%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : COL001-1 : 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 : n032.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 05:47:43 PM UTC 2025
% Result : Unsatisfiable 27.35s 14.94s
% Output : CNFRefutation 27.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 12 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 27 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ apply > #nlpp > s > k > combinator
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(s,type,
s: $i ).
tff(k,type,
k: $i ).
tff(combinator,type,
combinator: $i ).
tff(f_27,axiom,
! [X,Y,Z] : ( apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_29,axiom,
! [X,Y] : ( apply(apply(k,X),Y) = X ),
file(unknown,unknown) ).
tff(f_32,axiom,
! [Y] : ( Y != apply(combinator,Y) ),
file(unknown,unknown) ).
tff(c_17,plain,
! [X_10,Y_11,Z_12] : ( apply(apply(apply(s,X_10),Y_11),Z_12) = apply(apply(X_10,Z_12),apply(Y_11,Z_12)) ),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_4,plain,
! [X_4,Y_5] : ( apply(apply(k,X_4),Y_5) = X_4 ),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_43,plain,
! [Y_11,Z_12] : ( apply(apply(apply(s,k),Y_11),Z_12) = Z_12 ),
inference(superposition,[status(thm),theory(equality)],[c_17,c_4]) ).
tff(c_206,plain,
! [X_20,Y_21,Y_22] : ( apply(apply(apply(s,apply(k,X_20)),Y_21),Y_22) = apply(X_20,apply(Y_21,Y_22)) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_17]) ).
tff(c_2,plain,
! [X_1,Y_2,Z_3] : ( apply(apply(apply(s,X_1),Y_2),Z_3) = apply(apply(X_1,Z_3),apply(Y_2,Z_3)) ),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_6718,plain,
! [X_88,Y_89,Y_90] : ( apply(apply(apply(s,apply(s,apply(k,X_88))),Y_89),Y_90) = apply(X_88,apply(Y_90,apply(Y_89,Y_90))) ),
inference(superposition,[status(thm),theory(equality)],[c_206,c_2]) ).
tff(c_6,plain,
! [Y_6] : ( apply(combinator,Y_6) != Y_6 ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_11171,plain,
! [Y_118,Y_119] : ( apply(apply(apply(s,apply(s,apply(k,combinator))),Y_118),Y_119) != apply(Y_119,apply(Y_118,Y_119)) ),
inference(superposition,[status(thm),theory(equality)],[c_6718,c_6]) ).
tff(c_11527,plain,
! [Y_11,Z_12] : ( apply(apply(apply(s,apply(s,apply(k,combinator))),apply(apply(s,k),Y_11)),Z_12) != apply(Z_12,Z_12) ),
inference(superposition,[status(thm),theory(equality)],[c_43,c_11171]) ).
tff(c_58355,plain,
$false,
inference(reflexivity,[status(thm),theory(equality)],[c_11527]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : COL001-1 : TPTP v9.0.0. Released v1.0.0.
% 0.02/0.09 % 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
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Mon Apr 7 15:50:01 EDT 2025
% 0.08/0.28 % CPUTime :
% 27.35/14.94 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.35/14.95
% 27.35/14.95 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------