%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL144-1 : 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/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 : n001.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 11:11:20 AM UTC 2026
% Result : Unsatisfiable 23.24s 9.74s
% Output : CNFRefutation 23.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 53 unt; 0 typ; 0 def)
% Number of atoms : 69 ( 51 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 12 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 2 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 79 ( 79 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ ordered > implies > big_hat > big_V > #nlpp > not > z > 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(z,type,
z: $i ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff(f_92,axiom,
! [X,Y] :
( ( implies(X,Y) != truth )
| ordered(X,Y) ),
file(unknown,unknown) ).
tff(f_97,axiom,
( ordered(x,implies(y,z))
| ordered(y,implies(x,z)) ),
file(unknown,unknown) ).
tff(f_102,axiom,
( ~ ordered(x,implies(y,z))
| ~ ordered(y,implies(x,z)) ),
file(unknown,unknown) ).
tff(f_47,axiom,
! [X] : ( implies(truth,X) = X ),
file(unknown,unknown) ).
tff(f_79,axiom,
! [X,Y] : ( big_V(X,Y) = implies(implies(X,Y),Y) ),
file(unknown,unknown) ).
tff(f_51,axiom,
! [X,Y] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
file(unknown,unknown) ).
tff(f_49,axiom,
! [X,Y,Z] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
file(unknown,unknown) ).
tff(f_87,axiom,
! [X,Y] :
( ~ ordered(X,Y)
| ( implies(X,Y) = truth ) ),
file(unknown,unknown) ).
tff(f_53,axiom,
! [X,Y] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
file(unknown,unknown) ).
tff(c_16,plain,
! [X_15,Y_16] :
( ordered(X_15,Y_16)
| ( implies(X_15,Y_16) != truth ) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_18,plain,
( ordered(y,implies(x,z))
| ordered(x,implies(y,z)) ),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_244,plain,
ordered(x,implies(y,z)),
inference(splitLeft,[status(thm)],[c_18]) ).
tff(c_20,plain,
( ~ ordered(y,implies(x,z))
| ~ ordered(x,implies(y,z)) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_268,plain,
~ ordered(y,implies(x,z)),
inference(demodulation,[status(thm),theory(equality)],[c_244,c_20]) ).
tff(c_272,plain,
implies(y,implies(x,z)) != truth,
inference(resolution,[status(thm)],[c_16,c_268]) ).
tff(c_2,plain,
! [X_1] : ( implies(truth,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
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_79]) ).
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_51]) ).
tff(c_21,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_295,plain,
! [X_32,Y_33,Z_34] : ( implies(implies(X_32,Y_33),implies(implies(Y_33,Z_34),implies(X_32,Z_34))) = truth ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_400,plain,
! [X_1,Z_34] : ( implies(X_1,implies(implies(X_1,Z_34),implies(truth,Z_34))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_295]) ).
tff(c_424,plain,
! [X_35,Z_36] : ( implies(X_35,big_V(X_35,Z_36)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_2,c_400]) ).
tff(c_481,plain,
! [Z_37] : ( big_V(truth,Z_37) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_424,c_2]) ).
tff(c_591,plain,
! [X_40] : ( big_V(X_40,truth) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_21,c_481]) ).
tff(c_422,plain,
! [X_1,Z_34] : ( implies(X_1,big_V(X_1,Z_34)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_2,c_400]) ).
tff(c_599,plain,
! [X_40] : ( implies(X_40,truth) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_591,c_422]) ).
tff(c_502,plain,
! [X_5] : ( big_V(X_5,truth) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_21,c_481]) ).
tff(c_14,plain,
! [X_13,Y_14] :
( ( implies(X_13,Y_14) = truth )
| ~ ordered(X_13,Y_14) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_248,plain,
implies(x,implies(y,z)) = truth,
inference(resolution,[status(thm)],[c_244,c_14]) ).
tff(c_5270,plain,
! [X_114,X_115,Y_116] : ( implies(implies(X_114,implies(X_115,Y_116)),implies(big_V(X_115,Y_116),implies(X_114,Y_116))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_295]) ).
tff(c_5546,plain,
implies(truth,implies(big_V(y,z),implies(x,z))) = truth,
inference(superposition,[status(thm),theory(equality)],[c_248,c_5270]) ).
tff(c_142,plain,
! [X_29,Y_30] : ( implies(implies(not(X_29),not(Y_30)),implies(Y_30,X_29)) = truth ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_150,plain,
! [X_29,Y_30] : ( big_V(implies(not(X_29),not(Y_30)),implies(Y_30,X_29)) = implies(truth,implies(Y_30,X_29)) ),
inference(superposition,[status(thm),theory(equality)],[c_142,c_10]) ).
tff(c_176,plain,
! [X_29,Y_30] : ( big_V(implies(not(X_29),not(Y_30)),implies(Y_30,X_29)) = implies(Y_30,X_29) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_150]) ).
