TSTP Solution File: GRP124-9.004 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : GRP124-9.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n002.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 00:57:55 EDT 2023

% Result   : Unsatisfiable 3.08s 1.15s
% Output   : CNFRefutation 3.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :   20
% Syntax   : Number of clauses     :  118 (  27 unt;  38 nHn; 116 RR)
%            Number of literals    :  377 (   0 equ; 162 neg)
%            Maximal clause size   :   10 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :   96 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(c_51,plain,
    group_element(e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).

cnf(c_52,plain,
    group_element(e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).

cnf(c_53,plain,
    group_element(e_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).

cnf(c_54,plain,
    group_element(e_4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).

cnf(c_55,plain,
    ~ equalish(e_1,e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).

cnf(c_56,plain,
    ~ equalish(e_1,e_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).

cnf(c_57,plain,
    ~ equalish(e_1,e_4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).

cnf(c_58,plain,
    ~ equalish(e_2,e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).

cnf(c_59,plain,
    ~ equalish(e_2,e_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).

cnf(c_60,plain,
    ~ equalish(e_2,e_4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_4) ).

cnf(c_63,plain,
    ~ equalish(e_3,e_4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).

cnf(c_64,plain,
    ~ equalish(e_4,e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_1) ).

cnf(c_65,plain,
    ~ equalish(e_4,e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_2) ).

cnf(c_67,plain,
    ( ~ group_element(X0)
    | ~ group_element(X1)
    | product1(X0,X1,e_1)
    | product1(X0,X1,e_2)
    | product1(X0,X1,e_3)
    | product1(X0,X1,e_4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_total_function1) ).

cnf(c_69,plain,
    ( ~ product1(X0,X1,X2)
    | ~ product1(X0,X3,X2)
    | equalish(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_right_cancellation) ).

cnf(c_70,plain,
    ( ~ product1(X0,X1,X2)
    | ~ product1(X3,X1,X2)
    | equalish(X0,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_left_cancellation) ).

cnf(c_71,plain,
    product1(X0,X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_idempotence) ).

cnf(c_73,plain,
    ( ~ product2(X0,X1,X2)
    | ~ product2(X0,X1,X3)
    | equalish(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_total_function2) ).

cnf(c_76,plain,
    product2(X0,X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_idempotence) ).

cnf(c_77,negated_conjecture,
    ( ~ product1(X0,X1,X2)
    | ~ product1(X2,X0,X3)
    | product2(X3,X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2a) ).

cnf(c_78,plain,
    product2(e_1,e_1,e_1),
    inference(instantiation,[status(thm)],[c_76]) ).

cnf(c_79,plain,
    product1(e_1,e_1,e_1),
    inference(instantiation,[status(thm)],[c_71]) ).

cnf(c_234,plain,
    ( ~ product1(X0,e_1,X1)
    | ~ product1(X0,e_2,X1) ),
    inference(resolution,[status(thm)],[c_55,c_69]) ).

cnf(c_235,plain,
    ( ~ product1(e_1,e_1,e_1)
    | ~ product1(e_1,e_2,e_1) ),
    inference(instantiation,[status(thm)],[c_234]) ).

cnf(c_250,plain,
    ( ~ product1(e_1,X0,X1)
    | ~ product1(e_2,X0,X1) ),
    inference(resolution,[status(thm)],[c_55,c_70]) ).

cnf(c_251,plain,
    ( ~ product1(e_1,e_1,e_1)
    | ~ product1(e_2,e_1,e_1) ),
    inference(instantiation,[status(thm)],[c_250]) ).

cnf(c_298,plain,
    ( ~ product1(e_1,X0,X1)
    | ~ product1(e_3,X0,X1) ),
    inference(resolution,[status(thm)],[c_56,c_70]) ).

cnf(c_299,plain,
    ( ~ product1(e_1,e_1,e_1)
    | ~ product1(e_3,e_1,e_1) ),
    inference(instantiation,[status(thm)],[c_298]) ).

cnf(c_306,plain,
    ( ~ product2(X0,X1,e_1)
    | ~ product2(X0,X1,e_4) ),
    inference(resolution,[status(thm)],[c_57,c_73]) ).

cnf(c_307,plain,
    ( ~ product2(e_1,e_1,e_1)
    | ~ product2(e_1,e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_306]) ).

