%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP124-2.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:41:53 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.46s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 19
% Syntax : Number of clauses : 112 ( 50 unt; 38 nHn; 110 RR)
% Number of literals : 256 ( 0 equ; 104 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% 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 : 80 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_total_function1,axiom,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_4)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
cnf(product_left_cancellation,axiom,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(element_4,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
cnf(product_right_cancellation,axiom,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
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_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(qg2_2,negated_conjecture,
( ~ product(X6,X4,X5)
| ~ product(X6,X1,X2)
| ~ product(X4,X5,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg2_2) ).
cnf(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
cnf(e_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_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(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(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_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
cnf(c_0_19,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_4)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
inference(fof_simplification,[status(thm)],[product_total_function1]) ).
cnf(c_0_20,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
inference(fof_simplification,[status(thm)],[product_left_cancellation]) ).
cnf(c_0_21,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_4)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
c_0_19 ).
cnf(c_0_22,axiom,
group_element(e_4),
element_4 ).
cnf(c_0_23,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
inference(fof_simplification,[status(thm)],[product_right_cancellation]) ).
cnf(c_0_24,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_20 ).
cnf(c_0_25,axiom,
product(X1,X1,X1),
product_idempotence ).
cnf(c_0_26,plain,
( ~ group_element(X1)
| product(X1,e_4,e_1)
| product(X1,e_4,e_2)
| product(X1,e_4,e_3)
| product(X1,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_28,plain,
~ equalish(e_1,e_4),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_4]) ).
cnf(c_0_29,negated_conjecture,
( ~ product(X6,X4,X5)
| ~ product(X6,X1,X2)
| ~ product(X4,X5,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X5) ),
inference(fof_simplification,[status(thm)],[qg2_2]) ).
cnf(c_0_30,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_23 ).
cnf(c_0_31,plain,
( ~ product(X1,X2,X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
( product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
~ equalish(e_1,e_4),
c_0_28 ).
cnf(c_0_34,plain,
~ equalish(e_4,e_1),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_1]) ).
cnf(c_0_35,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_36,negated_conjecture,
( ~ product(X6,X4,X5)
| ~ product(X6,X1,X2)
| ~ product(X4,X5,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X5) ),
c_0_29 ).
cnf(c_0_37,plain,
( ~ product(X2,X1,X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_25]) ).
cnf(c_0_38,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_39,plain,
~ equalish(e_4,e_1),
c_0_34 ).
cnf(c_0_40,plain,
~ equalish(e_3,e_1),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_1]) ).
cnf(c_0_41,plain,
( ~ group_element(X1)
| product(X1,e_3,e_1)
| product(X1,e_3,e_2)
| product(X1,e_3,e_3)
| product(X1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_21,c_0_35]) ).
cnf(c_0_42,plain,
~ equalish(e_3,e_4),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_4]) ).
cnf(c_0_43,plain,
( ~ group_element(X1)
| product(X1,e_1,e_1)
| product(X1,e_1,e_2)
| product(X1,e_1,e_3)
| product(X1,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_21,c_0_27]) ).
cnf(c_0_44,negated_conjecture,
( ~ product(X3,X1,X4)
| ~ product(X2,X2,X4)
| ~ product(X2,X3,X1)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_25]) ).
cnf(c_0_45,plain,
( product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_46,plain,
~ equalish(e_3,e_1),
c_0_40 ).
cnf(c_0_47,plain,
( product(e_4,e_3,e_4)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_41,c_0_22]) ).
cnf(c_0_48,plain,
~ equalish(e_3,e_4),
c_0_42 ).
cnf(c_0_49,plain,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_43,c_0_22]) ).
cnf(c_0_50,negated_conjecture,
( ~ product(e_4,e_3,X1)
| ~ product(e_1,e_1,X1)
| product(e_1,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
cnf(c_0_51,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_47]),c_0_48]) ).