tff(c_25272,plain,
big_V(implies(not(implies(big_V(y,z),implies(x,z))),not(truth)),truth) = implies(truth,implies(big_V(y,z),implies(x,z))),
inference(superposition,[status(thm),theory(equality)],[c_5546,c_176]) ).
tff(c_25332,plain,
implies(big_V(y,z),implies(x,z)) = truth,
inference(demodulation,[status(thm),theory(equality)],[c_502,c_2,c_25272]) ).
tff(c_4,plain,
! [X_2,Y_3,Z_4] : ( implies(implies(X_2,Y_3),implies(implies(Y_3,Z_4),implies(X_2,Z_4))) = truth ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_16909,plain,
! [X_197,Z_198,Z_199] : ( implies(truth,implies(implies(big_V(X_197,Z_198),Z_199),implies(X_197,Z_199))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_424,c_4]) ).
tff(c_17329,plain,
! [X_197,Z_198,Z_199] : ( implies(implies(big_V(X_197,Z_198),Z_199),implies(X_197,Z_199)) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_16909]) ).
tff(c_25365,plain,
implies(truth,implies(y,implies(x,z))) = truth,
inference(superposition,[status(thm),theory(equality)],[c_25332,c_17329]) ).
tff(c_391,plain,
! [X_9,Y_10,Z_34] : ( implies(big_V(X_9,Y_10),implies(implies(Y_10,Z_34),implies(implies(X_9,Y_10),Z_34))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_295]) ).
tff(c_25572,plain,
! [X_9] : ( implies(big_V(X_9,truth),implies(truth,implies(implies(X_9,truth),implies(y,implies(x,z))))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_25365,c_391]) ).
tff(c_25650,plain,
implies(y,implies(x,z)) = truth,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_599,c_2,c_502,c_2,c_25572]) ).
tff(c_25652,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_272,c_25650]) ).
tff(c_25654,plain,
~ ordered(x,implies(y,z)),
inference(splitRight,[status(thm)],[c_18]) ).
tff(c_25662,plain,
implies(x,implies(y,z)) != truth,
inference(resolution,[status(thm)],[c_16,c_25654]) ).
tff(c_25687,plain,
! [X_238,Y_239,Z_240] : ( implies(implies(X_238,Y_239),implies(implies(Y_239,Z_240),implies(X_238,Z_240))) = truth ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_25792,plain,
! [X_1,Z_240] : ( implies(X_1,implies(implies(X_1,Z_240),implies(truth,Z_240))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_25687]) ).
tff(c_25816,plain,
! [X_241,Z_242] : ( implies(X_241,big_V(X_241,Z_242)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_2,c_25792]) ).
tff(c_25837,plain,
! [Z_242] : ( big_V(truth,Z_242) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_25816,c_2]) ).
tff(c_25653,plain,
ordered(y,implies(x,z)),
inference(splitRight,[status(thm)],[c_18]) ).
tff(c_25658,plain,
implies(y,implies(x,z)) = truth,
inference(resolution,[status(thm)],[c_25653,c_14]) ).
tff(c_25708,plain,
! [X_238,Y_239,Z_240] : ( big_V(implies(X_238,Y_239),implies(implies(Y_239,Z_240),implies(X_238,Z_240))) = implies(truth,implies(implies(Y_239,Z_240),implies(X_238,Z_240))) ),
inference(superposition,[status(thm),theory(equality)],[c_25687,c_10]) ).
tff(c_45205,plain,
! [X_430,Y_431,Z_432] : ( big_V(implies(X_430,Y_431),implies(implies(Y_431,Z_432),implies(X_430,Z_432))) = implies(implies(Y_431,Z_432),implies(X_430,Z_432)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_25708]) ).
tff(c_45701,plain,
! [Z_432] : ( big_V(truth,implies(implies(implies(x,z),Z_432),implies(y,Z_432))) = implies(implies(implies(x,z),Z_432),implies(y,Z_432)) ),
inference(superposition,[status(thm),theory(equality)],[c_25658,c_45205]) ).
tff(c_48113,plain,
! [Z_445] : ( implies(implies(implies(x,z),Z_445),implies(y,Z_445)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_25837,c_45701]) ).
tff(c_48415,plain,
implies(big_V(x,z),implies(y,z)) = truth,
inference(superposition,[status(thm),theory(equality)],[c_10,c_48113]) ).
tff(c_48842,plain,
! [X_446,Z_447,Z_448] : ( implies(truth,implies(implies(big_V(X_446,Z_447),Z_448),implies(X_446,Z_448))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_25816,c_4]) ).
tff(c_48996,plain,
implies(truth,implies(truth,implies(x,implies(y,z)))) = truth,
inference(superposition,[status(thm),theory(equality)],[c_48415,c_48842]) ).
tff(c_49356,plain,
implies(x,implies(y,z)) = truth,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_48996]) ).
tff(c_49358,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_25662,c_49356]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL144-1 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.10/0.36 % Computer : n001.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 03:35:30 UTC 2026
% 0.10/0.36 % CPUTime :
% 23.24/9.74 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.24/9.76
% 23.24/9.76 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------