%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL686+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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n011.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 11:12:33 AM UTC 2026
% Result : Theorem 4.39s 2.51s
% Output : CNFRefutation 4.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 23 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 89 ( 47 ~; 38 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 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 : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-1 aty)
% Number of variables : 20 ( 19 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ r1 > p3 > p2 > p1 > #nlpp > #skF_7 > #skF_5 > #skF_2 > #skF_3 > #skF_1 > #skF_4 > #skF_6
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(p3,type,
p3: $i > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $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(p1,type,
p1: $i > $o ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff(f_28,axiom,
! [X] : r1(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
tff(f_103,negated_conjecture,
~ ~ ? [X] :
~ ( ! [Y] :
( ~ r1(X,Y)
| ~ p3(Y)
| ! [X] :
( ~ r1(Y,X)
| ~ p1(X) ) )
| ! [Y] :
( ~ r1(X,Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ! [Y] :
( ~ r1(X,Y)
| $false )
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ( p2(Y)
& ~ p1(Y) )
| ( ~ p2(Y)
& p1(Y) ) ) )
| ! [Y] :
( ~ r1(X,Y)
| p3(Y) )
| ! [Y] :
( ~ r1(X,Y)
| ( ~ p1(Y)
& ~ p2(Y) )
| ( p2(Y)
& p1(Y) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).
tff(c_2,plain,
! [X_1] : r1(X_1,X_1),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_20,plain,
! [X_37] :
( r1(X_37,'#skF_7'(X_37))
| ~ r1('#skF_4',X_37) ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_107,plain,
! [Y_57,X_58] :
( p1(Y_57)
| ~ p2(Y_57)
| ~ r1(X_58,Y_57)
| ~ r1('#skF_4',X_58) ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_173,plain,
! [X_61] :
( p1(X_61)
| ~ p2(X_61)
| ~ r1('#skF_4',X_61) ),
inference(resolution,[status(thm)],[c_2,c_107]) ).
tff(c_189,plain,
( p1('#skF_7'('#skF_4'))
| ~ p2('#skF_7'('#skF_4'))
| ~ r1('#skF_4','#skF_4') ),
inference(resolution,[status(thm)],[c_20,c_173]) ).
tff(c_206,plain,
( p1('#skF_7'('#skF_4'))
| ~ p2('#skF_7'('#skF_4')) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_189]) ).
tff(c_215,plain,
~ p2('#skF_7'('#skF_4')),
inference(splitLeft,[status(thm)],[c_206]) ).
tff(c_75,plain,
! [Y_55,X_56] :
( ~ p1(Y_55)
| p2(Y_55)
| ~ r1(X_56,Y_55)
| ~ r1('#skF_4',X_56) ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_222,plain,
! [X_62] :
( ~ p1(X_62)
| p2(X_62)
| ~ r1('#skF_4',X_62) ),
inference(resolution,[status(thm)],[c_2,c_75]) ).
tff(c_238,plain,
( ~ p1('#skF_7'('#skF_4'))
| p2('#skF_7'('#skF_4'))
| ~ r1('#skF_4','#skF_4') ),
inference(resolution,[status(thm)],[c_20,c_222]) ).
tff(c_257,plain,
( ~ p1('#skF_7'('#skF_4'))
| p2('#skF_7'('#skF_4')) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_238]) ).
tff(c_258,plain,
~ p1('#skF_7'('#skF_4')),
inference(negUnitSimplification,[status(thm)],[c_215,c_257]) ).
tff(c_18,plain,
! [X_37] :
( p2('#skF_7'(X_37))
| p1('#skF_7'(X_37))
| ~ r1('#skF_4',X_37) ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_218,plain,
( p1('#skF_7'('#skF_4'))
| ~ r1('#skF_4','#skF_4') ),
inference(resolution,[status(thm)],[c_18,c_215]) ).
tff(c_221,plain,
p1('#skF_7'('#skF_4')),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_218]) ).
tff(c_267,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_258,c_221]) ).
tff(c_268,plain,
p1('#skF_7'('#skF_4')),
inference(splitRight,[status(thm)],[c_206]) ).
tff(c_269,plain,
p2('#skF_7'('#skF_4')),
inference(splitRight,[status(thm)],[c_206]) ).
tff(c_16,plain,
! [X_37] :
( ~ p1('#skF_7'(X_37))
| ~ p2('#skF_7'(X_37))
| ~ r1('#skF_4',X_37) ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_272,plain,
( ~ p1('#skF_7'('#skF_4'))
| ~ r1('#skF_4','#skF_4') ),
inference(resolution,[status(thm)],[c_269,c_16]) ).
tff(c_276,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_268,c_272]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL686+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.11/0.38 % Computer : n011.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 5 09:50:43 UTC 2026
% 0.11/0.39 % CPUTime :
% 4.39/2.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.39/2.52
% 4.39/2.52 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------