%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP127-3.004 : TPTP v9.0.0. Released v1.2.0.
% 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 06:25:11 PM UTC 2025
% Result : Unsatisfiable 11.58s 4.13s
% Output : CNFRefutation 11.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 28
% Syntax : Number of formulae : 149 ( 86 unt; 0 typ; 0 def)
% Number of atoms : 319 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 284 ( 114 ~; 170 |; 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 : 0 ( 0 >; 0 *; 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 : 84 ( 84 !; 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_137,axiom,
~ equalish(e_2,e_3),
file(unknown,unknown) ).
tff(f_131,axiom,
~ equalish(e_1,e_3),
file(unknown,unknown) ).
tff(f_147,axiom,
~ equalish(e_4,e_1),
file(unknown,unknown) ).
tff(f_133,axiom,
~ equalish(e_1,e_4),
file(unknown,unknown) ).
tff(f_149,axiom,
~ equalish(e_4,e_2),
file(unknown,unknown) ).
tff(f_124,axiom,
group_element(e_1),
file(unknown,unknown) ).
tff(f_127,axiom,
group_element(e_4),
file(unknown,unknown) ).
tff(f_165,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_191,axiom,
! [X] : product(X,X,X),
file(unknown,unknown) ).
tff(f_181,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_151,axiom,
~ equalish(e_4,e_3),
file(unknown,unknown) ).
tff(f_125,axiom,
group_element(e_2),
file(unknown,unknown) ).
tff(f_135,axiom,
~ equalish(e_2,e_1),
file(unknown,unknown) ).
tff(f_129,axiom,
~ equalish(e_1,e_2),
file(unknown,unknown) ).
tff(f_36,axiom,
greater(e_1,e_0),
file(unknown,unknown) ).
tff(f_34,axiom,
next(e_2,e_3),
file(unknown,unknown) ).
tff(f_123,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_37,axiom,
greater(e_2,e_0),
file(unknown,unknown) ).
tff(f_64,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_38,axiom,
greater(e_3,e_0),
file(unknown,unknown) ).
tff(f_44,axiom,
greater(e_4,e_2),
file(unknown,unknown) ).
tff(f_43,axiom,
greater(e_3,e_2),
file(unknown,unknown) ).
tff(f_109,axiom,
! [X,Y] :
( ~ cycle(X,e_0)
| ~ product(X,e_1,Y)
| ~ greater(Y,X) ),
file(unknown,unknown) ).
tff(f_189,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_199,axiom,
! [Y,X,Z1,Z2] :
( ~ product(Y,X,Z1)
| ~ product(Z1,Y,Z2)
| product(Z2,Y,X) ),
file(unknown,unknown) ).
tff(f_139,axiom,
~ equalish(e_2,e_4),
file(unknown,unknown) ).
tff(f_145,axiom,
~ equalish(e_3,e_4),
file(unknown,unknown) ).
tff(f_126,axiom,
group_element(e_3),
file(unknown,unknown) ).
tff(c_60,plain,
~ equalish(e_2,e_3),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_54,plain,
~ equalish(e_1,e_3),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_70,plain,
~ equalish(e_4,e_1),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_56,plain,
~ equalish(e_1,e_4),
inference(cnfTransformation,[status(thm)],[f_133]) ).
tff(c_72,plain,
~ equalish(e_4,e_2),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_44,plain,
group_element(e_1),
inference(cnfTransformation,[status(thm)],[f_124]) ).
tff(c_50,plain,
group_element(e_4),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_5224,plain,
! [X_431,Y_432] :
( product(X_431,Y_432,e_4)
| product(X_431,Y_432,e_3)
| product(X_431,Y_432,e_2)
| product(X_431,Y_432,e_1)
| ~ group_element(Y_432)
| ~ group_element(X_431) ),
inference(cnfTransformation,[status(thm)],[f_165]) ).
tff(c_84,plain,
! [X_35] : product(X_35,X_35,X_35),
inference(cnfTransformation,[status(thm)],[f_191]) ).
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_181]) ).