cnf(c_0_52,plain,
~ equalish(e_4,e_3),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_3]) ).
cnf(c_0_53,plain,
( product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_49]),c_0_33]) ).
cnf(c_0_54,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_25])]) ).
cnf(c_0_55,plain,
~ equalish(e_4,e_3),
c_0_52 ).
cnf(c_0_56,plain,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_53]),c_0_39]) ).
cnf(c_0_57,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_58,plain,
~ equalish(e_2,e_4),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_4]) ).
cnf(c_0_59,negated_conjecture,
( product(e_4,e_3,e_2)
| product(e_1,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_54]),c_0_55]) ).
cnf(c_0_60,negated_conjecture,
( ~ product(e_1,e_3,X1)
| ~ product(e_4,e_4,X1)
| product(e_4,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_56]),c_0_48]) ).
cnf(c_0_61,plain,
~ equalish(e_1,e_3),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_3]) ).
cnf(c_0_62,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_26,c_0_57]) ).
cnf(c_0_63,plain,
~ equalish(e_2,e_4),
c_0_58 ).
cnf(c_0_64,plain,
~ equalish(e_1,e_2),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_2]) ).
cnf(c_0_65,negated_conjecture,
( ~ product(e_4,X1,e_2)
| product(e_1,e_4,e_2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_30,c_0_59]) ).
cnf(c_0_66,negated_conjecture,
( ~ product(e_1,e_3,e_4)
| product(e_4,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_60,c_0_25]) ).
cnf(c_0_67,plain,
~ equalish(e_1,e_3),
c_0_61 ).
cnf(c_0_68,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_62]),c_0_63]) ).
cnf(c_0_69,plain,
~ equalish(e_1,e_2),
c_0_64 ).
cnf(c_0_70,plain,
~ equalish(e_2,e_1),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_1]) ).
cnf(c_0_71,negated_conjecture,
( ~ product(e_1,e_3,e_4)
| product(e_1,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]) ).
cnf(c_0_72,negated_conjecture,
( ~ product(e_4,e_1,X1)
| ~ product(e_2,e_2,X1)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_68]),c_0_69]) ).
cnf(c_0_73,plain,
~ equalish(e_2,e_1),
c_0_70 ).
cnf(c_0_74,negated_conjecture,
( ~ product(X1,e_4,e_2)
| ~ product(e_1,e_3,e_4)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_24,c_0_71]) ).
cnf(c_0_75,negated_conjecture,
( ~ product(e_4,e_1,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_72,c_0_25]) ).
cnf(c_0_76,negated_conjecture,
( ~ product(e_2,e_4,e_2)
| ~ product(e_1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_77,negated_conjecture,
( ~ product(e_1,e_3,e_4)
| product(e_2,e_4,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_66]),c_0_76]) ).
cnf(c_0_78,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_41,c_0_27]) ).
cnf(c_0_79,negated_conjecture,
( product(e_2,e_4,e_3)
| 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_77,c_0_78]) ).
cnf(c_0_80,negated_conjecture,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_2,e_4,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_79]),c_0_46]) ).
cnf(c_0_81,negated_conjecture,
( product(e_2,e_4,e_3)
| product(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_80]),c_0_67]) ).
cnf(c_0_82,negated_conjecture,
( ~ product(X1,e_3,e_2)
| product(e_1,e_4,e_2)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_24,c_0_59]) ).
cnf(c_0_83,negated_conjecture,
( ~ product(e_1,X1,e_2)
| product(e_2,e_4,e_3)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_30,c_0_81]) ).
cnf(c_0_84,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_2,e_4,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_81]),c_0_33]) ).
cnf(c_0_85,plain,
( ~ product(X1,e_4,e_3)
| product(e_1,e_4,e_2)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_24,c_0_45]) ).
cnf(c_0_86,negated_conjecture,
product(e_2,e_4,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_55]) ).
