%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : COL001-2 : 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/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 : n026.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 7.47s 2.82s
% Output : CNFRefutation 7.47s
% 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 ( 3 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 : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 21 ( 21 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ apply > #nlpp > x > s > k > i > combinator > b
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(i,type,
i: $i ).
tff(x,type,
x: $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(s,type,
s: $i ).
tff(k,type,
k: $i ).
tff(combinator,type,
combinator: $i ).
tff(b,type,
b: $i ).
tff(f_32,axiom,
! [X] : ( apply(i,X) = X ),
file(unknown,unknown) ).
tff(f_26,axiom,
! [X,Y,Z] : ( apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_30,axiom,
! [X,Y,Z] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_37,axiom,
! [Y] : ( Y != apply(combinator,Y) ),
file(unknown,unknown) ).
tff(c_8,plain,
! [X_9] : ( apply(i,X_9) = X_9 ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_41,plain,
! [X_19,Y_20,Z_21] : ( apply(apply(apply(s,X_19),Y_20),Z_21) = apply(apply(X_19,Z_21),apply(Y_20,Z_21)) ),
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_176,plain,
! [X_25,X_26] : ( apply(apply(apply(s,X_25),i),X_26) = apply(apply(X_25,X_26),X_26) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_41]) ).
tff(c_6,plain,
! [X_6,Y_7,Z_8] : ( apply(apply(apply(b,X_6),Y_7),Z_8) = apply(X_6,apply(Y_7,Z_8)) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_4583,plain,
! [X_79,X_80] : ( apply(apply(apply(s,apply(b,X_79)),i),X_80) = apply(X_79,apply(X_80,X_80)) ),
inference(superposition,[status(thm),theory(equality)],[c_176,c_6]) ).
tff(c_12,plain,
! [Y_11] : ( apply(combinator,Y_11) != Y_11 ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_4962,plain,
! [X_80] : ( apply(apply(apply(s,apply(b,combinator)),i),X_80) != apply(X_80,X_80) ),
inference(superposition,[status(thm),theory(equality)],[c_4583,c_12]) ).
tff(c_5710,plain,
$false,
inference(reflexivity,[status(thm),theory(equality)],[c_4962]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : COL001-2 : TPTP v9.0.0. Released v1.0.0.
% 0.08/0.12 % 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
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Apr 7 15:50:08 EDT 2025
% 0.12/0.33 % CPUTime :
% 7.47/2.82 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.47/2.82
% 7.47/2.82 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------