TSTP Solution File: GRP126-4.004 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP126-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n009.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 : Thu Aug 31 00:16:28 EDT 2023
% Result : Unsatisfiable 0.10s 0.53s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 33
% Syntax : Number of formulae : 203 ( 52 unt; 7 typ; 0 def)
% Number of atoms : 472 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 482 ( 206 ~; 276 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 113 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
group_element: $i > $o ).
tff(decl_23,type,
e_1: $i ).
tff(decl_24,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_25,type,
e_2: $i ).
tff(decl_26,type,
e_3: $i ).
tff(decl_27,type,
e_4: $i ).
tff(decl_28,type,
equalish: ( $i * $i ) > $o ).
cnf(product_total_function1,axiom,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| product(X1,X2,e_3)
| product(X1,X2,e_4)
| ~ group_element(X1)
| ~ group_element(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
cnf(product_right_cancellation,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(product_idempotence,axiom,
product(X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
cnf(column_surjectivity,axiom,
( product(X1,e_1,X2)
| product(X1,e_2,X2)
| product(X1,e_3,X2)
| product(X1,e_4,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',column_surjectivity) ).
cnf(element_4,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
cnf(product_total_function2,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
cnf(product_left_cancellation,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
cnf(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
cnf(e_1_is_not_e_4,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
cnf(e_3_is_not_e_4,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
cnf(e_2_is_not_e_4,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
cnf(qg4_1,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X3,X4,X2)
| ~ product(X2,X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg4_1) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
cnf(qg4,negated_conjecture,
( product(X3,X4,X2)
| ~ product(X1,X2,X3)
| ~ product(X2,X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg4) ).
cnf(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
cnf(row_surjectivity,axiom,
( product(e_1,X1,X2)
| product(e_2,X1,X2)
| product(e_3,X1,X2)
| product(e_4,X1,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',row_surjectivity) ).
cnf(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
cnf(qg4_2,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X4,X3,X1)
| ~ product(X2,X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg4_2) ).
cnf(c_0_26,axiom,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| product(X1,X2,e_3)
| product(X1,X2,e_4)
| ~ group_element(X1)
| ~ group_element(X2) ),
product_total_function1 ).
cnf(c_0_27,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_28,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_right_cancellation ).
cnf(c_0_29,axiom,
product(X1,X1,X1),
product_idempotence ).
cnf(c_0_30,plain,
( product(X1,e_3,e_4)
| product(X1,e_3,e_3)
| product(X1,e_3,e_2)
| product(X1,e_3,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_32,plain,
( equalish(X1,X2)
| ~ product(X2,X1,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,axiom,
~ equalish(e_3,e_1),
e_3_is_not_e_1 ).
cnf(c_0_35,axiom,
( product(X1,e_1,X2)
| product(X1,e_2,X2)
| product(X1,e_3,X2)
| product(X1,e_4,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
column_surjectivity ).
cnf(c_0_36,axiom,
group_element(e_4),
element_4 ).
cnf(c_0_37,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_38,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
product_total_function2 ).
cnf(c_0_39,plain,
( product(X1,e_4,e_4)
| product(X1,e_3,e_4)
| product(X1,e_2,e_4)
| product(X1,e_1,e_4)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
product_left_cancellation ).
cnf(c_0_41,axiom,
~ equalish(e_2,e_3),
e_2_is_not_e_3 ).
cnf(c_0_42,plain,
( equalish(X1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| ~ product(e_1,X1,e_4) ),
inference(spm,[status(thm)],[c_0_28,c_0_37]) ).
cnf(c_0_43,plain,
( equalish(X1,X2)
| ~ product(X2,X2,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_29]) ).
cnf(c_0_44,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_3,e_4)
| product(e_1,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_39,c_0_31]) ).
cnf(c_0_45,axiom,
~ equalish(e_4,e_1),
e_4_is_not_e_1 ).
cnf(c_0_46,plain,
( equalish(X1,X2)
| ~ product(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_29]) ).
cnf(c_0_47,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| ~ product(e_1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,axiom,
~ equalish(e_1,e_3),
e_1_is_not_e_3 ).
cnf(c_0_49,plain,
( product(X1,e_4,e_4)
| product(X1,e_4,e_3)
| product(X1,e_4,e_2)
| product(X1,e_4,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_36]) ).
