TSTP Solution File: GRP127-4.004 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP127-4.004 : 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 : n007.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 00:16:34 EDT 2023
% Result : Unsatisfiable 0.53s 0.64s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 30
% Syntax : Number of formulae : 154 ( 43 unt; 7 typ; 0 def)
% Number of atoms : 355 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 362 ( 154 ~; 208 |; 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 : 102 ( 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_4,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
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(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_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(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_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_1,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_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(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_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(qg3,negated_conjecture,
( product(X4,X1,X2)
| ~ product(X1,X2,X3)
| ~ product(X3,X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
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(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(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(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(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_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(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(qg3_1,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X4,X1,X2)
| ~ product(X3,X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3_1) ).
cnf(qg3_2,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X3,X2,X4)
| ~ product(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3_2) ).
cnf(c_0_23,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_24,axiom,
group_element(e_4),
element_4 ).
cnf(c_0_25,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_right_cancellation ).
cnf(c_0_26,axiom,
product(X1,X1,X1),
product_idempotence ).
cnf(c_0_27,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_23,c_0_24]) ).
cnf(c_0_28,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_29,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
product_left_cancellation ).
cnf(c_0_30,plain,
( equalish(X1,X2)
| ~ product(X2,X1,X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,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_27,c_0_28]) ).
cnf(c_0_32,axiom,
~ equalish(e_4,e_1),
e_4_is_not_e_1 ).
cnf(c_0_33,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_34,plain,
( equalish(X1,X2)
| ~ product(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_26]) ).
cnf(c_0_35,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_30,c_0_31]),c_0_32]) ).
cnf(c_0_36,axiom,
~ equalish(e_1,e_4),
e_1_is_not_e_4 ).
cnf(c_0_37,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_23,c_0_33]) ).
cnf(c_0_38,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_34,c_0_35]),c_0_36]) ).
cnf(c_0_39,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_37,c_0_28]) ).
cnf(c_0_40,axiom,
~ equalish(e_3,e_1),
e_3_is_not_e_1 ).
cnf(c_0_41,plain,
( equalish(X1,e_1)
| product(e_1,e_4,e_2)
| ~ product(X1,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_29,c_0_38]) ).
cnf(c_0_42,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_30,c_0_39]),c_0_40]) ).
cnf(c_0_43,plain,
( product(e_1,e_4,e_2)
| ~ product(e_4,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_32,c_0_41]) ).
cnf(c_0_44,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_29,c_0_42]) ).
cnf(c_0_45,axiom,
~ equalish(e_2,e_1),
e_2_is_not_e_1 ).
cnf(c_0_46,axiom,
~ equalish(e_3,e_4),
e_3_is_not_e_4 ).
cnf(c_0_47,plain,
( equalish(X1,e_4)
| ~ product(e_4,e_4,e_3)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_43]) ).
cnf(c_0_48,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_32,c_0_44]) ).
cnf(c_0_49,axiom,
~ equalish(e_1,e_3),
e_1_is_not_e_3 ).
cnf(c_0_50,negated_conjecture,
( product(X4,X1,X2)
| ~ product(X1,X2,X3)
| ~ product(X3,X1,X4) ),
qg3 ).
cnf(c_0_51,plain,
( product(e_1,e_4,e_2)
| ~ product(e_3,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_52,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_45,c_0_44]) ).
cnf(c_0_53,plain,
( ~ product(e_4,e_4,e_3)
| ~ product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_54,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_34,c_0_48]),c_0_49]) ).
cnf(c_0_55,negated_conjecture,
( product(X1,X1,X2)
| ~ product(X1,X2,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_26]) ).
cnf(c_0_56,plain,
( equalish(X1,e_4)
| ~ product(e_3,e_4,e_3)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_51]) ).
cnf(c_0_57,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_40,c_0_44]) ).
cnf(c_0_58,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_34,c_0_52]),c_0_49]) ).
cnf(c_0_59,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_37,c_0_24]) ).
cnf(c_0_60,plain,
~ product(e_4,e_3,e_4),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
cnf(c_0_61,plain,
( ~ product(e_3,e_4,e_3)
| ~ product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_46,c_0_56]) ).
cnf(c_0_62,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_34,c_0_57]),c_0_49]) ).
cnf(c_0_63,axiom,
~ equalish(e_4,e_3),
e_4_is_not_e_3 ).
cnf(c_0_64,plain,
( equalish(X1,e_3)
| ~ product(e_2,e_3,e_4)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_58]) ).
cnf(c_0_65,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_3,e_4,X1)
| ~ product(e_4,X1,e_1) ),
inference(spm,[status(thm)],[c_0_50,c_0_38]) ).
cnf(c_0_66,plain,
( product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(sr,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_67,plain,
~ product(e_3,e_4,e_3),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_55]) ).
cnf(c_0_68,plain,
( equalish(X1,e_1)
| ~ product(e_2,e_3,e_4)
| ~ product(X1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_29,c_0_58]) ).
