TSTP Solution File: GRP130-1.003 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP130-1.003 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n029.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 0.56s 0.71s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 20
% Syntax : Number of formulae : 184 ( 30 unt; 6 typ; 0 def)
% Number of atoms : 486 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 556 ( 248 ~; 308 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 93 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
e_1: $i ).
tff(decl_23,type,
group_element: $i > $o ).
tff(decl_24,type,
e_2: $i ).
tff(decl_25,type,
e_3: $i ).
tff(decl_26,type,
equalish: ( $i * $i ) > $o ).
tff(decl_27,type,
product: ( $i * $i * $i ) > $o ).
cnf(product_total_function1,axiom,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| product(X1,X2,e_3)
| ~ 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(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(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(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_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(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
cnf(qg3,negated_conjecture,
( product(X4,X2,X1)
| ~ product(X1,X2,X3)
| ~ product(X1,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
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_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_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_2,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_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(c_0_14,axiom,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| product(X1,X2,e_3)
| ~ group_element(X1)
| ~ group_element(X2) ),
product_total_function1 ).
cnf(c_0_15,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_16,plain,
( 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_14,c_0_15]) ).
cnf(c_0_17,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_18,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
product_left_cancellation ).
cnf(c_0_19,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_21,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_right_cancellation ).
cnf(c_0_22,axiom,
~ equalish(e_2,e_1),
e_2_is_not_e_1 ).
cnf(c_0_23,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| equalish(X1,e_1)
| ~ product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,axiom,
~ equalish(e_2,e_3),
e_2_is_not_e_3 ).
cnf(c_0_25,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| equalish(X1,e_3)
| ~ product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_26,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_27,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| equalish(X1,e_3)
| ~ product(e_1,X1,e_1) ),
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_28,negated_conjecture,
( product(X4,X2,X1)
| ~ product(X1,X2,X3)
| ~ product(X1,X3,X4) ),
qg3 ).
cnf(c_0_29,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| ~ product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_3)
| ~ product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_16,c_0_26]) ).
cnf(c_0_32,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| ~ product(e_1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_24,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_3,X1,e_1)
| ~ product(e_2,e_3,e_1)
| ~ product(e_1,X1,e_3) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
( product(e_3,e_3,e_2)
| equalish(X1,e_3)
| ~ product(e_2,e_3,e_1)
| ~ product(e_3,X1,e_3) ),
inference(spm,[status(thm)],[c_0_21,c_0_30]) ).
cnf(c_0_35,plain,
( 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_14,c_0_26]) ).
cnf(c_0_36,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| equalish(X1,e_3)
| ~ product(e_2,X1,e_1) ),
inference(spm,[status(thm)],[c_0_21,c_0_31]) ).
cnf(c_0_37,plain,
( product(e_1,e_3,e_2)
| equalish(X1,e_3)
| ~ product(e_1,e_2,e_1)
| ~ product(e_1,X1,e_3) ),
inference(spm,[status(thm)],[c_0_21,c_0_32]) ).
cnf(c_0_38,negated_conjecture,
( product(e_3,e_3,e_1)
| product(e_1,e_3,e_2)
| ~ product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_33,c_0_29]) ).
cnf(c_0_39,plain,
( product(e_3,e_3,e_2)
| ~ product(e_2,e_3,e_1)
| ~ product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_24,c_0_34]) ).
cnf(c_0_40,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_35,c_0_15]) ).
cnf(c_0_41,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
product_total_function2 ).
cnf(c_0_42,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_3)
| ~ product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_24,c_0_36]) ).
cnf(c_0_43,plain,
( product(e_1,e_3,e_2)
| ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_24,c_0_37]) ).
cnf(c_0_44,axiom,
~ equalish(e_3,e_1),
e_3_is_not_e_1 ).
cnf(c_0_45,negated_conjecture,
( product(e_3,e_3,e_1)
| equalish(X1,e_1)
| ~ product(e_2,e_3,e_1)
| ~ product(X1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_18,c_0_38]) ).
