%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL226-3 : 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 : n009.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 11:11:33 AM UTC 2026
% Result : Unsatisfiable 11.90s 4.59s
% Output : CNFRefutation 12.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 34 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 16 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 42 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ theorem > axiom > or > implies > #nlpp > not > s > r > q
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(r,type,
r: $i ).
tff(s,type,
s: $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(implies,type,
implies: ( $i * $i ) > $i ).
tff(f_54,axiom,
! [A,B,C] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
file(unknown,unknown) ).
tff(f_61,axiom,
! [X] :
( theorem(X)
| ~ axiom(X) ),
file(unknown,unknown) ).
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_69,axiom,
! [X,Y] :
( theorem(X)
| ~ theorem(implies(Y,X))
| ~ theorem(Y) ),
file(unknown,unknown) ).
tff(f_77,axiom,
~ theorem(implies(or(q,r),implies(or(not(r),s),or(q,s)))),
file(unknown,unknown) ).
tff(c_10,plain,
! [A_9,B_10,C_11] : axiom(implies(implies(A_9,B_10),implies(or(C_11,A_9),or(C_11,B_10)))),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_14,plain,
! [X_14] :
( ~ axiom(X_14)
| theorem(X_14) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
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_115,plain,
! [A_41,B_42,C_43] : axiom(implies(or(A_41,or(B_42,C_43)),or(B_42,or(A_41,C_43)))),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_132,plain,
! [A_41,X_12,C_43] : axiom(implies(or(A_41,or(not(X_12),C_43)),implies(X_12,or(A_41,C_43)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_115]) ).
tff(c_469,plain,
! [A_89,X_90,C_91] : axiom(implies(or(A_89,implies(X_90,C_91)),implies(X_90,or(A_89,C_91)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_132]) ).
tff(c_47,plain,
! [Y_27,X_28] :
( ~ theorem(Y_27)
| ~ theorem(implies(Y_27,X_28))
| theorem(X_28) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_51,plain,
! [Y_27,X_28] :
( ~ theorem(Y_27)
| theorem(X_28)
| ~ axiom(implies(Y_27,X_28)) ),
inference(resolution,[status(thm)],[c_14,c_47]) ).
tff(c_1264,plain,
! [A_181,X_182,C_183] :
( ~ theorem(or(A_181,implies(X_182,C_183)))
| theorem(implies(X_182,or(A_181,C_183))) ),
inference(resolution,[status(thm)],[c_469,c_51]) ).
tff(c_1313,plain,
! [X_12,X_182,C_183] :
( ~ theorem(implies(X_12,implies(X_182,C_183)))
| theorem(implies(X_182,or(not(X_12),C_183))) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_1264]) ).
tff(c_4110,plain,
! [X_349,X_350,C_351] :
( ~ theorem(implies(X_349,implies(X_350,C_351)))
| theorem(implies(X_350,implies(X_349,C_351))) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_1313]) ).
tff(c_6412,plain,
! [X_471,X_472,C_473] :
( theorem(implies(X_471,implies(X_472,C_473)))
| ~ axiom(implies(X_472,implies(X_471,C_473))) ),
inference(resolution,[status(thm)],[c_14,c_4110]) ).
tff(c_18,plain,
~ theorem(implies(or(q,r),implies(or(not(r),s),or(q,s)))),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_19,plain,
~ theorem(implies(or(q,r),implies(implies(r,s),or(q,s)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_18]) ).
tff(c_6452,plain,
~ axiom(implies(implies(r,s),implies(or(q,r),or(q,s)))),
inference(resolution,[status(thm)],[c_6412,c_19]) ).
tff(c_6469,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10,c_6452]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL226-3 : 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
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 5 11:45:36 UTC 2026
% 0.08/0.36 % CPUTime :
% 11.90/4.59 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.23/4.60
% 12.23/4.60 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------