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_5243,plain,
! [Y_432] :
( equalish(Y_432,e_4)
| product(e_4,Y_432,e_3)
| product(e_4,Y_432,e_2)
| product(e_4,Y_432,e_1)
| ~ group_element(Y_432)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_5224,c_241]) ).
tff(c_12886,plain,
! [Y_838] :
( equalish(Y_838,e_4)
| product(e_4,Y_838,e_3)
| product(e_4,Y_838,e_2)
| product(e_4,Y_838,e_1)
| ~ group_element(Y_838) ),
inference(demodulation,[status(thm),theory(equality)],[c_50,c_5243]) ).
tff(c_74,plain,
~ equalish(e_4,e_3),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_46,plain,
group_element(e_2),
inference(cnfTransformation,[status(thm)],[f_125]) ).
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_165]) ).
tff(c_58,plain,
~ equalish(e_2,e_1),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_52,plain,
~ equalish(e_1,e_2),
inference(cnfTransformation,[status(thm)],[f_129]) ).
tff(c_10,plain,
greater(e_1,e_0),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_6,plain,
next(e_2,e_3),
inference(cnfTransformation,[status(thm)],[f_34]) ).
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_123]) ).
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_5279,plain,
! [Y_433] :
( ~ greater(Y_433,e_0)
| ~ cycle(e_2,Y_433) ),
inference(splitLeft,[status(thm)],[c_293]) ).
tff(c_5295,plain,
~ cycle(e_2,e_1),
inference(resolution,[status(thm)],[c_10,c_5279]) ).
tff(c_12,plain,
greater(e_2,e_0),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_5294,plain,
~ cycle(e_2,e_2),
inference(resolution,[status(thm)],[c_12,c_5279]) ).
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_64]) ).
tff(c_14,plain,
greater(e_3,e_0),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_5292,plain,
~ cycle(e_2,e_3),
inference(resolution,[status(thm)],[c_14,c_5279]) ).
tff(c_5318,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_5292]) ).
tff(c_5321,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_5318]) ).
tff(c_6884,plain,
cycle(e_2,e_0),
inference(negUnitSimplification,[status(thm)],[c_5295,c_5294,c_5321]) ).
tff(c_26,plain,
greater(e_4,e_2),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_24,plain,
greater(e_3,e_2),
inference(cnfTransformation,[status(thm)],[f_43]) ).
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_109]) ).
tff(c_5255,plain,
! [X_431] :
( ~ greater(e_4,X_431)
| ~ cycle(X_431,e_0)
| product(X_431,e_1,e_3)
| product(X_431,e_1,e_2)
| product(X_431,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X_431) ),
inference(resolution,[status(thm)],[c_5224,c_40]) ).
tff(c_7606,plain,
! [X_593] :
( ~ greater(e_4,X_593)
| ~ cycle(X_593,e_0)
| product(X_593,e_1,e_3)
| product(X_593,e_1,e_2)
| product(X_593,e_1,e_1)
| ~ group_element(X_593) ),
inference(demodulation,[status(thm),theory(equality)],[c_44,c_5255]) ).
tff(c_9582,plain,
! [X_640] :
( ~ greater(e_3,X_640)
| ~ greater(e_4,X_640)
| ~ cycle(X_640,e_0)
| product(X_640,e_1,e_2)
| product(X_640,e_1,e_1)
| ~ group_element(X_640) ),
inference(resolution,[status(thm)],[c_7606,c_40]) ).
tff(c_9617,plain,
( equalish(e_1,e_2)
| ~ greater(e_3,e_2)
| ~ greater(e_4,e_2)
| ~ cycle(e_2,e_0)
| product(e_2,e_1,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_9582,c_241]) ).
tff(c_9658,plain,
( equalish(e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_46,c_6884,c_26,c_24,c_9617]) ).
tff(c_9659,plain,
product(e_2,e_1,e_1),
inference(negUnitSimplification,[status(thm)],[c_52,c_9658]) ).
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_189]) ).
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_9673,plain,
equalish(e_2,e_1),
inference(resolution,[status(thm)],[c_9659,c_102]) ).
tff(c_9694,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_58,c_9673]) ).
tff(c_9696,plain,
! [Z_641] :
( equalish(Z_641,e_3)
| ~ product(e_2,e_1,Z_641) ),
inference(splitRight,[status(thm)],[c_293]) ).
tff(c_9700,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_9696]) ).
tff(c_9703,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_9700]) ).
tff(c_9704,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_9703]) ).
tff(c_9705,plain,
product(e_2,e_1,e_1),
inference(splitLeft,[status(thm)],[c_9704]) ).
tff(c_9695,plain,
! [Z_112] :
( equalish(Z_112,e_3)
| ~ product(e_2,e_1,Z_112) ),
inference(splitRight,[status(thm)],[c_293]) ).
tff(c_9749,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_9705,c_9695]) ).
tff(c_9767,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_54,c_9749]) ).
tff(c_9768,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(splitRight,[status(thm)],[c_9704]) ).
tff(c_9770,plain,
product(e_2,e_1,e_3),
inference(splitLeft,[status(thm)],[c_9768]) ).
