TSTP Solution File: GRP124-1.004 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP124-1.004 : 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 : n019.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 00:16:12 EDT 2023
% Result : Unsatisfiable 0.19s 0.60s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 27
% Syntax : Number of formulae : 134 ( 39 unt; 7 typ; 0 def)
% Number of atoms : 292 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 314 ( 149 ~; 165 |; 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 : 62 ( 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,
e_4: $i ).
tff(decl_27,type,
equalish: ( $i * $i ) > $o ).
tff(decl_28,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)
| 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(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(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(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(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_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_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(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
cnf(qg2_2,negated_conjecture,
( equalish(X2,X5)
| ~ product(X1,X2,X3)
| ~ product(X4,X5,X3)
| ~ product(X6,X1,X2)
| ~ product(X6,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg2_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(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_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_4,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
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(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(c_0_20,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_21,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_22,axiom,
group_element(e_4),
element_4 ).
cnf(c_0_23,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_right_cancellation ).
cnf(c_0_24,axiom,
product(X1,X1,X1),
product_idempotence ).
cnf(c_0_25,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_20,c_0_21]) ).
cnf(c_0_26,axiom,
group_element(e_1),
element_1 ).
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_20,c_0_22]) ).
cnf(c_0_28,plain,
( equalish(X1,X2)
| ~ product(X2,X1,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,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_25,c_0_26]) ).
cnf(c_0_30,axiom,
~ equalish(e_3,e_1),
e_3_is_not_e_1 ).
cnf(c_0_31,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
product_left_cancellation ).
cnf(c_0_32,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_26]) ).
cnf(c_0_33,axiom,
~ equalish(e_4,e_1),
e_4_is_not_e_1 ).
cnf(c_0_34,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_28,c_0_29]),c_0_30]) ).
cnf(c_0_35,plain,
( equalish(X1,X2)
| ~ product(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_24]) ).
cnf(c_0_36,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_28,c_0_32]),c_0_33]) ).
cnf(c_0_37,axiom,
~ equalish(e_1,e_4),
e_1_is_not_e_4 ).
cnf(c_0_38,axiom,
~ equalish(e_2,e_3),
e_2_is_not_e_3 ).
cnf(c_0_39,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| equalish(X1,e_3)
| ~ product(e_1,X1,e_4) ),
inference(spm,[status(thm)],[c_0_23,c_0_34]) ).
cnf(c_0_40,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_35,c_0_36]),c_0_37]) ).
cnf(c_0_41,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_38,c_0_39]) ).
cnf(c_0_42,axiom,
~ equalish(e_1,e_3),
e_1_is_not_e_3 ).
cnf(c_0_43,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_44,negated_conjecture,
( equalish(X2,X5)
| ~ product(X1,X2,X3)
| ~ product(X4,X5,X3)
| ~ product(X6,X1,X2)
| ~ product(X6,X4,X5) ),
qg2_2 ).
cnf(c_0_45,axiom,
~ equalish(e_2,e_4),
e_2_is_not_e_4 ).
cnf(c_0_46,plain,
( product(e_1,e_4,e_2)
| equalish(X1,e_4)
| ~ product(e_1,X1,e_3) ),
inference(spm,[status(thm)],[c_0_23,c_0_40]) ).
cnf(c_0_47,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_35,c_0_41]),c_0_42]) ).
cnf(c_0_48,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_20,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
( equalish(X1,X2)
| ~ product(X2,X3,X1)
| ~ product(X2,X2,X4)
| ~ product(X3,X1,X4) ),
inference(spm,[status(thm)],[c_0_44,c_0_24]) ).
cnf(c_0_50,plain,
( product(e_1,e_4,e_2)
| ~ product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,axiom,
~ equalish(e_2,e_1),
e_2_is_not_e_1 ).
cnf(c_0_52,plain,
( equalish(X1,e_1)
| ~ product(e_1,e_2,e_4)
| ~ product(X1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_31,c_0_47]) ).
cnf(c_0_53,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_48,c_0_26]) ).
cnf(c_0_54,negated_conjecture,
( product(e_1,e_4,e_2)
| ~ product(e_1,e_1,X1)
| ~ product(e_4,e_3,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_40]),c_0_30]) ).
cnf(c_0_55,negated_conjecture,
( ~ product(e_1,e_2,e_3)
| ~ product(e_1,e_1,X1)
| ~ product(e_4,e_2,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
cnf(c_0_56,plain,
( ~ product(e_1,e_2,e_4)
| ~ product(e_4,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_52]) ).
cnf(c_0_57,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_28,c_0_53]),c_0_51]) ).