cnf(c_0_50,plain,
( product(e_1,e_4,e_4)
| product(e_1,e_3,e_4)
| product(e_1,e_2,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
cnf(c_0_51,axiom,
~ equalish(e_1,e_4),
e_1_is_not_e_4 ).
cnf(c_0_52,plain,
( product(e_1,e_3,e_2)
| ~ product(e_1,e_2,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_53,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_49,c_0_31]) ).
cnf(c_0_54,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_3,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_50]),c_0_51]) ).
cnf(c_0_55,axiom,
~ equalish(e_3,e_2),
e_3_is_not_e_2 ).
cnf(c_0_56,plain,
( equalish(X1,e_2)
| ~ product(e_1,e_2,e_4)
| ~ product(e_1,e_3,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_52]) ).
cnf(c_0_57,plain,
( product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_53]),c_0_45]) ).
cnf(c_0_58,plain,
( product(X1,e_4,e_3)
| product(X1,e_3,e_3)
| product(X1,e_2,e_3)
| product(X1,e_1,e_3)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_27]) ).
cnf(c_0_59,axiom,
~ equalish(e_3,e_4),
e_3_is_not_e_4 ).
cnf(c_0_60,plain,
( equalish(X1,e_4)
| product(e_1,e_2,e_4)
| ~ product(e_1,e_3,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_54]) ).
cnf(c_0_61,plain,
( ~ product(e_1,e_2,e_4)
| ~ product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_62,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_57]),c_0_51]) ).
cnf(c_0_63,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_3)
| product(e_1,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_58,c_0_31]) ).
cnf(c_0_64,plain,
~ product(e_1,e_3,e_3),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).
cnf(c_0_65,axiom,
~ equalish(e_2,e_4),
e_2_is_not_e_4 ).
cnf(c_0_66,plain,
( equalish(X1,e_4)
| product(e_1,e_4,e_2)
| ~ product(e_1,X1,e_3) ),
inference(spm,[status(thm)],[c_0_28,c_0_62]) ).
cnf(c_0_67,plain,
( product(X1,e_1,e_4)
| product(X1,e_1,e_3)
| product(X1,e_1,e_2)
| product(X1,e_1,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_31]) ).
cnf(c_0_68,plain,
( product(e_1,e_4,e_3)
| product(e_1,e_2,e_3)
| product(e_1,e_1,e_3) ),
inference(sr,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_69,plain,
( product(e_1,e_4,e_2)
| ~ product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_70,plain,
( product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_67,c_0_36]) ).
cnf(c_0_71,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_4,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_68]),c_0_34]) ).
cnf(c_0_72,axiom,
~ equalish(e_1,e_2),
e_1_is_not_e_2 ).
cnf(c_0_73,plain,
( equalish(X1,e_2)
| ~ product(e_1,e_2,e_3)
| ~ product(e_1,e_4,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_69]) ).
cnf(c_0_74,plain,
( equalish(X1,e_1)
| product(e_1,e_4,e_2)
| ~ product(X1,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_40,c_0_62]) ).
cnf(c_0_75,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X3,X4,X2)
| ~ product(X2,X1,X4) ),
qg4_1 ).
cnf(c_0_76,plain,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_70]),c_0_45]) ).
cnf(c_0_77,plain,
( equalish(X1,e_3)
| product(e_1,e_2,e_3)
| ~ product(e_1,e_4,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_71]) ).
cnf(c_0_78,plain,
( ~ product(e_1,e_2,e_3)
| ~ product(e_1,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_79,plain,
( product(e_1,e_4,e_2)
| ~ product(e_3,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_34,c_0_74]) ).
cnf(c_0_80,negated_conjecture,
( product(e_1,e_2,e_4)
| product(X1,e_4,e_1)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_75,c_0_54]) ).
cnf(c_0_81,plain,
( product(e_4,e_1,e_2)
| product(e_4,e_1,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_76]),c_0_51]) ).
cnf(c_0_82,plain,
~ product(e_1,e_4,e_1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_77]),c_0_78]) ).
cnf(c_0_83,axiom,
~ equalish(e_2,e_1),
e_2_is_not_e_1 ).
cnf(c_0_84,plain,
( equalish(X1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| ~ product(X1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_40,c_0_37]) ).