cnf(c_330,plain,
    ( ~ product1(X0,e_1,X1)
    | ~ product1(X0,e_4,X1) ),
    inference(resolution,[status(thm)],[c_57,c_69]) ).

cnf(c_331,plain,
    ( ~ product1(e_1,e_1,e_1)
    | ~ product1(e_1,e_4,e_1) ),
    inference(instantiation,[status(thm)],[c_330]) ).

cnf(c_346,plain,
    ( ~ product1(e_1,X0,X1)
    | ~ product1(e_4,X0,X1) ),
    inference(resolution,[status(thm)],[c_57,c_70]) ).

cnf(c_347,plain,
    ( ~ product1(e_1,e_1,e_1)
    | ~ product1(e_4,e_1,e_1) ),
    inference(instantiation,[status(thm)],[c_346]) ).

cnf(c_1068,plain,
    ( ~ product2(X0,X1,e_1)
    | ~ product2(X0,X1,e_2)
    | equalish(e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_73]) ).

cnf(c_1071,plain,
    ( ~ product1(X0,e_1,X1)
    | ~ product1(X0,e_2,X1)
    | equalish(e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_69]) ).

cnf(c_1073,plain,
    ( ~ product1(e_1,X0,X1)
    | ~ product1(e_2,X0,X1)
    | equalish(e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_70]) ).

cnf(c_1077,plain,
    ( ~ product1(X0,e_1,X1)
    | ~ product1(X0,e_3,X1)
    | equalish(e_1,e_3) ),
    inference(instantiation,[status(thm)],[c_69]) ).

cnf(c_1080,plain,
    ( ~ product2(X0,X1,e_1)
    | ~ product2(X0,X1,e_4)
    | equalish(e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_73]) ).

cnf(c_1083,plain,
    ( ~ product1(X0,e_1,X1)
    | ~ product1(X0,e_4,X1)
    | equalish(e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_69]) ).

cnf(c_1085,plain,
    ( ~ product1(e_1,X0,X1)
    | ~ product1(e_4,X0,X1)
    | equalish(e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_70]) ).

cnf(c_1097,plain,
    ( ~ product1(e_2,X0,X1)
    | ~ product1(e_3,X0,X1)
    | equalish(e_2,e_3) ),
    inference(instantiation,[status(thm)],[c_70]) ).

cnf(c_1098,plain,
    ( ~ product2(X0,X1,e_2)
    | ~ product2(X0,X1,e_4)
    | equalish(e_2,e_4) ),
    inference(instantiation,[status(thm)],[c_73]) ).

cnf(c_1103,plain,
    ( ~ product1(e_2,X0,X1)
    | ~ product1(e_4,X0,X1)
    | equalish(e_2,e_4) ),
    inference(instantiation,[status(thm)],[c_70]) ).

cnf(c_1119,plain,
    ( ~ product1(X0,e_3,X1)
    | ~ product1(X0,e_4,X1)
    | equalish(e_3,e_4) ),
    inference(instantiation,[status(thm)],[c_69]) ).

cnf(c_1133,plain,
    ( ~ product1(e_2,X0,X1)
    | ~ product1(e_4,X0,X1)
    | equalish(e_4,e_2) ),
    inference(instantiation,[status(thm)],[c_70]) ).

cnf(c_1142,plain,
    ( ~ product2(e_2,e_2,e_1)
    | ~ product2(e_2,e_2,e_2)
    | equalish(e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_1068]) ).

cnf(c_1143,plain,
    product2(e_2,e_2,e_2),
    inference(instantiation,[status(thm)],[c_76]) ).

cnf(c_1145,plain,
    product1(e_2,e_2,e_2),
    inference(instantiation,[status(thm)],[c_71]) ).

cnf(c_1165,plain,
    ( ~ group_element(X0)
    | ~ group_element(e_2)
    | product1(e_2,X0,e_1)
    | product1(e_2,X0,e_2)
    | product1(e_2,X0,e_3)
    | product1(e_2,X0,e_4) ),
    inference(instantiation,[status(thm)],[c_67]) ).

cnf(c_1166,plain,
    ( ~ group_element(e_1)
    | ~ group_element(e_2)
    | product1(e_2,e_1,e_1)
    | product1(e_2,e_1,e_2)
    | product1(e_2,e_1,e_3)
    | product1(e_2,e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_1165]) ).

