3
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff(p101,type,
p101: $i > $o ).
tff(p102,type,
p102: $i > $o ).
tff(p100,type,
p100: $i > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(r1,type,
r1: ( $i * $i ) > $o ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(p2,type,
p2: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff(p1,type,
p1: $i > $o ).
tff(f_241,negated_conjecture,
~ ~ ? [X] :
~ ( ~ ! [Y] :
( ~ r1(X,Y)
| p2(Y) )
| ~ ( ! [Y] :
( ~ r1(X,Y)
| ( ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p2(X)
& ~ p102(X)
& p101(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p2(X)
& ~ p102(X)
& p101(X) ) ) )
| ~ ( ~ p101(Y)
& p100(Y) ) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p2(X)
| ~ p101(X) )
| p2(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p2(X)
| ~ p101(X) )
| ~ p2(Y) ) )
| ~ p101(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p1(X)
| ~ p100(X) )
| p1(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p1(X)
| ~ p100(X) )
| ~ p1(Y) ) )
| ~ p100(Y) )
& ( p101(Y)
| ~ p102(Y) )
& ( p100(Y)
| ~ p101(Y) ) ) )
& ( ( ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ~ p2(Y)
& ~ p102(Y)
& p101(Y) ) )
& ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( p2(Y)
& ~ p102(Y)
& p101(Y) ) ) )
| ~ ( ~ p101(X)
& p100(X) ) )
& ( ( ( ! [Y] :
( ~ r1(X,Y)
| ~ p2(Y)
| ~ p101(Y) )
| p2(X) )
& ( ! [Y] :
( ~ r1(X,Y)
| p2(Y)
| ~ p101(Y) )
| ~ p2(X) ) )
| ~ p101(X) )
& ( ( ( ! [Y] :
( ~ r1(X,Y)
| ~ p1(Y)
| ~ p100(Y) )
| p1(X) )
& ( ! [Y] :
( ~ r1(X,Y)
| p1(Y)
| ~ p100(Y) )
| ~ p1(X) ) )
| ~ p100(X) )
& ( p101(X)
| ~ p102(X) )
& ( p100(X)
| ~ p101(X) )
& ~ p101(X)
& p100(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
tff(c_2,plain,
p100('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_241]) ).
tff(c_4,plain,
~ p101('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_241]) ).
tff(c_32,plain,
( ~ p2('#skF_4')
| ~ p100('#skF_1')
| p101('#skF_1') ),
inference(cnfTransformation,[status(thm)],[f_241]) ).
tff(c_71,plain,
( ~ p2('#skF_4')
| ~ p100('#skF_1') ),
inference(negUnitSimplification,[status(thm)],[c_4,c_32]) ).
tff(c_85,plain,
~ p2('#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_71]) ).
tff(c_34,plain,
( r1('#skF_1','#skF_4')
| ~ p100('#skF_1')
| p101('#skF_1') ),
inference(cnfTransformation,[status(thm)],[f_241]) ).
tff(c_67,plain,
( r1('#skF_1','#skF_4')
| ~ p100('#skF_1') ),
inference(negUnitSimplification,[status(thm)],[c_4,c_34]) ).
tff(c_83,plain,
r1('#skF_1','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_67]) ).
tff(c_10,plain,
! [Y_21] :
( p2(Y_21)
| ~ r1('#skF_1',Y_21) ),
inference(cnfTransformation,[status(thm)],[f_241]) ).
tff(c_100,plain,
p2('#skF_4'),
inference(resolution,[status(thm)],[c_83,c_10]) ).
tff(c_104,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_85,c_100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL636+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 5 13:24:35 UTC 2026
% 0.09/0.36 % CPUTime :
% 3.72/2.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.72/2.23
% 3.72/2.23 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------