cnf(c_0_85,plain,
( equalish(X1,e_4)
| ~ product(e_3,e_4,e_3)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_28,c_0_79]) ).
cnf(c_0_86,negated_conjecture,
( product(e_4,e_1,e_2)
| product(e_1,e_2,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]) ).
cnf(c_0_87,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_88,plain,
( product(e_1,e_4,e_2)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_83,c_0_74]) ).
cnf(c_0_89,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| ~ product(e_3,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_34,c_0_84]) ).
cnf(c_0_90,plain,
( ~ product(e_3,e_4,e_3)
| ~ product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_59,c_0_85]) ).
cnf(c_0_91,negated_conjecture,
( equalish(X1,e_1)
| product(e_4,e_1,e_2)
| ~ product(X1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_40,c_0_86]) ).
cnf(c_0_92,plain,
( product(X1,e_2,e_4)
| product(X1,e_2,e_3)
| product(X1,e_2,e_2)
| product(X1,e_2,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_87]) ).
cnf(c_0_93,plain,
( equalish(X1,e_4)
| ~ product(e_2,e_4,e_3)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_28,c_0_88]) ).
cnf(c_0_94,plain,
( product(e_1,e_3,e_2)
| ~ product(e_3,e_3,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_89]),c_0_48]) ).
cnf(c_0_95,plain,
( ~ product(e_3,e_4,e_3)
| ~ product(e_1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_90,c_0_52]) ).
cnf(c_0_96,negated_conjecture,
( product(e_4,e_1,e_2)
| ~ product(e_2,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_83,c_0_91]) ).
cnf(c_0_97,negated_conjecture,
( product(X3,X4,X2)
| ~ product(X1,X2,X3)
| ~ product(X2,X1,X4) ),
qg4 ).
cnf(c_0_98,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_92,c_0_31]) ).
cnf(c_0_99,plain,
( ~ product(e_2,e_4,e_3)
| ~ product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_59,c_0_93]) ).
cnf(c_0_100,axiom,
~ equalish(e_4,e_2),
e_4_is_not_e_2 ).
cnf(c_0_101,plain,
( equalish(X1,e_2)
| ~ product(e_3,e_3,e_4)
| ~ product(e_1,e_3,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_94]) ).
cnf(c_0_102,axiom,
( product(e_1,X1,X2)
| product(e_2,X1,X2)
| product(e_3,X1,X2)
| product(e_4,X1,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
row_surjectivity ).
cnf(c_0_103,negated_conjecture,
( product(e_4,e_1,e_2)
| ~ product(e_3,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_95,c_0_86]) ).
cnf(c_0_104,negated_conjecture,
( equalish(X1,e_1)
| ~ product(e_2,e_2,e_4)
| ~ product(e_4,X1,e_2) ),
inference(spm,[status(thm)],[c_0_28,c_0_96]) ).
cnf(c_0_105,negated_conjecture,
( product(X1,X2,X2)
| ~ product(X2,X2,X1) ),
inference(spm,[status(thm)],[c_0_97,c_0_29]) ).
cnf(c_0_106,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_98]),c_0_83]) ).
cnf(c_0_107,plain,
( ~ product(e_3,e_4,e_3)
| ~ product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_65,c_0_85]) ).
cnf(c_0_108,plain,
( ~ product(e_2,e_4,e_3)
| ~ product(e_1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_99,c_0_52]) ).
cnf(c_0_109,plain,
( equalish(X1,e_1)
| product(e_4,e_1,e_2)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_28,c_0_81]) ).
cnf(c_0_110,plain,
( ~ product(e_3,e_3,e_4)
| ~ product(e_1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_111,plain,
( product(e_4,X1,e_3)
| product(e_3,X1,e_3)
| product(e_2,X1,e_3)
| product(e_1,X1,e_3)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_102,c_0_27]) ).
cnf(c_0_112,negated_conjecture,
( product(X1,e_2,e_4)
| ~ product(e_3,e_4,e_3)
| ~ product(e_1,e_4,X1) ),
inference(spm,[status(thm)],[c_0_97,c_0_103]) ).
cnf(c_0_113,negated_conjecture,
~ product(e_2,e_2,e_4),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_104]),c_0_105]) ).
cnf(c_0_114,plain,
( product(e_1,e_2,e_3)
| ~ product(e_3,e_4,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_106]),c_0_107]) ).