cnf(c_0_87,plain,
~ equalish(e_3,e_2),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_2]) ).
cnf(c_0_88,negated_conjecture,
product(e_1,e_4,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_73]) ).
cnf(c_0_89,plain,
( product(e_3,e_4,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_26,c_0_35]) ).
cnf(c_0_90,plain,
~ equalish(e_3,e_2),
c_0_87 ).
cnf(c_0_91,negated_conjecture,
( ~ product(X1,e_4,e_3)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_24,c_0_86]) ).
cnf(c_0_92,negated_conjecture,
( ~ product(X1,e_4,e_2)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_24,c_0_88]) ).
cnf(c_0_93,plain,
( product(e_3,e_4,e_1)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_89]),c_0_48]) ).
cnf(c_0_94,negated_conjecture,
~ product(e_3,e_4,e_3),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_95,negated_conjecture,
~ product(e_3,e_4,e_2),
inference(spm,[status(thm)],[c_0_46,c_0_92]) ).
cnf(c_0_96,plain,
product(e_3,e_4,e_1),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_93,c_0_94]),c_0_95]) ).
cnf(c_0_97,negated_conjecture,
( ~ product(e_4,e_1,X1)
| ~ product(e_3,e_3,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_96]),c_0_67]) ).
cnf(c_0_98,negated_conjecture,
( ~ product(e_4,e_1,X1)
| ~ product(e_3,e_3,X1)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_93]),c_0_67]) ).
cnf(c_0_99,negated_conjecture,
product(e_4,e_1,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_56]),c_0_25])]) ).
cnf(c_0_100,negated_conjecture,
( ~ product(e_4,e_1,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_98,c_0_25]) ).
cnf(c_0_101,plain,
( ~ product(e_3,X1,e_1)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_30,c_0_96]) ).
cnf(c_0_102,negated_conjecture,
( ~ product(X1,e_1,e_2)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_24,c_0_99]) ).
cnf(c_0_103,negated_conjecture,
( ~ product(X3,X1,X2)
| ~ product(e_3,X3,X1)
| ~ product(e_4,e_1,X2)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_36,c_0_93]) ).
cnf(c_0_104,negated_conjecture,
( product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_4,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_100,c_0_56]) ).
cnf(c_0_105,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_43,c_0_35]) ).
cnf(c_0_106,plain,
~ product(e_3,e_1,e_1),
inference(spm,[status(thm)],[c_0_33,c_0_101]) ).
cnf(c_0_107,negated_conjecture,
~ product(e_3,e_1,e_2),
inference(spm,[status(thm)],[c_0_48,c_0_102]) ).
cnf(c_0_108,negated_conjecture,
( ~ product(X2,X1,e_2)
| ~ product(e_3,X2,X1)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_3)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_109,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_4) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_105,c_0_106]),c_0_107]) ).
cnf(c_0_110,negated_conjecture,
product(e_3,e_1,e_3),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_88])]),c_0_39]),c_0_94]),c_0_95]) ).
cnf(c_0_111,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_110]),c_0_67]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP124-2.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 19:58:40 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.46 % Version: 3.5.1
% 0.11/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.46 % Starting sh5l with 300s (1) cores
% 0.11/0.46 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 37721 completed with status 0
% 0.11/0.46 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.11/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.46 % No SInE strategy applied
% 0.11/0.46 % Search class: FGHNF-FFSM00-SFFFFFNN
% 0.11/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.11/0.46 % Starting G----_404_C05_02_F1_SE_CS_SP_PS_RG_S04AI with 136s (1) cores
% 0.11/0.46 % Starting new_bool_3 with 136s (1) cores
% 0.11/0.46 % Starting new_bool_1 with 136s (1) cores
% 0.11/0.46 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 37728 completed with status 0
% 0.11/0.46 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.11/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.46 % No SInE strategy applied
% 0.11/0.46 % Search class: FGHNF-FFSM00-SFFFFFNN
% 0.11/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.11/0.46 % Preprocessing time : 0.001 s
% 0.11/0.46 % Presaturation interreduction done
% 0.11/0.46
% 0.11/0.46 % Proof found!
