TSTP Solution File: GRP129-4.004 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP129-4.004 : 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 : n023.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 00:17:08 EDT 2023
% Result : Unsatisfiable 0.52s 0.78s
% Output : CNFRefutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 25
% Syntax : Number of formulae : 181 ( 37 unt; 7 typ; 0 def)
% Number of atoms : 486 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 539 ( 227 ~; 312 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 112 ( 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(qg3_1,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X3,X1,X4)
| ~ product(X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3_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_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(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_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(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
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(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(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
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(qg3_2,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X2,X4,X3)
| ~ product(X4,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3_2) ).
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(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(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(qg3,negated_conjecture,
( product(X3,X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
cnf(c_0_18,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_19,axiom,
group_element(e_4),
element_4 ).
cnf(c_0_20,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_18,c_0_19]) ).
cnf(c_0_21,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X3,X1,X4)
| ~ product(X2,X3,X4) ),
qg3_1 ).
cnf(c_0_22,plain,
( product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
( product(e_4,e_4,e_4)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| product(e_4,X1,e_4)
| ~ product(X1,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
product_left_cancellation ).
cnf(c_0_25,negated_conjecture,
( product(e_4,e_4,e_2)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_26,axiom,
~ equalish(e_3,e_4),
e_3_is_not_e_4 ).
cnf(c_0_27,negated_conjecture,
( equalish(X1,e_4)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| ~ product(X1,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
product_total_function2 ).
cnf(c_0_29,negated_conjecture,
( product(e_4,e_4,e_2)
| product(e_4,e_4,e_3)
| ~ product(e_3,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,axiom,
~ equalish(e_4,e_3),
e_4_is_not_e_3 ).
cnf(c_0_31,negated_conjecture,
( equalish(X1,e_3)
| product(e_4,e_4,e_2)
| ~ product(e_3,e_4,e_4)
| ~ product(e_4,e_4,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,negated_conjecture,
( product(e_4,e_4,e_2)
| product(e_4,X1,e_4)
| ~ product(e_3,e_4,e_4)
| ~ product(X1,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_21,c_0_29]) ).
cnf(c_0_33,negated_conjecture,
( product(e_4,e_4,e_2)
| ~ product(e_3,e_4,e_4)
| ~ product(e_4,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,negated_conjecture,
( product(e_4,e_4,e_2)
| ~ product(e_3,e_4,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_29]),c_0_33]) ).
cnf(c_0_35,negated_conjecture,
( product(e_4,X1,e_4)
| ~ product(e_3,e_4,e_4)
| ~ product(X1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_21,c_0_34]) ).
cnf(c_0_36,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_37,axiom,
~ equalish(e_4,e_2),
e_4_is_not_e_2 ).
cnf(c_0_38,negated_conjecture,
( equalish(X1,e_2)
| ~ product(e_3,e_4,e_4)
| ~ product(e_4,e_4,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
( product(e_4,e_4,e_4)
| ~ product(e_3,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_35,c_0_34]) ).
cnf(c_0_40,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_18,c_0_36]) ).
cnf(c_0_41,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_20,c_0_36]) ).
cnf(c_0_42,negated_conjecture,
~ product(e_3,e_4,e_4),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_43,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_40,c_0_36]) ).
cnf(c_0_44,plain,
( product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(sr,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,negated_conjecture,
( product(e_3,e_3,e_4)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,X1,e_3)
| ~ product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_21,c_0_43]) ).
cnf(c_0_46,axiom,
~ equalish(e_2,e_3),
e_2_is_not_e_3 ).
cnf(c_0_47,plain,
( equalish(X1,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_3)
| ~ product(X1,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_24,c_0_44]) ).
cnf(c_0_48,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_right_cancellation ).
cnf(c_0_49,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_50,negated_conjecture,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_45,c_0_43]) ).