cnf(c_0_115,negated_conjecture,
( product(e_4,e_1,e_2)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_108,c_0_86]) ).
cnf(c_0_116,plain,
( ~ product(e_2,e_4,e_3)
| ~ product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_65,c_0_93]) ).
cnf(c_0_117,plain,
( product(e_4,e_1,e_2)
| ~ product(e_4,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_34,c_0_109]) ).
cnf(c_0_118,plain,
( product(e_1,e_2,e_4)
| ~ product(e_3,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_110,c_0_54]) ).
cnf(c_0_119,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| ~ product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_120,negated_conjecture,
( equalish(X1,e_2)
| product(e_4,e_1,e_2)
| ~ product(e_1,X1,e_4) ),
inference(spm,[status(thm)],[c_0_28,c_0_86]) ).
cnf(c_0_121,plain,
( product(e_1,e_4,e_3)
| product(e_2,e_4,e_3)
| product(e_3,e_4,e_3)
| product(e_4,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_111,c_0_36]) ).
cnf(c_0_122,negated_conjecture,
~ product(e_3,e_4,e_3),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_69]),c_0_113]),c_0_114]) ).
cnf(c_0_123,negated_conjecture,
( product(X1,e_2,e_4)
| ~ product(e_2,e_4,e_3)
| ~ product(e_1,e_4,X1) ),
inference(spm,[status(thm)],[c_0_97,c_0_115]) ).
cnf(c_0_124,plain,
( product(e_1,e_2,e_3)
| ~ product(e_2,e_4,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_106]),c_0_116]) ).
cnf(c_0_125,axiom,
~ equalish(e_4,e_3),
e_4_is_not_e_3 ).
cnf(c_0_126,plain,
( equalish(X1,e_3)
| ~ product(e_3,e_3,e_4)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_28,c_0_94]) ).
cnf(c_0_127,negated_conjecture,
( product(X1,e_2,e_4)
| ~ product(e_4,e_3,e_3)
| ~ product(e_1,e_4,X1) ),
inference(spm,[status(thm)],[c_0_97,c_0_117]) ).
cnf(c_0_128,plain,
( equalish(X1,e_1)
| ~ product(e_3,e_3,e_4)
| ~ product(X1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_40,c_0_118]) ).
cnf(c_0_129,plain,
( product(e_1,e_3,e_2)
| ~ product(e_2,e_3,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_119]),c_0_48]) ).
cnf(c_0_130,negated_conjecture,
( product(e_4,e_1,e_2)
| ~ product(e_1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_55,c_0_120]) ).
cnf(c_0_131,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_4) ),
inference(sr,[status(thm)],[c_0_37,c_0_64]) ).
cnf(c_0_132,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| ~ product(e_4,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_45,c_0_84]) ).
cnf(c_0_133,plain,
( product(e_4,e_4,e_3)
| product(e_2,e_4,e_3)
| product(e_1,e_4,e_3) ),
inference(sr,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_134,negated_conjecture,
~ product(e_2,e_4,e_3),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_69]),c_0_113]),c_0_124]) ).
cnf(c_0_135,plain,
( ~ product(e_3,e_3,e_4)
| ~ product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_136,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_3,e_2,e_4)
| ~ product(e_4,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_127,c_0_62]) ).
cnf(c_0_137,plain,
( ~ product(e_3,e_3,e_4)
| ~ product(e_3,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_34,c_0_128]) ).
cnf(c_0_138,plain,
( equalish(X1,e_2)
| ~ product(e_2,e_3,e_4)
| ~ product(e_1,e_3,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_129]) ).
cnf(c_0_139,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_4,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_140,plain,
( product(e_1,e_3,e_2)
| ~ product(e_4,e_3,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_132]),c_0_48]) ).
cnf(c_0_141,negated_conjecture,
( product(e_4,e_1,e_2)
| product(X1,e_3,e_4)
| ~ product(e_1,e_4,X1) ),
inference(spm,[status(thm)],[c_0_97,c_0_81]) ).
cnf(c_0_142,plain,
( product(e_1,e_4,e_3)
| product(e_4,e_4,e_3) ),
inference(sr,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_143,negated_conjecture,
~ product(e_3,e_3,e_4),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_105]),c_0_137]) ).