cnf(c_0_46,plain,
( equalish(X1,e_3)
| ~ product(e_2,e_3,e_1)
| ~ product(e_3,e_2,e_3)
| ~ product(X1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_18,c_0_39]) ).
cnf(c_0_47,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| equalish(X1,e_3)
| ~ product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_18,c_0_40]) ).
cnf(c_0_48,axiom,
~ equalish(e_1,e_3),
e_1_is_not_e_3 ).
cnf(c_0_49,plain,
( product(e_2,e_3,e_2)
| equalish(X1,e_3)
| ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_3,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_50,plain,
( product(e_2,e_3,e_2)
| equalish(X1,e_3)
| ~ product(e_2,e_2,e_1)
| ~ product(e_2,X1,e_3) ),
inference(spm,[status(thm)],[c_0_21,c_0_42]) ).
cnf(c_0_51,axiom,
~ equalish(e_1,e_2),
e_1_is_not_e_2 ).
cnf(c_0_52,plain,
( equalish(X1,e_2)
| ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_2,e_3)
| ~ product(e_1,e_3,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_43]) ).
cnf(c_0_53,plain,
( product(e_3,e_3,e_2)
| equalish(X1,e_3)
| ~ product(e_2,e_3,e_1)
| ~ product(X1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_18,c_0_30]) ).
cnf(c_0_54,negated_conjecture,
( product(e_3,e_3,e_1)
| ~ product(e_2,e_3,e_1)
| ~ product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_55,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_35,c_0_17]) ).
cnf(c_0_56,plain,
( ~ product(e_2,e_3,e_1)
| ~ product(e_3,e_2,e_3)
| ~ product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_24,c_0_46]) ).
cnf(c_0_57,plain,
( product(e_3,e_2,e_2)
| product(e_3,e_2,e_3)
| ~ product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_24,c_0_47]) ).
cnf(c_0_58,plain,
( product(e_2,e_3,e_2)
| ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_59,plain,
( product(e_2,e_3,e_2)
| ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_24,c_0_50]) ).
cnf(c_0_60,plain,
( ~ product(e_1,e_2,e_3)
| ~ product(e_1,e_3,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_28]) ).
cnf(c_0_61,plain,
( product(e_3,e_3,e_2)
| ~ product(e_2,e_3,e_1)
| ~ product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_48,c_0_53]) ).
cnf(c_0_62,negated_conjecture,
( equalish(X1,e_1)
| ~ product(e_2,e_3,e_1)
| ~ product(e_3,e_3,e_2)
| ~ product(e_3,e_3,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_54]) ).
cnf(c_0_63,axiom,
~ equalish(e_3,e_2),
e_3_is_not_e_2 ).
cnf(c_0_64,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| equalish(X1,e_2)
| ~ product(e_1,X1,e_1) ),
inference(spm,[status(thm)],[c_0_21,c_0_55]) ).
cnf(c_0_65,plain,
( product(e_3,e_2,e_2)
| ~ product(e_2,e_3,e_1)
| ~ product(e_2,e_2,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]) ).
cnf(c_0_66,plain,
( equalish(X1,e_2)
| ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_2,e_3)
| ~ product(e_2,e_3,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_59]) ).
cnf(c_0_67,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| ~ product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_60,c_0_19]) ).
cnf(c_0_68,plain,
( product(e_1,e_3,e_2)
| product(e_3,e_3,e_2)
| ~ product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_61,c_0_29]) ).
cnf(c_0_69,negated_conjecture,
( ~ product(e_2,e_3,e_1)
| ~ product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_22,c_0_62]) ).
cnf(c_0_70,negated_conjecture,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,X1,e_1)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_28,c_0_55]) ).
cnf(c_0_71,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| ~ product(e_1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_72,negated_conjecture,
( product(e_2,X1,e_3)
| ~ product(e_2,e_3,e_1)
| ~ product(e_2,e_2,e_1)
| ~ product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_28,c_0_65]) ).
