%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL198-3 : 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 : n017.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 11:11:28 AM UTC 2026
% Result : Unsatisfiable 54.49s 40.71s
% Output : CNFRefutation 54.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 88 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 77 ( 40 ~; 37 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 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 : 115 ( 115 !; 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_54,axiom,
! [A,B,C] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
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_69,axiom,
! [X,Y] :
( theorem(X)
| ~ theorem(implies(Y,X))
| ~ theorem(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_46,axiom,
! [A] : axiom(implies(or(A,A),A)),
file(unknown,unknown) ).
tff(f_77,axiom,
~ theorem(implies(or(not(p),implies(p,q)),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_74,plain,
! [A_32,B_33,C_34] : axiom(implies(implies(A_32,B_33),implies(or(C_34,A_32),or(C_34,B_33)))),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_83,plain,
! [A_32,Y_13,X_12] : axiom(implies(implies(A_32,Y_13),implies(or(not(X_12),A_32),implies(X_12,Y_13)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_74]) ).
tff(c_86,plain,
! [A_32,Y_13,X_12] : axiom(implies(implies(A_32,Y_13),implies(implies(X_12,A_32),implies(X_12,Y_13)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_83]) ).
tff(c_6,plain,
! [A_4,B_5] : axiom(implies(or(A_4,B_5),or(B_5,A_4))),
inference(cnfTransformation,[status(thm)],[f_50]) ).
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_307,plain,
! [A_68,Y_69,X_70] : axiom(implies(implies(A_68,Y_69),implies(implies(X_70,A_68),implies(X_70,Y_69)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_83]) ).
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_983,plain,
! [A_157,Y_158,X_159] :
( ~ theorem(implies(A_157,Y_158))
| theorem(implies(implies(X_159,A_157),implies(X_159,Y_158))) ),
inference(resolution,[status(thm)],[c_307,c_51]) ).
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_4184,plain,
! [X_349,A_350,Y_351] :
( ~ theorem(implies(X_349,A_350))
| theorem(implies(X_349,Y_351))
| ~ theorem(implies(A_350,Y_351)) ),
inference(resolution,[status(thm)],[c_983,c_16]) ).
tff(c_6257,plain,
! [X_485,Y_486,A_487] :
( theorem(implies(X_485,Y_486))
| ~ theorem(implies(A_487,Y_486))
| ~ axiom(implies(X_485,A_487)) ),
inference(resolution,[status(thm)],[c_14,c_4184]) ).
tff(c_16864,plain,
! [X_895,Y_896,A_897] :
( theorem(implies(X_895,Y_896))
| ~ axiom(implies(X_895,A_897))
| ~ axiom(implies(A_897,Y_896)) ),
inference(resolution,[status(thm)],[c_14,c_6257]) ).
tff(c_18670,plain,
! [A_938,Y_939,B_940] :
( theorem(implies(A_938,Y_939))
| ~ axiom(implies(or(B_940,A_938),Y_939)) ),
inference(resolution,[status(thm)],[c_4,c_16864]) ).
tff(c_18700,plain,
! [B_5,A_4] : theorem(implies(B_5,or(B_5,A_4))),
inference(resolution,[status(thm)],[c_6,c_18670]) ).
tff(c_135,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_148,plain,
! [X_12,B_42,Y_13] : axiom(implies(or(not(X_12),or(B_42,Y_13)),or(B_42,implies(X_12,Y_13)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_135]) ).
tff(c_375,plain,
! [X_79,B_80,Y_81] : axiom(implies(implies(X_79,or(B_80,Y_81)),or(B_80,implies(X_79,Y_81)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_148]) ).
tff(c_386,plain,
! [X_79,B_80,Y_81] :
( ~ theorem(implies(X_79,or(B_80,Y_81)))
| theorem(or(B_80,implies(X_79,Y_81))) ),
inference(resolution,[status(thm)],[c_375,c_51]) ).
tff(c_2040,plain,
! [A_252,B_253,C_254] :
( ~ theorem(implies(A_252,B_253))
| theorem(implies(or(C_254,A_252),or(C_254,B_253))) ),
inference(resolution,[status(thm)],[c_74,c_51]) ).
tff(c_2376,plain,
! [C_276,A_277,B_278] :
( ~ theorem(or(C_276,A_277))
| theorem(or(C_276,B_278))
| ~ theorem(implies(A_277,B_278)) ),
inference(resolution,[status(thm)],[c_2040,c_16]) ).