cnf(c_0_51,plain,
( product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| ~ product(e_2,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,axiom,
~ equalish(e_2,e_4),
e_2_is_not_e_4 ).
cnf(c_0_53,negated_conjecture,
( equalish(X1,e_4)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| ~ product(e_4,X1,e_4) ),
inference(spm,[status(thm)],[c_0_48,c_0_25]) ).
cnf(c_0_54,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_18,c_0_49]) ).
cnf(c_0_55,negated_conjecture,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,X1,e_3)
| ~ product(X1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_21,c_0_50]) ).
cnf(c_0_56,plain,
( equalish(X1,e_4)
| product(e_3,e_4,e_2)
| ~ product(e_2,e_4,e_1)
| ~ product(e_3,X1,e_3) ),
inference(spm,[status(thm)],[c_0_48,c_0_51]) ).
cnf(c_0_57,negated_conjecture,
( product(e_4,e_4,e_2)
| product(e_4,e_4,e_3)
| ~ product(e_4,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_54,c_0_49]) ).
cnf(c_0_59,negated_conjecture,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_55,c_0_50]) ).
cnf(c_0_60,plain,
( product(e_3,e_4,e_2)
| ~ product(e_2,e_4,e_1)
| ~ product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_26,c_0_56]) ).
cnf(c_0_61,negated_conjecture,
( equalish(X1,e_3)
| product(e_4,e_4,e_2)
| ~ product(e_4,e_2,e_4)
| ~ product(e_4,e_4,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_57]) ).
cnf(c_0_62,negated_conjecture,
( product(e_4,e_4,e_2)
| product(e_4,e_4,e_3)
| ~ product(e_2,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_52,c_0_27]) ).
cnf(c_0_63,negated_conjecture,
( product(e_2,e_2,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,X1,e_2)
| ~ product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_21,c_0_58]) ).
cnf(c_0_64,negated_conjecture,
( equalish(X1,e_3)
| product(e_3,e_3,e_2)
| ~ product(X1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_24,c_0_59]) ).
cnf(c_0_65,plain,
( equalish(X1,e_3)
| ~ product(e_2,e_4,e_1)
| ~ product(e_3,e_3,e_3)
| ~ product(X1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_24,c_0_60]) ).
cnf(c_0_66,negated_conjecture,
( product(e_4,e_4,e_2)
| product(e_4,X1,e_4)
| ~ product(e_4,e_2,e_4)
| ~ product(X1,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_21,c_0_57]) ).
cnf(c_0_67,negated_conjecture,
( product(e_4,e_4,e_2)
| ~ product(e_4,e_2,e_4)
| ~ product(e_4,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_30,c_0_61]) ).
cnf(c_0_68,negated_conjecture,
( equalish(X1,e_3)
| product(e_4,e_4,e_2)
| ~ product(e_2,e_4,e_4)
| ~ product(e_4,e_4,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_62]) ).
cnf(c_0_69,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_63,c_0_58]) ).
cnf(c_0_70,plain,
( equalish(X1,e_4)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_3)
| ~ product(e_3,X1,e_1) ),
inference(spm,[status(thm)],[c_0_48,c_0_44]) ).
cnf(c_0_71,negated_conjecture,
( product(e_3,e_3,e_2)
| ~ product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_46,c_0_64]) ).
cnf(c_0_72,plain,
( ~ product(e_2,e_4,e_1)
| ~ product(e_3,e_3,e_3)
| ~ product(e_4,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_30,c_0_65]) ).
cnf(c_0_73,negated_conjecture,
( product(e_4,e_4,e_2)
| ~ product(e_4,e_2,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_57]),c_0_67]) ).
cnf(c_0_74,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X2,X4,X3)
| ~ product(X4,X1,X2) ),
qg3_2 ).
cnf(c_0_75,negated_conjecture,
( product(e_4,e_4,e_2)
| product(e_4,X1,e_4)
| ~ product(e_2,e_4,e_4)
| ~ product(X1,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_21,c_0_62]) ).
