%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL188-3 : 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 11:11:26 AM UTC 2026
% Result : Unsatisfiable 8.01s 3.55s
% Output : CNFRefutation 8.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 77 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 68 ( 36 ~; 32 |; 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 : 92 ( 92 !; 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_56,axiom,
! [X,Y] : ( implies(X,Y) = or(not(X),Y) ),
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_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_54,axiom,
! [A,B,C] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
file(unknown,unknown) ).
tff(f_77,axiom,
~ theorem(or(p,implies(or(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_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_14,plain,
! [X_14] :
( ~ axiom(X_14)
| theorem(X_14) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_117,plain,
! [A_40,B_41,C_42] : axiom(implies(or(A_40,or(B_41,C_42)),or(B_41,or(A_40,C_42)))),
inference(cnfTransformation,[status(thm)],[f_52]) ).
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_393,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_117,c_54]) ).
tff(c_2685,plain,
! [B_320,A_321,C_322] :
( theorem(or(B_320,or(A_321,C_322)))
| ~ axiom(or(A_321,or(B_320,C_322))) ),
inference(resolution,[status(thm)],[c_14,c_393]) ).
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_64,plain,
! [Y_32,X_33] :
( ~ theorem(Y_32)
| theorem(X_33)
| ~ axiom(implies(Y_32,X_33)) ),
inference(resolution,[status(thm)],[c_14,c_50]) ).
tff(c_84,plain,
! [A_2,B_3] :
( ~ theorem(A_2)
| theorem(or(B_3,A_2)) ),
inference(resolution,[status(thm)],[c_4,c_64]) ).
tff(c_519,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_84,c_393]) ).
tff(c_534,plain,
! [X_12,B_108,C_109] :
( theorem(implies(X_12,or(B_108,C_109)))
| ~ theorem(or(not(X_12),C_109)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_519]) ).
tff(c_711,plain,
! [X_122,B_123,C_124] :
( theorem(implies(X_122,or(B_123,C_124)))
| ~ theorem(implies(X_122,C_124)) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_534]) ).
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_878,plain,
! [X_141,B_142,C_143] :
( ~ theorem(X_141)
| theorem(or(B_142,C_143))
| ~ theorem(implies(X_141,C_143)) ),
inference(resolution,[status(thm)],[c_711,c_16]) ).
tff(c_922,plain,
! [X_148,B_149,C_150] :
( ~ theorem(X_148)
| theorem(or(B_149,C_150))
| ~ axiom(implies(X_148,C_150)) ),
inference(resolution,[status(thm)],[c_14,c_878]) ).
tff(c_1281,plain,
! [A_188,B_189,B_190] :
( ~ theorem(or(A_188,B_189))
| theorem(or(B_190,or(B_189,A_188))) ),
inference(resolution,[status(thm)],[c_6,c_922]) ).
tff(c_135,plain,
! [A_40,B_41,C_42] :
( ~ theorem(or(A_40,or(B_41,C_42)))
| theorem(or(B_41,or(A_40,C_42))) ),
inference(resolution,[status(thm)],[c_117,c_54]) ).
tff(c_1453,plain,
! [B_210,B_211,A_212] :
( theorem(or(B_210,or(B_211,A_212)))
| ~ theorem(or(A_212,B_210)) ),
inference(resolution,[status(thm)],[c_1281,c_135]) ).
tff(c_2,plain,
! [A_1] : axiom(implies(or(A_1,A_1),A_1)),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_83,plain,
! [A_1] :
( ~ theorem(or(A_1,A_1))
| theorem(A_1) ),
inference(resolution,[status(thm)],[c_2,c_64]) ).
tff(c_1489,plain,
! [B_211,A_212] :
( theorem(or(B_211,A_212))
| ~ theorem(or(A_212,or(B_211,A_212))) ),
inference(resolution,[status(thm)],[c_1453,c_83]) ).
tff(c_2782,plain,
! [A_327,C_328] :
( theorem(or(A_327,C_328))
| ~ axiom(or(A_327,or(C_328,C_328))) ),
inference(resolution,[status(thm)],[c_2685,c_1489]) ).
tff(c_2790,plain,
! [X_12,C_328] :
( theorem(or(not(X_12),C_328))
| ~ axiom(implies(X_12,or(C_328,C_328))) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_2782]) ).
tff(c_2981,plain,
! [X_337,C_338] :
( theorem(implies(X_337,C_338))
| ~ axiom(implies(X_337,or(C_338,C_338))) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_2790]) ).
tff(c_3015,plain,
! [A_2] : theorem(implies(A_2,A_2)),
inference(resolution,[status(thm)],[c_4,c_2981]) ).
tff(c_10,plain,
! [A_9,B_10,C_11] : axiom(implies(implies(A_9,B_10),implies(or(C_11,A_9),or(C_11,B_10)))),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_80,plain,
! [A_9,B_10,C_11] :
( ~ theorem(implies(A_9,B_10))
| theorem(implies(or(C_11,A_9),or(C_11,B_10))) ),
inference(resolution,[status(thm)],[c_10,c_64]) ).
tff(c_130,plain,
! [X_12,B_41,Y_13] : axiom(implies(or(not(X_12),or(B_41,Y_13)),or(B_41,implies(X_12,Y_13)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_117]) ).
tff(c_482,plain,
! [X_98,B_99,Y_100] : axiom(implies(implies(X_98,or(B_99,Y_100)),or(B_99,implies(X_98,Y_100)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_130]) ).
tff(c_2235,plain,
! [X_266,B_267,Y_268] :
( ~ theorem(implies(X_266,or(B_267,Y_268)))
| theorem(or(B_267,implies(X_266,Y_268))) ),
inference(resolution,[status(thm)],[c_482,c_54]) ).
tff(c_18,plain,
~ theorem(or(p,implies(or(p,q),q))),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_2278,plain,
~ theorem(implies(or(p,q),or(p,q))),
inference(resolution,[status(thm)],[c_2235,c_18]) ).
tff(c_2305,plain,
~ theorem(implies(q,q)),
inference(resolution,[status(thm)],[c_80,c_2278]) ).
tff(c_3020,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3015,c_2305]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL188-3 : 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
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 5 19:29:09 UTC 2026
% 0.10/0.36 % CPUTime :
% 8.01/3.55 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.01/3.56
% 8.01/3.56 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------