%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : COL020-1 : TPTP v9.0.0. Released v1.0.0.
% 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 : n019.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 : Wed Apr 9 05:47:48 PM UTC 2025
% Result : Unsatisfiable 5.52s 2.34s
% Output : CNFRefutation 5.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 4 avg)
% Maximal term depth : 6 ( 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; 4 con; 0-2 aty)
% Number of variables : 28 ( 28 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ apply > #nlpp > s > combinator > c > b
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(s,type,
s: $i ).
tff(combinator,type,
combinator: $i ).
tff(b,type,
b: $i ).
tff(c,type,
c: $i ).
tff(f_30,axiom,
! [X,Y,Z] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_32,axiom,
! [X,Y,Z] : ( apply(apply(apply(c,X),Y),Z) = apply(apply(X,Z),Y) ),
file(unknown,unknown) ).
tff(f_28,axiom,
! [X,Y,Z] : ( apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_35,axiom,
! [Y] : ( Y != apply(combinator,Y) ),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_4,Y_5,Z_6] : ( apply(apply(apply(b,X_4),Y_5),Z_6) = apply(X_4,apply(Y_5,Z_6)) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_6,plain,
! [X_7,Y_8,Z_9] : ( apply(apply(apply(c,X_7),Y_8),Z_9) = apply(apply(X_7,Z_9),Y_8) ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_28,plain,
! [X_18,Y_19,Z_20] : ( apply(apply(apply(s,X_18),Y_19),Z_20) = apply(apply(X_18,Z_20),apply(Y_19,Z_20)) ),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_778,plain,
! [X_32,Y_33,Y_34] : ( apply(apply(apply(s,apply(c,X_32)),Y_33),Y_34) = apply(apply(X_32,apply(Y_33,Y_34)),Y_34) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_28]) ).
tff(c_2067,plain,
! [X_45,Y_46,Z_47] : ( apply(apply(apply(s,apply(c,apply(b,X_45))),Y_46),Z_47) = apply(X_45,apply(apply(Y_46,Z_47),Z_47)) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_778]) ).
tff(c_8,plain,
! [Y_10] : ( apply(combinator,Y_10) != Y_10 ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_2369,plain,
! [Y_46,Z_47] : ( apply(apply(apply(s,apply(c,apply(b,combinator))),Y_46),Z_47) != apply(apply(Y_46,Z_47),Z_47) ),
inference(superposition,[status(thm),theory(equality)],[c_2067,c_8]) ).
tff(c_2620,plain,
$false,
inference(reflexivity,[status(thm),theory(equality)],[c_2369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COL020-1 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.13 % 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
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 7 15:54:32 EDT 2025
% 0.13/0.34 % CPUTime :
% 5.52/2.34 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.52/2.34
% 5.52/2.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------