TSTP Solution File: GRP126-3.004 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP126-3.004 : TPTP v8.1.2. Released v1.2.0.
% 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 : n015.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 : Tue Aug 22 10:39:59 EDT 2023
% Result : Unsatisfiable 10.66s 3.68s
% Output : CNFRefutation 11.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 42
% Syntax : Number of formulae : 211 ( 118 unt; 11 typ; 0 def)
% Number of atoms : 390 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 310 ( 120 ~; 190 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 6 >; 6 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 95 (; 95 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > next > greater > equalish > cycle > group_element > #nlpp > e_4 > e_3 > e_2 > e_1 > e_0
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(group_element,type,
group_element: $i > $o ).
tff(greater,type,
greater: ( $i * $i ) > $o ).
tff(cycle,type,
cycle: ( $i * $i ) > $o ).
tff(e_2,type,
e_2: $i ).
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(next,type,
next: ( $i * $i ) > $o ).
tff(e_0,type,
e_0: $i ).
tff(e_4,type,
e_4: $i ).
tff(e_3,type,
e_3: $i ).
tff(equalish,type,
equalish: ( $i * $i ) > $o ).
tff(e_1,type,
e_1: $i ).
tff(f_135,axiom,
~ equalish(e_2,e_3),
file(unknown,unknown) ).
tff(f_127,axiom,
~ equalish(e_1,e_2),
file(unknown,unknown) ).
tff(f_129,axiom,
~ equalish(e_1,e_3),
file(unknown,unknown) ).
tff(f_145,axiom,
~ equalish(e_4,e_1),
file(unknown,unknown) ).
tff(f_131,axiom,
~ equalish(e_1,e_4),
file(unknown,unknown) ).
tff(f_147,axiom,
~ equalish(e_4,e_2),
file(unknown,unknown) ).
tff(f_122,axiom,
group_element(e_1),
file(unknown,unknown) ).
tff(f_125,axiom,
group_element(e_4),
file(unknown,unknown) ).
tff(f_163,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(X,Y,e_1)
| product(X,Y,e_2)
| product(X,Y,e_3)
| product(X,Y,e_4) ),
file(unknown,unknown) ).
tff(f_189,axiom,
! [X] : product(X,X,X),
file(unknown,unknown) ).
tff(f_179,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_149,axiom,
~ equalish(e_4,e_3),
file(unknown,unknown) ).
tff(f_123,axiom,
group_element(e_2),
file(unknown,unknown) ).
tff(f_141,axiom,
~ equalish(e_3,e_2),
file(unknown,unknown) ).
tff(f_34,axiom,
greater(e_1,e_0),
file(unknown,unknown) ).
tff(f_32,axiom,
next(e_2,e_3),
file(unknown,unknown) ).
tff(f_121,axiom,
! [X,Y,Z,X1] :
( ~ cycle(X,Y)
| ~ product(X,e_1,Z)
| ~ greater(Y,e_0)
| ~ next(X,X1)
| equalish(Z,X1) ),
file(unknown,unknown) ).
tff(f_35,axiom,
greater(e_2,e_0),
file(unknown,unknown) ).
tff(f_62,axiom,
! [X] :
( ~ group_element(X)
| cycle(X,e_0)
| cycle(X,e_1)
| cycle(X,e_2)
| cycle(X,e_3) ),
file(unknown,unknown) ).
tff(f_36,axiom,
greater(e_3,e_0),
file(unknown,unknown) ).
tff(f_42,axiom,
greater(e_4,e_2),
file(unknown,unknown) ).
tff(f_41,axiom,
greater(e_3,e_2),
file(unknown,unknown) ).
tff(f_137,axiom,
~ equalish(e_2,e_4),
file(unknown,unknown) ).
tff(f_139,axiom,
~ equalish(e_3,e_1),
file(unknown,unknown) ).
tff(f_124,axiom,
group_element(e_3),
file(unknown,unknown) ).
tff(f_143,axiom,
~ equalish(e_3,e_4),
file(unknown,unknown) ).
tff(f_187,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_197,axiom,
! [X,Y,Z1,Z2] :
( ~ product(X,Y,Z1)
| ~ product(Y,X,Z2)
| product(Z1,Z2,Y) ),
file(unknown,unknown) ).