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_189]) ).
tff(c_9790,plain,
! [W_31] :
( equalish(W_31,e_2)
| ~ product(W_31,e_1,e_3) ),
inference(resolution,[status(thm)],[c_9770,c_82]) ).
tff(c_12898,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_12886,c_9790]) ).
tff(c_12930,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_12898]) ).
tff(c_12931,plain,
( product(e_4,e_1,e_2)
| product(e_4,e_1,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_56,c_72,c_12930]) ).
tff(c_13349,plain,
product(e_4,e_1,e_1),
inference(splitLeft,[status(thm)],[c_12931]) ).
tff(c_13360,plain,
equalish(e_4,e_1),
inference(resolution,[status(thm)],[c_13349,c_102]) ).
tff(c_13379,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_70,c_13360]) ).
tff(c_13380,plain,
product(e_4,e_1,e_2),
inference(splitRight,[status(thm)],[c_12931]) ).
tff(c_5247,plain,
! [X_431] :
( equalish(X_431,e_4)
| product(X_431,e_4,e_3)
| product(X_431,e_4,e_2)
| product(X_431,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(X_431) ),
inference(resolution,[status(thm)],[c_5224,c_102]) ).
tff(c_11892,plain,
! [X_812] :
( equalish(X_812,e_4)
| product(X_812,e_4,e_3)
| product(X_812,e_4,e_2)
| product(X_812,e_4,e_1)
| ~ group_element(X_812) ),
inference(demodulation,[status(thm),theory(equality)],[c_50,c_5247]) ).
tff(c_86,plain,
! [Z2_39,Y_36,X_37,Z1_38] :
( product(Z2_39,Y_36,X_37)
| ~ product(Z1_38,Y_36,Z2_39)
| ~ product(Y_36,X_37,Z1_38) ),
inference(cnfTransformation,[status(thm)],[f_199]) ).
tff(c_9826,plain,
! [X_650] :
( product(e_3,e_1,X_650)
| ~ product(e_1,X_650,e_2) ),
inference(resolution,[status(thm)],[c_9770,c_86]) ).
tff(c_9861,plain,
! [X_650,X_37] :
( product(X_650,e_1,X_37)
| ~ product(e_1,X_37,e_3)
| ~ product(e_1,X_650,e_2) ),
inference(resolution,[status(thm)],[c_9826,c_86]) ).
tff(c_11895,plain,
! [X_650] :
( product(X_650,e_1,e_4)
| ~ product(e_1,X_650,e_2)
| 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_11892,c_9861]) ).
tff(c_11925,plain,
! [X_650] :
( product(X_650,e_1,e_4)
| ~ product(e_1,X_650,e_2)
| 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_11895]) ).
tff(c_11926,plain,
! [X_650] :
( product(X_650,e_1,e_4)
| ~ product(e_1,X_650,e_2)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_56,c_11925]) ).
tff(c_12492,plain,
product(e_1,e_4,e_1),
inference(splitLeft,[status(thm)],[c_11926]) ).
tff(c_62,plain,
~ equalish(e_2,e_4),
inference(cnfTransformation,[status(thm)],[f_139]) ).
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_181]) ).
tff(c_9789,plain,
! [W_28] :
( equalish(W_28,e_1)
| ~ product(e_2,W_28,e_3) ),
inference(resolution,[status(thm)],[c_9770,c_80]) ).
tff(c_11903,plain,
( equalish(e_4,e_1)
| 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_11892,c_9789]) ).
tff(c_11933,plain,
( equalish(e_4,e_1)
| 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_11903]) ).
tff(c_11934,plain,
( product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_62,c_70,c_11933]) ).
tff(c_12341,plain,
product(e_2,e_4,e_1),
inference(splitLeft,[status(thm)],[c_11934]) ).
tff(c_12353,plain,
! [W_31] :
( equalish(W_31,e_2)
| ~ product(W_31,e_4,e_1) ),
inference(resolution,[status(thm)],[c_12341,c_82]) ).
