%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL235-3 : 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 : n027.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 11:11:35 AM UTC 2026
% Result : Unsatisfiable 22.03s 11.33s
% Output : CNFRefutation 22.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 70 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 116 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 96 ( 50 ~; 46 |; 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 146 ( 146 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ theorem > axiom > or > implies > and > #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(and,type,
and: ( $i * $i ) > $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_96,axiom,
! [P,Q] : ( and(P,Q) = not(or(not(P),not(Q))) ),
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_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_100,axiom,
~ theorem(implies(not(and(p,q)),or(not(p),not(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_18,plain,
! [P_17,Q_18] : ( not(or(not(P_17),not(Q_18))) = and(P_17,Q_18) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_43,plain,
! [P_27,Q_28] : ( not(implies(P_27,not(Q_28))) = and(P_27,Q_28) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_18]) ).
tff(c_52,plain,
! [P_27,Q_28,Y_13] : ( implies(implies(P_27,not(Q_28)),Y_13) = or(and(P_27,Q_28),Y_13) ),
inference(superposition,[status(thm),theory(equality)],[c_43,c_12]) ).
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_82,plain,
! [A_34,B_35,C_36] : axiom(implies(or(A_34,or(B_35,C_36)),or(B_35,or(A_34,C_36)))),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_89,plain,
! [X_12,B_35,C_36] : axiom(implies(implies(X_12,or(B_35,C_36)),or(B_35,or(not(X_12),C_36)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_82]) ).
tff(c_738,plain,
! [X_114,B_115,C_116] : axiom(implies(implies(X_114,or(B_115,C_116)),or(B_115,implies(X_114,C_116)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_89]) ).
tff(c_68,plain,
! [Y_31,X_32] :
( ~ theorem(Y_31)
| ~ theorem(implies(Y_31,X_32))
| theorem(X_32) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_72,plain,
! [Y_31,X_32] :
( ~ theorem(Y_31)
| theorem(X_32)
| ~ axiom(implies(Y_31,X_32)) ),
inference(resolution,[status(thm)],[c_14,c_68]) ).
tff(c_756,plain,
! [X_114,B_115,C_116] :
( ~ theorem(implies(X_114,or(B_115,C_116)))
| theorem(or(B_115,implies(X_114,C_116))) ),
inference(resolution,[status(thm)],[c_738,c_72]) ).
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_101,plain,
! [Y_37,X_38] :
( ~ theorem(Y_37)
| theorem(X_38)
| ~ axiom(implies(Y_37,X_38)) ),
inference(resolution,[status(thm)],[c_14,c_68]) ).
tff(c_125,plain,
! [A_2,B_3] :
( ~ theorem(A_2)
| theorem(or(B_3,A_2)) ),
inference(resolution,[status(thm)],[c_4,c_101]) ).
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_52]) ).
tff(c_1032,plain,
! [A_160,B_161,C_162] :
( ~ theorem(or(A_160,or(B_161,C_162)))
| theorem(or(B_161,or(A_160,C_162))) ),
inference(resolution,[status(thm)],[c_8,c_101]) ).
tff(c_1165,plain,
! [B_181,B_182,C_183] :
( theorem(or(B_181,or(B_182,C_183)))
| ~ theorem(or(B_181,C_183)) ),
inference(resolution,[status(thm)],[c_125,c_1032]) ).
tff(c_1180,plain,
! [X_12,B_182,C_183] :
( theorem(implies(X_12,or(B_182,C_183)))
| ~ theorem(or(not(X_12),C_183)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_1165]) ).
tff(c_1314,plain,
! [X_193,B_194,C_195] :
( theorem(implies(X_193,or(B_194,C_195)))
| ~ theorem(implies(X_193,C_195)) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_1180]) ).