tff(f_171,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_107,axiom,
! [X,Y] :
( ~ cycle(X,e_0)
| ~ product(X,e_1,Y)
| ~ greater(Y,X) ),
file(unknown,unknown) ).
tff(f_133,axiom,
~ equalish(e_2,e_1),
file(unknown,unknown) ).
tff(c_60,plain,
~ equalish(e_2,e_3),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_52,plain,
~ equalish(e_1,e_2),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_54,plain,
~ equalish(e_1,e_3),
inference(cnfTransformation,[status(thm)],[f_129]) ).
tff(c_70,plain,
~ equalish(e_4,e_1),
inference(cnfTransformation,[status(thm)],[f_145]) ).
tff(c_56,plain,
~ equalish(e_1,e_4),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_72,plain,
~ equalish(e_4,e_2),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_44,plain,
group_element(e_1),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_50,plain,
group_element(e_4),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_4215,plain,
! [X_283,Y_284] :
( product(X_283,Y_284,e_4)
| product(X_283,Y_284,e_3)
| product(X_283,Y_284,e_2)
| product(X_283,Y_284,e_1)
| ~ group_element(Y_284)
| ~ group_element(X_283) ),
inference(cnfTransformation,[status(thm)],[f_163]) ).
tff(c_84,plain,
! [X_35] : product(X_35,X_35,X_35),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_238,plain,
! [W_89,Z_90,X_91,Y_92] :
( equalish(W_89,Z_90)
| ~ product(X_91,Z_90,Y_92)
| ~ product(X_91,W_89,Y_92) ),
inference(cnfTransformation,[status(thm)],[f_179]) ).
tff(c_241,plain,
! [W_89,X_35] :
( equalish(W_89,X_35)
| ~ product(X_35,W_89,X_35) ),
inference(resolution,[status(thm)],[c_84,c_238]) ).
tff(c_4234,plain,
! [Y_284] :
( equalish(Y_284,e_4)
| product(e_4,Y_284,e_3)
| product(e_4,Y_284,e_2)
| product(e_4,Y_284,e_1)
| ~ group_element(Y_284)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_4215,c_241]) ).
tff(c_11911,plain,
! [Y_774] :
( equalish(Y_774,e_4)
| product(e_4,Y_774,e_3)
| product(e_4,Y_774,e_2)
| product(e_4,Y_774,e_1)
| ~ group_element(Y_774) ),
inference(demodulation,[status(thm),theory(equality)],[c_50,c_4234]) ).
tff(c_74,plain,
~ equalish(e_4,e_3),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_46,plain,
group_element(e_2),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_76,plain,
! [X_21,Y_22] :
( product(X_21,Y_22,e_4)
| product(X_21,Y_22,e_3)
| product(X_21,Y_22,e_2)
| product(X_21,Y_22,e_1)
| ~ group_element(Y_22)
| ~ group_element(X_21) ),
inference(cnfTransformation,[status(thm)],[f_163]) ).
tff(c_66,plain,
~ equalish(e_3,e_2),
inference(cnfTransformation,[status(thm)],[f_141]) ).
tff(c_10,plain,
greater(e_1,e_0),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_6,plain,
next(e_2,e_3),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_281,plain,
! [Z_112,X1_113,X_114,Y_115] :
( equalish(Z_112,X1_113)
| ~ next(X_114,X1_113)
| ~ greater(Y_115,e_0)
| ~ product(X_114,e_1,Z_112)
| ~ cycle(X_114,Y_115) ),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_293,plain,
! [Z_112,Y_115] :
( equalish(Z_112,e_3)
| ~ greater(Y_115,e_0)
| ~ product(e_2,e_1,Z_112)
| ~ cycle(e_2,Y_115) ),
inference(resolution,[status(thm)],[c_6,c_281]) ).
tff(c_4268,plain,
! [Y_285] :
( ~ greater(Y_285,e_0)
| ~ cycle(e_2,Y_285) ),
inference(splitLeft,[status(thm)],[c_293]) ).
tff(c_4284,plain,
~ cycle(e_2,e_1),
inference(resolution,[status(thm)],[c_10,c_4268]) ).
tff(c_12,plain,
greater(e_2,e_0),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_4283,plain,
~ cycle(e_2,e_2),
inference(resolution,[status(thm)],[c_12,c_4268]) ).