cnf(c_0_76,negated_conjecture,
( product(e_4,e_4,e_2)
| ~ product(e_2,e_4,e_4)
| ~ product(e_4,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_30,c_0_68]) ).
cnf(c_0_77,negated_conjecture,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,X1,e_2)
| ~ product(X1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_21,c_0_69]) ).
cnf(c_0_78,plain,
( product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| ~ product(e_3,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_52,c_0_70]) ).
cnf(c_0_79,axiom,
~ equalish(e_3,e_2),
e_3_is_not_e_2 ).
cnf(c_0_80,negated_conjecture,
( equalish(X1,e_2)
| ~ product(e_2,e_3,e_3)
| ~ product(e_3,e_3,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_71]) ).
cnf(c_0_81,negated_conjecture,
( ~ product(e_2,e_4,e_1)
| ~ product(e_3,e_3,e_3)
| ~ product(e_4,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_82,negated_conjecture,
( product(e_4,e_2,X1)
| ~ product(e_2,e_4,e_1)
| ~ product(e_3,e_3,e_3)
| ~ product(e_2,e_3,X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_60]) ).
cnf(c_0_83,negated_conjecture,
( equalish(X1,e_3)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| ~ product(X1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_24,c_0_50]) ).
cnf(c_0_84,negated_conjecture,
( product(e_4,e_4,e_2)
| ~ product(e_2,e_4,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_62]),c_0_76]) ).
cnf(c_0_85,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_77,c_0_69]) ).
cnf(c_0_86,plain,
( equalish(X1,e_4)
| product(e_3,e_4,e_2)
| ~ product(e_3,e_2,e_1)
| ~ product(e_3,X1,e_3) ),
inference(spm,[status(thm)],[c_0_48,c_0_78]) ).
cnf(c_0_87,negated_conjecture,
( product(e_3,X1,e_3)
| ~ product(e_2,e_3,e_3)
| ~ product(X1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_21,c_0_71]) ).
cnf(c_0_88,negated_conjecture,
( ~ product(e_2,e_3,e_3)
| ~ product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_89,negated_conjecture,
( ~ product(e_2,e_4,e_1)
| ~ product(e_3,e_3,e_3)
| ~ product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_90,negated_conjecture,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_3)
| ~ product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_46,c_0_83]) ).
cnf(c_0_91,negated_conjecture,
( equalish(X1,e_2)
| ~ product(e_2,e_4,e_4)
| ~ product(e_4,e_4,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_84]) ).
cnf(c_0_92,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_2,X1,e_2)
| ~ product(X1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_21,c_0_85]) ).
cnf(c_0_93,plain,
( product(e_3,e_4,e_2)
| ~ product(e_3,e_2,e_1)
| ~ product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_26,c_0_86]) ).
cnf(c_0_94,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_40,c_0_49]) ).
cnf(c_0_95,negated_conjecture,
~ product(e_2,e_3,e_3),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_71]),c_0_88]) ).
cnf(c_0_96,negated_conjecture,
( product(e_3,e_3,e_2)
| ~ product(e_2,e_4,e_1)
| ~ product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_97,negated_conjecture,
( product(e_4,X1,e_4)
| ~ product(e_2,e_4,e_4)
| ~ product(X1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_21,c_0_84]) ).
cnf(c_0_98,negated_conjecture,
( ~ product(e_2,e_4,e_4)
| ~ product(e_4,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_37,c_0_91]) ).
cnf(c_0_99,negated_conjecture,
product(e_2,e_2,e_2),
inference(spm,[status(thm)],[c_0_92,c_0_85]) ).
cnf(c_0_100,plain,
( equalish(X1,e_3)
| ~ product(e_3,e_2,e_1)
| ~ product(e_3,e_3,e_3)
| ~ product(X1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_24,c_0_93]) ).