cnf(c_0_58,plain,
( product(e_1,e_4,e_2)
| equalish(X1,e_1)
| ~ product(X1,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_31,c_0_40]) ).
cnf(c_0_59,negated_conjecture,
( product(e_1,e_4,e_2)
| ~ product(e_4,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_54,c_0_24]) ).
cnf(c_0_60,negated_conjecture,
( ~ product(e_1,e_2,e_3)
| ~ product(e_4,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_55,c_0_24]) ).
cnf(c_0_61,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| ~ product(e_4,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_62,plain,
( product(e_1,e_4,e_2)
| ~ product(e_3,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_30,c_0_58]) ).
cnf(c_0_63,negated_conjecture,
( ~ product(e_4,e_3,e_1)
| ~ product(e_1,e_1,X1)
| ~ product(e_4,e_2,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_59]),c_0_51]) ).
cnf(c_0_64,negated_conjecture,
( product(e_1,e_2,e_2)
| ~ product(e_4,e_2,e_1)
| ~ product(e_4,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_65,axiom,
~ equalish(e_1,e_2),
e_1_is_not_e_2 ).
cnf(c_0_66,axiom,
~ equalish(e_3,e_4),
e_3_is_not_e_4 ).
cnf(c_0_67,plain,
( equalish(X1,e_4)
| ~ product(e_3,e_4,e_3)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_23,c_0_62]) ).
cnf(c_0_68,negated_conjecture,
( ~ product(e_4,e_3,e_1)
| ~ product(e_4,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_63,c_0_24]) ).
cnf(c_0_69,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_25,c_0_22]) ).
cnf(c_0_70,negated_conjecture,
( ~ product(e_4,e_2,e_1)
| ~ product(e_4,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_64]),c_0_65]) ).
cnf(c_0_71,plain,
( ~ product(e_3,e_4,e_3)
| ~ product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_72,negated_conjecture,
( product(e_4,e_3,e_4)
| product(e_4,e_3,e_3)
| ~ product(e_4,e_2,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]) ).
cnf(c_0_73,plain,
( product(e_1,e_4,e_2)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_51,c_0_58]) ).
cnf(c_0_74,plain,
( ~ product(e_3,e_4,e_3)
| ~ product(e_1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_71,c_0_47]) ).
cnf(c_0_75,plain,
( ~ product(e_3,e_4,e_3)
| ~ product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_45,c_0_67]) ).
cnf(c_0_76,negated_conjecture,
( product(e_4,e_3,e_3)
| ~ product(e_4,e_2,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_72]),c_0_66]) ).
cnf(c_0_77,axiom,
~ equalish(e_4,e_3),
e_4_is_not_e_3 ).
cnf(c_0_78,plain,
( equalish(X1,e_1)
| ~ product(e_1,e_2,e_3)
| ~ product(X1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_31,c_0_50]) ).
cnf(c_0_79,plain,
( equalish(X1,e_4)
| ~ product(e_2,e_4,e_3)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_23,c_0_73]) ).
cnf(c_0_80,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_74,c_0_57]),c_0_75]) ).
cnf(c_0_81,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_48,c_0_22]) ).
cnf(c_0_82,negated_conjecture,
~ product(e_4,e_2,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_76]),c_0_77]) ).
cnf(c_0_83,plain,
( ~ product(e_1,e_2,e_3)
| ~ product(e_3,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_30,c_0_78]) ).
cnf(c_0_84,plain,
( ~ product(e_2,e_4,e_3)
| ~ product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_66,c_0_79]) ).
cnf(c_0_85,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| ~ product(e_1,e_1,X1)
| ~ product(e_3,e_4,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_34]),c_0_33]) ).
cnf(c_0_86,plain,
( equalish(X1,e_1)
| ~ product(e_3,e_4,e_3)
| ~ product(X1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_31,c_0_80]) ).
cnf(c_0_87,plain,
( product(e_4,e_2,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_2) ),
inference(sr,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_88,negated_conjecture,
( equalish(X1,e_1)
| ~ product(e_4,e_3,e_1)
| ~ product(X1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_31,c_0_59]) ).
cnf(c_0_89,plain,
( product(e_1,e_2,e_2)
| ~ product(e_3,e_4,e_2)
| ~ product(e_4,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_83,c_0_61]) ).
cnf(c_0_90,plain,
( ~ product(e_2,e_4,e_3)
| ~ product(e_1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_84,c_0_47]) ).
cnf(c_0_91,plain,
( ~ product(e_2,e_4,e_3)
| ~ product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_45,c_0_79]) ).
cnf(c_0_92,negated_conjecture,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| ~ product(e_3,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_85,c_0_24]) ).