cnf(c_0_73,plain,
( ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_2,e_3)
| ~ product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_51,c_0_66]) ).
cnf(c_0_74,plain,
( product(e_1,e_3,e_2)
| equalish(X1,e_3)
| ~ product(e_1,e_2,e_3)
| ~ product(e_1,X1,e_3) ),
inference(spm,[status(thm)],[c_0_21,c_0_67]) ).
cnf(c_0_75,plain,
( product(e_3,e_3,e_2)
| equalish(X1,e_3)
| ~ product(e_2,e_3,e_1)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_21,c_0_68]) ).
cnf(c_0_76,negated_conjecture,
( product(e_2,X1,e_1)
| ~ product(e_2,e_3,e_1)
| ~ product(e_1,X1,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_68]),c_0_69]) ).
cnf(c_0_77,negated_conjecture,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| ~ product(e_2,e_3,e_1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_68]),c_0_69]),c_0_71]) ).
cnf(c_0_78,negated_conjecture,
( ~ product(e_2,e_3,e_1)
| ~ product(e_2,e_2,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_65]),c_0_73]) ).
cnf(c_0_79,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| equalish(X1,e_1)
| ~ product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_18,c_0_55]) ).
cnf(c_0_80,plain,
( product(e_1,e_3,e_2)
| ~ product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_24,c_0_74]) ).
cnf(c_0_81,plain,
( product(e_3,e_3,e_2)
| ~ product(e_2,e_3,e_1)
| ~ product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_24,c_0_75]) ).
cnf(c_0_82,negated_conjecture,
( product(e_1,e_2,e_2)
| ~ product(e_2,e_3,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]) ).
cnf(c_0_83,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| ~ product(e_3,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_44,c_0_79]) ).
cnf(c_0_84,plain,
( product(e_3,e_2,e_2)
| equalish(X1,e_3)
| ~ product(e_2,e_2,e_1)
| ~ product(X1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_18,c_0_57]) ).
cnf(c_0_85,plain,
( equalish(X1,e_1)
| ~ product(e_1,e_2,e_3)
| ~ product(X1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_18,c_0_80]) ).
cnf(c_0_86,negated_conjecture,
~ product(e_2,e_3,e_1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_69]) ).
cnf(c_0_87,plain,
( product(e_1,e_2,e_2)
| equalish(X1,e_1)
| ~ product(e_3,e_2,e_1)
| ~ product(X1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_18,c_0_83]) ).
cnf(c_0_88,plain,
( product(e_3,e_2,e_2)
| ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_24,c_0_84]) ).
cnf(c_0_89,plain,
( ~ product(e_1,e_2,e_3)
| ~ product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_44,c_0_85]) ).
cnf(c_0_90,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2) ),
inference(sr,[status(thm)],[c_0_31,c_0_86]) ).
cnf(c_0_91,plain,
( ~ product(e_1,e_2,e_3)
| ~ product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_22,c_0_85]) ).
cnf(c_0_92,plain,
( product(e_1,e_2,e_2)
| ~ product(e_3,e_2,e_1)
| ~ product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_22,c_0_87]) ).
cnf(c_0_93,plain,
( equalish(X1,e_2)
| ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_2,e_3)
| ~ product(e_3,e_2,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_88]) ).
cnf(c_0_94,plain,
( product(e_1,e_2,e_2)
| ~ product(e_3,e_3,e_2)
| ~ product(e_3,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_89,c_0_83]) ).
cnf(c_0_95,plain,
( product(e_2,e_3,e_2)
| equalish(X1,e_2)
| ~ product(X1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_18,c_0_90]) ).
cnf(c_0_96,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| equalish(X1,e_3)
| ~ product(e_3,X1,e_1) ),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_97,plain,
( product(e_1,e_2,e_2)
| ~ product(e_2,e_3,e_2)
| ~ product(e_3,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_91,c_0_83]) ).
cnf(c_0_98,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_35,c_0_26]) ).
