%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL138-1 : 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 : n012.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 11:11:19 AM UTC 2026
% Result : Unsatisfiable 16.40s 7.32s
% Output : CNFRefutation 16.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 44 ( 44 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ implies > #nlpp > not > z > y > x > truth
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(truth,type,
truth: $i ).
tff(x,type,
x: $i ).
tff(y,type,
y: $i ).
tff(not,type,
not: $i > $i ).
tff(z,type,
z: $i ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff(f_47,axiom,
! [X] : ( implies(truth,X) = X ),
file(unknown,unknown) ).
tff(f_49,axiom,
! [X,Y,Z] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
file(unknown,unknown) ).
tff(f_51,axiom,
! [X,Y] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
file(unknown,unknown) ).
tff(f_57,axiom,
implies(x,implies(y,z)) != implies(y,implies(x,z)),
file(unknown,unknown) ).
tff(c_2,plain,
! [X_1] : ( implies(truth,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_187,plain,
! [X_17,Y_18,Z_19] : ( implies(implies(X_17,Y_18),implies(implies(Y_18,Z_19),implies(X_17,Z_19))) = truth ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_4,plain,
! [X_2,Y_3,Z_4] : ( implies(implies(X_2,Y_3),implies(implies(Y_3,Z_4),implies(X_2,Z_4))) = truth ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_21190,plain,
! [Y_150,Z_151,X_152,Z_153] : ( implies(truth,implies(implies(implies(implies(Y_150,Z_151),implies(X_152,Z_151)),Z_153),implies(implies(X_152,Y_150),Z_153))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_187,c_4]) ).
tff(c_22066,plain,
! [Y_150,X_1,Z_153] : ( implies(truth,implies(implies(implies(implies(Y_150,X_1),X_1),Z_153),implies(implies(truth,Y_150),Z_153))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_21190]) ).
tff(c_56244,plain,
! [Y_253,X_254,Z_255] : ( implies(implies(implies(implies(Y_253,X_254),X_254),Z_255),implies(Y_253,Z_255)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_22066]) ).
tff(c_190,plain,
! [Y_18,Z_19,X_17,Z_4] : ( implies(truth,implies(implies(implies(implies(Y_18,Z_19),implies(X_17,Z_19)),Z_4),implies(implies(X_17,Y_18),Z_4))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_187,c_4]) ).
tff(c_56435,plain,
! [X_17,Y_253,X_254] : ( implies(truth,implies(truth,implies(implies(X_17,implies(Y_253,X_254)),implies(Y_253,implies(X_17,X_254))))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_56244,c_190]) ).
tff(c_57405,plain,
! [X_17,Y_253,X_254] : ( implies(implies(X_17,implies(Y_253,X_254)),implies(Y_253,implies(X_17,X_254))) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_56435]) ).
tff(c_90188,plain,
! [X_323,Y_324,X_325] : ( implies(implies(X_323,implies(Y_324,X_325)),implies(Y_324,implies(X_323,X_325))) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_56435]) ).
tff(c_6,plain,
! [Y_6,X_5] : ( implies(implies(Y_6,X_5),X_5) = implies(implies(X_5,Y_6),Y_6) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_90693,plain,
! [Y_324,X_323,X_325] : ( implies(implies(implies(Y_324,implies(X_323,X_325)),implies(X_323,implies(Y_324,X_325))),implies(X_323,implies(Y_324,X_325))) = implies(truth,implies(Y_324,implies(X_323,X_325))) ),
inference(superposition,[status(thm),theory(equality)],[c_90188,c_6]) ).
tff(c_92067,plain,
! [Y_324,X_323,X_325] : ( implies(Y_324,implies(X_323,X_325)) = implies(X_323,implies(Y_324,X_325)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_57405,c_2,c_90693]) ).
tff(c_10,plain,
implies(y,implies(x,z)) != implies(x,implies(y,z)),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_92438,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_92067,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL138-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % 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
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Sat Sep 5 00:09:42 UTC 2026
% 0.05/0.31 % CPUTime :
% 16.40/7.32 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.40/7.32
% 16.40/7.32 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------