tff(c_11757,plain,
! [B_703,B_704,X_705,Y_706] :
( theorem(or(B_703,B_704))
| ~ theorem(implies(implies(X_705,Y_706),B_704))
| ~ theorem(implies(X_705,or(B_703,Y_706))) ),
inference(resolution,[status(thm)],[c_386,c_2376]) ).
tff(c_83707,plain,
! [B_2574,B_2575,X_2576,Y_2577] :
( theorem(or(B_2574,B_2575))
| ~ theorem(implies(X_2576,or(B_2574,Y_2577)))
| ~ axiom(implies(implies(X_2576,Y_2577),B_2575)) ),
inference(resolution,[status(thm)],[c_14,c_11757]) ).
tff(c_84106,plain,
! [B_2578,B_2579,A_2580] :
( theorem(or(B_2578,B_2579))
| ~ axiom(implies(implies(B_2578,A_2580),B_2579)) ),
inference(resolution,[status(thm)],[c_18700,c_83707]) ).
tff(c_84152,plain,
! [A_2581,X_2582,Y_2583] : theorem(or(A_2581,implies(implies(X_2582,A_2581),implies(X_2582,Y_2583)))),
inference(resolution,[status(thm)],[c_86,c_84106]) ).
tff(c_53,plain,
! [Y_30,X_31] :
( ~ theorem(Y_30)
| theorem(X_31)
| ~ axiom(implies(Y_30,X_31)) ),
inference(resolution,[status(thm)],[c_14,c_47]) ).
tff(c_70,plain,
! [A_4,B_5] :
( ~ theorem(or(A_4,B_5))
| theorem(or(B_5,A_4)) ),
inference(resolution,[status(thm)],[c_6,c_53]) ).
tff(c_84289,plain,
! [X_2590,A_2591,Y_2592] : theorem(or(implies(implies(X_2590,A_2591),implies(X_2590,Y_2592)),A_2591)),
inference(resolution,[status(thm)],[c_84152,c_70]) ).
tff(c_73,plain,
! [A_2,B_3] :
( ~ theorem(A_2)
| theorem(or(B_3,A_2)) ),
inference(resolution,[status(thm)],[c_4,c_53]) ).
tff(c_390,plain,
! [A_83,B_84,C_85] :
( ~ theorem(or(A_83,or(B_84,C_85)))
| theorem(or(B_84,or(A_83,C_85))) ),
inference(resolution,[status(thm)],[c_135,c_51]) ).
tff(c_516,plain,
! [B_107,B_108,C_109] :
( theorem(or(B_107,or(B_108,C_109)))
| ~ theorem(or(B_107,C_109)) ),
inference(resolution,[status(thm)],[c_73,c_390]) ).
tff(c_2,plain,
! [A_1] : axiom(implies(or(A_1,A_1),A_1)),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_72,plain,
! [A_1] :
( ~ theorem(or(A_1,A_1))
| theorem(A_1) ),
inference(resolution,[status(thm)],[c_2,c_53]) ).
tff(c_558,plain,
! [B_113,C_114] :
( theorem(or(B_113,C_114))
| ~ theorem(or(or(B_113,C_114),C_114)) ),
inference(resolution,[status(thm)],[c_516,c_72]) ).
tff(c_597,plain,
! [X_12,Y_13] :
( theorem(or(not(X_12),Y_13))
| ~ theorem(or(implies(X_12,Y_13),Y_13)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_558]) ).
tff(c_610,plain,
! [X_12,Y_13] :
( theorem(implies(X_12,Y_13))
| ~ theorem(or(implies(X_12,Y_13),Y_13)) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_597]) ).
tff(c_84341,plain,
! [X_2590,Y_2592] : theorem(implies(implies(X_2590,implies(X_2590,Y_2592)),implies(X_2590,Y_2592))),
inference(resolution,[status(thm)],[c_84289,c_610]) ).
tff(c_18,plain,
~ theorem(implies(or(not(p),implies(p,q)),implies(p,q))),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_19,plain,
~ theorem(implies(implies(p,implies(p,q)),implies(p,q))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_18]) ).
tff(c_85309,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_84341,c_19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL198-3 : 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
% 0.08/0.35 % Computer : n017.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 : Fri Sep 4 13:04:50 UTC 2026
% 0.12/0.36 % CPUTime :
% 54.49/40.71 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 54.49/40.72
% 54.49/40.72 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------