%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL164-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : n028.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 11:11:22 AM UTC 2026
% Result : Unsatisfiable 6.27s 3.06s
% Output : CNFRefutation 6.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 30 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 40 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ xor > implies > and_star > #nlpp > not > y > x > truth > falsehood
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(truth,type,
truth: $i ).
tff(x,type,
x: $i ).
tff(falsehood,type,
falsehood: $i ).
tff(xor,type,
xor: ( $i * $i ) > $i ).
tff(y,type,
y: $i ).
tff(not,type,
not: $i > $i ).
tff(and_star,type,
and_star: ( $i * $i ) > $i ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff(f_50,axiom,
! [X] : ( xor(X,falsehood) = X ),
file(unknown,unknown) ).
tff(f_52,axiom,
! [X] : ( xor(X,X) = falsehood ),
file(unknown,unknown) ).
tff(f_48,axiom,
! [X] : ( not(X) = xor(X,truth) ),
file(unknown,unknown) ).
tff(f_60,axiom,
! [X,Y] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ),
file(unknown,unknown) ).
tff(f_69,axiom,
! [X,Y] : ( xor(X,Y) = xor(Y,X) ),
file(unknown,unknown) ).
tff(f_58,axiom,
! [X] : ( and_star(xor(truth,X),X) = falsehood ),
file(unknown,unknown) ).
tff(f_78,axiom,
! [X,Y] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ),
file(unknown,unknown) ).
tff(f_73,axiom,
! [X,Y] : ( and_star(X,Y) = and_star(Y,X) ),
file(unknown,unknown) ).
tff(f_80,axiom,
implies(implies(not(x),not(y)),implies(y,x)) != truth,
file(unknown,unknown) ).
tff(c_4,plain,
! [X_2] : ( xor(X_2,falsehood) = X_2 ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_6,plain,
! [X_3] : ( xor(X_3,X_3) = falsehood ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_2,plain,
! [X_1] : ( xor(X_1,truth) = not(X_1) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_14,plain,
! [X_7,Y_8] : ( xor(xor(X_7,truth),Y_8) = xor(X_7,xor(truth,Y_8)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_433,plain,
! [X_33,Y_34] : ( xor(not(X_33),Y_34) = xor(X_33,xor(truth,Y_34)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14]) ).
tff(c_472,plain,
! [X_33] : ( xor(X_33,xor(truth,truth)) = not(not(X_33)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_433]) ).
tff(c_489,plain,
! [X_33] : ( not(not(X_33)) = X_33 ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_6,c_472]) ).
tff(c_136,plain,
! [Y_26,X_27] : ( xor(Y_26,X_27) = xor(X_27,Y_26) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_187,plain,
! [X_1] : ( xor(truth,X_1) = not(X_1) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_136]) ).
tff(c_12,plain,
! [X_6] : ( and_star(xor(truth,X_6),X_6) = falsehood ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_527,plain,
! [X_36,Y_37] : ( xor(truth,and_star(X_36,xor(truth,Y_37))) = implies(X_36,Y_37) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_570,plain,
! [Y_37] : ( implies(xor(truth,xor(truth,Y_37)),Y_37) = xor(truth,falsehood) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_527]) ).
tff(c_588,plain,
! [Y_37] : ( implies(xor(truth,xor(truth,Y_37)),Y_37) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_570]) ).
tff(c_1410,plain,
! [Y_37] : ( implies(Y_37,Y_37) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_489,c_187,c_187,c_588]) ).
tff(c_26,plain,
! [X_18,Y_19] : ( xor(truth,and_star(X_18,xor(truth,Y_19))) = implies(X_18,Y_19) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_698,plain,
! [X_18,Y_19] : ( not(and_star(X_18,not(Y_19))) = implies(X_18,Y_19) ),
inference(demodulation,[status(thm),theory(equality)],[c_187,c_187,c_26]) ).
tff(c_22,plain,
! [Y_17,X_16] : ( and_star(Y_17,X_16) = and_star(X_16,Y_17) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_1570,plain,
! [X_58,Y_59] : ( not(and_star(X_58,not(Y_59))) = implies(X_58,Y_59) ),
inference(demodulation,[status(thm),theory(equality)],[c_187,c_187,c_26]) ).
tff(c_1637,plain,
! [X_58,X_33] : ( implies(X_58,not(X_33)) = not(and_star(X_58,X_33)) ),
inference(superposition,[status(thm),theory(equality)],[c_489,c_1570]) ).
tff(c_28,plain,
implies(implies(not(x),not(y)),implies(y,x)) != truth,
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_2368,plain,
implies(not(and_star(not(x),y)),implies(y,x)) != truth,
inference(demodulation,[status(thm),theory(equality)],[c_1637,c_28]) ).
tff(c_2371,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1410,c_698,c_22,c_2368]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL164-1 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.13/0.38 % Computer : n028.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sat Sep 5 06:44:29 UTC 2026
% 0.13/0.38 % CPUTime :
% 6.27/3.06 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.27/3.07
% 6.27/3.07 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------