cnf(c_0_99,negated_conjecture,
( product(e_2,X1,e_1)
| ~ product(e_3,e_2,e_1)
| ~ product(e_2,e_2,e_3)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_28,c_0_92]) ).
cnf(c_0_100,plain,
( ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_2,e_3)
| ~ product(e_3,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_51,c_0_93]) ).
cnf(c_0_101,plain,
( equalish(X1,e_1)
| ~ product(e_3,e_3,e_2)
| ~ product(e_3,e_2,e_1)
| ~ product(X1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_18,c_0_94]) ).
cnf(c_0_102,plain,
( product(e_2,e_3,e_2)
| ~ product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_63,c_0_95]) ).
cnf(c_0_103,plain,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_3)
| ~ product(e_3,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_24,c_0_96]) ).
cnf(c_0_104,plain,
( equalish(X1,e_1)
| ~ product(e_2,e_3,e_2)
| ~ product(e_3,e_2,e_1)
| ~ product(X1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_18,c_0_97]) ).
cnf(c_0_105,plain,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| equalish(X1,e_2)
| ~ product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_18,c_0_98]) ).
cnf(c_0_106,negated_conjecture,
( ~ product(e_3,e_2,e_1)
| ~ product(e_2,e_2,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_92]),c_0_100]) ).
cnf(c_0_107,plain,
( ~ product(e_3,e_3,e_2)
| ~ product(e_3,e_2,e_1)
| ~ product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_22,c_0_101]) ).
cnf(c_0_108,plain,
( product(e_3,e_3,e_2)
| product(e_2,e_3,e_2)
| ~ product(e_3,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_109,plain,
( ~ product(e_2,e_3,e_2)
| ~ product(e_3,e_2,e_1)
| ~ product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_22,c_0_104]) ).
cnf(c_0_110,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| ~ product(e_3,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_63,c_0_105]) ).
cnf(c_0_111,negated_conjecture,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| ~ product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_106,c_0_40]) ).
cnf(c_0_112,plain,
( ~ product(e_3,e_2,e_1)
| ~ product(e_2,e_2,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109]) ).
cnf(c_0_113,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_2,e_2,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_40]),c_0_111]) ).
cnf(c_0_114,plain,
( product(e_2,e_3,e_2)
| equalish(X1,e_3)
| ~ product(e_2,X1,e_3) ),
inference(spm,[status(thm)],[c_0_21,c_0_90]) ).
cnf(c_0_115,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_40]),c_0_113]) ).
cnf(c_0_116,plain,
( product(e_2,e_3,e_2)
| ~ product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_24,c_0_114]) ).
cnf(c_0_117,plain,
( product(e_3,e_2,e_2)
| equalish(X1,e_3)
| ~ product(X1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_18,c_0_115]) ).
cnf(c_0_118,plain,
( equalish(X1,e_2)
| ~ product(e_2,e_2,e_3)
| ~ product(X1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_18,c_0_116]) ).
cnf(c_0_119,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_3,X1,e_1)
| ~ product(e_1,e_2,e_1)
| ~ product(e_1,X1,e_3) ),
inference(spm,[status(thm)],[c_0_28,c_0_32]) ).
cnf(c_0_120,plain,
( product(e_3,e_2,e_2)
| ~ product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_24,c_0_117]) ).
cnf(c_0_121,plain,
( ~ product(e_2,e_2,e_3)
| ~ product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_51,c_0_118]) ).
cnf(c_0_122,negated_conjecture,
( product(e_3,e_3,e_1)
| product(e_1,e_3,e_2)
| ~ product(e_1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_119,c_0_32]) ).
cnf(c_0_123,plain,
( 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_14,c_0_17]) ).
cnf(c_0_124,plain,
( equalish(X1,e_3)
| ~ product(e_2,e_2,e_3)
| ~ product(X1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_18,c_0_120]) ).
cnf(c_0_125,plain,
( ~ product(e_2,e_2,e_3)
| ~ product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_121,c_0_80]) ).
