%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : COL003-16 : TPTP v9.0.0. Released v2.1.0.
% 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 : n016.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 05:47:44 PM UTC 2025
% Result : Unsatisfiable 28.25s 16.54s
% Output : CNFRefutation 28.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 22 ( 21 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 8 ( 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 : 32 ( 32 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ apply > #nlpp > w > strong_fixed_point > fixed_pt > b
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(w,type,
w: $i ).
tff(fixed_pt,type,
fixed_pt: $i ).
tff(b,type,
b: $i ).
tff(strong_fixed_point,type,
strong_fixed_point: $i ).
tff(f_29,axiom,
! [X,Y,Z] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_32,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(b,apply(w,w)),w)),b)),b),
file(unknown,unknown) ).
tff(f_31,axiom,
! [X,Y] : ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) ),
file(unknown,unknown) ).
tff(f_34,axiom,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
file(unknown,unknown) ).
tff(c_2,plain,
! [X_1,Y_2,Z_3] : ( apply(apply(apply(b,X_1),Y_2),Z_3) = apply(X_1,apply(Y_2,Z_3)) ),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_6,plain,
apply(apply(b,apply(apply(b,apply(apply(b,apply(w,w)),w)),b)),b) = strong_fixed_point,
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_1719,plain,
! [Z_30] : ( apply(apply(apply(b,apply(apply(b,apply(w,w)),w)),b),apply(b,Z_30)) = apply(strong_fixed_point,Z_30) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_2]) ).
tff(c_1811,plain,
! [Z_31] : ( apply(apply(apply(b,apply(w,w)),w),apply(b,apply(b,Z_31))) = apply(strong_fixed_point,Z_31) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1719]) ).
tff(c_1832,plain,
! [Z_31] : ( apply(apply(w,w),apply(w,apply(b,apply(b,Z_31)))) = apply(strong_fixed_point,Z_31) ),
inference(superposition,[status(thm),theory(equality)],[c_1811,c_2]) ).
tff(c_9,plain,
! [X_6,Y_7] : ( apply(apply(w,X_6),Y_7) = apply(apply(X_6,Y_7),Y_7) ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_4,plain,
! [X_4,Y_5] : ( apply(apply(w,X_4),Y_5) = apply(apply(X_4,Y_5),Y_5) ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_13,plain,
! [Y_7] : ( apply(apply(w,w),Y_7) = apply(apply(Y_7,Y_7),Y_7) ),
inference(superposition,[status(thm),theory(equality)],[c_9,c_4]) ).
tff(c_91,plain,
! [X_9,Y_10,Z_11] : ( apply(apply(apply(b,X_9),Y_10),Z_11) = apply(X_9,apply(Y_10,Z_11)) ),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_1208,plain,
! [X_26,Y_27,Z_28] : ( apply(apply(w,apply(apply(b,X_26),Y_27)),Z_28) = apply(apply(X_26,apply(Y_27,Z_28)),Z_28) ),
inference(superposition,[status(thm),theory(equality)],[c_91,c_4]) ).
tff(c_10077,plain,
! [X_71,Y_72,Z_73] : ( apply(apply(w,apply(apply(b,apply(b,X_71)),Y_72)),Z_73) = apply(X_71,apply(apply(Y_72,Z_73),Z_73)) ),
inference(superposition,[status(thm),theory(equality)],[c_1208,c_2]) ).
tff(c_41707,plain,
! [X_138,Y_139] : ( apply(apply(w,apply(apply(b,apply(b,X_138)),Y_139)),Y_139) = apply(X_138,apply(apply(w,w),Y_139)) ),
inference(superposition,[status(thm),theory(equality)],[c_13,c_10077]) ).
tff(c_604,plain,
! [X_19,Y_20] : ( apply(apply(apply(w,X_19),Y_20),Y_20) = apply(apply(w,apply(X_19,Y_20)),Y_20) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_9]) ).
tff(c_682,plain,
! [X_19] : ( apply(apply(w,apply(X_19,apply(w,X_19))),apply(w,X_19)) = apply(apply(w,w),apply(w,X_19)) ),
inference(superposition,[status(thm),theory(equality)],[c_13,c_604]) ).
tff(c_41823,plain,
! [X_138] : ( apply(X_138,apply(apply(w,w),apply(w,apply(b,apply(b,X_138))))) = apply(apply(w,w),apply(w,apply(b,apply(b,X_138)))) ),
inference(superposition,[status(thm),theory(equality)],[c_41707,c_682]) ).
tff(c_42188,plain,
! [X_138] : ( apply(X_138,apply(strong_fixed_point,X_138)) = apply(strong_fixed_point,X_138) ),
inference(demodulation,[status(thm),theory(equality)],[c_1832,c_1832,c_41823]) ).
tff(c_8,plain,
apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) != apply(strong_fixed_point,fixed_pt),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_42216,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_42188,c_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COL003-16 : TPTP v9.0.0. Released v2.1.0.
% 0.11/0.13 % 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
% 0.14/0.33 % Computer : n016.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 : Mon Apr 7 15:51:23 EDT 2025
% 0.14/0.34 % CPUTime :
% 28.25/16.54 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.25/16.55
% 28.25/16.55 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------