%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL674+1.005 : 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 : n026.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 11:12:29 AM UTC 2026
% Result : Theorem 8.40s 2.99s
% Output : CNFRefutation 8.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 38 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 217 ( 0 equ)
% Maximal formula atoms : 121 ( 5 avg)
% Number of connectives : 338 ( 159 ~; 123 |; 55 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 14 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 1 con; 0-1 aty)
% Number of variables : 46 ( 45 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ r1 > p6 > p5 > p4 > p3 > p2 > p106 > p105 > p104 > p103 > p102 > p101 > p100 > p1 > #nlpp > #skF_9 > #skF_7 > #skF_5 > #skF_2 > #skF_4 > #skF_8 > #skF_10 > #skF_1 > #skF_3 > #skF_11 > #skF_6
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_9',type,
'#skF_9': $i > $i ).
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(p3,type,
p3: $i > $o ).
tff(p106,type,
p106: $i > $o ).
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(p101,type,
p101: $i > $o ).
tff(p102,type,
p102: $i > $o ).
tff(p100,type,
p100: $i > $o ).
tff('#skF_8',type,
'#skF_8': $i > $i ).
tff(p103,type,
p103: $i > $o ).
tff('#skF_10',type,
'#skF_10': $i > $i ).
tff(p5,type,
p5: $i > $o ).
tff(p4,type,
p4: $i > $o ).
tff(p6,type,
p6: $i > $o ).
tff(r1,type,
r1: ( $i * $i ) > $o ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(p2,type,
p2: $i > $o ).
tff(p105,type,
p105: $i > $o ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff('#skF_11',type,
'#skF_11': $i > $i ).
tff(p104,type,
p104: $i > $o ).
tff(p1,type,
p1: $i > $o ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff(f_412,negated_conjecture,
~ ~ ? [X] :
~ ( ~ ! [Y] :
( ~ r1(X,Y)
| p3(Y) )
| ~ ( ! [Y] :
( ~ r1(X,Y)
| ( ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p6(X)
& ~ p106(X)
& p105(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p6(X)
& ~ p106(X)
& p105(X) ) ) )
| ~ ( ~ p105(Y)
& p104(Y) ) )
& ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p5(X)
& ~ p105(X)
& p104(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p5(X)
& ~ p105(X)
& p104(X) ) ) )
| ~ ( ~ p104(Y)
& p103(Y) ) )
& ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p4(X)
& ~ p104(X)
& p103(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p4(X)
& ~ p104(X)
& p103(X) ) ) )
| ~ ( ~ p103(Y)
& p102(Y) ) )
& ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p3(X)
& ~ p103(X)
& p102(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p3(X)
& ~ p103(X)
& p102(X) ) ) )
| ~ ( ~ p102(Y)
& p101(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)
| ~ p6(X)
| ~ p105(X) )
| p6(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p6(X)
| ~ p105(X) )
| ~ p6(Y) ) )
| ~ p105(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p5(X)
| ~ p104(X) )
| p5(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p5(X)
| ~ p104(X) )
| ~ p5(Y) ) )
| ~ p104(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p4(X)
| ~ p103(X) )
| p4(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p4(X)
| ~ p103(X) )
| ~ p4(Y) ) )
| ~ p103(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p3(X)
| ~ p102(X) )
| p3(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p3(X)
| ~ p102(X) )
| ~ p3(Y) ) )
| ~ p102(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) )
& ( p105(Y)
| ~ p106(Y) )
& ( p104(Y)
| ~ p105(Y) )
& ( p103(Y)
| ~ p104(Y) )
& ( p102(Y)
| ~ p103(Y) )
& ( p101(Y)
| ~ p102(Y) )
& ( p100(Y)
| ~ p101(Y) ) ) )
& ~ p101(X)
& p100(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
tff(f_29,axiom,
! [X] : r1(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
tff(f_35,axiom,
! [X,Y,Z] :
( ( r1(X,Y)
& r1(Y,Z) )
=> r1(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
tff(c_8,plain,
~ p101('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_412]) ).
tff(c_2,plain,
! [X_1] : r1(X_1,X_1),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_6,plain,
p100('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_412]) ).
tff(c_828,plain,
! [Y_138] :
( r1(Y_138,'#skF_10'(Y_138))
| ~ p100(Y_138)
| p101(Y_138)
| ~ r1('#skF_1',Y_138) ),
inference(cnfTransformation,[status(thm)],[f_412]) ).
tff(c_14,plain,
! [Y_52] :
( ~ p102(Y_52)
| p101(Y_52)
| ~ r1('#skF_1',Y_52) ),
inference(cnfTransformation,[status(thm)],[f_412]) ).
tff(c_842,plain,
( ~ p102('#skF_10'('#skF_1'))
| p101('#skF_10'('#skF_1'))
| ~ p100('#skF_1')
| p101('#skF_1')
| ~ r1('#skF_1','#skF_1') ),
inference(resolution,[status(thm)],[c_828,c_14]) ).
tff(c_870,plain,
( ~ p102('#skF_10'('#skF_1'))
| p101('#skF_10'('#skF_1'))
| p101('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6,c_842]) ).
tff(c_871,plain,
( ~ p102('#skF_10'('#skF_1'))
| p101('#skF_10'('#skF_1')) ),
inference(negUnitSimplification,[status(thm)],[c_8,c_870]) ).
tff(c_923,plain,
~ p102('#skF_10'('#skF_1')),
inference(splitLeft,[status(thm)],[c_871]) ).