cnf(c_0_69,plain,
( ~ product(e_2,e_3,e_4)
| ~ product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_70,negated_conjecture,
( product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| product(e_1,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]) ).
cnf(c_0_71,plain,
( ~ product(e_2,e_3,e_4)
| ~ product(e_4,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_32,c_0_68]) ).
cnf(c_0_72,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_73,negated_conjecture,
( product(e_4,e_3,e_3)
| ~ product(e_2,e_3,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).
cnf(c_0_74,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_72,c_0_24]) ).
cnf(c_0_75,negated_conjecture,
~ product(e_2,e_3,e_4),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_73]),c_0_63]) ).
cnf(c_0_76,plain,
( equalish(X1,e_3)
| ~ product(e_3,e_3,e_4)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_62]) ).
cnf(c_0_77,plain,
( equalish(X1,e_4)
| product(e_1,e_4,e_2)
| ~ product(e_1,X1,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_38]) ).
cnf(c_0_78,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_79,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
product_total_function2 ).
cnf(c_0_80,plain,
( product(e_1,e_3,e_4)
| product(e_3,e_3,e_4) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_33]),c_0_60]),c_0_75]) ).
cnf(c_0_81,plain,
( ~ product(e_3,e_3,e_4)
| ~ product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_63,c_0_76]) ).
cnf(c_0_82,plain,
( product(e_1,e_4,e_2)
| ~ product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_46,c_0_77]) ).
cnf(c_0_83,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_78,c_0_33]) ).
cnf(c_0_84,plain,
( equalish(X1,e_4)
| product(e_3,e_3,e_4)
| ~ product(e_1,e_3,X1) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_85,plain,
( ~ product(e_3,e_3,e_4)
| ~ product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_86,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_83,c_0_28]) ).
cnf(c_0_87,plain,
~ product(e_1,e_3,e_3),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_84]),c_0_85]) ).
cnf(c_0_88,axiom,
~ equalish(e_2,e_4),
e_2_is_not_e_4 ).
cnf(c_0_89,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_23,c_0_28]) ).
cnf(c_0_90,plain,
( equalish(X1,X2)
| ~ product(X2,X2,X1) ),
inference(spm,[status(thm)],[c_0_79,c_0_26]) ).
cnf(c_0_91,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_86,c_0_87]) ).
cnf(c_0_92,plain,
( product(e_1,e_4,e_2)
| ~ product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_88,c_0_77]) ).
cnf(c_0_93,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_89,c_0_24]) ).
cnf(c_0_94,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_90,c_0_91]),c_0_40]) ).
cnf(c_0_95,axiom,
~ equalish(e_4,e_2),
e_4_is_not_e_2 ).
cnf(c_0_96,plain,
( equalish(X1,e_2)
| ~ product(e_1,e_2,e_3)
| ~ product(e_1,e_4,X1) ),
inference(spm,[status(thm)],[c_0_79,c_0_92]) ).
cnf(c_0_97,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_34,c_0_93]),c_0_32]) ).
cnf(c_0_98,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_78,c_0_24]) ).
cnf(c_0_99,plain,
( equalish(X1,e_3)
| product(e_1,e_2,e_3)
| ~ product(e_1,e_4,X1) ),
inference(spm,[status(thm)],[c_0_79,c_0_94]) ).
cnf(c_0_100,plain,
( ~ product(e_1,e_2,e_3)
| ~ product(e_1,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_101,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_30,c_0_97]),c_0_36]) ).
cnf(c_0_102,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_98,c_0_28]) ).
cnf(c_0_103,plain,
~ product(e_1,e_4,e_4),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_99]),c_0_100]) ).
cnf(c_0_104,plain,
( equalish(X1,e_1)
| product(e_4,e_1,e_2)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_101]) ).
cnf(c_0_105,axiom,
~ equalish(e_2,e_3),
e_2_is_not_e_3 ).
cnf(c_0_106,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_25,c_0_42]) ).
cnf(c_0_107,plain,
( equalish(X1,e_2)
| ~ product(e_3,e_3,e_4)
| ~ product(e_1,e_3,X1) ),
inference(spm,[status(thm)],[c_0_79,c_0_62]) ).
cnf(c_0_108,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_1,e_4) ),
inference(sr,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_109,plain,
( product(e_4,e_1,e_2)
| ~ product(e_4,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_40,c_0_104]) ).
cnf(c_0_110,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_105,c_0_106]) ).
cnf(c_0_111,plain,
( ~ product(e_3,e_3,e_4)
| ~ product(e_1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_95,c_0_107]) ).
cnf(c_0_112,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_90,c_0_108]),c_0_32]) ).
cnf(c_0_113,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X4,X1,X2)
| ~ product(X3,X1,X4) ),
qg3_1 ).
cnf(c_0_114,plain,
( equalish(X1,e_4)
| ~ product(e_4,e_3,e_3)
| ~ product(X1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_29,c_0_109]) ).
cnf(c_0_115,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_34,c_0_110]),c_0_49]) ).