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_1567,plain,
! [X_214,B_215,C_216] :
( ~ theorem(X_214)
| theorem(or(B_215,C_216))
| ~ theorem(implies(X_214,C_216)) ),
inference(resolution,[status(thm)],[c_1314,c_16]) ).
tff(c_1716,plain,
! [X_230,B_231,C_232] :
( ~ theorem(X_230)
| theorem(or(B_231,C_232))
| ~ axiom(implies(X_230,C_232)) ),
inference(resolution,[status(thm)],[c_14,c_1567]) ).
tff(c_2211,plain,
! [A_279,B_280,B_281] :
( ~ theorem(or(A_279,B_280))
| theorem(or(B_281,or(B_280,A_279))) ),
inference(resolution,[status(thm)],[c_6,c_1716]) ).
tff(c_120,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_101]) ).
tff(c_2463,plain,
! [B_296,B_297,A_298] :
( theorem(or(B_296,or(B_297,A_298)))
| ~ theorem(or(A_298,B_296)) ),
inference(resolution,[status(thm)],[c_2211,c_120]) ).
tff(c_2,plain,
! [A_1] : axiom(implies(or(A_1,A_1),A_1)),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_124,plain,
! [A_1] :
( ~ theorem(or(A_1,A_1))
| theorem(A_1) ),
inference(resolution,[status(thm)],[c_2,c_101]) ).
tff(c_2817,plain,
! [B_333,A_334] :
( theorem(or(B_333,A_334))
| ~ theorem(or(A_334,or(B_333,A_334))) ),
inference(resolution,[status(thm)],[c_2463,c_124]) ).
tff(c_2908,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_2817]) ).
tff(c_2984,plain,
! [X_338,Y_339] :
( theorem(implies(X_338,Y_339))
| ~ theorem(or(Y_339,implies(X_338,Y_339))) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_2908]) ).
tff(c_3283,plain,
! [X_355,C_356] :
( theorem(implies(X_355,C_356))
| ~ theorem(implies(X_355,or(C_356,C_356))) ),
inference(resolution,[status(thm)],[c_756,c_2984]) ).
tff(c_3388,plain,
! [X_359,C_360] :
( theorem(implies(X_359,C_360))
| ~ axiom(implies(X_359,or(C_360,C_360))) ),
inference(resolution,[status(thm)],[c_14,c_3283]) ).
tff(c_3429,plain,
! [A_361] : theorem(implies(A_361,A_361)),
inference(resolution,[status(thm)],[c_4,c_3388]) ).
tff(c_4379,plain,
! [P_400,Q_401] : theorem(or(and(P_400,Q_401),implies(P_400,not(Q_401)))),
inference(superposition,[status(thm),theory(equality)],[c_52,c_3429]) ).
tff(c_122,plain,
! [A_4,B_5] :
( ~ theorem(or(A_4,B_5))
| theorem(or(B_5,A_4)) ),
inference(resolution,[status(thm)],[c_6,c_101]) ).
tff(c_4408,plain,
! [P_400,Q_401] : theorem(or(implies(P_400,not(Q_401)),and(P_400,Q_401))),
inference(resolution,[status(thm)],[c_4379,c_122]) ).
tff(c_445,plain,
! [P_89,Q_90,Y_91] : ( implies(implies(P_89,not(Q_90)),Y_91) = or(and(P_89,Q_90),Y_91) ),
inference(superposition,[status(thm),theory(equality)],[c_43,c_12]) ).
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_4780,plain,
! [P_420,Q_421,C_422] : axiom(or(and(P_420,Q_421),implies(or(C_422,P_420),or(C_422,not(Q_421))))),
inference(superposition,[status(thm),theory(equality)],[c_445,c_10]) ).
tff(c_61,plain,
! [A_29,B_30] : axiom(implies(or(A_29,B_30),or(B_30,A_29))),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_286,plain,
! [Y_61,X_62] : axiom(implies(or(Y_61,not(X_62)),implies(X_62,Y_61))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_61]) ).
