%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL186-3 : 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 : n016.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 11:11:26 AM UTC 2026
% Result : Unsatisfiable 18.52s 7.37s
% Output : CNFRefutation 18.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 44 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 20 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 53 !; 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_50,axiom,
! [A,B] : axiom(implies(or(A,B),or(B,A))),
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_54,axiom,
! [A,B,C] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
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(p,q))),
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_43,plain,
! [A_25,B_26] : axiom(implies(or(A_25,B_26),or(B_26,A_25))),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_49,plain,
! [Y_13,X_12] : axiom(implies(or(Y_13,not(X_12)),implies(X_12,Y_13))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_43]) ).
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_14,plain,
! [X_14] :
( ~ axiom(X_14)
| theorem(X_14) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_121,plain,
! [A_37,B_38,C_39] : axiom(implies(implies(A_37,B_38),implies(or(C_39,A_37),or(C_39,B_38)))),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_127,plain,
! [Y_13,B_38,X_12] : axiom(implies(implies(Y_13,B_38),implies(implies(X_12,Y_13),or(not(X_12),B_38)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_121]) ).
tff(c_656,plain,
! [Y_114,B_115,X_116] : axiom(implies(implies(Y_114,B_115),implies(implies(X_116,Y_114),implies(X_116,B_115)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_127]) ).
tff(c_50,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_54,plain,
! [Y_27,X_28] :
( ~ theorem(Y_27)
| theorem(X_28)
| ~ axiom(implies(Y_27,X_28)) ),
inference(resolution,[status(thm)],[c_14,c_50]) ).
tff(c_1007,plain,
! [Y_160,B_161,X_162] :
( ~ theorem(implies(Y_160,B_161))
| theorem(implies(implies(X_162,Y_160),implies(X_162,B_161))) ),
inference(resolution,[status(thm)],[c_656,c_54]) ).
tff(c_16,plain,
! [Y_16,X_15] :
( ~ theorem(Y_16)
| ~ theorem(implies(Y_16,X_15))
| theorem(X_15) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_3507,plain,
! [X_314,Y_315,B_316] :
( ~ theorem(implies(X_314,Y_315))
| theorem(implies(X_314,B_316))
| ~ theorem(implies(Y_315,B_316)) ),
inference(resolution,[status(thm)],[c_1007,c_16]) ).
tff(c_5654,plain,
! [X_439,B_440,Y_441] :
( theorem(implies(X_439,B_440))
| ~ theorem(implies(Y_441,B_440))
| ~ axiom(implies(X_439,Y_441)) ),
inference(resolution,[status(thm)],[c_14,c_3507]) ).
tff(c_16150,plain,
! [X_868,B_869,Y_870] :
( theorem(implies(X_868,B_869))
| ~ axiom(implies(X_868,Y_870))
| ~ axiom(implies(Y_870,B_869)) ),
inference(resolution,[status(thm)],[c_14,c_5654]) ).
tff(c_17835,plain,
! [A_903,B_904,B_905] :
( theorem(implies(A_903,B_904))
| ~ axiom(implies(or(B_905,A_903),B_904)) ),
inference(resolution,[status(thm)],[c_4,c_16150]) ).
tff(c_17863,plain,
! [X_12,Y_13] : theorem(implies(not(X_12),implies(X_12,Y_13))),
inference(resolution,[status(thm)],[c_49,c_17835]) ).
tff(c_18,plain,
~ theorem(implies(not(p),implies(p,q))),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_18024,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_17863,c_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL186-3 : 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
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 4 19:15:43 UTC 2026
% 0.09/0.35 % CPUTime :
% 18.52/7.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.52/7.38
% 18.52/7.38 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------