cnf(c_0_101,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(sr,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_102,negated_conjecture,
( product(e_3,X1,e_3)
| ~ product(e_2,e_4,e_1)
| ~ product(e_2,e_3,e_4)
| ~ product(X1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_21,c_0_96]) ).
cnf(c_0_103,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_20,c_0_49]) ).
cnf(c_0_104,negated_conjecture,
~ product(e_2,e_4,e_4),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_84]),c_0_98]) ).
cnf(c_0_105,negated_conjecture,
( equalish(X1,e_2)
| ~ product(e_2,X1,e_2) ),
inference(spm,[status(thm)],[c_0_48,c_0_99]) ).
cnf(c_0_106,plain,
( ~ product(e_3,e_2,e_1)
| ~ product(e_3,e_3,e_3)
| ~ product(e_4,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_30,c_0_100]) ).
cnf(c_0_107,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_108,plain,
( equalish(X1,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_4)
| ~ product(e_2,X1,e_1) ),
inference(spm,[status(thm)],[c_0_48,c_0_101]) ).
cnf(c_0_109,negated_conjecture,
( ~ product(e_2,e_4,e_1)
| ~ product(e_2,e_3,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_96]),c_0_89]) ).
cnf(c_0_110,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(sr,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_111,negated_conjecture,
~ product(e_2,e_4,e_2),
inference(spm,[status(thm)],[c_0_37,c_0_105]) ).
cnf(c_0_112,negated_conjecture,
( ~ product(e_3,e_2,e_1)
| ~ product(e_3,e_3,e_3)
| ~ product(e_4,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_106,c_0_73]) ).
cnf(c_0_113,negated_conjecture,
( product(e_4,e_2,X1)
| ~ product(e_3,e_2,e_1)
| ~ product(e_3,e_3,e_3)
| ~ product(e_2,e_3,X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_93]) ).
cnf(c_0_114,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_107,c_0_19]) ).
cnf(c_0_115,plain,
( product(e_2,e_3,e_2)
| ~ product(e_2,e_4,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_108]),c_0_109]) ).
cnf(c_0_116,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_3) ),
inference(sr,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_117,negated_conjecture,
~ product(e_2,e_3,e_2),
inference(spm,[status(thm)],[c_0_79,c_0_105]) ).
cnf(c_0_118,negated_conjecture,
( equalish(X1,e_3)
| product(e_3,e_3,e_2)
| ~ product(e_3,X1,e_3) ),
inference(spm,[status(thm)],[c_0_48,c_0_59]) ).
cnf(c_0_119,negated_conjecture,
( ~ product(e_3,e_2,e_1)
| ~ product(e_3,e_3,e_3)
| ~ product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_120,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_3,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_36]),c_0_42]) ).
cnf(c_0_121,plain,
product(e_2,e_4,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_117]) ).
cnf(c_0_122,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_2,e_4)
| product(e_2,e_3,e_4)
| product(e_2,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_114,c_0_49]) ).
cnf(c_0_123,negated_conjecture,
( equalish(X1,e_4)
| ~ product(e_4,e_2,e_4)
| ~ product(e_4,X1,e_2) ),
inference(spm,[status(thm)],[c_0_48,c_0_73]) ).
cnf(c_0_124,negated_conjecture,
( product(e_3,e_3,e_2)
| ~ product(e_3,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_30,c_0_118]) ).
cnf(c_0_125,negated_conjecture,
( equalish(X1,e_4)
| ~ product(e_4,e_2,e_4)
| ~ product(X1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_24,c_0_73]) ).
cnf(c_0_126,negated_conjecture,
( product(e_3,e_3,e_2)
| ~ product(e_3,e_2,e_1)
| ~ product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_119,c_0_90]) ).
cnf(c_0_127,plain,
( equalish(X1,e_3)
| product(e_3,e_3,e_4)
| product(e_3,e_2,e_4)
| ~ product(X1,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_24,c_0_120]) ).
