%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL134-1 : 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 : n017.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 3.36s 2.38s
% Output : CNFRefutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 17 ( 16 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 23 ( 23 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ implies > #nlpp > not > x > truth
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(truth,type,
truth: $i ).
tff(x,type,
x: $i ).
tff(not,type,
not: $i > $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,truth) != truth,
file(unknown,unknown) ).
tff(c_2,plain,
! [X_1] : ( implies(truth,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_91,plain,
! [X_15,Y_16,Z_17] : ( implies(implies(X_15,Y_16),implies(implies(Y_16,Z_17),implies(X_15,Z_17))) = truth ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_183,plain,
! [Y_16,X_1] : ( implies(implies(truth,Y_16),implies(implies(Y_16,X_1),X_1)) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_91]) ).
tff(c_327,plain,
! [Y_20,X_21] : ( implies(Y_20,implies(implies(Y_20,X_21),X_21)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_183]) ).
tff(c_358,plain,
! [X_21] : ( implies(implies(truth,X_21),X_21) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_327,c_2]) ).
tff(c_416,plain,
! [X_21] : ( implies(X_21,X_21) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_358]) ).
tff(c_46,plain,
! [Y_13,X_14] : ( implies(implies(Y_13,X_14),X_14) = implies(implies(X_14,Y_13),Y_13) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_79,plain,
! [X_1] : ( implies(implies(X_1,truth),truth) = implies(X_1,X_1) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_46]) ).
tff(c_480,plain,
! [X_23] : ( implies(implies(X_23,truth),truth) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_416,c_79]) ).
tff(c_193,plain,
! [Y_16,X_1] : ( implies(Y_16,implies(implies(Y_16,X_1),X_1)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_183]) ).
tff(c_490,plain,
! [X_23] : ( implies(X_23,truth) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_480,c_193]) ).
tff(c_10,plain,
implies(x,truth) != truth,
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_568,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_490,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL134-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 4 18:11:36 UTC 2026
% 0.11/0.37 % CPUTime :
% 3.36/2.38 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.36/2.38
% 3.36/2.38 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------