cnf(c_1174,plain,
    product1(e_3,e_3,e_3),
    inference(instantiation,[status(thm)],[c_71]) ).

cnf(c_1183,plain,
    ( ~ group_element(X0)
    | ~ group_element(e_3)
    | product1(X0,e_3,e_1)
    | product1(X0,e_3,e_2)
    | product1(X0,e_3,e_3)
    | product1(X0,e_3,e_4) ),
    inference(instantiation,[status(thm)],[c_67]) ).

cnf(c_1194,plain,
    ( ~ group_element(X0)
    | ~ group_element(e_3)
    | product1(e_3,X0,e_1)
    | product1(e_3,X0,e_2)
    | product1(e_3,X0,e_3)
    | product1(e_3,X0,e_4) ),
    inference(instantiation,[status(thm)],[c_67]) ).

cnf(c_1195,plain,
    ( ~ group_element(e_1)
    | ~ group_element(e_3)
    | product1(e_3,e_1,e_1)
    | product1(e_3,e_1,e_2)
    | product1(e_3,e_1,e_3)
    | product1(e_3,e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_1194]) ).

cnf(c_1198,plain,
    ( ~ product1(X0,e_4,X1)
    | ~ product1(e_4,X2,X0)
    | product2(X1,X2,e_4) ),
    inference(instantiation,[status(thm)],[c_77]) ).

cnf(c_1200,plain,
    ( ~ product2(e_4,e_4,e_1)
    | ~ product2(e_4,e_4,e_4)
    | equalish(e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_1080]) ).

cnf(c_1201,plain,
    product2(e_4,e_4,e_4),
    inference(instantiation,[status(thm)],[c_76]) ).

cnf(c_1203,plain,
    product1(e_4,e_4,e_4),
    inference(instantiation,[status(thm)],[c_71]) ).

cnf(c_1207,plain,
    ( ~ product1(X0,X1,X2)
    | ~ product1(X1,e_4,X0)
    | product2(X2,e_4,X1) ),
    inference(instantiation,[status(thm)],[c_77]) ).

cnf(c_1229,plain,
    ( ~ product1(e_4,X0,X1)
    | ~ group_element(X0)
    | ~ group_element(X2)
    | product2(X1,X2,X0)
    | product1(X0,X2,e_1)
    | product1(X0,X2,e_2)
    | product1(X0,X2,e_3) ),
    inference(superposition,[status(thm)],[c_67,c_77]) ).

cnf(c_1258,plain,
    ( ~ group_element(X0)
    | ~ group_element(e_4)
    | product1(X0,e_4,e_1)
    | product1(X0,e_4,e_2)
    | product1(X0,e_4,e_3)
    | product1(X0,e_4,e_4) ),
    inference(instantiation,[status(thm)],[c_67]) ).

cnf(c_1259,plain,
    ( ~ group_element(e_1)
    | ~ group_element(e_4)
    | product1(e_1,e_4,e_1)
    | product1(e_1,e_4,e_2)
    | product1(e_1,e_4,e_3)
    | product1(e_1,e_4,e_4) ),
    inference(instantiation,[status(thm)],[c_1258]) ).

cnf(c_1282,plain,
    ( ~ group_element(X0)
    | ~ group_element(X1)
    | ~ group_element(e_4)
    | product1(X0,X1,e_1)
    | product1(X0,X1,e_2)
    | product1(X0,X1,e_3)
    | product2(e_4,X1,X0)
    | product1(e_4,X0,e_1)
    | product1(e_4,X0,e_2)
    | product1(e_4,X0,e_3) ),
    inference(superposition,[status(thm)],[c_67,c_1229]) ).

cnf(c_1283,plain,
    ( ~ group_element(X0)
    | ~ group_element(X1)
    | product1(X0,X1,e_1)
    | product1(X0,X1,e_2)
    | product1(X0,X1,e_3)
    | product2(e_4,X1,X0)
    | product1(e_4,X0,e_1)
    | product1(e_4,X0,e_2)
    | product1(e_4,X0,e_3) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_1282,c_54]) ).

cnf(c_1319,plain,
    ( ~ group_element(X0)
    | ~ group_element(e_4)
    | product1(e_4,X0,e_1)
    | product1(e_4,X0,e_2)
    | product1(e_4,X0,e_3)
    | product1(e_4,X0,e_4) ),
    inference(instantiation,[status(thm)],[c_67]) ).

