%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL176-3 : 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 : n007.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 11:11:24 AM UTC 2026
% Result : Unsatisfiable 7.47s 3.47s
% Output : CNFRefutation 7.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 70 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 62 ( 32 ~; 30 |; 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 : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 84 ( 84 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ theorem > axiom > or > implies > #nlpp > not > 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(axiom,type,
axiom: $i > $o ).
tff(p,type,
p: $i ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff(f_49,axiom,
! [A,B] : axiom(implies(A,or(B,A))),
file(unknown,unknown) ).
tff(f_62,axiom,
! [X] :
( theorem(X)
| ~ axiom(X) ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [X,Y] : ( implies(X,Y) = or(not(X),Y) ),
file(unknown,unknown) ).
tff(f_53,axiom,
! [A,B,C] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
file(unknown,unknown) ).
tff(f_70,axiom,
! [X,Y] :
( theorem(X)
| ~ theorem(implies(Y,X))
| ~ theorem(Y) ),
file(unknown,unknown) ).
tff(f_51,axiom,
! [A,B] : axiom(implies(or(A,B),or(B,A))),
file(unknown,unknown) ).
tff(f_47,axiom,
! [A] : axiom(implies(or(A,A),A)),
file(unknown,unknown) ).
tff(f_78,axiom,
~ theorem(implies(p,p)),
file(unknown,unknown) ).
tff(c_4,plain,
! [A_2,B_3] : axiom(implies(A_2,or(B_3,A_2))),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_14,plain,
! [X_14] :
( ~ axiom(X_14)
| theorem(X_14) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_12,plain,
! [X_12,Y_13] : ( or(not(X_12),Y_13) = implies(X_12,Y_13) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_55,plain,
! [A_29,B_30,C_31] : axiom(implies(or(A_29,or(B_30,C_31)),or(B_30,or(A_29,C_31)))),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_62,plain,
! [X_12,B_30,C_31] : axiom(implies(implies(X_12,or(B_30,C_31)),or(B_30,or(not(X_12),C_31)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_55]) ).
tff(c_262,plain,
! [X_62,B_63,C_64] : axiom(implies(implies(X_62,or(B_63,C_64)),or(B_63,implies(X_62,C_64)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_62]) ).
tff(c_43,plain,
! [Y_25,X_26] :
( ~ theorem(Y_25)
| ~ theorem(implies(Y_25,X_26))
| theorem(X_26) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_47,plain,
! [Y_25,X_26] :
( ~ theorem(Y_25)
| theorem(X_26)
| ~ axiom(implies(Y_25,X_26)) ),
inference(resolution,[status(thm)],[c_14,c_43]) ).
tff(c_273,plain,
! [X_62,B_63,C_64] :
( ~ theorem(implies(X_62,or(B_63,C_64)))
| theorem(or(B_63,implies(X_62,C_64))) ),
inference(resolution,[status(thm)],[c_262,c_47]) ).
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_51]) ).
tff(c_74,plain,
! [Y_32,X_33] :
( ~ theorem(Y_32)
| theorem(X_33)
| ~ axiom(implies(Y_32,X_33)) ),
inference(resolution,[status(thm)],[c_14,c_43]) ).
tff(c_94,plain,
! [A_2,B_3] :
( ~ theorem(A_2)
| theorem(or(B_3,A_2)) ),
inference(resolution,[status(thm)],[c_4,c_74]) ).
tff(c_8,plain,
! [A_6,B_7,C_8] : axiom(implies(or(A_6,or(B_7,C_8)),or(B_7,or(A_6,C_8)))),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_403,plain,
! [A_89,B_90,C_91] :
( ~ theorem(or(A_89,or(B_90,C_91)))
| theorem(or(B_90,or(A_89,C_91))) ),
inference(resolution,[status(thm)],[c_8,c_74]) ).
tff(c_525,plain,
! [B_113,B_114,C_115] :
( theorem(or(B_113,or(B_114,C_115)))
| ~ theorem(or(B_113,C_115)) ),
inference(resolution,[status(thm)],[c_94,c_403]) ).
tff(c_540,plain,
! [X_12,B_114,C_115] :
( theorem(implies(X_12,or(B_114,C_115)))
| ~ theorem(or(not(X_12),C_115)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_525]) ).
tff(c_715,plain,
! [X_133,B_134,C_135] :
( theorem(implies(X_133,or(B_134,C_135)))
| ~ theorem(implies(X_133,C_135)) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_540]) ).
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_70]) ).
tff(c_884,plain,
! [X_150,B_151,C_152] :
( ~ theorem(X_150)
| theorem(or(B_151,C_152))
| ~ theorem(implies(X_150,C_152)) ),
inference(resolution,[status(thm)],[c_715,c_16]) ).
tff(c_955,plain,
! [X_161,B_162,C_163] :
( ~ theorem(X_161)
| theorem(or(B_162,C_163))
| ~ axiom(implies(X_161,C_163)) ),
inference(resolution,[status(thm)],[c_14,c_884]) ).
tff(c_1402,plain,
! [A_208,B_209,B_210] :
( ~ theorem(or(A_208,B_209))
| theorem(or(B_210,or(B_209,A_208))) ),
inference(resolution,[status(thm)],[c_6,c_955]) ).
tff(c_90,plain,
! [A_6,B_7,C_8] :
( ~ theorem(or(A_6,or(B_7,C_8)))
| theorem(or(B_7,or(A_6,C_8))) ),
inference(resolution,[status(thm)],[c_8,c_74]) ).
tff(c_1608,plain,
! [B_225,B_226,A_227] :
( theorem(or(B_225,or(B_226,A_227)))
| ~ theorem(or(A_227,B_225)) ),
inference(resolution,[status(thm)],[c_1402,c_90]) ).
tff(c_1673,plain,
! [B_236,X_237,Y_238] :
( theorem(or(B_236,implies(X_237,Y_238)))
| ~ theorem(or(Y_238,B_236)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_1608]) ).
tff(c_2,plain,
! [A_1] : axiom(implies(or(A_1,A_1),A_1)),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_93,plain,
! [A_1] :
( ~ theorem(or(A_1,A_1))
| theorem(A_1) ),
inference(resolution,[status(thm)],[c_2,c_74]) ).
tff(c_2101,plain,
! [X_266,Y_267] :
( theorem(implies(X_266,Y_267))
| ~ theorem(or(Y_267,implies(X_266,Y_267))) ),
inference(resolution,[status(thm)],[c_1673,c_93]) ).
tff(c_2254,plain,
! [X_272,C_273] :
( theorem(implies(X_272,C_273))
| ~ theorem(implies(X_272,or(C_273,C_273))) ),
inference(resolution,[status(thm)],[c_273,c_2101]) ).
tff(c_2341,plain,
! [X_276,C_277] :
( theorem(implies(X_276,C_277))
| ~ axiom(implies(X_276,or(C_277,C_277))) ),
inference(resolution,[status(thm)],[c_14,c_2254]) ).
tff(c_2375,plain,
! [A_2] : theorem(implies(A_2,A_2)),
inference(resolution,[status(thm)],[c_4,c_2341]) ).
tff(c_18,plain,
~ theorem(implies(p,p)),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_2378,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2375,c_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL176-3 : 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
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 5 09:20:09 UTC 2026
% 0.08/0.36 % CPUTime :
% 7.47/3.47 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.47/3.48
% 7.47/3.48 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------