%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL172-3 : TPTP v9.3.1. Released v2.3.0.
% 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 11:11:23 AM UTC 2026
% Result : Unsatisfiable 4.74s 2.76s
% Output : CNFRefutation 4.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 24 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ theorem > axiom > or > implies > #nlpp > not > r > q > p
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(r,type,
r: $i ).
tff(theorem,type,
theorem: $i > $o ).
tff(or,type,
or: ( $i * $i ) > $i ).
tff(not,type,
not: $i > $i ).
tff(q,type,
q: $i ).
tff(axiom,type,
axiom: $i > $o ).
tff(p,type,
p: $i ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff(f_56,axiom,
! [X,Y] : ( implies(X,Y) = or(not(X),Y) ),
file(unknown,unknown) ).
tff(f_52,axiom,
! [A,B,C] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
file(unknown,unknown) ).
tff(f_61,axiom,
! [X] :
( theorem(X)
| ~ axiom(X) ),
file(unknown,unknown) ).
tff(f_77,axiom,
~ theorem(implies(implies(p,implies(q,r)),implies(q,implies(p,r)))),
file(unknown,unknown) ).
tff(c_12,plain,
! [X_12,Y_13] : ( or(not(X_12),Y_13) = implies(X_12,Y_13) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_112,plain,
! [A_37,B_38,C_39] : axiom(implies(or(A_37,or(B_38,C_39)),or(B_38,or(A_37,C_39)))),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_118,plain,
! [A_37,X_12,Y_13] : axiom(implies(or(A_37,implies(X_12,Y_13)),or(not(X_12),or(A_37,Y_13)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_112]) ).
tff(c_405,plain,
! [A_83,X_84,Y_85] : axiom(implies(or(A_83,implies(X_84,Y_85)),implies(X_84,or(A_83,Y_85)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_118]) ).
tff(c_412,plain,
! [X_12,X_84,Y_85] : axiom(implies(implies(X_12,implies(X_84,Y_85)),implies(X_84,or(not(X_12),Y_85)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_405]) ).
tff(c_417,plain,
! [X_12,X_84,Y_85] : axiom(implies(implies(X_12,implies(X_84,Y_85)),implies(X_84,implies(X_12,Y_85)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_412]) ).
tff(c_14,plain,
! [X_14] :
( ~ axiom(X_14)
| theorem(X_14) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_18,plain,
~ theorem(implies(implies(p,implies(q,r)),implies(q,implies(p,r)))),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_76,plain,
~ axiom(implies(implies(p,implies(q,r)),implies(q,implies(p,r)))),
inference(resolution,[status(thm)],[c_14,c_18]) ).
tff(c_561,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_417,c_76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL172-3 : TPTP v9.3.1. Released v2.3.0.
% 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 : n014.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 : Sat Sep 5 13:27:27 UTC 2026
% 0.10/0.37 % CPUTime :
% 4.74/2.76 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.74/2.77
% 4.74/2.77 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------