cnf(c_0_126,negated_conjecture,
( product(e_3,e_3,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_122]),c_0_55]),c_0_71]) ).
cnf(c_0_127,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_123,c_0_26]) ).
cnf(c_0_128,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| ~ product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_22,c_0_79]) ).
cnf(c_0_129,plain,
( ~ product(e_2,e_2,e_3)
| ~ product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_48,c_0_124]) ).
cnf(c_0_130,negated_conjecture,
( product(e_1,e_2,e_2)
| product(e_3,e_3,e_1)
| ~ product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_131,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| ~ product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_44,c_0_23]) ).
cnf(c_0_132,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| equalish(X1,e_1)
| ~ product(e_2,X1,e_1) ),
inference(spm,[status(thm)],[c_0_21,c_0_127]) ).
cnf(c_0_133,plain,
( product(e_1,e_2,e_2)
| ~ product(e_2,e_3,e_2)
| ~ product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_91,c_0_128]) ).
cnf(c_0_134,negated_conjecture,
( product(e_3,e_3,e_1)
| ~ product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_135,plain,
( product(e_1,e_3,e_2)
| equalish(X1,e_1)
| ~ product(e_3,e_3,e_1)
| ~ product(X1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_18,c_0_131]) ).
cnf(c_0_136,plain,
( product(e_2,e_3,e_2)
| ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_48,c_0_50]) ).
cnf(c_0_137,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| ~ product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_22,c_0_132]) ).
cnf(c_0_138,plain,
( equalish(X1,e_2)
| ~ product(e_2,e_3,e_2)
| ~ product(e_2,e_2,e_1)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_21,c_0_133]) ).
cnf(c_0_139,negated_conjecture,
( equalish(X1,e_3)
| ~ product(e_2,e_2,e_3)
| ~ product(e_3,X1,e_1) ),
inference(spm,[status(thm)],[c_0_21,c_0_134]) ).
cnf(c_0_140,plain,
( equalish(X1,e_2)
| ~ product(e_2,e_2,e_3)
| ~ product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_21,c_0_120]) ).
cnf(c_0_141,plain,
( product(e_1,e_3,e_2)
| ~ product(e_3,e_3,e_1)
| ~ product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_44,c_0_135]) ).
cnf(c_0_142,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_3,e_2)
| ~ product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_143,plain,
( ~ product(e_2,e_3,e_2)
| ~ product(e_2,e_2,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_138]),c_0_28]) ).
cnf(c_0_144,negated_conjecture,
( ~ product(e_2,e_2,e_3)
| ~ product(e_3,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_48,c_0_139]) ).
cnf(c_0_145,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_123,c_0_15]) ).
cnf(c_0_146,plain,
( ~ product(e_2,e_2,e_3)
| ~ product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_51,c_0_140]) ).
cnf(c_0_147,plain,
( equalish(X1,e_2)
| ~ product(e_3,e_3,e_1)
| ~ product(e_3,e_3,e_3)
| ~ product(e_1,e_3,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_141]) ).
cnf(c_0_148,plain,
( equalish(X1,e_2)
| ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_1,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_142]),c_0_143]) ).
cnf(c_0_149,negated_conjecture,
( product(e_3,e_1,e_3)
| ~ product(e_2,e_2,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_146]) ).
cnf(c_0_150,plain,
( ~ product(e_3,e_3,e_1)
| ~ product(e_3,e_3,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_147]),c_0_28]) ).
cnf(c_0_151,plain,
( ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_63,c_0_148]) ).
cnf(c_0_152,negated_conjecture,
( product(e_3,X1,e_3)
| ~ product(e_2,e_2,e_3)
| ~ product(e_3,X1,e_1) ),
inference(spm,[status(thm)],[c_0_28,c_0_149]) ).
cnf(c_0_153,negated_conjecture,
( ~ product(e_3,e_3,e_3)
| ~ product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_150,c_0_134]) ).
cnf(c_0_154,plain,
( product(e_2,e_1,e_2)
| ~ product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_151,c_0_137]) ).
