%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : HEN010-7 : TPTP v9.0.0. 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 : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Apr 9 06:45:57 PM UTC 2025
% Result : Unsatisfiable 19.76s 8.07s
% Output : CNFRefutation 20.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 53 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 106 ( 8 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 113 ( 60 ~; 53 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 82 ( 82 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ quotient > less_equal > divide > #nlpp > zero > identity > idQa_Q__idQ_idQa > idQa > idQ_idQa > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(less_equal,type,
less_equal: ( $i * $i ) > $o ).
tff(a,type,
a: $i ).
tff(divide,type,
divide: ( $i * $i ) > $i ).
tff(idQa,type,
idQa: $i ).
tff(idQa_Q__idQ_idQa,type,
idQa_Q__idQ_idQa: $i ).
tff(quotient,type,
quotient: ( $i * $i * $i ) > $o ).
tff(identity,type,
identity: $i ).
tff(idQ_idQa,type,
idQ_idQa: $i ).
tff(zero,type,
zero: $i ).
tff(f_158,axiom,
quotient(identity,idQa,idQ_idQa),
file(unknown,unknown) ).
tff(f_115,axiom,
! [X] : quotient(X,zero,X),
file(unknown,unknown) ).
tff(f_59,axiom,
! [X,Y,Z] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) ),
file(unknown,unknown) ).
tff(f_95,axiom,
! [X,Y] : quotient(X,Y,divide(X,Y)),
file(unknown,unknown) ).
tff(f_134,axiom,
! [W1,Z,X,Y,W2] :
( ~ quotient(X,Y,W1)
| ~ less_equal(W1,Z)
| ~ quotient(X,Z,W2)
| less_equal(W2,Y) ),
file(unknown,unknown) ).
tff(f_157,axiom,
quotient(identity,a,idQa),
file(unknown,unknown) ).
tff(f_123,axiom,
! [X,Y,Z] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,Z)
| less_equal(X,Z) ),
file(unknown,unknown) ).
tff(f_89,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,X)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_113,axiom,
! [X] : quotient(X,X,zero),
file(unknown,unknown) ).
tff(f_161,axiom,
idQa != idQa_Q__idQ_idQa,
file(unknown,unknown) ).
tff(f_159,axiom,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
file(unknown,unknown) ).
tff(f_77,axiom,
! [V3,V5,Z,V1,X,Y,V2,V4] :
( ~ quotient(X,Y,V1)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Z,V3)
| ~ quotient(V3,V2,V4)
| ~ quotient(V1,Z,V5)
| less_equal(V4,V5) ),
file(unknown,unknown) ).
tff(c_38,plain,
quotient(identity,idQa,idQ_idQa),
inference(cnfTransformation,[status(thm)],[f_158]) ).
tff(c_26,plain,
! [X_29] : quotient(X_29,zero,X_29),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_51,plain,
! [Z_58,X_59,Y_60] :
( less_equal(Z_58,X_59)
| ~ quotient(X_59,Y_60,Z_58) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_90,plain,
! [X_29] : less_equal(X_29,X_29),
inference(resolution,[status(thm)],[c_26,c_51]) ).
tff(c_16,plain,
! [X_20,Y_21] : quotient(X_20,Y_21,divide(X_20,Y_21)),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_559,plain,
! [W2_104,Z_107,Y_106,W1_103,X_105] :
( less_equal(W2_104,Y_106)
| ~ quotient(X_105,Z_107,W2_104)
| ~ less_equal(W1_103,Z_107)
| ~ quotient(X_105,Y_106,W1_103) ),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_12986,plain,
! [X_356,Y_357,Y_358,W1_359] :
( less_equal(divide(X_356,Y_357),Y_358)
| ~ less_equal(W1_359,Y_357)
| ~ quotient(X_356,Y_358,W1_359) ),
inference(resolution,[status(thm)],[c_16,c_559]) ).
tff(c_13098,plain,
! [X_356,X_29,Y_358] :
( less_equal(divide(X_356,X_29),Y_358)
| ~ quotient(X_356,Y_358,X_29) ),
inference(resolution,[status(thm)],[c_90,c_12986]) ).
tff(c_20125,plain,
! [X_514,X_515,Y_516] :
( less_equal(divide(X_514,X_515),Y_516)
| ~ quotient(X_514,Y_516,X_515) ),
inference(resolution,[status(thm)],[c_90,c_12986]) ).
tff(c_36,plain,
quotient(identity,a,idQa),
inference(cnfTransformation,[status(thm)],[f_157]) ).
tff(c_3639,plain,
! [Y_202,W1_203] :
( less_equal(idQ_idQa,Y_202)
| ~ less_equal(W1_203,idQa)
| ~ quotient(identity,Y_202,W1_203) ),
inference(resolution,[status(thm)],[c_38,c_559]) ).
tff(c_3665,plain,
( less_equal(idQ_idQa,a)
| ~ less_equal(idQa,idQa) ),
inference(resolution,[status(thm)],[c_36,c_3639]) ).
tff(c_3681,plain,
less_equal(idQ_idQa,a),
inference(demodulation,[status(thm),theory(equality)],[c_90,c_3665]) ).
tff(c_28,plain,
! [X_30,Z_32,Y_31] :
( less_equal(X_30,Z_32)
| ~ less_equal(Y_31,Z_32)
| ~ less_equal(X_30,Y_31) ),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_3690,plain,
! [X_30] :
( less_equal(X_30,a)
| ~ less_equal(X_30,idQ_idQa) ),
inference(resolution,[status(thm)],[c_3681,c_28]) ).