tff(c_320,plain,
! [Y_66,X_67] :
( ~ theorem(or(Y_66,not(X_67)))
| theorem(implies(X_67,Y_66)) ),
inference(resolution,[status(thm)],[c_286,c_72]) ).
tff(c_342,plain,
! [X_12,X_67] :
( ~ theorem(implies(X_12,not(X_67)))
| theorem(implies(X_67,not(X_12))) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_320]) ).
tff(c_3459,plain,
! [X_67] : theorem(implies(X_67,not(not(X_67)))),
inference(resolution,[status(thm)],[c_3429,c_342]) ).
tff(c_4228,plain,
! [P_394,Q_395,Y_396] :
( ~ theorem(implies(P_394,not(Q_395)))
| theorem(Y_396)
| ~ axiom(or(and(P_394,Q_395),Y_396)) ),
inference(superposition,[status(thm),theory(equality)],[c_445,c_72]) ).
tff(c_4265,plain,
! [Y_396,X_67] :
( theorem(Y_396)
| ~ axiom(or(and(X_67,not(X_67)),Y_396)) ),
inference(resolution,[status(thm)],[c_3459,c_4228]) ).
tff(c_19706,plain,
! [C_1070,P_1071] : theorem(implies(or(C_1070,P_1071),or(C_1070,not(not(P_1071))))),
inference(resolution,[status(thm)],[c_4780,c_4265]) ).
tff(c_174,plain,
! [A_45,B_46,C_47] : axiom(implies(implies(A_45,B_46),implies(or(C_47,A_45),or(C_47,B_46)))),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_184,plain,
! [A_45,B_46,C_47] :
( ~ theorem(implies(A_45,B_46))
| theorem(implies(or(C_47,A_45),or(C_47,B_46))) ),
inference(resolution,[status(thm)],[c_174,c_72]) ).
tff(c_3352,plain,
! [B_357,A_358] :
( theorem(implies(or(B_357,A_358),B_357))
| ~ theorem(implies(A_358,B_357)) ),
inference(resolution,[status(thm)],[c_184,c_3283]) ).
tff(c_3666,plain,
! [B_375,A_376] :
( ~ theorem(or(B_375,A_376))
| theorem(B_375)
| ~ theorem(implies(A_376,B_375)) ),
inference(resolution,[status(thm)],[c_3352,c_16]) ).
tff(c_3812,plain,
! [B_3,A_2] :
( theorem(B_3)
| ~ theorem(implies(A_2,B_3))
| ~ theorem(A_2) ),
inference(resolution,[status(thm)],[c_125,c_3666]) ).
tff(c_30251,plain,
! [C_1366,P_1367] :
( theorem(or(C_1366,not(not(P_1367))))
| ~ theorem(or(C_1366,P_1367)) ),
inference(resolution,[status(thm)],[c_19706,c_3812]) ).
tff(c_297,plain,
! [Y_61,X_62] :
( ~ theorem(or(Y_61,not(X_62)))
| theorem(implies(X_62,Y_61)) ),
inference(resolution,[status(thm)],[c_286,c_72]) ).
tff(c_30354,plain,
! [P_1368,C_1369] :
( theorem(implies(not(P_1368),C_1369))
| ~ theorem(or(C_1369,P_1368)) ),
inference(resolution,[status(thm)],[c_30251,c_297]) ).
tff(c_20,plain,
~ theorem(implies(not(and(p,q)),or(not(p),not(q)))),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_22,plain,
~ theorem(implies(not(and(p,q)),implies(p,not(q)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_20]) ).
tff(c_30489,plain,
~ theorem(or(implies(p,not(q)),and(p,q))),
inference(resolution,[status(thm)],[c_30354,c_22]) ).
tff(c_30558,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4408,c_30489]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL235-3 : 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
% 0.10/0.36 % Computer : n027.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % 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 16:00:43 UTC 2026
% 0.10/0.36 % CPUTime :
% 22.03/11.33 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.03/11.35
% 22.03/11.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------