%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL079-1 : 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 : n001.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 11:11:12 AM UTC 2026
% Result : Unsatisfiable 2.98s 1.96s
% Output : CNFRefutation 2.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 15 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 28 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_a_theorem > implies > #nlpp > not > c > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(is_a_theorem,type,
is_a_theorem: $i > $o ).
tff(b,type,
b: $i ).
tff(not,type,
not: $i > $i ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff(c,type,
c: $i ).
tff(f_42,axiom,
~ is_a_theorem(implies(a,c)),
file(unknown,unknown) ).
tff(f_40,axiom,
is_a_theorem(implies(b,c)),
file(unknown,unknown) ).
tff(f_39,axiom,
is_a_theorem(implies(a,b)),
file(unknown,unknown) ).
tff(f_34,axiom,
! [X,Y] : is_a_theorem(implies(X,implies(Y,X))),
file(unknown,unknown) ).
tff(f_32,axiom,
! [X,Y] :
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ),
file(unknown,unknown) ).
tff(f_36,axiom,
! [X,Y,Z] : is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))),
file(unknown,unknown) ).
tff(c_14,plain,
~ is_a_theorem(implies(a,c)),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_12,plain,
is_a_theorem(implies(b,c)),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_10,plain,
is_a_theorem(implies(a,b)),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_4,plain,
! [X_3,Y_4] : is_a_theorem(implies(X_3,implies(Y_4,X_3))),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_16,plain,
! [Y_12,X_13] :
( is_a_theorem(Y_12)
| ~ is_a_theorem(X_13)
| ~ is_a_theorem(implies(X_13,Y_12)) ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_26,plain,
! [Y_4,X_3] :
( is_a_theorem(implies(Y_4,X_3))
| ~ is_a_theorem(X_3) ),
inference(resolution,[status(thm)],[c_4,c_16]) ).
tff(c_36,plain,
! [X_16,Y_17,Z_18] : is_a_theorem(implies(implies(X_16,implies(Y_17,Z_18)),implies(implies(X_16,Y_17),implies(X_16,Z_18)))),
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_32]) ).
tff(c_84,plain,
! [X_25,Y_26,Z_27] :
( is_a_theorem(implies(implies(X_25,Y_26),implies(X_25,Z_27)))
| ~ is_a_theorem(implies(X_25,implies(Y_26,Z_27))) ),
inference(resolution,[status(thm)],[c_36,c_2]) ).
tff(c_100,plain,
! [X_35,Z_36,Y_37] :
( is_a_theorem(implies(X_35,Z_36))
| ~ is_a_theorem(implies(X_35,Y_37))
| ~ is_a_theorem(implies(X_35,implies(Y_37,Z_36))) ),
inference(resolution,[status(thm)],[c_84,c_2]) ).
tff(c_167,plain,
! [Y_41,Z_42,Y_43] :
( is_a_theorem(implies(Y_41,Z_42))
| ~ is_a_theorem(implies(Y_41,Y_43))
| ~ is_a_theorem(implies(Y_43,Z_42)) ),
inference(resolution,[status(thm)],[c_26,c_100]) ).
tff(c_195,plain,
! [Z_44] :
( is_a_theorem(implies(a,Z_44))
| ~ is_a_theorem(implies(b,Z_44)) ),
inference(resolution,[status(thm)],[c_10,c_167]) ).
tff(c_210,plain,
is_a_theorem(implies(a,c)),
inference(resolution,[status(thm)],[c_12,c_195]) ).
tff(c_218,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14,c_210]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL079-1 : 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
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 6 01:10:03 UTC 2026
% 0.10/0.36 % CPUTime :
% 2.98/1.96 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.98/1.97
% 2.98/1.97 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------