%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL189-3 : 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 : n026.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 8.50s 3.65s
% Output : CNFRefutation 8.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 79 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 71 ( 37 ~; 34 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 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 : 93 ( 93 !; 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_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_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_50,axiom,
! [A,B] : axiom(implies(or(A,B),or(B,A))),
file(unknown,unknown) ).
tff(f_46,axiom,
! [A] : axiom(implies(or(A,A),A)),
file(unknown,unknown) ).
tff(f_77,axiom,
~ theorem(or(not(p),implies(implies(p,q),q))),
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_48]) ).
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_121,plain,
! [A_39,B_40,C_41] : axiom(implies(or(A_39,or(B_40,C_41)),or(B_40,or(A_39,C_41)))),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_134,plain,
! [X_12,B_40,Y_13] : axiom(implies(or(not(X_12),or(B_40,Y_13)),or(B_40,implies(X_12,Y_13)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_121]) ).
tff(c_308,plain,
! [X_68,B_69,Y_70] : axiom(implies(implies(X_68,or(B_69,Y_70)),or(B_69,implies(X_68,Y_70)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_134]) ).
tff(c_51,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_55,plain,
! [Y_27,X_28] :
( ~ theorem(Y_27)
| theorem(X_28)
| ~ axiom(implies(Y_27,X_28)) ),
inference(resolution,[status(thm)],[c_14,c_51]) ).
tff(c_319,plain,
! [X_68,B_69,Y_70] :
( ~ theorem(implies(X_68,or(B_69,Y_70)))
| theorem(or(B_69,implies(X_68,Y_70))) ),
inference(resolution,[status(thm)],[c_308,c_55]) ).
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_65,plain,
! [Y_32,X_33] :
( ~ theorem(Y_32)
| theorem(X_33)
| ~ axiom(implies(Y_32,X_33)) ),
inference(resolution,[status(thm)],[c_14,c_51]) ).
tff(c_85,plain,
! [A_2,B_3] :
( ~ theorem(A_2)
| theorem(or(B_3,A_2)) ),
inference(resolution,[status(thm)],[c_4,c_65]) ).
tff(c_400,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_121,c_55]) ).
tff(c_513,plain,
! [B_104,B_105,C_106] :
( theorem(or(B_104,or(B_105,C_106)))
| ~ theorem(or(B_104,C_106)) ),
inference(resolution,[status(thm)],[c_85,c_400]) ).
tff(c_528,plain,
! [X_12,B_105,C_106] :
( theorem(implies(X_12,or(B_105,C_106)))
| ~ theorem(or(not(X_12),C_106)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_513]) ).
tff(c_666,plain,
! [X_119,B_120,C_121] :
( theorem(implies(X_119,or(B_120,C_121)))
| ~ theorem(implies(X_119,C_121)) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_528]) ).
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_697,plain,
! [X_125,B_126,C_127] :
( ~ theorem(X_125)
| theorem(or(B_126,C_127))
| ~ theorem(implies(X_125,C_127)) ),
inference(resolution,[status(thm)],[c_666,c_16]) ).
tff(c_978,plain,
! [X_156,B_157,C_158] :
( ~ theorem(X_156)
| theorem(or(B_157,C_158))
| ~ axiom(implies(X_156,C_158)) ),
inference(resolution,[status(thm)],[c_14,c_697]) ).
tff(c_1411,plain,
! [A_202,B_203,B_204] :
( ~ theorem(or(A_202,B_203))
| theorem(or(B_204,or(B_203,A_202))) ),
inference(resolution,[status(thm)],[c_6,c_978]) ).
tff(c_139,plain,
! [A_39,B_40,C_41] :
( ~ theorem(or(A_39,or(B_40,C_41)))
| theorem(or(B_40,or(A_39,C_41))) ),
inference(resolution,[status(thm)],[c_121,c_55]) ).
tff(c_1503,plain,
! [B_213,B_214,A_215] :
( theorem(or(B_213,or(B_214,A_215)))
| ~ theorem(or(A_215,B_213)) ),
inference(resolution,[status(thm)],[c_1411,c_139]) ).
tff(c_2,plain,
! [A_1] : axiom(implies(or(A_1,A_1),A_1)),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_84,plain,
! [A_1] :
( ~ theorem(or(A_1,A_1))
| theorem(A_1) ),
inference(resolution,[status(thm)],[c_2,c_65]) ).
tff(c_1635,plain,
! [B_231,A_232] :
( theorem(or(B_231,A_232))
| ~ theorem(or(A_232,or(B_231,A_232))) ),
inference(resolution,[status(thm)],[c_1503,c_84]) ).
tff(c_1710,plain,
! [X_12,Y_13] :
( theorem(or(not(X_12),Y_13))
| ~ theorem(or(Y_13,implies(X_12,Y_13))) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_1635]) ).
tff(c_1824,plain,
! [X_240,Y_241] :
( theorem(implies(X_240,Y_241))
| ~ theorem(or(Y_241,implies(X_240,Y_241))) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_1710]) ).
tff(c_2109,plain,
! [X_260,Y_261] :
( theorem(implies(X_260,Y_261))
| ~ theorem(implies(X_260,or(Y_261,Y_261))) ),
inference(resolution,[status(thm)],[c_319,c_1824]) ).
tff(c_2163,plain,
! [X_262,Y_263] :
( theorem(implies(X_262,Y_263))
| ~ axiom(implies(X_262,or(Y_263,Y_263))) ),
inference(resolution,[status(thm)],[c_14,c_2109]) ).
tff(c_2197,plain,
! [A_2] : theorem(implies(A_2,A_2)),
inference(resolution,[status(thm)],[c_4,c_2163]) ).
tff(c_897,plain,
! [X_144,B_145,Y_146] :
( ~ theorem(implies(X_144,or(B_145,Y_146)))
| theorem(or(B_145,implies(X_144,Y_146))) ),
inference(resolution,[status(thm)],[c_308,c_55]) ).
tff(c_921,plain,
! [X_144,X_12,Y_146] :
( ~ theorem(implies(X_144,or(not(X_12),Y_146)))
| theorem(implies(X_12,implies(X_144,Y_146))) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_897]) ).
tff(c_3319,plain,
! [X_299,X_300,Y_301] :
( ~ theorem(implies(X_299,implies(X_300,Y_301)))
| theorem(implies(X_300,implies(X_299,Y_301))) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_921]) ).
tff(c_3356,plain,
! [X_300,Y_301] : theorem(implies(X_300,implies(implies(X_300,Y_301),Y_301))),
inference(resolution,[status(thm)],[c_2197,c_3319]) ).
tff(c_18,plain,
~ theorem(or(not(p),implies(implies(p,q),q))),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_19,plain,
~ theorem(implies(p,implies(implies(p,q),q))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_18]) ).
tff(c_3366,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3356,c_19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL189-3 : 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
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Fri Sep 4 18:51:55 UTC 2026
% 0.12/0.38 % CPUTime :
% 8.50/3.65 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.50/3.66
% 8.50/3.66 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------