%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL212-3 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n026.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 11:11:31 AM UTC 2026
% Result : Unsatisfiable 3.51s 2.37s
% Output : CNFRefutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 20 ( 20 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ theorem > axiom > or > implies > #nlpp > not > q > p
%Foreground sorts:
%Background operators:
%Foreground operators:
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_48,axiom,
! [A,B] : axiom(implies(A,or(B,A))),
file(unknown,unknown) ).
tff(f_61,axiom,
! [X] :
( theorem(X)
| ~ axiom(X) ),
file(unknown,unknown) ).
tff(f_69,axiom,
! [X,Y] :
( theorem(X)
| ~ theorem(implies(Y,X))
| ~ theorem(Y) ),
file(unknown,unknown) ).
tff(f_77,axiom,
~ theorem(implies(not(p),implies(q,implies(implies(p,q),q)))),
file(unknown,unknown) ).
tff(c_22,plain,
! [X_21,Y_22] : ( or(not(X_21),Y_22) = implies(X_21,Y_22) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_4,plain,
! [A_2,B_3] : axiom(implies(A_2,or(B_3,A_2))),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_32,plain,
! [Y_22,X_21] : axiom(implies(Y_22,implies(X_21,Y_22))),
inference(superposition,[status(thm),theory(equality)],[c_22,c_4]) ).
tff(c_14,plain,
! [X_14] :
( ~ axiom(X_14)
| theorem(X_14) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_39,plain,
! [Y_25,X_26] :
( ~ theorem(Y_25)
| ~ theorem(implies(Y_25,X_26))
| theorem(X_26) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_52,plain,
! [Y_30,X_31] :
( ~ theorem(Y_30)
| theorem(X_31)
| ~ axiom(implies(Y_30,X_31)) ),
inference(resolution,[status(thm)],[c_14,c_39]) ).
tff(c_81,plain,
! [Y_34,X_35] :
( ~ theorem(Y_34)
| theorem(implies(X_35,Y_34)) ),
inference(resolution,[status(thm)],[c_32,c_52]) ).
tff(c_18,plain,
~ theorem(implies(not(p),implies(q,implies(implies(p,q),q)))),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_88,plain,
~ theorem(implies(q,implies(implies(p,q),q))),
inference(resolution,[status(thm)],[c_81,c_18]) ).
tff(c_220,plain,
~ axiom(implies(q,implies(implies(p,q),q))),
inference(resolution,[status(thm)],[c_14,c_88]) ).
tff(c_226,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_32,c_220]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL212-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.10/0.36 % Computer : n026.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 20:18:26 UTC 2026
% 0.10/0.36 % CPUTime :
% 3.51/2.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.51/2.38
% 3.51/2.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------