cnf(c_0_128,axiom,
~ equalish(e_1,e_2),
e_1_is_not_e_2 ).
cnf(c_0_129,plain,
( equalish(X1,e_2)
| ~ product(X1,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_24,c_0_121]) ).
cnf(c_0_130,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_2,e_4)
| product(e_2,e_1,e_4) ),
inference(sr,[status(thm)],[c_0_122,c_0_104]) ).
cnf(c_0_131,negated_conjecture,
( equalish(X1,e_2)
| ~ product(e_2,e_2,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_99]) ).
cnf(c_0_132,plain,
( product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_54,c_0_19]) ).
cnf(c_0_133,negated_conjecture,
( ~ product(e_4,e_2,e_4)
| ~ product(e_4,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_26,c_0_123]) ).
cnf(c_0_134,negated_conjecture,
( product(e_3,e_4,e_2)
| product(e_4,e_3,X1)
| ~ product(e_3,e_2,e_1)
| ~ product(e_3,e_3,X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_78]) ).
cnf(c_0_135,negated_conjecture,
( product(e_3,e_4,e_2)
| product(e_3,e_3,e_2)
| ~ product(e_3,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_124,c_0_78]) ).
cnf(c_0_136,negated_conjecture,
( ~ product(e_4,e_2,e_4)
| ~ product(e_3,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_26,c_0_125]) ).
cnf(c_0_137,negated_conjecture,
( equalish(X1,e_3)
| ~ product(e_3,e_2,e_1)
| ~ product(e_2,e_3,e_4)
| ~ product(X1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_24,c_0_126]) ).
cnf(c_0_138,negated_conjecture,
( equalish(X1,e_3)
| ~ product(e_3,e_2,e_1)
| ~ product(e_2,e_3,e_4)
| ~ product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_48,c_0_126]) ).
cnf(c_0_139,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_3,e_4)
| ~ product(e_2,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_46,c_0_127]) ).
cnf(c_0_140,plain,
~ product(e_1,e_4,e_3),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_141,negated_conjecture,
( product(e_2,e_2,e_4)
| product(e_2,e_3,e_4)
| product(e_1,e_4,X1)
| ~ product(e_4,e_2,X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_130]) ).
cnf(c_0_142,negated_conjecture,
~ product(e_2,e_2,e_4),
inference(spm,[status(thm)],[c_0_37,c_0_131]) ).
cnf(c_0_143,plain,
( equalish(X1,e_4)
| product(e_4,e_2,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_2)
| ~ product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_24,c_0_132]) ).
cnf(c_0_144,negated_conjecture,
( ~ product(e_4,e_2,e_4)
| ~ product(e_3,e_2,e_1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_135]),c_0_136]) ).
cnf(c_0_145,negated_conjecture,
( equalish(X1,e_2)
| ~ product(X1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_24,c_0_99]) ).
cnf(c_0_146,negated_conjecture,
( ~ product(e_3,e_2,e_1)
| ~ product(e_2,e_3,e_4)
| ~ product(e_4,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_30,c_0_137]) ).
cnf(c_0_147,negated_conjecture,
( ~ product(e_3,e_2,e_1)
| ~ product(e_2,e_3,e_4)
| ~ product(e_3,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_30,c_0_138]) ).
cnf(c_0_148,negated_conjecture,
( product(e_4,e_3,X1)
| ~ product(e_3,e_2,X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_121]) ).
cnf(c_0_149,negated_conjecture,
( product(X3,X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X2,X3,X4) ),
qg3 ).
cnf(c_0_150,plain,
( equalish(X1,e_4)
| product(e_3,e_2,e_4)
| ~ product(e_2,e_1,e_4)
| ~ product(e_3,e_3,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_139]) ).
cnf(c_0_151,negated_conjecture,
( equalish(X1,e_3)
| product(e_3,e_3,e_2)
| ~ product(e_2,e_3,e_4)
| ~ product(e_3,X1,e_3) ),
inference(spm,[status(thm)],[c_0_48,c_0_90]) ).