cnf(c_0_144,plain,
( product(e_4,e_1,e_2)
| ~ product(e_4,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_45,c_0_109]) ).
cnf(c_0_145,plain,
( equalish(X1,e_1)
| ~ product(e_1,e_2,e_4)
| ~ product(X1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_40,c_0_52]) ).
cnf(c_0_146,plain,
( ~ product(e_2,e_3,e_4)
| ~ product(e_1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_100,c_0_138]) ).
cnf(c_0_147,negated_conjecture,
( equalish(X1,e_3)
| product(e_4,e_1,e_2)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_28,c_0_139]) ).
cnf(c_0_148,negated_conjecture,
( product(e_1,e_4,e_2)
| product(X1,e_3,e_1)
| ~ product(e_4,e_1,X1) ),
inference(spm,[status(thm)],[c_0_97,c_0_62]) ).
cnf(c_0_149,plain,
( equalish(X1,e_2)
| ~ product(e_4,e_3,e_4)
| ~ product(e_1,e_3,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_140]) ).
cnf(c_0_150,negated_conjecture,
product(e_4,e_1,e_2),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_143]),c_0_144]) ).
cnf(c_0_151,plain,
( ~ product(e_1,e_2,e_4)
| ~ product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_34,c_0_145]) ).
cnf(c_0_152,plain,
( product(e_1,e_2,e_4)
| ~ product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_146,c_0_54]) ).
cnf(c_0_153,negated_conjecture,
( product(e_4,e_1,e_2)
| ~ product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_125,c_0_147]) ).
cnf(c_0_154,negated_conjecture,
( product(e_4,e_1,e_2)
| product(e_3,e_3,e_1)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_148,c_0_81]) ).
cnf(c_0_155,plain,
( ~ product(e_4,e_3,e_4)
| ~ product(e_1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_100,c_0_149]) ).
cnf(c_0_156,negated_conjecture,
( product(X1,e_2,e_4)
| ~ product(e_1,e_4,X1) ),
inference(spm,[status(thm)],[c_0_97,c_0_150]) ).
cnf(c_0_157,plain,
( ~ product(e_1,e_2,e_4)
| ~ product(e_4,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_45,c_0_145]) ).
cnf(c_0_158,negated_conjecture,
( product(e_4,e_1,e_2)
| ~ product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_151,c_0_86]) ).
cnf(c_0_159,plain,
( product(e_4,X1,e_4)
| product(e_3,X1,e_4)
| product(e_2,X1,e_4)
| product(e_1,X1,e_4)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_102,c_0_36]) ).
cnf(c_0_160,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X4,X3,X1)
| ~ product(X2,X1,X4) ),
qg4_2 ).
cnf(c_0_161,negated_conjecture,
( product(X1,e_4,e_1)
| ~ product(e_2,e_3,e_4)
| ~ product(e_4,X1,e_2) ),
inference(spm,[status(thm)],[c_0_75,c_0_152]) ).
cnf(c_0_162,negated_conjecture,
( product(e_3,e_3,e_1)
| product(e_4,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_153,c_0_154]) ).
cnf(c_0_163,plain,
( equalish(X1,e_3)
| ~ product(e_2,e_3,e_4)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_28,c_0_129]) ).
cnf(c_0_164,plain,
( product(e_1,e_2,e_4)
| ~ product(e_4,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_155,c_0_54]) ).
cnf(c_0_165,negated_conjecture,
~ product(e_1,e_2,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_69]),c_0_113]) ).
cnf(c_0_166,negated_conjecture,
( product(e_4,e_1,e_2)
| ~ product(e_4,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_157,c_0_86]) ).
cnf(c_0_167,negated_conjecture,
( product(X1,e_2,e_4)
| ~ product(e_3,e_3,e_2)
| ~ product(e_1,e_4,X1) ),
inference(spm,[status(thm)],[c_0_97,c_0_158]) ).
cnf(c_0_168,plain,
( product(e_1,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_3,e_3,e_4)
| product(e_4,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_159,c_0_27]) ).
cnf(c_0_169,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_3,X1,e_4)
| ~ product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_160,c_0_62]) ).
cnf(c_0_170,negated_conjecture,
( product(e_3,e_3,e_1)
| ~ product(e_2,e_3,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_82]) ).
