%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL133-1 : 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 : n007.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 3.62s 2.49s
% Output : CNFRefutation 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 28 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 37 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ implies > #nlpp > not > 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(implies,type,
implies: ( $i * $i ) > $i ).
tff(f_57,axiom,
! [X,Y] : ( implies(X,Y) = implies(Y,X) ),
file(unknown,unknown) ).
tff(f_47,axiom,
! [X] : ( implies(truth,X) = X ),
file(unknown,unknown) ).
tff(f_51,axiom,
! [X,Y] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
file(unknown,unknown) ).
tff(f_53,axiom,
! [X,Y] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
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_59,axiom,
x != y,
file(unknown,unknown) ).
tff(c_22,plain,
! [Y_12,X_13] : ( implies(Y_12,X_13) = implies(X_13,Y_12) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_2,plain,
! [X_1] : ( implies(truth,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_38,plain,
! [Y_12] : ( implies(Y_12,truth) = Y_12 ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_2]) ).
tff(c_190,plain,
! [Y_18,X_19] : ( implies(implies(Y_18,X_19),X_19) = implies(implies(X_19,Y_18),Y_18) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_285,plain,
! [X_1] : ( implies(implies(X_1,truth),truth) = implies(X_1,X_1) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_190]) ).
tff(c_305,plain,
! [X_1] : ( implies(X_1,X_1) = X_1 ),
inference(demodulation,[status(thm),theory(equality)],[c_38,c_38,c_285]) ).
tff(c_10,plain,
! [Y_10,X_9] : ( implies(Y_10,X_9) = implies(X_9,Y_10) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_307,plain,
! [X_20] : ( implies(X_20,X_20) = X_20 ),
inference(demodulation,[status(thm),theory(equality)],[c_38,c_38,c_285]) ).
tff(c_8,plain,
! [X_7,Y_8] : ( implies(implies(not(X_7),not(Y_8)),implies(Y_8,X_7)) = truth ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_321,plain,
! [X_20] : ( implies(implies(not(X_20),not(X_20)),X_20) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_307,c_8]) ).
tff(c_343,plain,
! [X_20] : ( implies(X_20,not(X_20)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_305,c_321]) ).
tff(c_571,plain,
! [X_25] : ( implies(X_25,not(X_25)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_305,c_321]) ).
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_585,plain,
! [X_25] : ( implies(implies(not(X_25),X_25),X_25) = implies(truth,not(X_25)) ),
inference(superposition,[status(thm),theory(equality)],[c_571,c_6]) ).
tff(c_610,plain,
! [X_25] : ( not(X_25) = X_25 ),
inference(demodulation,[status(thm),theory(equality)],[c_38,c_343,c_10,c_10,c_2,c_585]) ).
tff(c_353,plain,
! [X_21,Y_22,Z_23] : ( implies(implies(X_21,Y_22),implies(implies(Y_22,Z_23),implies(X_21,Z_23))) = truth ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_449,plain,
! [Y_8] : ( implies(implies(Y_8,not(not(Y_8))),truth) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_353]) ).
tff(c_616,plain,
! [Y_8] : ( implies(implies(Y_8,Y_8),truth) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_610,c_610,c_449]) ).
tff(c_619,plain,
! [Y_8] : ( truth = Y_8 ),
inference(demodulation,[status(thm),theory(equality)],[c_38,c_305,c_616]) ).
tff(c_630,plain,
! [Y_27] : ( truth = Y_27 ),
inference(demodulation,[status(thm),theory(equality)],[c_38,c_305,c_616]) ).
tff(c_12,plain,
y != x,
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_652,plain,
x != truth,
inference(superposition,[status(thm),theory(equality)],[c_630,c_12]) ).
tff(c_658,plain,
$false,
inference(superposition,[status(thm),theory(equality)],[c_619,c_652]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL133-1 : 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 : n007.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 : Sat Sep 5 08:04:09 UTC 2026
% 0.11/0.37 % CPUTime :
% 3.62/2.49 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.96/2.50
% 3.96/2.50 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------