%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL109-10 : TPTP v9.3.1. Released v7.5.0.
% 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 : n020.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 11:11:15 AM UTC 2026
% Result : Unsatisfiable 160.52s 128.06s
% Output : CNFRefutation 160.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 33 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 32 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 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; 3 con; 0-4 aty)
% Number of variables : 57 ( 57 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ ifeq > implies > #nlpp > not > truth > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(truth,type,
truth: $i ).
tff(a,type,
a: $i ).
tff(b,type,
b: $i ).
tff(not,type,
not: $i > $i ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff(ifeq,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(f_46,axiom,
! [X,Y,Z] : ( implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)) ),
file(unknown,unknown) ).
tff(f_26,axiom,
! [X] : ( implies(truth,X) = X ),
file(unknown,unknown) ).
tff(f_52,axiom,
! [X,Y] : ( implies(not(X),not(Y)) = implies(Y,X) ),
file(unknown,unknown) ).
tff(f_40,axiom,
! [X,Y] : ( implies(X,implies(Y,X)) = truth ),
file(unknown,unknown) ).
tff(f_50,axiom,
! [X] : ( not(not(X)) = X ),
file(unknown,unknown) ).
tff(f_48,axiom,
! [X] : ( implies(X,not(truth)) = not(X) ),
file(unknown,unknown) ).
tff(f_30,axiom,
! [X,Y] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
file(unknown,unknown) ).
tff(f_28,axiom,
! [X,Y,Z] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
file(unknown,unknown) ).
tff(f_54,axiom,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
file(unknown,unknown) ).
tff(c_24,plain,
! [Y_25,X_24,Z_26] : ( implies(Y_25,implies(X_24,Z_26)) = implies(X_24,implies(Y_25,Z_26)) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_4,plain,
! [X_4] : ( implies(truth,X_4) = X_4 ),
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_259,plain,
! [X_43,Y_44] : ( implies(not(X_43),not(Y_44)) = implies(Y_44,X_43) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_18,plain,
! [X_16,Y_17] : ( implies(X_16,implies(Y_17,X_16)) = truth ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_269,plain,
! [Y_44,X_43] : ( implies(not(Y_44),implies(Y_44,X_43)) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_259,c_18]) ).
tff(c_28,plain,
! [X_28] : ( not(not(X_28)) = X_28 ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_298,plain,
! [X_43,X_28] : ( implies(not(X_43),X_28) = implies(not(X_28),X_43) ),
inference(superposition,[status(thm),theory(equality)],[c_28,c_259]) ).
tff(c_30,plain,
! [X_29,Y_30] : ( implies(not(X_29),not(Y_30)) = implies(Y_30,X_29) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_26,plain,
! [X_27] : ( implies(X_27,not(truth)) = not(X_27) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_295,plain,
! [Y_44,X_28] : ( implies(Y_44,not(X_28)) = implies(X_28,not(Y_44)) ),
inference(superposition,[status(thm),theory(equality)],[c_28,c_259]) ).
tff(c_910,plain,
! [Y_55,X_56] : ( implies(implies(Y_55,X_56),X_56) = implies(implies(X_56,Y_55),Y_55) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_1045,plain,
! [Y_30,X_29] : ( implies(implies(not(Y_30),not(X_29)),not(X_29)) = implies(implies(Y_30,X_29),not(Y_30)) ),
inference(superposition,[status(thm),theory(equality)],[c_30,c_910]) ).
tff(c_12681,plain,
! [Y_167,X_168] : ( implies(implies(Y_167,X_168),not(Y_167)) = implies(X_168,not(implies(X_168,Y_167))) ),
inference(demodulation,[status(thm),theory(equality)],[c_295,c_30,c_1045]) ).
tff(c_1115,plain,
! [Y_30,X_29] : ( implies(implies(Y_30,X_29),not(Y_30)) = implies(X_29,not(implies(X_29,Y_30))) ),
inference(demodulation,[status(thm),theory(equality)],[c_295,c_30,c_1045]) ).
tff(c_12687,plain,
! [Y_167,X_168] : ( implies(not(Y_167),not(implies(not(Y_167),implies(Y_167,X_168)))) = implies(implies(X_168,not(implies(X_168,Y_167))),not(implies(Y_167,X_168))) ),
inference(superposition,[status(thm),theory(equality)],[c_12681,c_1115]) ).
tff(c_13202,plain,
! [X_168,Y_167] : ( implies(implies(X_168,not(implies(X_168,Y_167))),not(implies(Y_167,X_168))) = Y_167 ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_26,c_269,c_12687]) ).
tff(c_8,plain,
! [Y_9,X_8] : ( implies(implies(Y_9,X_8),X_8) = implies(implies(X_8,Y_9),Y_9) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_1956,plain,
! [X_67,Y_68,Z_69] : ( implies(implies(X_67,Y_68),implies(implies(Y_68,Z_69),implies(X_67,Z_69))) = truth ),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_353034,plain,
! [Y_726,X_727,Y_728] : ( implies(implies(implies(Y_726,X_727),Y_728),implies(implies(Y_728,X_727),implies(implies(X_727,Y_726),Y_726))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_1956]) ).
tff(c_354885,plain,
! [Y_167,X_168] : ( implies(Y_167,implies(implies(not(implies(Y_167,X_168)),not(implies(X_168,Y_167))),implies(implies(not(implies(X_168,Y_167)),X_168),X_168))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_13202,c_353034]) ).
tff(c_357062,plain,
! [Y_167,X_168] : ( implies(Y_167,implies(implies(Y_167,implies(implies(X_168,Y_167),X_168)),X_168)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_4,c_269,c_298,c_30,c_354885]) ).
tff(c_32,plain,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_33,plain,
implies(b,implies(implies(b,implies(implies(a,b),a)),a)) != truth,
inference(demodulation,[status(thm),theory(equality)],[c_24,c_24,c_32]) ).
tff(c_361182,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_357062,c_33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL109-10 : TPTP v9.3.1. Released v7.5.0.
% 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
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 5 22:10:27 UTC 2026
% 0.09/0.36 % CPUTime :
% 160.52/128.06 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 160.52/128.07
% 160.52/128.07 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------