cnf(c_1320,plain,
    ( ~ group_element(e_1)
    | ~ group_element(e_4)
    | product1(e_4,e_1,e_1)
    | product1(e_4,e_1,e_2)
    | product1(e_4,e_1,e_3)
    | product1(e_4,e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_1319]) ).

cnf(c_1620,plain,
    ( ~ product1(e_2,e_1,e_2)
    | ~ product1(e_2,e_2,e_2)
    | equalish(e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_1071]) ).

cnf(c_1622,plain,
    ( ~ product1(e_1,e_2,e_2)
    | ~ product1(e_2,e_2,e_2)
    | equalish(e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_1073]) ).

cnf(c_1779,plain,
    ( ~ product1(e_3,e_1,e_3)
    | ~ product1(e_3,e_3,e_3)
    | equalish(e_1,e_3) ),
    inference(instantiation,[status(thm)],[c_1077]) ).

cnf(c_1796,plain,
    ( ~ product1(X0,X1,X0)
    | equalish(X0,X1) ),
    inference(superposition,[status(thm)],[c_71,c_69]) ).

cnf(c_1830,plain,
    ( ~ product1(X0,X1,X1)
    | equalish(X1,X0) ),
    inference(superposition,[status(thm)],[c_71,c_70]) ).

cnf(c_1863,plain,
    ( ~ product2(e_4,e_4,e_2)
    | ~ product2(e_4,e_4,e_4)
    | equalish(e_2,e_4) ),
    inference(instantiation,[status(thm)],[c_1098]) ).

cnf(c_1886,plain,
    ( ~ product2(e_4,X0,X1)
    | ~ group_element(X0)
    | ~ group_element(X2)
    | product1(X2,X0,e_1)
    | product1(X2,X0,e_2)
    | product1(X2,X0,e_3)
    | product1(e_4,X2,e_1)
    | product1(e_4,X2,e_2)
    | product1(e_4,X2,e_3)
    | equalish(X2,X1) ),
    inference(superposition,[status(thm)],[c_1283,c_73]) ).

cnf(c_1972,plain,
    ( ~ product1(e_4,e_3,e_4)
    | ~ product1(e_4,e_4,e_4)
    | equalish(e_3,e_4) ),
    inference(instantiation,[status(thm)],[c_1119]) ).

cnf(c_1974,plain,
    ( ~ product1(e_4,e_1,e_4)
    | ~ product1(e_4,e_4,e_4)
    | equalish(e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_1083]) ).

cnf(c_1979,plain,
    ( ~ product1(e_2,e_4,e_4)
    | ~ product1(e_4,e_4,e_4)
    | equalish(e_2,e_4) ),
    inference(instantiation,[status(thm)],[c_1103]) ).

cnf(c_1980,plain,
    ( ~ product1(e_1,e_4,e_4)
    | ~ product1(e_4,e_4,e_4)
    | equalish(e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_1085]) ).

cnf(c_2288,plain,
    ( ~ group_element(X0)
    | ~ group_element(e_4)
    | product1(X0,e_4,e_1)
    | product1(X0,e_4,e_2)
    | product1(X0,e_4,e_3)
    | product1(e_4,X0,e_1)
    | product1(e_4,X0,e_2)
    | product1(e_4,X0,e_3)
    | equalish(X0,e_4) ),
    inference(superposition,[status(thm)],[c_76,c_1886]) ).

cnf(c_2292,plain,
    ( ~ group_element(X0)
    | product1(X0,e_4,e_1)
    | product1(X0,e_4,e_2)
    | product1(X0,e_4,e_3)
    | product1(e_4,X0,e_1)
    | product1(e_4,X0,e_2)
    | product1(e_4,X0,e_3)
    | equalish(X0,e_4) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_2288,c_54]) ).

cnf(c_2450,plain,
    ( ~ group_element(e_3)
    | product1(e_3,e_4,e_1)
    | product1(e_3,e_4,e_2)
    | product1(e_4,e_3,e_1)
    | product1(e_4,e_3,e_2)
    | product1(e_4,e_3,e_3)
    | equalish(e_3,e_4) ),
    inference(superposition,[status(thm)],[c_2292,c_1796]) ).

