%------------------------------------------------------------------------------
% 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/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 : n006.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 06:56:35 PM UTC 2026
% Result : Theorem 3.54s 2.02s
% Output : CNFRefutation 4.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 24 ( 23 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 : 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; 1 con; 0-2 aty)
% Number of variables : 25 ( 24 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ x22 > x2 > #nlpp > s > proj1S > z
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(x22,type,
x22: ( $i * $i ) > $i ).
tff(proj1S,type,
proj1S: $i > $i ).
tff(s,type,
s: $i > $i ).
tff(x2,type,
x2: ( $i * $i ) > $i ).
tff(z,type,
z: $i ).
tff(f_29,axiom,
! [X] : ( z != s(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
tff(f_26,axiom,
! [X] : ( proj1S(s(X)) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
tff(f_31,axiom,
! [Y] : ( x2(z,Y) = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
tff(f_33,axiom,
! [Y,N] : ( x2(s(N),Y) = s(x2(N,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
tff(f_35,axiom,
! [Y] : ( x22(z,Y) = z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
tff(f_37,axiom,
! [Y,N] : ( x22(s(N),Y) = x2(Y,x22(N,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
tff(f_41,negated_conjecture,
~ ? [X] : ( x22(X,X) != X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_007) ).
tff(c_4,plain,
! [X_2] : ( s(X_2) != z ),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_2,plain,
! [X_1] : ( proj1S(s(X_1)) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_6,plain,
! [Y_3] : ( x2(z,Y_3) = Y_3 ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_8,plain,
! [N_5,Y_4] : ( x2(s(N_5),Y_4) = s(x2(N_5,Y_4)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_10,plain,
! [Y_6] : ( x22(z,Y_6) = z ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_69,plain,
! [N_17,Y_18] : ( x22(s(N_17),Y_18) = x2(Y_18,x22(N_17,Y_18)) ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_374,plain,
! [N_25,N_26] : ( s(x2(N_25,x22(N_26,s(N_25)))) = x22(s(N_26),s(N_25)) ),
inference(superposition,[status(thm),theory(equality)],[c_69,c_8]) ).
tff(c_435,plain,
! [N_25] : ( x22(s(z),s(N_25)) = s(x2(N_25,z)) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_374]) ).
tff(c_14,plain,
! [X_9] : ( x22(X_9,X_9) = X_9 ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_902,plain,
! [N_48,N_49] : ( x2(N_48,x22(N_49,s(N_48))) = proj1S(x22(s(N_49),s(N_48))) ),
inference(superposition,[status(thm),theory(equality)],[c_374,c_2]) ).
tff(c_986,plain,
! [N_49] : ( x2(N_49,x22(N_49,s(N_49))) = proj1S(s(N_49)) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_902]) ).
tff(c_1010,plain,
! [N_50] : ( x2(N_50,x22(N_50,s(N_50))) = N_50 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_986]) ).
tff(c_1038,plain,
x2(s(z),s(x2(s(z),z))) = s(z),
inference(superposition,[status(thm),theory(equality)],[c_435,c_1010]) ).
tff(c_1064,plain,
s(s(s(z))) = s(z),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_8,c_6,c_8,c_1038]) ).
tff(c_1255,plain,
s(s(z)) = proj1S(s(z)),
inference(superposition,[status(thm),theory(equality)],[c_1064,c_2]) ).
tff(c_1294,plain,
s(s(z)) = z,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1255]) ).
tff(c_1296,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4,c_1294]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX204+1 : TPTP v9.3.0. Released v9.3.0.
% 0.13/0.13 % 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
% 0.18/0.34 % Computer : n006.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue May 5 11:28:45 EDT 2026
% 0.18/0.35 % CPUTime :
% 3.54/2.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.54/2.02
% 3.54/2.02 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------