tff(c_32,plain,
! [X_4] :
( cycle(X_4,e_3)
| cycle(X_4,e_2)
| cycle(X_4,e_1)
| cycle(X_4,e_0)
| ~ group_element(X_4) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_14,plain,
greater(e_3,e_0),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_4281,plain,
~ cycle(e_2,e_3),
inference(resolution,[status(thm)],[c_14,c_4268]) ).
tff(c_4287,plain,
( cycle(e_2,e_2)
| cycle(e_2,e_1)
| cycle(e_2,e_0)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_32,c_4281]) ).
tff(c_4290,plain,
( cycle(e_2,e_2)
| cycle(e_2,e_1)
| cycle(e_2,e_0) ),
inference(demodulation,[status(thm),theory(equality)],[c_46,c_4287]) ).
tff(c_6385,plain,
cycle(e_2,e_0),
inference(negUnitSimplification,[status(thm)],[c_4284,c_4283,c_4290]) ).
tff(c_26,plain,
greater(e_4,e_2),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_24,plain,
greater(e_3,e_2),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_62,plain,
~ equalish(e_2,e_4),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_64,plain,
~ equalish(e_3,e_1),
inference(cnfTransformation,[status(thm)],[f_139]) ).
tff(c_48,plain,
group_element(e_3),
inference(cnfTransformation,[status(thm)],[f_124]) ).
tff(c_68,plain,
~ equalish(e_3,e_4),
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_99,plain,
! [W_47,Z_48,Y_49,X_50] :
( equalish(W_47,Z_48)
| ~ product(Z_48,Y_49,X_50)
| ~ product(W_47,Y_49,X_50) ),
inference(cnfTransformation,[status(thm)],[f_187]) ).
tff(c_102,plain,
! [W_47,X_35] :
( equalish(W_47,X_35)
| ~ product(W_47,X_35,X_35) ),
inference(resolution,[status(thm)],[c_84,c_99]) ).
tff(c_4238,plain,
! [X_283] :
( equalish(X_283,e_4)
| product(X_283,e_4,e_3)
| product(X_283,e_4,e_2)
| product(X_283,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(X_283) ),
inference(resolution,[status(thm)],[c_4215,c_102]) ).
tff(c_7144,plain,
! [X_498] :
( equalish(X_498,e_4)
| product(X_498,e_4,e_3)
| product(X_498,e_4,e_2)
| product(X_498,e_4,e_1)
| ~ group_element(X_498) ),
inference(demodulation,[status(thm),theory(equality)],[c_50,c_4238]) ).
tff(c_7159,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_7144,c_241]) ).
tff(c_7175,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_7159]) ).
tff(c_7176,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_68,c_74,c_7175]) ).
tff(c_7226,plain,
product(e_3,e_4,e_1),
inference(splitLeft,[status(thm)],[c_7176]) ).
tff(c_86,plain,
! [Z1_38,Z2_39,Y_37,X_36] :
( product(Z1_38,Z2_39,Y_37)
| ~ product(Y_37,X_36,Z2_39)
| ~ product(X_36,Y_37,Z1_38) ),
inference(cnfTransformation,[status(thm)],[f_197]) ).
tff(c_7273,plain,
! [Z1_503] :
( product(Z1_503,e_1,e_3)
| ~ product(e_4,e_3,Z1_503) ),
inference(resolution,[status(thm)],[c_7226,c_86]) ).
tff(c_7276,plain,
( product(e_4,e_1,e_3)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_76,c_7273]) ).
tff(c_7279,plain,
( product(e_4,e_1,e_3)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_50,c_48,c_7276]) ).
tff(c_7291,plain,
product(e_4,e_3,e_1),
inference(splitLeft,[status(thm)],[c_7279]) ).
tff(c_7235,plain,
! [Z1_38] :
( product(Z1_38,e_1,e_3)
| ~ product(e_4,e_3,Z1_38) ),
inference(resolution,[status(thm)],[c_7226,c_86]) ).
tff(c_7302,plain,
product(e_1,e_1,e_3),
inference(resolution,[status(thm)],[c_7291,c_7235]) ).
tff(c_258,plain,
! [W_99,Z_100,X_101,Y_102] :
( equalish(W_99,Z_100)
| ~ product(X_101,Y_102,Z_100)
| ~ product(X_101,Y_102,W_99) ),
inference(cnfTransformation,[status(thm)],[f_171]) ).