cnf(c_0_152,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_4,e_2,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_142]) ).
cnf(c_0_153,plain,
( product(e_4,e_2,e_2)
| product(e_4,e_2,e_3)
| ~ product(e_3,e_2,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_143]),c_0_144]) ).
cnf(c_0_154,negated_conjecture,
~ product(e_4,e_2,e_2),
inference(spm,[status(thm)],[c_0_37,c_0_145]) ).
cnf(c_0_155,negated_conjecture,
( ~ product(e_3,e_2,e_1)
| ~ product(e_2,e_3,e_4) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_134]),c_0_126]),c_0_147]) ).
cnf(c_0_156,negated_conjecture,
( equalish(X1,X2)
| ~ product(e_4,e_3,X1)
| ~ product(e_3,e_2,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_148]) ).
cnf(c_0_157,negated_conjecture,
( product(e_4,X1,e_3)
| ~ product(X1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_149,c_0_121]) ).
cnf(c_0_158,plain,
( product(e_3,e_2,e_4)
| ~ product(e_2,e_1,e_4)
| ~ product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_26,c_0_150]) ).
cnf(c_0_159,plain,
( product(e_3,e_2,e_4)
| ~ product(e_2,e_1,e_4)
| ~ product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_52,c_0_150]) ).
cnf(c_0_160,negated_conjecture,
( product(e_3,e_3,e_2)
| ~ product(e_2,e_3,e_4)
| ~ product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_46,c_0_151]) ).
cnf(c_0_161,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_54,c_0_36]) ).
cnf(c_0_162,negated_conjecture,
~ product(e_3,e_2,e_2),
inference(spm,[status(thm)],[c_0_79,c_0_145]) ).
cnf(c_0_163,negated_conjecture,
~ product(e_3,e_2,e_1),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_154]),c_0_155]) ).
cnf(c_0_164,negated_conjecture,
~ product(e_3,e_2,e_4),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_156]),c_0_157]) ).
cnf(c_0_165,negated_conjecture,
( product(e_3,e_2,e_4)
| ~ product(e_2,e_1,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_59]),c_0_159]) ).
cnf(c_0_166,negated_conjecture,
( equalish(X1,e_2)
| ~ product(e_2,e_3,e_4)
| ~ product(e_3,e_2,e_3)
| ~ product(e_3,e_3,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_160]) ).
cnf(c_0_167,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_3) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_161,c_0_162]),c_0_163]) ).
cnf(c_0_168,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_3,e_4) ),
inference(sr,[status(thm)],[c_0_130,c_0_142]) ).
cnf(c_0_169,negated_conjecture,
~ product(e_2,e_1,e_4),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_170,negated_conjecture,
( ~ product(e_2,e_3,e_4)
| ~ product(e_3,e_2,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_166]),c_0_149]) ).
cnf(c_0_171,plain,
product(e_3,e_2,e_3),
inference(sr,[status(thm)],[c_0_167,c_0_164]) ).
cnf(c_0_172,plain,
product(e_2,e_3,e_4),
inference(sr,[status(thm)],[c_0_168,c_0_169]) ).
cnf(c_0_173,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_171])]),c_0_172])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP129-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.10/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 20:32:55 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.52/0.58 start to proof: theBenchmark
% 0.52/0.78 % Version : CSE_E---1.5
% 0.52/0.78 % Problem : theBenchmark.p
% 0.52/0.78 % Proof found
% 0.52/0.78 % SZS status Theorem for theBenchmark.p
% 0.52/0.78 % SZS output start Proof
% See solution above
% 0.52/0.79 % Total time : 0.192000 s
% 0.52/0.79 % SZS output end Proof
% 0.52/0.79 % Total time : 0.194000 s
%------------------------------------------------------------------------------