cnf(c_0_93,plain,
( ~ product(e_3,e_4,e_3)
| ~ product(e_4,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_33,c_0_86]) ).
cnf(c_0_94,plain,
( product(e_4,e_2,e_2)
| product(e_4,e_2,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_87]),c_0_45]) ).
cnf(c_0_95,negated_conjecture,
( ~ product(e_4,e_3,e_1)
| ~ product(e_3,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_30,c_0_88]) ).
cnf(c_0_96,plain,
( ~ product(e_3,e_4,e_2)
| ~ product(e_4,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_89]),c_0_65]) ).
cnf(c_0_97,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_90,c_0_57]),c_0_91]) ).
cnf(c_0_98,plain,
( equalish(X1,e_4)
| ~ product(e_1,e_2,e_3)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_23,c_0_50]) ).
cnf(c_0_99,negated_conjecture,
( product(e_1,e_3,e_2)
| ~ product(e_3,e_4,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_92]),c_0_42]) ).
cnf(c_0_100,plain,
( product(e_4,e_2,e_2)
| ~ product(e_3,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_101,axiom,
~ equalish(e_4,e_2),
e_4_is_not_e_2 ).
cnf(c_0_102,negated_conjecture,
( product(e_4,e_3,e_4)
| product(e_4,e_3,e_3)
| ~ product(e_3,e_4,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_69]),c_0_96]) ).
cnf(c_0_103,plain,
( equalish(X1,e_1)
| ~ product(e_2,e_4,e_3)
| ~ product(X1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_31,c_0_97]) ).
cnf(c_0_104,plain,
( ~ product(e_1,e_2,e_3)
| ~ product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_66,c_0_98]) ).
cnf(c_0_105,negated_conjecture,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| ~ product(e_1,e_1,X1)
| ~ product(e_2,e_4,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_57]),c_0_33]) ).
cnf(c_0_106,negated_conjecture,
( equalish(X1,e_3)
| ~ product(e_3,e_4,e_1)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_23,c_0_99]) ).
cnf(c_0_107,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_21]) ).
cnf(c_0_108,plain,
~ product(e_3,e_4,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_100]),c_0_101]) ).
cnf(c_0_109,negated_conjecture,
( product(e_4,e_3,e_3)
| ~ product(e_3,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_102]),c_0_66]) ).
cnf(c_0_110,plain,
( ~ product(e_2,e_4,e_3)
| ~ product(e_4,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_33,c_0_103]) ).
cnf(c_0_111,negated_conjecture,
( ~ product(e_1,e_2,e_3)
| ~ product(e_3,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_104,c_0_99]) ).
cnf(c_0_112,negated_conjecture,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| ~ product(e_2,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_105,c_0_24]) ).
cnf(c_0_113,negated_conjecture,
( ~ product(e_3,e_4,e_1)
| ~ product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_38,c_0_106]) ).
cnf(c_0_114,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_107,c_0_108]) ).
cnf(c_0_115,negated_conjecture,
~ product(e_3,e_4,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_109]),c_0_77]) ).
cnf(c_0_116,plain,
( product(e_4,e_2,e_2)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_110,c_0_94]) ).
cnf(c_0_117,negated_conjecture,
( ~ product(e_3,e_4,e_1)
| ~ product(e_2,e_4,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_113]) ).
cnf(c_0_118,plain,
( product(e_3,e_4,e_1)
| product(e_3,e_4,e_4) ),
inference(sr,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_119,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_27,c_0_43]) ).
cnf(c_0_120,plain,
~ product(e_2,e_4,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_116]),c_0_101]) ).
cnf(c_0_121,negated_conjecture,
( product(e_3,e_4,e_4)
| ~ product(e_2,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_122,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(sr,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_123,negated_conjecture,
~ product(e_2,e_4,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_121]),c_0_66]) ).
cnf(c_0_124,plain,
( product(e_2,e_4,e_2)
| product(e_2,e_4,e_4) ),
inference(sr,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_125,plain,
product(e_2,e_4,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_124]),c_0_45]) ).
cnf(c_0_126,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_125]),c_0_101]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP124-1.004 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 28 23:15:13 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 0.19/0.60 % Version : CSE_E---1.5
% 0.19/0.60 % Problem : theBenchmark.p
% 0.19/0.60 % Proof found
% 0.19/0.60 % SZS status Theorem for theBenchmark.p
% 0.19/0.60 % SZS output start Proof
% See solution above
% 0.19/0.61 % Total time : 0.041000 s
% 0.19/0.61 % SZS output end Proof
% 0.19/0.61 % Total time : 0.044000 s
%------------------------------------------------------------------------------