%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWX204-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/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 : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:56:36 PM UTC 2026
% Result : Unsatisfiable 4.95s 2.21s
% Output : CNFRefutation 4.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 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 : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 30 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ x22 > x2 > eq2 > eq > #nlpp > s > mul_idem > z > btrue > bfalse
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(eq,type,
eq: ( $i * $i ) > $i ).
tff(x22,type,
x22: ( $i * $i ) > $i ).
tff(mul_idem,type,
mul_idem: $i > $i ).
tff(s,type,
s: $i > $i ).
tff(x2,type,
x2: ( $i * $i ) > $i ).
tff(z,type,
z: $i ).
tff(bfalse,type,
bfalse: $i ).
tff(eq2,type,
eq2: ( $i * $i ) > $i ).
tff(btrue,type,
btrue: $i ).
tff(f_43,axiom,
! [X] : ( eq2(X,X) = btrue ),
file(unknown,unknown) ).
tff(f_39,axiom,
! [X] : ( eq(s(X),z) = bfalse ),
file(unknown,unknown) ).
tff(f_23,axiom,
! [Y] : ( x2(z,Y) = Y ),
file(unknown,unknown) ).
tff(f_27,axiom,
! [Y] : ( x22(z,Y) = z ),
file(unknown,unknown) ).
tff(f_25,axiom,
! [N,Y] : ( x2(s(N),Y) = s(x2(N,Y)) ),
file(unknown,unknown) ).
tff(f_29,axiom,
! [N,Y] : ( x22(s(N),Y) = x2(Y,x22(N,Y)) ),
file(unknown,unknown) ).
tff(f_31,axiom,
! [X] : ( mul_idem(X) = eq(x22(X,X),X) ),
file(unknown,unknown) ).
tff(f_35,axiom,
! [X,Y] : ( eq(s(X),s(Y)) = eq(X,Y) ),
file(unknown,unknown) ).
tff(f_46,axiom,
! [X] : ( eq2(mul_idem(X),bfalse) != btrue ),
file(unknown,unknown) ).
tff(c_24,plain,
! [X_13] : ( eq2(X_13,X_13) = btrue ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_20,plain,
! [X_11] : ( eq(s(X_11),z) = bfalse ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_2,plain,
! [Y_1] : ( x2(z,Y_1) = Y_1 ),
inference(cnfTransformation,[status(thm)],[f_23]) ).
tff(c_6,plain,
! [Y_4] : ( x22(z,Y_4) = z ),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_4,plain,
! [N_2,Y_3] : ( x2(s(N_2),Y_3) = s(x2(N_2,Y_3)) ),
inference(cnfTransformation,[status(thm)],[f_25]) ).
tff(c_129,plain,
! [N_27,Y_28] : ( x22(s(N_27),Y_28) = x2(Y_28,x22(N_27,Y_28)) ),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_310,plain,
! [N_33,N_34] : ( s(x2(N_33,x22(N_34,s(N_33)))) = x22(s(N_34),s(N_33)) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_129]) ).
tff(c_1781,plain,
! [N_89,N_90] : ( s(s(x2(N_89,x22(N_90,s(s(N_89)))))) = x22(s(N_90),s(s(N_89))) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_310]) ).
tff(c_1954,plain,
! [N_89] : ( x22(s(z),s(s(N_89))) = s(s(x2(N_89,z))) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_1781]) ).
tff(c_2138,plain,
! [N_93] : ( s(s(x22(N_93,s(s(z))))) = x22(s(N_93),s(s(z))) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1781]) ).
tff(c_2295,plain,
x22(s(s(z)),s(s(z))) = s(s(s(s(x2(z,z))))),
inference(superposition,[status(thm),theory(equality)],[c_1954,c_2138]) ).
tff(c_2332,plain,
x22(s(s(z)),s(s(z))) = s(s(s(s(z)))),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2295]) ).
tff(c_10,plain,
! [X_7] : ( eq(x22(X_7,X_7),X_7) = mul_idem(X_7) ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_2532,plain,
eq(s(s(s(s(z)))),s(s(z))) = mul_idem(s(s(z))),
inference(superposition,[status(thm),theory(equality)],[c_2332,c_10]) ).
tff(c_16,plain,
! [X_8,Y_9] : ( eq(s(X_8),s(Y_9)) = eq(X_8,Y_9) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_2564,plain,
eq(s(s(s(z))),s(z)) = mul_idem(s(s(z))),
inference(superposition,[status(thm),theory(equality)],[c_2532,c_16]) ).
tff(c_2574,plain,
eq(s(s(z)),z) = mul_idem(s(s(z))),
inference(superposition,[status(thm),theory(equality)],[c_2564,c_16]) ).
tff(c_2580,plain,
mul_idem(s(s(z))) = bfalse,
inference(demodulation,[status(thm),theory(equality)],[c_20,c_2574]) ).
tff(c_26,plain,
! [X_14] : ( eq2(mul_idem(X_14),bfalse) != btrue ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_2587,plain,
eq2(bfalse,bfalse) != btrue,
inference(superposition,[status(thm),theory(equality)],[c_2580,c_26]) ).
tff(c_2592,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_24,c_2587]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX204-1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.17/0.34 % Computer : n007.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 11:29:23 EDT 2026
% 0.17/0.34 % CPUTime :
% 4.95/2.21 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.95/2.21
% 4.95/2.21 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------