cnf(c_0_171,plain,
( ~ product(e_2,e_3,e_4)
| ~ product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_125,c_0_163]) ).
cnf(c_0_172,plain,
( equalish(X1,e_1)
| ~ product(e_4,e_3,e_4)
| ~ product(X1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_40,c_0_164]) ).
cnf(c_0_173,plain,
product(e_1,e_4,e_3),
inference(sr,[status(thm)],[c_0_71,c_0_165]) ).
cnf(c_0_174,plain,
( product(e_4,X1,e_2)
| product(e_3,X1,e_2)
| product(e_2,X1,e_2)
| product(e_1,X1,e_2)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_102,c_0_87]) ).
cnf(c_0_175,negated_conjecture,
( equalish(X1,e_1)
| ~ product(e_4,e_3,e_2)
| ~ product(e_4,X1,e_2) ),
inference(spm,[status(thm)],[c_0_28,c_0_166]) ).
cnf(c_0_176,negated_conjecture,
( ~ product(e_3,e_3,e_2)
| ~ product(e_1,e_2,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_69]),c_0_113]) ).
cnf(c_0_177,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| ~ product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_151,c_0_106]) ).
cnf(c_0_178,plain,
( product(e_4,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_1,e_3,e_4) ),
inference(sr,[status(thm)],[c_0_168,c_0_143]) ).
cnf(c_0_179,negated_conjecture,
~ product(e_2,e_3,e_4),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_143]),c_0_171]) ).
cnf(c_0_180,plain,
( ~ product(e_4,e_3,e_4)
| ~ product(e_3,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_34,c_0_172]) ).
cnf(c_0_181,negated_conjecture,
product(e_3,e_2,e_4),
inference(spm,[status(thm)],[c_0_156,c_0_173]) ).
cnf(c_0_182,plain,
( product(e_1,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_3,e_3,e_2)
| product(e_4,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_174,c_0_27]) ).
cnf(c_0_183,negated_conjecture,
~ product(e_4,e_3,e_2),
inference(spm,[status(thm)],[c_0_34,c_0_175]) ).
cnf(c_0_184,negated_conjecture,
( product(e_1,e_2,e_2)
| ~ product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_176,c_0_177]) ).
cnf(c_0_185,plain,
( product(e_1,e_3,e_4)
| product(e_4,e_3,e_4) ),
inference(sr,[status(thm)],[c_0_178,c_0_179]) ).
cnf(c_0_186,plain,
~ product(e_4,e_3,e_4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_180,c_0_181])]) ).
cnf(c_0_187,plain,
( product(e_3,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[c_0_182,c_0_183]) ).
cnf(c_0_188,negated_conjecture,
~ product(e_3,e_3,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_184]),c_0_72]) ).
cnf(c_0_189,plain,
( ~ product(e_1,e_2,e_4)
| ~ product(e_1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_100,c_0_56]) ).
cnf(c_0_190,plain,
product(e_1,e_3,e_4),
inference(sr,[status(thm)],[c_0_185,c_0_186]) ).
cnf(c_0_191,plain,
( product(e_1,e_2,e_4)
| ~ product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_65,c_0_60]) ).
cnf(c_0_192,plain,
( product(e_1,e_3,e_2)
| product(e_2,e_3,e_2) ),
inference(sr,[status(thm)],[c_0_187,c_0_188]) ).
cnf(c_0_193,plain,
~ product(e_1,e_2,e_4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_189,c_0_190])]) ).
cnf(c_0_194,plain,
product(e_2,e_3,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_192]),c_0_193]) ).
cnf(c_0_195,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_194]),c_0_55]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : GRP126-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.07 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.07/0.26 % Computer : n009.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Tue Aug 29 02:12:05 EDT 2023
% 0.07/0.26 % CPUTime :
% 0.10/0.41 start to proof: theBenchmark
% 0.10/0.53 % Version : CSE_E---1.5
% 0.10/0.53 % Problem : theBenchmark.p
% 0.10/0.53 % Proof found
% 0.10/0.53 % SZS status Theorem for theBenchmark.p
% 0.10/0.53 % SZS output start Proof
% See solution above
% 0.10/0.54 % Total time : 0.112000 s
% 0.10/0.54 % SZS output end Proof
% 0.10/0.54 % Total time : 0.115000 s
%------------------------------------------------------------------------------