%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL109-5 : TPTP v9.3.1. Released v1.0.0.
% 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 : n013.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 11:11:16 AM UTC 2026
% Result : Unsatisfiable 6.73s 3.21s
% Output : CNFRefutation 6.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 63 ( 27 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 34 ( 19 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 75 ( 75 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ ordered > implies > big_hat > big_V > #nlpp > not > y > x > truth
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(truth,type,
truth: $i ).
tff(big_V,type,
big_V: ( $i * $i ) > $i ).
tff(ordered,type,
ordered: ( $i * $i ) > $o ).
tff(x,type,
x: $i ).
tff(y,type,
y: $i ).
tff(not,type,
not: $i > $i ).
tff(big_hat,type,
big_hat: ( $i * $i ) > $i ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff(f_48,axiom,
! [X] : ( implies(truth,X) = X ),
file(unknown,unknown) ).
tff(f_80,axiom,
! [X,Y] : ( big_V(X,Y) = implies(implies(X,Y),Y) ),
file(unknown,unknown) ).
tff(f_50,axiom,
! [X,Y,Z] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
file(unknown,unknown) ).
tff(f_52,axiom,
! [X,Y] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
file(unknown,unknown) ).
tff(f_93,axiom,
! [X,Y] :
( ( implies(X,Y) != truth )
| ordered(X,Y) ),
file(unknown,unknown) ).
tff(f_116,axiom,
! [Y,X,Z] :
( ~ ordered(Y,implies(X,Z))
| ordered(X,implies(Y,Z)) ),
file(unknown,unknown) ).
tff(f_101,axiom,
! [X,Y,Z] :
( ~ ordered(X,Y)
| ordered(implies(X,Z),implies(Y,Z)) ),
file(unknown,unknown) ).
tff(f_88,axiom,
! [X,Y] :
( ~ ordered(X,Y)
| ( implies(X,Y) = truth ) ),
file(unknown,unknown) ).
tff(f_126,axiom,
big_V(implies(x,y),implies(y,x)) != truth,
file(unknown,unknown) ).
tff(c_2,plain,
! [X_1] : ( implies(truth,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_10,plain,
! [X_9,Y_10] : ( implies(implies(X_9,Y_10),Y_10) = big_V(X_9,Y_10) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_885,plain,
! [X_80,Y_81,Z_82] : ( implies(implies(X_80,Y_81),implies(implies(Y_81,Z_82),implies(X_80,Z_82))) = truth ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_1007,plain,
! [X_1,Z_82] : ( implies(X_1,implies(implies(X_1,Z_82),implies(truth,Z_82))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_885]) ).
tff(c_1027,plain,
! [X_83,Z_84] : ( implies(X_83,big_V(X_83,Z_84)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_2,c_1007]) ).
tff(c_1065,plain,
! [Z_84] : ( big_V(truth,Z_84) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_1027,c_2]) ).
tff(c_94,plain,
! [X_48,Y_49] : ( implies(implies(X_48,Y_49),Y_49) = big_V(X_48,Y_49) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_109,plain,
! [X_1] : ( implies(X_1,X_1) = big_V(truth,X_1) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_94]) ).
tff(c_1100,plain,
! [X_1] : ( implies(X_1,X_1) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_1065,c_109]) ).
tff(c_6,plain,
! [Y_6,X_5] : ( implies(implies(Y_6,X_5),X_5) = implies(implies(X_5,Y_6),Y_6) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_36,plain,
! [Y_6,X_5] : ( big_V(Y_6,X_5) = big_V(X_5,Y_6) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_10,c_6]) ).
tff(c_1102,plain,
! [Z_85] : ( big_V(truth,Z_85) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_1027,c_2]) ).
tff(c_1127,plain,
! [X_5] : ( big_V(X_5,truth) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_36,c_1102]) ).