tff(c_56,plain,
! [Y_52] :
( p101('#skF_10'(Y_52))
| ~ p100(Y_52)
| p101(Y_52)
| ~ r1('#skF_1',Y_52) ),
inference(cnfTransformation,[status(thm)],[f_412]) ).
tff(c_12,plain,
! [Y_52] :
( ~ p101(Y_52)
| p100(Y_52)
| ~ r1('#skF_1',Y_52) ),
inference(cnfTransformation,[status(thm)],[f_412]) ).
tff(c_854,plain,
( ~ p101('#skF_10'('#skF_1'))
| p100('#skF_10'('#skF_1'))
| ~ p100('#skF_1')
| p101('#skF_1')
| ~ r1('#skF_1','#skF_1') ),
inference(resolution,[status(thm)],[c_828,c_12]) ).
tff(c_882,plain,
( ~ p101('#skF_10'('#skF_1'))
| p100('#skF_10'('#skF_1'))
| p101('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6,c_854]) ).
tff(c_883,plain,
( ~ p101('#skF_10'('#skF_1'))
| p100('#skF_10'('#skF_1')) ),
inference(negUnitSimplification,[status(thm)],[c_8,c_882]) ).
tff(c_958,plain,
~ p101('#skF_10'('#skF_1')),
inference(splitLeft,[status(thm)],[c_883]) ).
tff(c_961,plain,
( ~ p100('#skF_1')
| p101('#skF_1')
| ~ r1('#skF_1','#skF_1') ),
inference(resolution,[status(thm)],[c_56,c_958]) ).
tff(c_964,plain,
p101('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6,c_961]) ).
tff(c_966,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8,c_964]) ).
tff(c_968,plain,
p101('#skF_10'('#skF_1')),
inference(splitRight,[status(thm)],[c_883]) ).
tff(c_62,plain,
! [Y_52] :
( r1(Y_52,'#skF_10'(Y_52))
| ~ p100(Y_52)
| p101(Y_52)
| ~ r1('#skF_1',Y_52) ),
inference(cnfTransformation,[status(thm)],[f_412]) ).
tff(c_708,plain,
! [Y_136] :
( r1(Y_136,'#skF_8'(Y_136))
| ~ p101(Y_136)
| p102(Y_136)
| ~ r1('#skF_1',Y_136) ),
inference(cnfTransformation,[status(thm)],[f_412]) ).
tff(c_4,plain,
! [X_2,Z_4,Y_3] :
( r1(X_2,Z_4)
| ~ r1(Y_3,Z_4)
| ~ r1(X_2,Y_3) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_2085,plain,
! [X_248,Y_249] :
( r1(X_248,'#skF_8'(Y_249))
| ~ r1(X_248,Y_249)
| ~ p101(Y_249)
| p102(Y_249)
| ~ r1('#skF_1',Y_249) ),
inference(resolution,[status(thm)],[c_708,c_4]) ).
tff(c_10,plain,
! [Y_51] :
( p3(Y_51)
| ~ r1('#skF_1',Y_51) ),
inference(cnfTransformation,[status(thm)],[f_412]) ).
tff(c_2157,plain,
! [Y_250] :
( p3('#skF_8'(Y_250))
| ~ p101(Y_250)
| p102(Y_250)
| ~ r1('#skF_1',Y_250) ),
inference(resolution,[status(thm)],[c_2085,c_10]) ).
tff(c_76,plain,
! [Y_52] :
( ~ p3('#skF_8'(Y_52))
| ~ p101(Y_52)
| p102(Y_52)
| ~ r1('#skF_1',Y_52) ),
inference(cnfTransformation,[status(thm)],[f_412]) ).
tff(c_2162,plain,
! [Y_251] :
( ~ p101(Y_251)
| p102(Y_251)
| ~ r1('#skF_1',Y_251) ),
inference(resolution,[status(thm)],[c_2157,c_76]) ).
tff(c_2198,plain,
( ~ p101('#skF_10'('#skF_1'))
| p102('#skF_10'('#skF_1'))
| ~ p100('#skF_1')
| p101('#skF_1')
| ~ r1('#skF_1','#skF_1') ),
inference(resolution,[status(thm)],[c_62,c_2162]) ).
tff(c_2241,plain,
( p102('#skF_10'('#skF_1'))
| p101('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6,c_968,c_2198]) ).
tff(c_2243,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8,c_923,c_2241]) ).
tff(c_2245,plain,
p102('#skF_10'('#skF_1')),
inference(splitRight,[status(thm)],[c_871]) ).
tff(c_58,plain,
! [Y_52] :
( ~ p102('#skF_10'(Y_52))
| ~ p100(Y_52)
| p101(Y_52)
| ~ r1('#skF_1',Y_52) ),
inference(cnfTransformation,[status(thm)],[f_412]) ).
tff(c_2282,plain,
( ~ p100('#skF_1')
| p101('#skF_1')
| ~ r1('#skF_1','#skF_1') ),
inference(resolution,[status(thm)],[c_2245,c_58]) ).
tff(c_2285,plain,
p101('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6,c_2282]) ).
tff(c_2287,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8,c_2285]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL674+1.005 : 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
% 0.07/0.36 % Computer : n026.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Sat Sep 5 02:08:40 UTC 2026
% 0.12/0.36 % CPUTime :
% 8.40/2.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.40/2.99
% 8.40/2.99 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------