%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL236-3 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n029.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 8.52s 3.76s
% Output : CNFRefutation 8.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 83 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 69 ( 37 ~; 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 100 ( 100 !; 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_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_96,axiom,
! [P,Q] : ( and(P,Q) = not(or(not(P),not(Q))) ),
file(unknown,unknown) ).
tff(f_100,axiom,
~ theorem(implies(or(not(p),not(q)),not(and(p,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_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_92,plain,
! [X_12,B_35,Y_13] : axiom(implies(or(not(X_12),or(B_35,Y_13)),or(B_35,implies(X_12,Y_13)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_82]) ).
tff(c_752,plain,
! [X_114,B_115,Y_116] : axiom(implies(implies(X_114,or(B_115,Y_116)),or(B_115,implies(X_114,Y_116)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_92]) ).
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_770,plain,
! [X_114,B_115,Y_116] :
( ~ theorem(implies(X_114,or(B_115,Y_116)))
| theorem(or(B_115,implies(X_114,Y_116))) ),
inference(resolution,[status(thm)],[c_752,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_959,plain,
! [A_139,B_140,C_141] :
( ~ theorem(or(A_139,or(B_140,C_141)))
| theorem(or(B_140,or(A_139,C_141))) ),
inference(resolution,[status(thm)],[c_8,c_101]) ).
tff(c_1088,plain,
! [B_160,B_161,C_162] :
( theorem(or(B_160,or(B_161,C_162)))
| ~ theorem(or(B_160,C_162)) ),
inference(resolution,[status(thm)],[c_125,c_959]) ).
tff(c_1103,plain,
! [X_12,B_161,C_162] :
( theorem(implies(X_12,or(B_161,C_162)))
| ~ theorem(or(not(X_12),C_162)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_1088]) ).
tff(c_1237,plain,
! [X_172,B_173,C_174] :
( theorem(implies(X_172,or(B_173,C_174)))
| ~ theorem(implies(X_172,C_174)) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_1103]) ).
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_1289,plain,
! [X_181,B_182,C_183] :
( ~ theorem(X_181)
| theorem(or(B_182,C_183))
| ~ theorem(implies(X_181,C_183)) ),
inference(resolution,[status(thm)],[c_1237,c_16]) ).
tff(c_1606,plain,
! [X_209,B_210,C_211] :
( ~ theorem(X_209)
| theorem(or(B_210,C_211))
| ~ axiom(implies(X_209,C_211)) ),
inference(resolution,[status(thm)],[c_14,c_1289]) ).
tff(c_2111,plain,
! [A_264,B_265,B_266] :
( ~ theorem(or(A_264,B_265))
| theorem(or(B_266,or(B_265,A_264))) ),
inference(resolution,[status(thm)],[c_6,c_1606]) ).
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_2318,plain,
! [B_281,B_282,A_283] :
( theorem(or(B_281,or(B_282,A_283)))
| ~ theorem(or(A_283,B_281)) ),
inference(resolution,[status(thm)],[c_2111,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_2637,plain,
! [B_315,A_316] :
( theorem(or(B_315,A_316))
| ~ theorem(or(A_316,or(B_315,A_316))) ),
inference(resolution,[status(thm)],[c_2318,c_124]) ).
tff(c_2732,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_2637]) ).
tff(c_2774,plain,
! [X_320,Y_321] :
( theorem(implies(X_320,Y_321))
| ~ theorem(or(Y_321,implies(X_320,Y_321))) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_2732]) ).
tff(c_3164,plain,
! [X_339,Y_340] :
( theorem(implies(X_339,Y_340))
| ~ theorem(implies(X_339,or(Y_340,Y_340))) ),
inference(resolution,[status(thm)],[c_770,c_2774]) ).
tff(c_3269,plain,
! [X_343,Y_344] :
( theorem(implies(X_343,Y_344))
| ~ axiom(implies(X_343,or(Y_344,Y_344))) ),
inference(resolution,[status(thm)],[c_14,c_3164]) ).
tff(c_3309,plain,
! [A_2] : theorem(implies(A_2,A_2)),
inference(resolution,[status(thm)],[c_4,c_3269]) ).
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_234,plain,
! [X_55,Y_56] : axiom(implies(implies(X_55,Y_56),or(Y_56,not(X_55)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_61]) ).
tff(c_245,plain,
! [X_55,Y_56] :
( ~ theorem(implies(X_55,Y_56))
| theorem(or(Y_56,not(X_55))) ),
inference(resolution,[status(thm)],[c_234,c_72]) ).
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_20,plain,
~ theorem(implies(or(not(p),not(q)),not(and(p,q)))),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_22,plain,
~ theorem(implies(implies(p,not(q)),not(and(p,q)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_20]) ).
tff(c_388,plain,
~ theorem(or(and(p,q),not(and(p,q)))),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_22]) ).
tff(c_524,plain,
~ theorem(implies(and(p,q),and(p,q))),
inference(resolution,[status(thm)],[c_245,c_388]) ).
tff(c_3312,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3309,c_524]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL236-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.09/0.35 % Computer : n029.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 10:26:10 UTC 2026
% 0.09/0.35 % CPUTime :
% 8.52/3.76 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.52/3.77
% 8.52/3.77 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------