tff(c_16,plain,
! [X_15,Y_16] :
( ordered(X_15,Y_16)
| ( implies(X_15,Y_16) != truth ) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_244,plain,
! [X_57,Y_58,Z_59] :
( ordered(X_57,implies(Y_58,Z_59))
| ~ ordered(Y_58,implies(X_57,Z_59)) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_259,plain,
! [Y_60,X_61] :
( ordered(truth,implies(Y_60,X_61))
| ~ ordered(Y_60,X_61) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_244]) ).
tff(c_273,plain,
! [X_1] :
( ordered(truth,big_V(truth,X_1))
| ~ ordered(X_1,X_1) ),
inference(superposition,[status(thm),theory(equality)],[c_109,c_259]) ).
tff(c_1097,plain,
! [X_1] :
( ordered(truth,truth)
| ~ ordered(X_1,X_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_1065,c_273]) ).
tff(c_1658,plain,
! [X_97] : ~ ordered(X_97,X_97),
inference(splitLeft,[status(thm)],[c_1097]) ).
tff(c_1670,plain,
! [Y_16] : ( implies(Y_16,Y_16) != truth ),
inference(resolution,[status(thm)],[c_16,c_1658]) ).
tff(c_1676,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1100,c_1670]) ).
tff(c_1677,plain,
ordered(truth,truth),
inference(splitRight,[status(thm)],[c_1097]) ).
tff(c_770,plain,
! [X_77,Z_78,Y_79] :
( ordered(implies(X_77,Z_78),implies(Y_79,Z_78))
| ~ ordered(X_77,Y_79) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_1678,plain,
! [X_98,X_99] :
( ordered(implies(X_98,X_99),X_99)
| ~ ordered(X_98,truth) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_770]) ).
tff(c_1708,plain,
! [X_1] :
( ordered(X_1,X_1)
| ~ ordered(truth,truth) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1678]) ).
tff(c_1826,plain,
! [X_102] : ordered(X_102,X_102),
inference(demodulation,[status(thm),theory(equality)],[c_1677,c_1708]) ).
tff(c_24,plain,
! [X_27,Y_26,Z_28] :
( ordered(X_27,implies(Y_26,Z_28))
| ~ ordered(Y_26,implies(X_27,Z_28)) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_1829,plain,
! [X_27,Z_28] : ordered(X_27,implies(implies(X_27,Z_28),Z_28)),
inference(resolution,[status(thm)],[c_1826,c_24]) ).
tff(c_1837,plain,
! [X_103,Z_104] : ordered(X_103,big_V(X_103,Z_104)),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_1829]) ).
tff(c_1843,plain,
! [X_5] : ordered(X_5,truth),
inference(superposition,[status(thm),theory(equality)],[c_1127,c_1837]) ).
tff(c_820,plain,
! [X_77,X_1] :
( ordered(implies(X_77,X_1),X_1)
| ~ ordered(X_77,truth) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_770]) ).
tff(c_1907,plain,
! [X_108,X_109] : ordered(implies(X_108,X_109),X_109),
inference(demodulation,[status(thm),theory(equality)],[c_1843,c_820]) ).
tff(c_1947,plain,
! [X_110] : ordered(truth,X_110),
inference(superposition,[status(thm),theory(equality)],[c_1100,c_1907]) ).
tff(c_14,plain,
! [X_13,Y_14] :
( ( implies(X_13,Y_14) = truth )
| ~ ordered(X_13,Y_14) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_1974,plain,
! [X_113] : ( implies(truth,X_113) = truth ),
inference(resolution,[status(thm)],[c_1947,c_14]) ).
tff(c_2015,plain,
! [X_113] : ( implies(truth,X_113) = big_V(truth,X_113) ),
inference(superposition,[status(thm),theory(equality)],[c_1974,c_10]) ).
tff(c_2054,plain,
! [X_114] : ( truth = X_114 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1065,c_2015]) ).
tff(c_34,plain,
big_V(implies(x,y),implies(y,x)) != truth,
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_2147,plain,
$false,
inference(superposition,[status(thm),theory(equality)],[c_2054,c_34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL109-5 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.08/0.35 % Computer : n013.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 4 19:50:05 UTC 2026
% 0.08/0.35 % CPUTime :
% 6.73/3.21 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.73/3.22
% 6.73/3.22 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------