%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL157-1 : 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 11:11:21 AM UTC 2026
% Result : Unsatisfiable 9.63s 3.97s
% Output : CNFRefutation 9.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 54 ( 54 unt; 0 typ; 0 def)
% Number of atoms : 54 ( 53 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 70 ( 70 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ xor > or > implies > and_star > and > #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(or,type,
or: ( $i * $i ) > $i ).
tff(not,type,
not: $i > $i ).
tff(and_star,type,
and_star: ( $i * $i ) > $i ).
tff(and,type,
and: ( $i * $i ) > $i ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff(f_129,axiom,
not(truth) = falsehood,
file(unknown,unknown) ).
tff(f_48,axiom,
! [X] : ( implies(truth,X) = X ),
file(unknown,unknown) ).
tff(f_50,axiom,
! [X,Y,Z] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
file(unknown,unknown) ).
tff(f_52,axiom,
! [X,Y] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
file(unknown,unknown) ).
tff(f_81,axiom,
! [X,Y] : ( or(X,Y) = implies(not(X),Y) ),
file(unknown,unknown) ).
tff(f_85,axiom,
! [X,Y] : ( or(X,Y) = or(Y,X) ),
file(unknown,unknown) ).
tff(f_54,axiom,
! [X,Y] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
file(unknown,unknown) ).
tff(f_87,axiom,
! [X,Y] : ( and(X,Y) = not(or(not(X),not(Y))) ),
file(unknown,unknown) ).
tff(f_122,axiom,
! [X,Y] : ( and_star(X,Y) = not(or(not(X),not(Y))) ),
file(unknown,unknown) ).
tff(f_127,axiom,
! [X,Y] : ( and_star(X,Y) = and_star(Y,X) ),
file(unknown,unknown) ).
tff(f_133,axiom,
and_star(x,falsehood) != falsehood,
file(unknown,unknown) ).
tff(c_32,plain,
not(truth) = falsehood,
inference(cnfTransformation,[status(thm)],[f_129]) ).
tff(c_2,plain,
! [X_1] : ( implies(truth,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_919,plain,
! [X_68,Y_69,Z_70] : ( implies(implies(X_68,Y_69),implies(implies(Y_69,Z_70),implies(X_68,Z_70))) = truth ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_1070,plain,
! [X_1,Z_70] : ( implies(X_1,implies(implies(X_1,Z_70),implies(truth,Z_70))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_919]) ).
tff(c_1098,plain,
! [X_71,Z_72] : ( implies(X_71,implies(implies(X_71,Z_72),Z_72)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1070]) ).
tff(c_1136,plain,
! [Z_72] : ( implies(implies(truth,Z_72),Z_72) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_1098,c_2]) ).
tff(c_1205,plain,
! [Z_72] : ( implies(Z_72,Z_72) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1136]) ).
tff(c_516,plain,
! [Y_58,X_59] : ( implies(implies(Y_58,X_59),X_59) = implies(implies(X_59,Y_58),Y_58) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_555,plain,
! [X_1] : ( implies(implies(X_1,truth),truth) = implies(X_1,X_1) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_516]) ).
tff(c_1159,plain,
! [X_1] : ( implies(X_1,implies(X_1,X_1)) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_555,c_1098]) ).
tff(c_1958,plain,
! [X_83] : ( implies(X_83,truth) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_1205,c_1159]) ).
tff(c_10,plain,
! [X_9,Y_10] : ( implies(not(X_9),Y_10) = or(X_9,Y_10) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_2002,plain,
! [X_9] : ( or(X_9,truth) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_1958,c_10]) ).
tff(c_14,plain,
! [Y_15,X_14] : ( or(Y_15,X_14) = or(X_14,Y_15) ),
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_163,plain,
! [X_43,Y_44] : ( implies(not(X_43),Y_44) = or(X_43,Y_44) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_175,plain,
! [Y_45] : ( or(truth,Y_45) = implies(falsehood,Y_45) ),
inference(superposition,[status(thm),theory(equality)],[c_32,c_163]) ).
