%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL029-1 : TPTP v9.3.1. 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 : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 11:11:06 AM UTC 2026
% Result : Unsatisfiable 17.86s 6.76s
% Output : CNFRefutation 18.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 52 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 47 ( 25 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 61 ( 61 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_a_theorem > implies > #nlpp > falsehood > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(is_a_theorem,type,
is_a_theorem: $i > $o ).
tff(falsehood,type,
falsehood: $i ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff(f_42,axiom,
! [X] : is_a_theorem(implies(falsehood,X)),
file(unknown,unknown) ).
tff(f_36,axiom,
! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
file(unknown,unknown) ).
tff(f_38,axiom,
! [X,Y] : is_a_theorem(implies(X,implies(Y,X))),
file(unknown,unknown) ).
tff(f_34,axiom,
! [X,Y] :
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ),
file(unknown,unknown) ).
tff(f_40,axiom,
! [X,Y] : is_a_theorem(implies(implies(implies(X,Y),X),X)),
file(unknown,unknown) ).
tff(f_44,axiom,
~ is_a_theorem(implies(implies(implies(a,falsehood),falsehood),a)),
file(unknown,unknown) ).
tff(c_10,plain,
! [X_10] : is_a_theorem(implies(falsehood,X_10)),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_4,plain,
! [X_3,Y_4,Z_5] : is_a_theorem(implies(implies(X_3,Y_4),implies(implies(Y_4,Z_5),implies(X_3,Z_5)))),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_6,plain,
! [X_6,Y_7] : is_a_theorem(implies(X_6,implies(Y_7,X_6))),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_15,plain,
! [Y_14,X_15] :
( is_a_theorem(Y_14)
| ~ is_a_theorem(X_15)
| ~ is_a_theorem(implies(X_15,Y_14)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_22,plain,
! [Y_7,X_6] :
( is_a_theorem(implies(Y_7,X_6))
| ~ is_a_theorem(X_6) ),
inference(resolution,[status(thm)],[c_6,c_15]) ).
tff(c_39,plain,
! [X_20,Y_21,Z_22] : is_a_theorem(implies(implies(X_20,Y_21),implies(implies(Y_21,Z_22),implies(X_20,Z_22)))),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_2,plain,
! [Y_2,X_1] :
( is_a_theorem(Y_2)
| ~ is_a_theorem(X_1)
| ~ is_a_theorem(implies(X_1,Y_2)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_43,plain,
! [Y_21,Z_22,X_20] :
( is_a_theorem(implies(implies(Y_21,Z_22),implies(X_20,Z_22)))
| ~ is_a_theorem(implies(X_20,Y_21)) ),
inference(resolution,[status(thm)],[c_39,c_2]) ).
tff(c_50,plain,
! [Y_25,Z_26,X_27] :
( is_a_theorem(implies(implies(Y_25,Z_26),implies(X_27,Z_26)))
| ~ is_a_theorem(implies(X_27,Y_25)) ),
inference(resolution,[status(thm)],[c_39,c_2]) ).
tff(c_34,plain,
! [X_18,Y_19] : is_a_theorem(implies(implies(implies(X_18,Y_19),X_18),X_18)),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_38,plain,
! [X_18,Y_19] :
( is_a_theorem(X_18)
| ~ is_a_theorem(implies(implies(X_18,Y_19),X_18)) ),
inference(resolution,[status(thm)],[c_34,c_2]) ).
tff(c_60,plain,
! [X_28,Z_29] :
( is_a_theorem(implies(X_28,Z_29))
| ~ is_a_theorem(implies(X_28,implies(X_28,Z_29))) ),
inference(resolution,[status(thm)],[c_50,c_38]) ).
tff(c_284,plain,
! [Y_53,Z_54] :
( is_a_theorem(implies(implies(Y_53,Z_54),Z_54))
| ~ is_a_theorem(implies(implies(Y_53,Z_54),Y_53)) ),
inference(resolution,[status(thm)],[c_43,c_60]) ).
tff(c_310,plain,
! [X_55,Z_56] :
( is_a_theorem(implies(implies(X_55,Z_56),Z_56))
| ~ is_a_theorem(X_55) ),
inference(resolution,[status(thm)],[c_22,c_284]) ).
tff(c_59,plain,
! [X_27,Z_26,Y_25] :
( is_a_theorem(implies(X_27,Z_26))
| ~ is_a_theorem(implies(Y_25,Z_26))
| ~ is_a_theorem(implies(X_27,Y_25)) ),
inference(resolution,[status(thm)],[c_50,c_2]) ).
tff(c_1914,plain,
! [X_138,Z_139,X_140] :
( is_a_theorem(implies(X_138,Z_139))
| ~ is_a_theorem(implies(X_138,implies(X_140,Z_139)))
| ~ is_a_theorem(X_140) ),
inference(resolution,[status(thm)],[c_310,c_59]) ).
tff(c_3068,plain,
! [X_171,Y_172,Z_173] :
( is_a_theorem(implies(implies(X_171,Y_172),implies(X_171,Z_173)))
| ~ is_a_theorem(implies(Y_172,Z_173)) ),
inference(resolution,[status(thm)],[c_4,c_1914]) ).
tff(c_8,plain,
! [X_8,Y_9] : is_a_theorem(implies(implies(implies(X_8,Y_9),X_8),X_8)),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_93,plain,
! [X_31,Z_32,Y_33] :
( is_a_theorem(implies(X_31,Z_32))
| ~ is_a_theorem(implies(Y_33,Z_32))
| ~ is_a_theorem(implies(X_31,Y_33)) ),
inference(resolution,[status(thm)],[c_50,c_2]) ).
tff(c_111,plain,
! [X_31,X_8,Y_9] :
( is_a_theorem(implies(X_31,X_8))
| ~ is_a_theorem(implies(X_31,implies(implies(X_8,Y_9),X_8))) ),
inference(resolution,[status(thm)],[c_8,c_93]) ).
tff(c_30301,plain,
! [Z_620,Y_621,Y_622] :
( is_a_theorem(implies(implies(implies(Z_620,Y_621),Y_622),Z_620))
| ~ is_a_theorem(implies(Y_622,Z_620)) ),
inference(resolution,[status(thm)],[c_3068,c_111]) ).
tff(c_12,plain,
~ is_a_theorem(implies(implies(implies(a,falsehood),falsehood),a)),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_30530,plain,
~ is_a_theorem(implies(falsehood,a)),
inference(resolution,[status(thm)],[c_30301,c_12]) ).
tff(c_30614,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10,c_30530]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL029-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % 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
% 0.08/0.40 % Computer : n014.cluster.edu
% 0.08/0.40 % Model : x86_64 x86_64
% 0.08/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.40 % Memory : 8046.5625MB
% 0.08/0.40 % OS : Linux 6.8.0-71-generic
% 0.08/0.40 % CPULimit : 300
% 0.08/0.40 % WCLimit : 300
% 0.08/0.40 % DateTime : Fri Sep 4 12:30:58 UTC 2026
% 0.08/0.41 % CPUTime :
% 17.86/6.76 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.86/6.77
% 17.86/6.77 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------