cnf(c_0_155,negated_conjecture,
~ product(e_2,e_2,e_3),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_134]),c_0_153]) ).
cnf(c_0_156,negated_conjecture,
( product(e_2,X1,e_2)
| ~ product(e_2,e_2,e_1)
| ~ product(e_2,X1,e_1) ),
inference(spm,[status(thm)],[c_0_28,c_0_154]) ).
cnf(c_0_157,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(sr,[status(thm)],[c_0_98,c_0_155]) ).
cnf(c_0_158,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_2,X1,e_2)
| ~ product(e_2,X1,e_1) ),
inference(spm,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_159,negated_conjecture,
product(e_2,e_2,e_2),
inference(spm,[status(thm)],[c_0_158,c_0_157]) ).
cnf(c_0_160,negated_conjecture,
( equalish(X1,e_2)
| ~ product(e_2,X1,e_2) ),
inference(spm,[status(thm)],[c_0_21,c_0_159]) ).
cnf(c_0_161,negated_conjecture,
~ product(e_2,e_3,e_2),
inference(spm,[status(thm)],[c_0_63,c_0_160]) ).
cnf(c_0_162,plain,
product(e_2,e_3,e_3),
inference(sr,[status(thm)],[c_0_90,c_0_161]) ).
cnf(c_0_163,plain,
( product(e_3,e_2,e_2)
| equalish(X1,e_2)
| ~ product(e_3,X1,e_3) ),
inference(spm,[status(thm)],[c_0_21,c_0_115]) ).
cnf(c_0_164,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| equalish(X1,e_3)
| ~ product(X1,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_18,c_0_145]) ).
cnf(c_0_165,plain,
( equalish(X1,e_3)
| ~ product(e_2,X1,e_3) ),
inference(spm,[status(thm)],[c_0_21,c_0_162]) ).
cnf(c_0_166,plain,
( product(e_3,e_2,e_2)
| ~ product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_51,c_0_163]) ).
cnf(c_0_167,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| ~ product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_24,c_0_164]) ).
cnf(c_0_168,negated_conjecture,
~ product(e_2,e_1,e_2),
inference(spm,[status(thm)],[c_0_51,c_0_160]) ).
cnf(c_0_169,plain,
~ product(e_2,e_1,e_3),
inference(spm,[status(thm)],[c_0_48,c_0_165]) ).
cnf(c_0_170,negated_conjecture,
( equalish(X1,e_2)
| ~ product(X1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_18,c_0_159]) ).
cnf(c_0_171,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_2,e_2)
| ~ product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_166,c_0_167]) ).
cnf(c_0_172,plain,
product(e_2,e_1,e_1),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_127,c_0_168]),c_0_169]) ).
cnf(c_0_173,negated_conjecture,
~ product(e_3,e_2,e_2),
inference(spm,[status(thm)],[c_0_63,c_0_170]) ).
cnf(c_0_174,negated_conjecture,
( product(e_3,e_2,e_2)
| product(e_3,X1,e_3)
| ~ product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_28,c_0_115]) ).
cnf(c_0_175,plain,
product(e_3,e_1,e_2),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_171,c_0_172])]),c_0_173]) ).
cnf(c_0_176,negated_conjecture,
product(e_3,e_1,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_175]),c_0_173]) ).
cnf(c_0_177,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_166,c_0_176])]),c_0_173]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP130-1.003 : TPTP v8.1.2. Released v1.2.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 23:20:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.56/0.59 start to proof: theBenchmark
% 0.56/0.71 % Version : CSE_E---1.5
% 0.56/0.71 % Problem : theBenchmark.p
% 0.56/0.71 % Proof found
% 0.56/0.71 % SZS status Theorem for theBenchmark.p
% 0.56/0.71 % SZS output start Proof
% See solution above
% 0.56/0.72 % Total time : 0.109000 s
% 0.56/0.72 % SZS output end Proof
% 0.56/0.72 % Total time : 0.113000 s
%------------------------------------------------------------------------------