cnf(c_0_116,negated_conjecture,
( product(e_2,e_1,X1)
| ~ product(e_4,e_3,e_3)
| ~ product(e_1,X1,e_4) ),
inference(spm,[status(thm)],[c_0_50,c_0_109]) ).
cnf(c_0_117,plain,
( product(e_1,e_2,e_4)
| ~ product(e_3,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_118,negated_conjecture,
( product(X1,X1,X2)
| ~ product(X2,X1,X1) ),
inference(spm,[status(thm)],[c_0_113,c_0_26]) ).
cnf(c_0_119,plain,
( ~ product(e_4,e_3,e_3)
| ~ product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_88,c_0_114]) ).
cnf(c_0_120,plain,
( equalish(X1,e_3)
| ~ product(e_1,e_2,e_4)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_115]) ).
cnf(c_0_121,negated_conjecture,
~ product(e_4,e_3,e_3),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_118]),c_0_119]) ).
cnf(c_0_122,plain,
( equalish(X1,e_1)
| ~ product(e_1,e_2,e_4)
| ~ product(X1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_29,c_0_115]) ).
cnf(c_0_123,plain,
( ~ product(e_1,e_2,e_4)
| ~ product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_63,c_0_120]) ).
cnf(c_0_124,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_4,e_3,e_2) ),
inference(sr,[status(thm)],[c_0_70,c_0_121]) ).
cnf(c_0_125,plain,
( ~ product(e_1,e_2,e_4)
| ~ product(e_4,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_32,c_0_122]) ).
cnf(c_0_126,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X3,X2,X4)
| ~ product(X2,X4,X1) ),
qg3_2 ).
cnf(c_0_127,negated_conjecture,
~ product(e_1,e_2,e_4),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_125]) ).
cnf(c_0_128,plain,
( equalish(X1,e_3)
| product(e_4,e_1,e_2)
| ~ product(e_4,e_1,X1) ),
inference(spm,[status(thm)],[c_0_79,c_0_101]) ).
cnf(c_0_129,negated_conjecture,
( product(e_4,e_1,e_2)
| product(X1,e_1,e_4)
| ~ product(e_1,e_3,X1) ),
inference(spm,[status(thm)],[c_0_126,c_0_101]) ).
cnf(c_0_130,plain,
product(e_1,e_3,e_4),
inference(sr,[status(thm)],[c_0_112,c_0_127]) ).
cnf(c_0_131,plain,
( product(e_4,e_1,e_2)
| ~ product(e_4,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_63,c_0_128]) ).
cnf(c_0_132,negated_conjecture,
product(e_4,e_1,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_131]) ).
cnf(c_0_133,plain,
( product(e_1,e_2,e_3)
| ~ product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_105,c_0_99]) ).
cnf(c_0_134,negated_conjecture,
( equalish(X1,e_1)
| ~ product(e_4,X1,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_132]) ).
cnf(c_0_135,plain,
( equalish(X1,e_1)
| ~ product(e_1,e_2,e_3)
| ~ product(X1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_29,c_0_92]) ).
cnf(c_0_136,negated_conjecture,
( product(e_4,e_3,e_2)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_133,c_0_124]) ).
cnf(c_0_137,negated_conjecture,
~ product(e_4,e_3,e_2),
inference(spm,[status(thm)],[c_0_40,c_0_134]) ).
cnf(c_0_138,plain,
( product(e_3,e_4,e_1)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_27,c_0_33]) ).
cnf(c_0_139,negated_conjecture,
( product(e_4,e_3,X1)
| ~ product(e_3,X1,e_1) ),
inference(spm,[status(thm)],[c_0_50,c_0_130]) ).
cnf(c_0_140,plain,
( ~ product(e_1,e_2,e_3)
| ~ product(e_3,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_40,c_0_135]) ).
cnf(c_0_141,negated_conjecture,
product(e_1,e_2,e_3),
inference(sr,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_142,plain,
( product(e_3,e_4,e_4)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(sr,[status(thm)],[c_0_138,c_0_67]) ).
cnf(c_0_143,negated_conjecture,
~ product(e_3,e_4,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_139]),c_0_46]) ).
cnf(c_0_144,plain,
~ product(e_3,e_4,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_140,c_0_141])]) ).
cnf(c_0_145,plain,
product(e_3,e_4,e_4),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_142,c_0_143]),c_0_144]) ).
cnf(c_0_146,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_145]),c_0_46]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP127-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.06/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n007.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 : Tue Aug 29 02:01:28 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.48/0.57 start to proof: theBenchmark
% 0.53/0.64 % Version : CSE_E---1.5
% 0.53/0.64 % Problem : theBenchmark.p
% 0.53/0.64 % Proof found
% 0.53/0.64 % SZS status Theorem for theBenchmark.p
% 0.53/0.64 % SZS output start Proof
% See solution above
% 0.53/0.64 % Total time : 0.063000 s
% 0.53/0.64 % SZS output end Proof
% 0.53/0.64 % Total time : 0.066000 s
%------------------------------------------------------------------------------