%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL161-1 : 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/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 : n015.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 11:11:21 AM UTC 2026
% Result : Unsatisfiable 5.22s 2.78s
% Output : CNFRefutation 5.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 27 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 27 ( 26 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 1 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 34 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ xor > implies > and_star > #nlpp > not > 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(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_73,axiom,
! [X,Y] : ( and_star(X,Y) = and_star(Y,X) ),
file(unknown,unknown) ).
tff(f_54,axiom,
! [X] : ( and_star(X,truth) = X ),
file(unknown,unknown) ).
tff(f_69,axiom,
! [X,Y] : ( xor(X,Y) = xor(Y,X) ),
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_80,axiom,
implies(truth,x) != x,
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_506,plain,
! [X_35,Y_36] : ( xor(not(X_35),Y_36) = xor(X_35,xor(truth,Y_36)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14]) ).
tff(c_545,plain,
! [X_35] : ( xor(X_35,xor(truth,truth)) = not(not(X_35)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_506]) ).
tff(c_562,plain,
! [X_35] : ( not(not(X_35)) = X_35 ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_6,c_545]) ).
tff(c_212,plain,
! [Y_28,X_29] : ( and_star(Y_28,X_29) = and_star(X_29,Y_28) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_8,plain,
! [X_4] : ( and_star(X_4,truth) = X_4 ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_232,plain,
! [Y_28] : ( and_star(truth,Y_28) = Y_28 ),
inference(superposition,[status(thm),theory(equality)],[c_212,c_8]) ).
tff(c_96,plain,
! [Y_25,X_26] : ( xor(Y_25,X_26) = xor(X_26,Y_25) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_116,plain,
! [Y_25] : ( xor(truth,Y_25) = not(Y_25) ),
inference(superposition,[status(thm),theory(equality)],[c_96,c_2]) ).
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_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_116,c_116,c_26]) ).
tff(c_1645,plain,
! [Y_59] : ( not(not(Y_59)) = implies(truth,Y_59) ),
inference(superposition,[status(thm),theory(equality)],[c_232,c_1570]) ).
tff(c_1668,plain,
! [Y_59] : ( implies(truth,Y_59) = Y_59 ),
inference(demodulation,[status(thm),theory(equality)],[c_562,c_1645]) ).
tff(c_28,plain,
implies(truth,x) != x,
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_1673,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1668,c_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL161-1 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.09/0.42 % Computer : n015.cluster.edu
% 0.09/0.42 % Model : x86_64 x86_64
% 0.09/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.42 % Memory : 8046.5625MB
% 0.09/0.42 % OS : Linux 6.8.0-71-generic
% 0.09/0.42 % CPULimit : 300
% 0.09/0.42 % WCLimit : 300
% 0.09/0.42 % DateTime : Sat Sep 5 08:56:57 UTC 2026
% 0.09/0.42 % CPUTime :
% 5.22/2.78 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.22/2.79
% 5.22/2.79 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------