tff(c_261,plain,
! [W_99,X_35] :
( equalish(W_99,X_35)
| ~ product(X_35,X_35,W_99) ),
inference(resolution,[status(thm)],[c_84,c_258]) ).
tff(c_7313,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_7302,c_261]) ).
tff(c_7328,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_64,c_7313]) ).
tff(c_7329,plain,
( product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| product(e_4,e_1,e_3) ),
inference(splitRight,[status(thm)],[c_7279]) ).
tff(c_7375,plain,
product(e_4,e_1,e_3),
inference(splitLeft,[status(thm)],[c_7329]) ).
tff(c_4259,plain,
! [X_283] :
( equalish(X_283,e_4)
| product(X_283,e_4,e_3)
| product(X_283,e_4,e_2)
| product(X_283,e_4,e_1)
| ~ group_element(X_283) ),
inference(demodulation,[status(thm),theory(equality)],[c_50,c_4238]) ).
tff(c_7472,plain,
! [Z1_514] :
( product(Z1_514,e_3,e_4)
| ~ product(e_1,e_4,Z1_514) ),
inference(resolution,[status(thm)],[c_7375,c_86]) ).
tff(c_7475,plain,
( product(e_3,e_3,e_4)
| equalish(e_1,e_4)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_4259,c_7472]) ).
tff(c_7481,plain,
( product(e_3,e_3,e_4)
| equalish(e_1,e_4)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_44,c_7475]) ).
tff(c_7482,plain,
( product(e_3,e_3,e_4)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_56,c_7481]) ).
tff(c_7486,plain,
product(e_1,e_4,e_1),
inference(splitLeft,[status(thm)],[c_7482]) ).
tff(c_82,plain,
! [W_31,Z_34,Y_32,X_33] :
( equalish(W_31,Z_34)
| ~ product(Z_34,Y_32,X_33)
| ~ product(W_31,Y_32,X_33) ),
inference(cnfTransformation,[status(thm)],[f_187]) ).
tff(c_7238,plain,
! [W_31] :
( equalish(W_31,e_3)
| ~ product(W_31,e_4,e_1) ),
inference(resolution,[status(thm)],[c_7226,c_82]) ).
tff(c_7491,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_7486,c_7238]) ).
tff(c_7507,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_54,c_7491]) ).
tff(c_7508,plain,
( product(e_1,e_4,e_2)
| product(e_3,e_3,e_4) ),
inference(splitRight,[status(thm)],[c_7482]) ).
tff(c_7510,plain,
product(e_3,e_3,e_4),
inference(splitLeft,[status(thm)],[c_7508]) ).
tff(c_7521,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_7510,c_261]) ).
tff(c_7539,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_74,c_7521]) ).
tff(c_7540,plain,
product(e_1,e_4,e_2),
inference(splitRight,[status(thm)],[c_7508]) ).
tff(c_7705,plain,
! [Z1_524] :
( product(Z1_524,e_2,e_1)
| ~ product(e_4,e_1,Z1_524) ),
inference(resolution,[status(thm)],[c_7540,c_86]) ).
tff(c_7714,plain,
product(e_3,e_2,e_1),
inference(resolution,[status(thm)],[c_7375,c_7705]) ).
tff(c_80,plain,
! [W_28,Z_30,X_27,Y_29] :
( equalish(W_28,Z_30)
| ~ product(X_27,Z_30,Y_29)
| ~ product(X_27,W_28,Y_29) ),
inference(cnfTransformation,[status(thm)],[f_179]) ).
tff(c_7237,plain,
! [W_28] :
( equalish(W_28,e_4)
| ~ product(e_3,W_28,e_1) ),
inference(resolution,[status(thm)],[c_7226,c_80]) ).
tff(c_7769,plain,
equalish(e_2,e_4),
inference(resolution,[status(thm)],[c_7714,c_7237]) ).
tff(c_7788,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_62,c_7769]) ).
tff(c_7789,plain,
( product(e_4,e_3,e_3)
| product(e_4,e_3,e_2) ),
inference(splitRight,[status(thm)],[c_7329]) ).
tff(c_7797,plain,
product(e_4,e_3,e_2),
inference(splitLeft,[status(thm)],[c_7789]) ).