tff(c_191,plain,
! [Y_15] : ( or(Y_15,truth) = implies(falsehood,Y_15) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_175]) ).
tff(c_2047,plain,
! [Y_15] : ( implies(falsehood,Y_15) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2002,c_191]) ).
tff(c_172,plain,
! [Y_44] : ( or(truth,Y_44) = implies(falsehood,Y_44) ),
inference(superposition,[status(thm),theory(equality)],[c_32,c_163]) ).
tff(c_1220,plain,
! [Z_73] : ( implies(Z_73,Z_73) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1136]) ).
tff(c_1347,plain,
! [X_76] : ( or(X_76,not(X_76)) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_1220]) ).
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_54]) ).
tff(c_305,plain,
! [X_50,Y_51] : ( implies(or(X_50,not(Y_51)),implies(Y_51,X_50)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_8]) ).
tff(c_339,plain,
! [X_1] : ( implies(or(X_1,not(truth)),X_1) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_305]) ).
tff(c_347,plain,
! [X_52] : ( implies(or(X_52,falsehood),X_52) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_339]) ).
tff(c_362,plain,
! [X_14] : ( implies(or(falsehood,X_14),X_14) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_347]) ).
tff(c_1372,plain,
implies(truth,not(falsehood)) = truth,
inference(superposition,[status(thm),theory(equality)],[c_1347,c_362]) ).
tff(c_1096,plain,
! [X_1,Z_70] : ( implies(X_1,implies(implies(X_1,Z_70),Z_70)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1070]) ).
tff(c_1617,plain,
implies(truth,implies(truth,not(falsehood))) = truth,
inference(superposition,[status(thm),theory(equality)],[c_1372,c_1096]) ).
tff(c_1647,plain,
not(falsehood) = truth,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_1617]) ).
tff(c_198,plain,
! [X_46,Y_47] : ( not(or(not(X_46),not(Y_47))) = and(X_46,Y_47) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_222,plain,
! [Y_47,X_46] : ( not(or(not(Y_47),not(X_46))) = and(X_46,Y_47) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_198]) ).
tff(c_1682,plain,
! [Y_47] : ( not(or(not(Y_47),truth)) = and(falsehood,Y_47) ),
inference(superposition,[status(thm),theory(equality)],[c_1647,c_222]) ).
tff(c_1709,plain,
! [Y_47] : ( not(implies(falsehood,not(Y_47))) = and(falsehood,Y_47) ),
inference(demodulation,[status(thm),theory(equality)],[c_172,c_14,c_1682]) ).
tff(c_7385,plain,
! [Y_47] : ( and(falsehood,Y_47) = falsehood ),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_2047,c_1709]) ).
tff(c_16,plain,
! [X_16,Y_17] : ( not(or(not(X_16),not(Y_17))) = and(X_16,Y_17) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_26,plain,
! [X_27,Y_28] : ( not(or(not(X_27),not(Y_28))) = and_star(X_27,Y_28) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_36,plain,
! [X_27,Y_28] : ( and_star(X_27,Y_28) = and(X_27,Y_28) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_26]) ).
tff(c_30,plain,
! [Y_33,X_32] : ( and_star(Y_33,X_32) = and_star(X_32,Y_33) ),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_34,plain,
and_star(x,falsehood) != falsehood,
inference(cnfTransformation,[status(thm)],[f_133]) ).
tff(c_35,plain,
and_star(falsehood,x) != falsehood,
inference(demodulation,[status(thm),theory(equality)],[c_30,c_34]) ).
tff(c_38,plain,
and(falsehood,x) != falsehood,
inference(demodulation,[status(thm),theory(equality)],[c_36,c_35]) ).
tff(c_7390,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_7385,c_38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL157-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % 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
% 0.10/0.38 % Computer : n017.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Fri Sep 4 19:42:36 UTC 2026
% 0.10/0.38 % CPUTime :
% 9.63/3.97 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.63/3.99
% 9.63/3.99 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------