%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL096-10 : TPTP v9.3.1. Released v7.3.0.
% 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 : n002.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 11:11:14 AM UTC 2026
% Result : Unsatisfiable 76.60s 55.04s
% Output : CNFRefutation 76.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 26 ( 25 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 10 ( 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 : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 103 ( 103 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ ifeq > equivalent > #nlpp > is_a_theorem > true > c > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(is_a_theorem,type,
is_a_theorem: $i > $i ).
tff(a,type,
a: $i ).
tff(b,type,
b: $i ).
tff(true,type,
true: $i ).
tff(equivalent,type,
equivalent: ( $i * $i ) > $i ).
tff(ifeq,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(c,type,
c: $i ).
tff(f_24,axiom,
! [A,B,C] : ( ifeq(A,A,B,C) = B ),
file(unknown,unknown) ).
tff(f_30,axiom,
! [U,Z,X,Y,V] : ( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),equivalent(equivalent(Y,Z),U)),V),V)) = true ),
file(unknown,unknown) ).
tff(f_32,axiom,
! [U,Z,X,Y,V] : ( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),Z),U),equivalent(equivalent(equivalent(X,V),Z),equivalent(equivalent(Y,V),U)))) = true ),
file(unknown,unknown) ).
tff(f_26,axiom,
! [X,Y] : ( ifeq(is_a_theorem(equivalent(X,Y)),true,ifeq(is_a_theorem(X),true,is_a_theorem(Y),true),true) = true ),
file(unknown,unknown) ).
tff(f_28,axiom,
! [X,Y,Z,U] : ( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),U),U)) = true ),
file(unknown,unknown) ).
tff(f_34,axiom,
is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)) != true,
file(unknown,unknown) ).
tff(c_2,plain,
! [A_1,B_2,C_3] : ( ifeq(A_1,A_1,B_2,C_3) = B_2 ),
inference(cnfTransformation,[status(thm)],[f_24]) ).
tff(c_8,plain,
! [V_14,Z_11,U_10,Y_13,X_12] : ( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_12,Y_13),equivalent(X_12,Z_11)),U_10),equivalent(equivalent(Y_13,Z_11),U_10)),V_14),V_14)) = true ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_63,plain,
! [X_36,U_35,Y_38,Z_37,V_34] : ( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_36,Y_38),Z_37),U_35),equivalent(equivalent(equivalent(X_36,V_34),Z_37),equivalent(equivalent(Y_38,V_34),U_35)))) = true ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_4,plain,
! [X_4,Y_5] : ( ifeq(is_a_theorem(equivalent(X_4,Y_5)),true,ifeq(is_a_theorem(X_4),true,is_a_theorem(Y_5),true),true) = true ),
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_305,plain,
! [Y_64,V_65,X_62,Z_63,U_66] : ( ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X_62,Y_64),Z_63),U_66)),true,is_a_theorem(equivalent(equivalent(equivalent(X_62,V_65),Z_63),equivalent(equivalent(Y_64,V_65),U_66))),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_63,c_4]) ).
tff(c_335,plain,
! [V_14,V_65,Z_11,U_10,Y_13,X_12] : ( ifeq(true,true,ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_12,Y_13),equivalent(X_12,Z_11)),U_10),V_65),V_14),equivalent(equivalent(equivalent(equivalent(Y_13,Z_11),U_10),V_65),V_14))),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_305]) ).
tff(c_13428,plain,
! [X_382,Y_383,V_381,V_384,Z_386,U_385] : ( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_382,Y_383),equivalent(X_382,Z_386)),U_385),V_381),V_384),equivalent(equivalent(equivalent(equivalent(Y_383,Z_386),U_385),V_381),V_384))) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_335]) ).
tff(c_46,plain,
! [X_29,V_31,U_32,Z_33,Y_30] : ( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_29,Y_30),equivalent(X_29,Z_33)),U_32),equivalent(equivalent(Y_30,Z_33),U_32)),V_31),V_31)) = true ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_54,plain,
! [X_29,V_31,U_32,Y_5,Z_33,Y_30] : ( ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_29,Y_30),equivalent(X_29,Z_33)),U_32),equivalent(equivalent(Y_30,Z_33),U_32)),V_31),V_31),Y_5)),true,ifeq(true,true,is_a_theorem(Y_5),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_46,c_4]) ).
tff(c_61,plain,
! [X_29,V_31,U_32,Y_5,Z_33,Y_30] : ( ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_29,Y_30),equivalent(X_29,Z_33)),U_32),equivalent(equivalent(Y_30,Z_33),U_32)),V_31),V_31),Y_5)),true,is_a_theorem(Y_5),true) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_54]) ).
tff(c_187756,plain,
! [Y_1717,V_1719,Z_1720,X_1716,Z_1718] : ( ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_1716,Z_1720),Z_1718),equivalent(equivalent(Y_1717,Z_1720),equivalent(equivalent(X_1716,Y_1717),Z_1718))),V_1719),V_1719)),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_13428,c_61]) ).
tff(c_187761,plain,
! [Y_1717,V_1719,Z_1720,X_1716,Z_1718] : ( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_1716,Z_1720),Z_1718),equivalent(equivalent(Y_1717,Z_1720),equivalent(equivalent(X_1716,Y_1717),Z_1718))),V_1719),V_1719)) = true ),
inference(superposition,[status(thm),theory(equality)],[c_187756,c_2]) ).
tff(c_6,plain,
! [X_6,Y_7,Z_8,U_9] : ( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_6,Y_7),equivalent(X_6,Z_8)),equivalent(Y_7,Z_8)),U_9),U_9)) = true ),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_342,plain,
! [Z_8,V_65,X_6,Y_7,U_9] : ( ifeq(true,true,ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_6,Y_7),equivalent(X_6,Z_8)),V_65),U_9),equivalent(equivalent(equivalent(Y_7,Z_8),V_65),U_9))),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_305]) ).
tff(c_3588,plain,
! [V_201,X_200,Y_203,U_202,Z_199] : ( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_200,Y_203),equivalent(X_200,Z_199)),V_201),U_202),equivalent(equivalent(equivalent(Y_203,Z_199),V_201),U_202))) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_342]) ).
tff(c_219777,plain,
! [Y_1982,U_1981,X_1983,V_1980,Z_1984] : ( ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_1983,Y_1982),equivalent(X_1983,Z_1984)),V_1980),U_1981)),true,is_a_theorem(equivalent(equivalent(equivalent(Y_1982,Z_1984),V_1980),U_1981)),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_3588,c_4]) ).
tff(c_220023,plain,
! [Z_1718,Y_1717,V_1719] : ( ifeq(true,true,ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(Z_1718,equivalent(equivalent(Y_1717,Y_1717),Z_1718)),V_1719),V_1719)),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_187761,c_219777]) ).
tff(c_221642,plain,
! [Z_1718,Y_1717,V_1719] : ( is_a_theorem(equivalent(equivalent(equivalent(Z_1718,equivalent(equivalent(Y_1717,Y_1717),Z_1718)),V_1719),V_1719)) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_220023]) ).
tff(c_12,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)) != true,
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_221889,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_221642,c_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL096-10 : TPTP v9.3.1. Released v7.3.0.
% 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
% 0.12/0.37 % Computer : n002.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 4 13:21:20 UTC 2026
% 0.12/0.38 % CPUTime :
% 76.60/55.04 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 76.60/55.04
% 76.60/55.04 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------