tff(c_36945,plain,
! [X_735,X_736] :
( less_equal(divide(X_735,X_736),a)
| ~ quotient(X_735,idQ_idQa,X_736) ),
inference(resolution,[status(thm)],[c_20125,c_3690]) ).
tff(c_2050,plain,
! [Y_164,W1_165] :
( less_equal(idQa,Y_164)
| ~ less_equal(W1_165,a)
| ~ quotient(identity,Y_164,W1_165) ),
inference(resolution,[status(thm)],[c_36,c_559]) ).
tff(c_2080,plain,
! [Y_21] :
( less_equal(idQa,Y_21)
| ~ less_equal(divide(identity,Y_21),a) ),
inference(resolution,[status(thm)],[c_16,c_2050]) ).
tff(c_37140,plain,
! [X_737] :
( less_equal(idQa,X_737)
| ~ quotient(identity,idQ_idQa,X_737) ),
inference(resolution,[status(thm)],[c_36945,c_2080]) ).
tff(c_37157,plain,
less_equal(idQa,divide(identity,idQ_idQa)),
inference(resolution,[status(thm)],[c_16,c_37140]) ).
tff(c_12,plain,
! [Y_18,X_17] :
( ( Y_18 = X_17 )
| ~ less_equal(Y_18,X_17)
| ~ less_equal(X_17,Y_18) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_37214,plain,
( ( divide(identity,idQ_idQa) = idQa )
| ~ less_equal(divide(identity,idQ_idQa),idQa) ),
inference(resolution,[status(thm)],[c_37157,c_12]) ).
tff(c_62243,plain,
~ less_equal(divide(identity,idQ_idQa),idQa),
inference(splitLeft,[status(thm)],[c_37214]) ).
tff(c_62267,plain,
~ quotient(identity,idQa,idQ_idQa),
inference(resolution,[status(thm)],[c_13098,c_62243]) ).
tff(c_62290,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_38,c_62267]) ).
tff(c_62291,plain,
divide(identity,idQ_idQa) = idQa,
inference(splitRight,[status(thm)],[c_37214]) ).
tff(c_62657,plain,
quotient(identity,idQ_idQa,idQa),
inference(superposition,[status(thm),theory(equality)],[c_62291,c_16]) ).
tff(c_24,plain,
! [X_28] : quotient(X_28,X_28,zero),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_42,plain,
idQa_Q__idQ_idQa != idQa,
inference(cnfTransformation,[status(thm)],[f_161]) ).
tff(c_40,plain,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_93,plain,
less_equal(idQa_Q__idQ_idQa,idQa),
inference(resolution,[status(thm)],[c_40,c_51]) ).
tff(c_122,plain,
! [Y_66,X_67] :
( ( Y_66 = X_67 )
| ~ less_equal(Y_66,X_67)
| ~ less_equal(X_67,Y_66) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_126,plain,
( ( idQa_Q__idQ_idQa = idQa )
| ~ less_equal(idQa,idQa_Q__idQ_idQa) ),
inference(resolution,[status(thm)],[c_93,c_122]) ).
tff(c_136,plain,
~ less_equal(idQa,idQa_Q__idQ_idQa),
inference(negUnitSimplification,[status(thm)],[c_42,c_126]) ).
tff(c_666,plain,
! [V3_111,X_114,V4_112,V2_110,Y_116,V1_115,Z_113,V5_117] :
( less_equal(V4_112,V5_117)
| ~ quotient(V1_115,Z_113,V5_117)
| ~ quotient(V3_111,V2_110,V4_112)
| ~ quotient(X_114,Z_113,V3_111)
| ~ quotient(Y_116,Z_113,V2_110)
| ~ quotient(X_114,Y_116,V1_115) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_18293,plain,
! [V2_478,V4_481,V3_480,Y_479,X_477] :
( less_equal(V4_481,idQa_Q__idQ_idQa)
| ~ quotient(V3_480,V2_478,V4_481)
| ~ quotient(X_477,idQ_idQa,V3_480)
| ~ quotient(Y_479,idQ_idQa,V2_478)
| ~ quotient(X_477,Y_479,idQa) ),
inference(resolution,[status(thm)],[c_40,c_666]) ).
tff(c_18410,plain,
! [X_29,X_477,Y_479] :
( less_equal(X_29,idQa_Q__idQ_idQa)
| ~ quotient(X_477,idQ_idQa,X_29)
| ~ quotient(Y_479,idQ_idQa,zero)
| ~ quotient(X_477,Y_479,idQa) ),
inference(resolution,[status(thm)],[c_26,c_18293]) ).
tff(c_62765,plain,
! [Y_479] :
( less_equal(idQa,idQa_Q__idQ_idQa)
| ~ quotient(Y_479,idQ_idQa,zero)
| ~ quotient(identity,Y_479,idQa) ),
inference(resolution,[status(thm)],[c_62657,c_18410]) ).
tff(c_65591,plain,
! [Y_993] :
( ~ quotient(Y_993,idQ_idQa,zero)
| ~ quotient(identity,Y_993,idQa) ),
inference(negUnitSimplification,[status(thm)],[c_136,c_62765]) ).
tff(c_65645,plain,
~ quotient(identity,idQ_idQa,idQa),
inference(resolution,[status(thm)],[c_24,c_65591]) ).
tff(c_65669,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_62657,c_65645]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN010-7 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.13 % 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
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 7 22:52:36 EDT 2025
% 0.12/0.34 % CPUTime :
% 19.76/8.07 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.76/8.08
% 19.76/8.08 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------