cnf(c_2453,plain,
    ( product1(e_3,e_4,e_1)
    | product1(e_3,e_4,e_2)
    | product1(e_4,e_3,e_1)
    | product1(e_4,e_3,e_2)
    | product1(e_4,e_3,e_3) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_2450,c_63,c_53]) ).

cnf(c_2662,plain,
    ( ~ group_element(e_2)
    | ~ group_element(e_4)
    | product1(e_2,e_4,e_1)
    | product1(e_2,e_4,e_2)
    | product1(e_2,e_4,e_3)
    | product1(e_2,e_4,e_4) ),
    inference(instantiation,[status(thm)],[c_1165]) ).

cnf(c_3041,plain,
    ( ~ group_element(e_3)
    | ~ group_element(e_4)
    | product1(e_4,e_3,e_1)
    | product1(e_4,e_3,e_2)
    | product1(e_4,e_3,e_3)
    | product1(e_4,e_3,e_4) ),
    inference(instantiation,[status(thm)],[c_1183]) ).

cnf(c_3109,plain,
    ( product1(e_4,e_3,e_1)
    | product1(e_4,e_3,e_2)
    | product1(e_4,e_3,e_3) ),
    inference(global_subsumption_just,[status(thm)],[c_2453,c_54,c_53,c_63,c_1203,c_1972,c_3041]) ).

cnf(c_3122,plain,
    ( product1(e_4,e_3,e_1)
    | product1(e_4,e_3,e_2)
    | equalish(e_3,e_4) ),
    inference(superposition,[status(thm)],[c_3109,c_1830]) ).

cnf(c_3123,plain,
    ( product1(e_4,e_3,e_1)
    | product1(e_4,e_3,e_2) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3122,c_63]) ).

cnf(c_3282,plain,
    ( ~ product1(e_2,X0,X1)
    | ~ product1(X0,e_4,e_2)
    | product2(X1,e_4,X0) ),
    inference(instantiation,[status(thm)],[c_1207]) ).

cnf(c_3350,plain,
    ( ~ product1(e_2,e_4,X0)
    | ~ product1(e_4,X1,e_2)
    | product2(X0,X1,e_4) ),
    inference(instantiation,[status(thm)],[c_1198]) ).

cnf(c_3351,plain,
    ( ~ product1(e_2,e_4,e_1)
    | ~ product1(e_4,e_1,e_2)
    | product2(e_1,e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_3350]) ).

cnf(c_3435,plain,
    ( ~ product1(e_2,e_4,X0)
    | product2(X0,e_3,e_4)
    | product1(e_4,e_3,e_1) ),
    inference(superposition,[status(thm)],[c_3123,c_77]) ).

cnf(c_3723,plain,
    ( ~ product1(X0,e_4,e_2)
    | ~ product1(e_2,X0,e_4)
    | product2(e_4,e_4,X0) ),
    inference(instantiation,[status(thm)],[c_3282]) ).

cnf(c_3724,plain,
    ( ~ product1(e_1,e_4,e_2)
    | ~ product1(e_2,e_1,e_4)
    | product2(e_4,e_4,e_1) ),
    inference(instantiation,[status(thm)],[c_3723]) ).

cnf(c_3813,plain,
    ( ~ group_element(e_2)
    | ~ group_element(e_4)
    | product1(e_2,e_4,e_1)
    | product1(e_2,e_4,e_2)
    | product1(e_2,e_4,e_3)
    | product1(e_4,e_3,e_1)
    | product2(e_4,e_3,e_4) ),
    inference(superposition,[status(thm)],[c_67,c_3435]) ).

cnf(c_3815,plain,
    ( product1(e_2,e_4,e_1)
    | product1(e_2,e_4,e_2)
    | product1(e_2,e_4,e_3)
    | product1(e_4,e_3,e_1)
    | product2(e_4,e_3,e_4) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3813,c_54,c_52]) ).

cnf(c_3972,plain,
    ( ~ product1(e_2,X0,e_4)
    | ~ product1(e_3,X0,e_4)
    | equalish(e_2,e_3) ),
    inference(instantiation,[status(thm)],[c_1097]) ).

cnf(c_3975,plain,
    ( ~ product1(e_2,e_1,e_4)
    | ~ product1(e_3,e_1,e_4)
    | equalish(e_2,e_3) ),
    inference(instantiation,[status(thm)],[c_3972]) ).