tff(c_12495,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[c_12492,c_12353]) ).
tff(c_12514,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_12495]) ).
tff(c_12516,plain,
~ product(e_1,e_4,e_1),
inference(splitRight,[status(thm)],[c_11926]) ).
tff(c_13062,plain,
product(e_4,e_1,e_1),
inference(splitLeft,[status(thm)],[c_12931]) ).
tff(c_68,plain,
~ equalish(e_3,e_4),
inference(cnfTransformation,[status(thm)],[f_145]) ).
tff(c_48,plain,
group_element(e_3),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_12910,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_12886,c_102]) ).
tff(c_12940,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_12910]) ).
tff(c_12941,plain,
( product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_68,c_74,c_12940]) ).
tff(c_12948,plain,
product(e_4,e_3,e_1),
inference(splitLeft,[status(thm)],[c_12941]) ).
tff(c_12981,plain,
! [W_28] :
( equalish(W_28,e_3)
| ~ product(e_4,W_28,e_1) ),
inference(resolution,[status(thm)],[c_12948,c_80]) ).
tff(c_13065,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_13062,c_12981]) ).
tff(c_13087,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_54,c_13065]) ).
tff(c_13088,plain,
product(e_4,e_1,e_2),
inference(splitRight,[status(thm)],[c_12931]) ).
tff(c_12350,plain,
! [X_37] :
( product(e_1,e_4,X_37)
| ~ product(e_4,X_37,e_2) ),
inference(resolution,[status(thm)],[c_12341,c_86]) ).
tff(c_13092,plain,
product(e_1,e_4,e_1),
inference(resolution,[status(thm)],[c_13088,c_12350]) ).
tff(c_13111,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12516,c_13092]) ).
tff(c_13112,plain,
product(e_4,e_3,e_2),
inference(splitRight,[status(thm)],[c_12941]) ).
tff(c_13150,plain,
! [W_28] :
( equalish(W_28,e_3)
| ~ product(e_4,W_28,e_2) ),
inference(resolution,[status(thm)],[c_13112,c_80]) ).
tff(c_13397,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_13380,c_13150]) ).
tff(c_13419,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_54,c_13397]) ).
tff(c_13420,plain,
product(e_2,e_4,e_2),
inference(splitRight,[status(thm)],[c_11934]) ).
tff(c_12137,plain,
product(e_2,e_4,e_1),
inference(splitLeft,[status(thm)],[c_11934]) ).
tff(c_11918,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_11892,c_241]) ).
tff(c_11947,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_11918]) ).
tff(c_11948,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_68,c_74,c_11947]) ).
tff(c_11951,plain,
product(e_3,e_4,e_1),
inference(splitLeft,[status(thm)],[c_11948]) ).
tff(c_12058,plain,
! [W_31] :
( equalish(W_31,e_3)
| ~ product(W_31,e_4,e_1) ),
inference(resolution,[status(thm)],[c_11951,c_82]) ).
tff(c_12140,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_12137,c_12058]) ).
tff(c_12152,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_60,c_12140]) ).
tff(c_12153,plain,
product(e_2,e_4,e_2),
inference(splitRight,[status(thm)],[c_11934]) ).
tff(c_12163,plain,
equalish(e_4,e_2),
inference(resolution,[status(thm)],[c_12153,c_241]) ).
tff(c_12174,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_72,c_12163]) ).
tff(c_12175,plain,
product(e_3,e_4,e_2),
inference(splitRight,[status(thm)],[c_11948]) ).
tff(c_12284,plain,
! [W_31] :
( equalish(W_31,e_3)
| ~ product(W_31,e_4,e_2) ),
inference(resolution,[status(thm)],[c_12175,c_82]) ).
tff(c_13424,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_13420,c_12284]) ).
tff(c_13441,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_60,c_13424]) ).
tff(c_13442,plain,
product(e_2,e_1,e_2),
inference(splitRight,[status(thm)],[c_9768]) ).
tff(c_13446,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_13442,c_9695]) ).
tff(c_13466,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_60,c_13446]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP127-3.004 : TPTP v9.0.0. Released v1.2.0.
% 0.12/0.13 % 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
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 7 21:23:05 EDT 2025
% 0.13/0.35 % CPUTime :
% 11.58/4.13 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.58/4.15
% 11.58/4.15 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------