%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL174-3 : 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 : n008.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 10.85s 4.24s
% Output : CNFRefutation 10.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 13 ~; 10 |; 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 : 48 ( 48 !; 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_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_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(implies(p,q),implies(implies(q,r),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_164,plain,
! [A_46,B_47,C_48] : axiom(implies(implies(A_46,B_47),implies(or(C_48,A_46),or(C_48,B_47)))),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_170,plain,
! [Y_13,B_47,X_12] : axiom(implies(implies(Y_13,B_47),implies(implies(X_12,Y_13),or(not(X_12),B_47)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_164]) ).
tff(c_175,plain,
! [Y_13,B_47,X_12] : axiom(implies(implies(Y_13,B_47),implies(implies(X_12,Y_13),implies(X_12,B_47)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_170]) ).
tff(c_14,plain,
! [X_14] :
( ~ axiom(X_14)
| theorem(X_14) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_109,plain,
! [A_38,B_39,C_40] : axiom(implies(or(A_38,or(B_39,C_40)),or(B_39,or(A_38,C_40)))),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_122,plain,
! [X_12,B_39,Y_13] : axiom(implies(or(not(X_12),or(B_39,Y_13)),or(B_39,implies(X_12,Y_13)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_109]) ).
tff(c_406,plain,
! [X_83,B_84,Y_85] : axiom(implies(implies(X_83,or(B_84,Y_85)),or(B_84,implies(X_83,Y_85)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_122]) ).
tff(c_412,plain,
! [X_83,X_12,Y_13] : axiom(implies(implies(X_83,implies(X_12,Y_13)),or(not(X_12),implies(X_83,Y_13)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_406]) ).
tff(c_435,plain,
! [X_89,X_90,Y_91] : axiom(implies(implies(X_89,implies(X_90,Y_91)),implies(X_90,implies(X_89,Y_91)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_412]) ).
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_43,plain,
! [Y_25,X_26] :
( ~ theorem(Y_25)
| theorem(X_26)
| ~ axiom(implies(Y_25,X_26)) ),
inference(resolution,[status(thm)],[c_14,c_39]) ).
tff(c_1564,plain,
! [X_213,X_214,Y_215] :
( ~ theorem(implies(X_213,implies(X_214,Y_215)))
| theorem(implies(X_214,implies(X_213,Y_215))) ),
inference(resolution,[status(thm)],[c_435,c_43]) ).
tff(c_5244,plain,
! [X_435,X_436,Y_437] :
( theorem(implies(X_435,implies(X_436,Y_437)))
| ~ axiom(implies(X_436,implies(X_435,Y_437))) ),
inference(resolution,[status(thm)],[c_14,c_1564]) ).
tff(c_18,plain,
~ theorem(implies(implies(p,q),implies(implies(q,r),implies(p,r)))),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_5286,plain,
~ axiom(implies(implies(q,r),implies(implies(p,q),implies(p,r)))),
inference(resolution,[status(thm)],[c_5244,c_18]) ).
tff(c_5303,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_175,c_5286]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL174-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.05 % 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
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 5 11:34:53 UTC 2026
% 0.11/0.38 % CPUTime :
% 10.85/4.24 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.85/4.25
% 10.85/4.25 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------