cnf(c_3988,plain,
    ( product1(e_2,e_4,e_1)
    | product1(e_2,e_4,e_2)
    | product1(e_2,e_4,e_3) ),
    inference(global_subsumption_just,[status(thm)],[c_3815,c_54,c_52,c_60,c_1203,c_1979,c_2662]) ).

cnf(c_3996,plain,
    ( ~ product1(X0,e_4,e_3)
    | product1(e_2,e_4,e_1)
    | product1(e_2,e_4,e_2)
    | equalish(e_2,X0) ),
    inference(superposition,[status(thm)],[c_3988,c_70]) ).

cnf(c_3997,plain,
    ( ~ product1(e_2,X0,e_3)
    | product1(e_2,e_4,e_1)
    | product1(e_2,e_4,e_2)
    | equalish(e_4,X0) ),
    inference(superposition,[status(thm)],[c_3988,c_69]) ).

cnf(c_3999,plain,
    ( ~ product1(e_3,e_2,X0)
    | product2(X0,e_4,e_2)
    | product1(e_2,e_4,e_1)
    | product1(e_2,e_4,e_2) ),
    inference(superposition,[status(thm)],[c_3988,c_77]) ).

cnf(c_4021,plain,
    ( ~ product1(e_2,e_1,e_3)
    | product1(e_2,e_4,e_1)
    | product1(e_2,e_4,e_2)
    | equalish(e_4,e_1) ),
    inference(instantiation,[status(thm)],[c_3997]) ).

cnf(c_4022,plain,
    ( ~ product1(e_1,e_4,e_3)
    | product1(e_2,e_4,e_1)
    | product1(e_2,e_4,e_2)
    | equalish(e_2,e_1) ),
    inference(instantiation,[status(thm)],[c_3996]) ).

cnf(c_4037,plain,
    ( ~ product1(e_2,X0,e_3)
    | ~ product1(e_4,X0,e_3)
    | equalish(e_4,e_2) ),
    inference(instantiation,[status(thm)],[c_1133]) ).

cnf(c_4046,plain,
    ( ~ product1(e_2,e_1,e_3)
    | ~ product1(e_4,e_1,e_3)
    | equalish(e_4,e_2) ),
    inference(instantiation,[status(thm)],[c_4037]) ).

cnf(c_4099,plain,
    ( product1(e_2,e_4,e_1)
    | product1(e_2,e_4,e_2) ),
    inference(global_subsumption_just,[status(thm)],[c_3999,c_54,c_52,c_51,c_79,c_64,c_58,c_57,c_55,c_251,c_331,c_1145,c_1166,c_1200,c_1201,c_1203,c_1259,c_1620,c_1980,c_3724,c_4021,c_4022]) ).

cnf(c_4109,plain,
    ( product1(e_2,e_4,e_1)
    | equalish(e_2,e_4) ),
    inference(superposition,[status(thm)],[c_4099,c_1796]) ).

cnf(c_4111,plain,
    product1(e_2,e_4,e_1),
    inference(forward_subsumption_resolution,[status(thm)],[c_4109,c_60]) ).

cnf(c_4116,plain,
    ( ~ product1(e_1,e_2,X0)
    | product2(X0,e_4,e_2) ),
    inference(superposition,[status(thm)],[c_4111,c_77]) ).

cnf(c_4172,plain,
    ( ~ group_element(e_1)
    | ~ group_element(e_2)
    | product1(e_1,e_2,e_1)
    | product1(e_1,e_2,e_2)
    | product1(e_1,e_2,e_3)
    | product2(e_4,e_4,e_2) ),
    inference(superposition,[status(thm)],[c_67,c_4116]) ).

cnf(c_4173,plain,
    ( product1(e_1,e_2,e_1)
    | product1(e_1,e_2,e_2)
    | product1(e_1,e_2,e_3)
    | product2(e_4,e_4,e_2) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4172,c_52,c_51]) ).

cnf(c_4484,plain,
    product1(e_1,e_2,e_3),
    inference(global_subsumption_just,[status(thm)],[c_4173,c_79,c_60,c_55,c_235,c_1145,c_1201,c_1622,c_1863,c_4173]) ).

