%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL076-3 : 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 : n013.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 11:11:11 AM UTC 2026
% Result : Unsatisfiable 7.91s 3.46s
% Output : CNFRefutation 8.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 21 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 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; 1 con; 0-2 aty)
% Number of variables : 60 ( 60 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_a_theorem > implies > #nlpp > not > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(is_a_theorem,type,
is_a_theorem: $i > $o ).
tff(not,type,
not: $i > $i ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff(f_38,axiom,
! [X,Y] : is_a_theorem(implies(X,implies(Y,X))),
file(unknown,unknown) ).
tff(f_42,axiom,
! [X,Y] : is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))),
file(unknown,unknown) ).
tff(f_50,axiom,
! [X1,X2,X3] :
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X2,X3))
| is_a_theorem(implies(X1,X3)) ),
file(unknown,unknown) ).
tff(f_40,axiom,
! [X,Y,Z] : is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))),
file(unknown,unknown) ).
tff(f_36,axiom,
! [X,Y] :
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ),
file(unknown,unknown) ).
tff(f_52,axiom,
~ is_a_theorem(implies(a,not(not(a)))),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_3,Y_4] : is_a_theorem(implies(X_3,implies(Y_4,X_3))),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_8,plain,
! [X_8,Y_9] : is_a_theorem(implies(implies(not(X_8),not(Y_9)),implies(Y_9,X_8))),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_51,plain,
! [X1_25,X3_26,X2_27] :
( is_a_theorem(implies(X1_25,X3_26))
| ~ is_a_theorem(implies(X2_27,X3_26))
| ~ is_a_theorem(implies(X1_25,X2_27)) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_260,plain,
! [X1_81,Y_82,X_83] :
( is_a_theorem(implies(X1_81,implies(Y_82,X_83)))
| ~ is_a_theorem(implies(X1_81,implies(not(X_83),not(Y_82)))) ),
inference(resolution,[status(thm)],[c_8,c_51]) ).
tff(c_311,plain,
! [Y_84,X_85] : is_a_theorem(implies(not(Y_84),implies(Y_84,X_85))),
inference(resolution,[status(thm)],[c_4,c_260]) ).
tff(c_61,plain,
! [X1_25,Y_9,X_8] :
( is_a_theorem(implies(X1_25,implies(Y_9,X_8)))
| ~ is_a_theorem(implies(X1_25,implies(not(X_8),not(Y_9)))) ),
inference(resolution,[status(thm)],[c_8,c_51]) ).
tff(c_327,plain,
! [X_8,Y_9] : is_a_theorem(implies(not(not(X_8)),implies(Y_9,X_8))),
inference(resolution,[status(thm)],[c_311,c_61]) ).
tff(c_91,plain,
! [X_37,Y_38,Z_39] : is_a_theorem(implies(implies(X_37,implies(Y_38,Z_39)),implies(implies(X_37,Y_38),implies(X_37,Z_39)))),
inference(cnfTransformation,[status(thm)],[f_40]) ).
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_36]) ).
tff(c_179,plain,
! [X_60,Y_61,Z_62] :
( is_a_theorem(implies(implies(X_60,Y_61),implies(X_60,Z_62)))
| ~ is_a_theorem(implies(X_60,implies(Y_61,Z_62))) ),
inference(resolution,[status(thm)],[c_91,c_2]) ).
tff(c_10,plain,
! [X1_10,X3_12,X2_11] :
( is_a_theorem(implies(X1_10,X3_12))
| ~ is_a_theorem(implies(X2_11,X3_12))
| ~ is_a_theorem(implies(X1_10,X2_11)) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_1741,plain,
! [X1_203,X_204,Z_205,Y_206] :
( is_a_theorem(implies(X1_203,implies(X_204,Z_205)))
| ~ is_a_theorem(implies(X1_203,implies(X_204,Y_206)))
| ~ is_a_theorem(implies(X_204,implies(Y_206,Z_205))) ),
inference(resolution,[status(thm)],[c_179,c_10]) ).
tff(c_2119,plain,
! [X_229,Y_230,Z_231] :
( is_a_theorem(implies(X_229,implies(Y_230,Z_231)))
| ~ is_a_theorem(implies(Y_230,implies(X_229,Z_231))) ),
inference(resolution,[status(thm)],[c_4,c_1741]) ).
tff(c_2344,plain,
! [Y_236,X_237] : is_a_theorem(implies(Y_236,implies(not(not(X_237)),X_237))),
inference(resolution,[status(thm)],[c_327,c_2119]) ).
tff(c_2396,plain,
! [X_237,Y_236] :
( is_a_theorem(implies(not(not(X_237)),X_237))
| ~ is_a_theorem(Y_236) ),
inference(resolution,[status(thm)],[c_2344,c_2]) ).
tff(c_2488,plain,
! [Y_236] : ~ is_a_theorem(Y_236),
inference(splitLeft,[status(thm)],[c_2396]) ).
tff(c_2389,plain,
! [Y_236,Y_9] : is_a_theorem(implies(Y_236,implies(Y_9,not(not(Y_9))))),
inference(resolution,[status(thm)],[c_2344,c_61]) ).
tff(c_2563,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2488,c_2389]) ).
tff(c_2610,plain,
! [X_245] : is_a_theorem(implies(not(not(X_245)),X_245)),
inference(splitRight,[status(thm)],[c_2396]) ).
tff(c_28,plain,
! [X_19,Y_20] : is_a_theorem(implies(implies(not(X_19),not(Y_20)),implies(Y_20,X_19))),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_32,plain,
! [Y_20,X_19] :
( is_a_theorem(implies(Y_20,X_19))
| ~ is_a_theorem(implies(not(X_19),not(Y_20))) ),
inference(resolution,[status(thm)],[c_28,c_2]) ).
tff(c_2681,plain,
! [Y_20] : is_a_theorem(implies(Y_20,not(not(Y_20)))),
inference(resolution,[status(thm)],[c_2610,c_32]) ).
tff(c_12,plain,
~ is_a_theorem(implies(a,not(not(a)))),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_2685,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2681,c_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL076-3 : 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
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 4 23:07:35 UTC 2026
% 0.09/0.36 % CPUTime :
% 7.91/3.46 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.91/3.47
% 7.91/3.47 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------