tff(c_7889,plain,
product(e_2,e_1,e_3),
inference(resolution,[status(thm)],[c_7797,c_7235]) ).
tff(c_40,plain,
! [Y_16,X_15] :
( ~ greater(Y_16,X_15)
| ~ product(X_15,e_1,Y_16)
| ~ cycle(X_15,e_0) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_7904,plain,
( ~ greater(e_3,e_2)
| ~ cycle(e_2,e_0) ),
inference(resolution,[status(thm)],[c_7889,c_40]) ).
tff(c_7912,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6385,c_24,c_7904]) ).
tff(c_7913,plain,
product(e_4,e_3,e_3),
inference(splitRight,[status(thm)],[c_7789]) ).
tff(c_7923,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_7913,c_102]) ).
tff(c_7934,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_74,c_7923]) ).
tff(c_7935,plain,
product(e_3,e_4,e_2),
inference(splitRight,[status(thm)],[c_7176]) ).
tff(c_7993,plain,
! [Z1_535] :
( product(Z1_535,e_2,e_3)
| ~ product(e_4,e_3,Z1_535) ),
inference(resolution,[status(thm)],[c_7935,c_86]) ).
tff(c_7996,plain,
( product(e_4,e_2,e_3)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_76,c_7993]) ).
tff(c_7999,plain,
( product(e_4,e_2,e_3)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_50,c_48,c_7996]) ).
tff(c_8001,plain,
product(e_4,e_3,e_1),
inference(splitLeft,[status(thm)],[c_7999]) ).
tff(c_8135,plain,
! [Z1_545] :
( product(Z1_545,e_1,e_4)
| ~ product(e_3,e_4,Z1_545) ),
inference(resolution,[status(thm)],[c_8001,c_86]) ).
tff(c_8144,plain,
product(e_2,e_1,e_4),
inference(resolution,[status(thm)],[c_7935,c_8135]) ).
tff(c_8167,plain,
( ~ greater(e_4,e_2)
| ~ cycle(e_2,e_0) ),
inference(resolution,[status(thm)],[c_8144,c_40]) ).
tff(c_8181,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6385,c_26,c_8167]) ).
tff(c_8182,plain,
( product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| product(e_4,e_2,e_3) ),
inference(splitRight,[status(thm)],[c_7999]) ).
tff(c_8210,plain,
product(e_4,e_2,e_3),
inference(splitLeft,[status(thm)],[c_8182]) ).
tff(c_8271,plain,
! [Z1_552] :
( product(Z1_552,e_3,e_4)
| ~ product(e_2,e_4,Z1_552) ),
inference(resolution,[status(thm)],[c_8210,c_86]) ).
tff(c_8274,plain,
( product(e_3,e_3,e_4)
| equalish(e_2,e_4)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_4259,c_8271]) ).
tff(c_8280,plain,
( product(e_3,e_3,e_4)
| equalish(e_2,e_4)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_46,c_8274]) ).
tff(c_8281,plain,
( product(e_3,e_3,e_4)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_62,c_8280]) ).
tff(c_8296,plain,
product(e_2,e_4,e_1),
inference(splitLeft,[status(thm)],[c_8281]) ).
tff(c_8457,plain,
! [Z1_565] :
( product(Z1_565,e_1,e_2)
| ~ product(e_4,e_2,Z1_565) ),
inference(resolution,[status(thm)],[c_8296,c_86]) ).
tff(c_8463,plain,
product(e_3,e_1,e_2),
inference(resolution,[status(thm)],[c_8210,c_8457]) ).
tff(c_7947,plain,
! [W_28] :
( equalish(W_28,e_4)
| ~ product(e_3,W_28,e_2) ),
inference(resolution,[status(thm)],[c_7935,c_80]) ).
tff(c_8473,plain,
equalish(e_1,e_4),
inference(resolution,[status(thm)],[c_8463,c_7947]) ).
tff(c_8498,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_56,c_8473]) ).
tff(c_8499,plain,
( product(e_2,e_4,e_2)
| product(e_3,e_3,e_4) ),
inference(splitRight,[status(thm)],[c_8281]) ).
tff(c_8565,plain,
product(e_3,e_3,e_4),
inference(splitLeft,[status(thm)],[c_8499]) ).
tff(c_8578,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_8565,c_261]) ).
tff(c_8599,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_74,c_8578]) ).