cnf(c_4489,plain,
    ( ~ product1(e_3,e_1,X0)
    | product2(X0,e_2,e_1) ),
    inference(superposition,[status(thm)],[c_4484,c_77]) ).

cnf(c_4570,plain,
    ( ~ group_element(e_1)
    | ~ group_element(e_3)
    | product1(e_3,e_1,e_1)
    | product1(e_3,e_1,e_2)
    | product1(e_3,e_1,e_3)
    | product2(e_4,e_2,e_1) ),
    inference(superposition,[status(thm)],[c_67,c_4489]) ).

cnf(c_4571,plain,
    ( product1(e_3,e_1,e_1)
    | product1(e_3,e_1,e_2)
    | product1(e_3,e_1,e_3)
    | product2(e_4,e_2,e_1) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4570,c_53,c_51]) ).

cnf(c_4689,plain,
    product1(e_3,e_1,e_2),
    inference(global_subsumption_just,[status(thm)],[c_4571,c_54,c_53,c_52,c_51,c_78,c_79,c_65,c_59,c_57,c_56,c_55,c_251,c_299,c_307,c_347,c_1145,c_1166,c_1174,c_1195,c_1203,c_1320,c_1620,c_1779,c_1974,c_3351,c_3975,c_4046,c_4111]) ).

cnf(c_4696,plain,
    product2(e_2,e_2,e_1),
    inference(superposition,[status(thm)],[c_4689,c_4489]) ).

cnf(c_4712,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_4696,c_1143,c_1142,c_55]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP124-9.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.13/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n002.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 21:23:35 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.08/1.15  % SZS status Started for theBenchmark.p
% 3.08/1.15  % SZS status Unsatisfiable for theBenchmark.p
% 3.08/1.15  
% 3.08/1.15  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.08/1.15  
% 3.08/1.15  ------  iProver source info
% 3.08/1.15  
% 3.08/1.15  git: date: 2023-05-31 18:12:56 +0000
% 3.08/1.15  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.08/1.15  git: non_committed_changes: false
% 3.08/1.15  git: last_make_outside_of_git: false
% 3.08/1.15  
% 3.08/1.15  ------ Parsing...successful
% 3.08/1.15  
% 3.08/1.15  ------  preprocesses with Option_epr_non_horn_non_eq
% 3.08/1.15  
% 3.08/1.15  
% 3.08/1.15  ------ Preprocessing... sf_s  rm: 2 0s  sf_e  pe_s  pe_e  sf_s  rm: 0 0s  sf_e  pe_s  pe_e 
% 3.08/1.15  
% 3.08/1.15  ------ Preprocessing...------  preprocesses with Option_epr_non_horn_non_eq
% 3.08/1.15   gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.08/1.15  ------ Proving...
% 3.08/1.15  ------ Problem Properties 
% 3.08/1.15  
% 3.08/1.15  
% 3.08/1.15  clauses                                 27
% 3.08/1.15  conjectures                             1
% 3.08/1.15  EPR                                     27
% 3.08/1.15  Horn                                    25
% 3.08/1.15  unary                                   18
% 3.08/1.15  binary                                  0
% 3.08/1.15  lits                                    51
% 3.08/1.15  lits eq                                 0
% 3.08/1.15  fd_pure                                 0
% 3.08/1.15  fd_pseudo                               0
% 3.08/1.15  fd_cond                                 0
% 3.08/1.15  fd_pseudo_cond                          0
% 3.08/1.15  AC symbols                              0
% 3.08/1.15  
% 3.08/1.15  ------ Schedule EPR non Horn non eq is on
% 3.08/1.15  
% 3.08/1.15  ------ no equalities: superposition off 
% 3.08/1.15  
% 3.08/1.15  ------ Input Options "--resolution_flag false" Time Limit: 70.
% 3.08/1.15  
% 3.08/1.15  
% 3.08/1.15  ------ 
% 3.08/1.15  Current options:
% 3.08/1.15  ------ 
% 3.08/1.15  
% 3.08/1.15  
% 3.08/1.15  
% 3.08/1.15  
% 3.08/1.15  ------ Proving...
% 3.08/1.15  
% 3.08/1.15  
% 3.08/1.15  % SZS status Unsatisfiable for theBenchmark.p
% 3.08/1.15  
% 3.08/1.15  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.08/1.16  
% 3.08/1.16  
%------------------------------------------------------------------------------