%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWX206-1 : 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 : n023.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 2.61s 1.62s
% Output : CNFRefutation 2.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 19 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 18 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 : 4 ( 1 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 : 13 ( 13 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ x2 > impl > eq2 > eq > #nlpp > s > plus_not_idem > z > btrue > bfalse
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(eq,type,
eq: ( $i * $i ) > $i ).
tff(s,type,
s: $i > $i ).
tff(impl,type,
impl: ( $i * $i ) > $i ).
tff(x2,type,
x2: ( $i * $i ) > $i ).
tff(z,type,
z: $i ).
tff(plus_not_idem,type,
plus_not_idem: $i > $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_23,axiom,
! [Q] : ( impl(btrue,Q) = Q ),
file(unknown,unknown) ).
tff(f_41,axiom,
! [X] : ( eq(X,X) = btrue ),
file(unknown,unknown) ).
tff(f_27,axiom,
! [Y] : ( x2(z,Y) = Y ),
file(unknown,unknown) ).
tff(f_33,axiom,
eq2(btrue,bfalse) = bfalse,
file(unknown,unknown) ).
tff(f_31,axiom,
! [X] : ( plus_not_idem(X) = impl(eq(x2(X,X),X),eq2(btrue,bfalse)) ),
file(unknown,unknown) ).
tff(f_46,axiom,
! [X] : ( eq2(plus_not_idem(X),bfalse) != btrue ),
file(unknown,unknown) ).
tff(c_24,plain,
! [X_12] : ( eq2(X_12,X_12) = btrue ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_2,plain,
! [Q_1] : ( impl(btrue,Q_1) = Q_1 ),
inference(cnfTransformation,[status(thm)],[f_23]) ).
tff(c_22,plain,
! [X_11] : ( eq(X_11,X_11) = btrue ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_6,plain,
! [Y_3] : ( x2(z,Y_3) = Y_3 ),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_14,plain,
eq2(btrue,bfalse) = bfalse,
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_10,plain,
! [X_6] : ( impl(eq(x2(X_6,X_6),X_6),eq2(btrue,bfalse)) = plus_not_idem(X_6) ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_118,plain,
! [X_26] : ( impl(eq(x2(X_26,X_26),X_26),bfalse) = plus_not_idem(X_26) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_10]) ).
tff(c_132,plain,
impl(eq(z,z),bfalse) = plus_not_idem(z),
inference(superposition,[status(thm),theory(equality)],[c_6,c_118]) ).
tff(c_136,plain,
plus_not_idem(z) = bfalse,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22,c_132]) ).
tff(c_26,plain,
! [X_13] : ( eq2(plus_not_idem(X_13),bfalse) != btrue ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_139,plain,
eq2(bfalse,bfalse) != btrue,
inference(superposition,[status(thm),theory(equality)],[c_136,c_26]) ).
tff(c_144,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_24,c_139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX206-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.13 % 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
% 0.14/0.33 % Computer : n023.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 11:35:08 EDT 2026
% 0.14/0.34 % CPUTime :
% 2.61/1.62 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.61/1.62
% 2.61/1.62 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------