tff(c_8600,plain,
product(e_2,e_4,e_2),
inference(splitRight,[status(thm)],[c_8499]) ).
tff(c_7948,plain,
! [W_31] :
( equalish(W_31,e_3)
| ~ product(W_31,e_4,e_2) ),
inference(resolution,[status(thm)],[c_7935,c_82]) ).
tff(c_8614,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_8600,c_7948]) ).
tff(c_8634,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_60,c_8614]) ).
tff(c_8635,plain,
( product(e_4,e_3,e_3)
| product(e_4,e_3,e_2) ),
inference(splitRight,[status(thm)],[c_8182]) ).
tff(c_8647,plain,
product(e_4,e_3,e_2),
inference(splitLeft,[status(thm)],[c_8635]) ).
tff(c_7945,plain,
! [Z1_38] :
( product(Z1_38,e_2,e_3)
| ~ product(e_4,e_3,Z1_38) ),
inference(resolution,[status(thm)],[c_7935,c_86]) ).
tff(c_8664,plain,
product(e_2,e_2,e_3),
inference(resolution,[status(thm)],[c_8647,c_7945]) ).
tff(c_8677,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_8664,c_261]) ).
tff(c_8693,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_66,c_8677]) ).
tff(c_8694,plain,
product(e_4,e_3,e_3),
inference(splitRight,[status(thm)],[c_8635]) ).
tff(c_8754,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_8694,c_102]) ).
tff(c_8769,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_74,c_8754]) ).
tff(c_8771,plain,
! [Z_571] :
( equalish(Z_571,e_3)
| ~ product(e_2,e_1,Z_571) ),
inference(splitRight,[status(thm)],[c_293]) ).
tff(c_8775,plain,
( equalish(e_4,e_3)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_76,c_8771]) ).
tff(c_8778,plain,
( equalish(e_4,e_3)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_46,c_44,c_8775]) ).
tff(c_8779,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_74,c_8778]) ).
tff(c_8780,plain,
product(e_2,e_1,e_1),
inference(splitLeft,[status(thm)],[c_8779]) ).
tff(c_8770,plain,
! [Z_112] :
( equalish(Z_112,e_3)
| ~ product(e_2,e_1,Z_112) ),
inference(splitRight,[status(thm)],[c_293]) ).
tff(c_8783,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_8780,c_8770]) ).
tff(c_8801,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_54,c_8783]) ).
tff(c_8802,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(splitRight,[status(thm)],[c_8779]) ).
tff(c_8824,plain,
product(e_2,e_1,e_3),
inference(splitLeft,[status(thm)],[c_8802]) ).
tff(c_8844,plain,
! [W_31] :
( equalish(W_31,e_2)
| ~ product(W_31,e_1,e_3) ),
inference(resolution,[status(thm)],[c_8824,c_82]) ).
tff(c_11924,plain,
( equalish(e_4,e_2)
| equalish(e_1,e_4)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_11911,c_8844]) ).
tff(c_11962,plain,
( equalish(e_4,e_2)
| equalish(e_1,e_4)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_44,c_11924]) ).
tff(c_11963,plain,
( product(e_4,e_1,e_2)
| product(e_4,e_1,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_56,c_72,c_11962]) ).
tff(c_11983,plain,
product(e_4,e_1,e_1),
inference(splitLeft,[status(thm)],[c_11963]) ).
tff(c_11992,plain,
equalish(e_4,e_1),
inference(resolution,[status(thm)],[c_11983,c_102]) ).
tff(c_12009,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_70,c_11992]) ).
tff(c_12010,plain,
product(e_4,e_1,e_2),
inference(splitRight,[status(thm)],[c_11963]) ).
tff(c_58,plain,
~ equalish(e_2,e_1),
inference(cnfTransformation,[status(thm)],[f_133]) ).
tff(c_8860,plain,
! [Z1_577] :
( product(Z1_577,e_3,e_2)
| ~ product(e_1,e_2,Z1_577) ),
inference(resolution,[status(thm)],[c_8824,c_86]) ).
tff(c_8863,plain,
( product(e_4,e_3,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_76,c_8860]) ).
tff(c_8866,plain,
( product(e_4,e_3,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_44,c_46,c_8863]) ).
tff(c_10855,plain,
product(e_1,e_2,e_1),
inference(splitLeft,[status(thm)],[c_8866]) ).
tff(c_10864,plain,
equalish(e_2,e_1),
inference(resolution,[status(thm)],[c_10855,c_241]) ).
tff(c_10875,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_58,c_10864]) ).
tff(c_10876,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_4,e_3,e_2) ),
inference(splitRight,[status(thm)],[c_8866]) ).
tff(c_10907,plain,
product(e_4,e_3,e_2),
inference(splitLeft,[status(thm)],[c_10876]) ).
tff(c_10918,plain,
! [W_28] :
( equalish(W_28,e_3)
| ~ product(e_4,W_28,e_2) ),
inference(resolution,[status(thm)],[c_10907,c_80]) ).
tff(c_12023,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_12010,c_10918]) ).
tff(c_12042,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_54,c_12023]) ).
tff(c_12043,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2) ),
inference(splitRight,[status(thm)],[c_10876]) ).
tff(c_12045,plain,
product(e_1,e_2,e_2),
inference(splitLeft,[status(thm)],[c_12043]) ).
tff(c_12121,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[c_12045,c_102]) ).
tff(c_12132,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_12121]) ).
tff(c_12133,plain,
product(e_1,e_2,e_3),
inference(splitRight,[status(thm)],[c_12043]) ).
tff(c_8841,plain,
! [Z1_38] :
( product(Z1_38,e_3,e_2)
| ~ product(e_1,e_2,Z1_38) ),
inference(resolution,[status(thm)],[c_8824,c_86]) ).
tff(c_12145,plain,
product(e_3,e_3,e_2),
inference(resolution,[status(thm)],[c_12133,c_8841]) ).
tff(c_12170,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_12145,c_261]) ).
tff(c_12182,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_60,c_12170]) ).
tff(c_12183,plain,
product(e_2,e_1,e_2),
inference(splitRight,[status(thm)],[c_8802]) ).
tff(c_12187,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_12183,c_8770]) ).
tff(c_12205,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_60,c_12187]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : GRP126-3.004 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.15 % 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
% 0.15/0.37 % Computer : n015.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.22/0.37 % WCLimit : 300
% 0.22/0.37 % DateTime : Thu Aug 3 22:17:59 EDT 2023
% 0.22/0.37 % CPUTime :
% 10.66/3.68 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.66/3.70
% 10.66/3.70 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.00/3.76
% 11.00/3.76 Inference rules
% 11.00/3.76 ----------------------
% 11.00/3.76 #Ref : 0
% 11.00/3.76 #Sup : 2487
% 11.00/3.76 #Fact : 0
% 11.00/3.76 #Define : 0
% 11.00/3.76 #Split : 70
% 11.00/3.76 #Chain : 0
% 11.00/3.76 #Close : 0
% 11.00/3.76
% 11.00/3.76 Ordering : KBO
% 11.00/3.76
% 11.00/3.76 Simplification rules
% 11.00/3.76 ----------------------
% 11.00/3.76 #Subsume : 987
% 11.00/3.76 #Demod : 1850
% 11.00/3.76 #Tautology : 493
% 11.00/3.76 #SimpNegUnit : 503
% 11.00/3.76 #BackRed : 0
% 11.00/3.76
% 11.00/3.76 #Partial instantiations: 0
% 11.00/3.76 #Strategies tried : 1
% 11.00/3.76
% 11.00/3.76 Timing (in seconds)
% 11.00/3.76 ----------------------
% 11.00/3.76 Preprocessing : 0.53
% 11.00/3.76 Parsing : 0.30
% 11.00/3.76 CNF conversion : 0.03
% 11.00/3.76 Main loop : 1.96
% 11.00/3.76 Inferencing : 0.65
% 11.00/3.76 Reduction : 0.63
% 11.00/3.76 Demodulation : 0.41
% 11.00/3.76 BG Simplification : 0.05
% 11.00/3.76 Subsumption : 0.53
% 11.00/3.76 Abstraction : 0.05
% 11.00/3.76 MUC search : 0.00
% 11.00/3.76 Cooper : 0.00
% 11.00/3.76 Total : 2.58
% 11.00/3.76 Index Insertion : 0.00
% 11.00/3.76 Index Deletion : 0.00
% 11.00/3.76 Index Matching : 0.00
% 11.00/3.76 BG Taut test : 0.00
%------------------------------------------------------------------------------