% 0.11/0.46 % SZS status Unsatisfiable
% 0.11/0.46 % SZS output start CNFRefutation
% See solution above
% 0.11/0.46 % Parsed axioms : 33
% 0.11/0.46 % Removed by relevancy pruning/SinE : 0
% 0.11/0.46 % Initial clauses : 33
% 0.11/0.46 % Removed in clause preprocessing : 0
% 0.11/0.46 % Initial clauses in saturation : 33
% 0.11/0.46 % Processed clauses : 436
% 0.11/0.46 % ...of these trivial : 1
% 0.11/0.46 % ...subsumed : 85
% 0.11/0.46 % ...remaining for further processing : 350
% 0.11/0.46 % Other redundant clauses eliminated : 0
% 0.11/0.46 % Clauses deleted for lack of memory : 0
% 0.11/0.46 % Backward-subsumed : 136
% 0.11/0.46 % Backward-rewritten : 36
% 0.11/0.46 % Generated clauses : 852
% 0.11/0.46 % ...of the previous two non-redundant : 745
% 0.11/0.46 % ...aggressively subsumed : 0
% 0.11/0.46 % Contextual simplify-reflections : 3
% 0.11/0.46 % Paramodulations : 839
% 0.11/0.46 % Factorizations : 0
% 0.11/0.46 % NegExts : 0
% 0.11/0.46 % Equation resolutions : 0
% 0.11/0.46 % Disequality decompositions : 0
% 0.11/0.46 % Total rewrite steps : 148
% 0.11/0.46 % ...of those cached : 133
% 0.11/0.46 % Propositional unsat checks : 0
% 0.11/0.46 % Propositional check models : 0
% 0.11/0.46 % Propositional check unsatisfiable : 0
% 0.11/0.46 % Propositional clauses : 0
% 0.11/0.46 % Propositional clauses after purity: 0
% 0.11/0.46 % Propositional unsat core size : 0
% 0.11/0.46 % Propositional preprocessing time : 0.000
% 0.11/0.46 % Propositional encoding time : 0.000
% 0.11/0.46 % Propositional solver time : 0.000
% 0.11/0.46 % Success case prop preproc time : 0.000
% 0.11/0.46 % Success case prop encoding time : 0.000
% 0.11/0.46 % Success case prop solver time : 0.000
% 0.11/0.46 % Current number of processed clauses : 132
% 0.11/0.46 % Positive orientable unit clauses : 22
% 0.11/0.46 % Positive unorientable unit clauses: 0
% 0.11/0.46 % Negative unit clauses : 50
% 0.11/0.46 % Non-unit-clauses : 60
% 0.11/0.46 % Current number of unprocessed clauses: 309
% 0.11/0.46 % ...number of literals in the above : 1498
% 0.11/0.46 % Current number of archived formulas : 0
% 0.11/0.46 % Current number of archived clauses : 218
% 0.11/0.46 % Clause-clause subsumption calls (NU) : 5987
% 0.11/0.46 % Rec. Clause-clause subsumption calls : 3404
% 0.11/0.46 % Non-unit clause-clause subsumptions : 137
% 0.11/0.46 % Unit Clause-clause subsumption calls : 1036
% 0.11/0.46 % Rewrite failures with RHS unbound : 0
% 0.11/0.46 % BW rewrite match attempts : 48
% 0.11/0.46 % BW rewrite match successes : 6
% 0.11/0.46 % Condensation attempts : 0
% 0.11/0.46 % Condensation successes : 0
% 0.11/0.46 % Termbank termtop insertions : 13124
% 0.11/0.46 % Search garbage collected termcells : 65
% 0.11/0.46
% 0.11/0.46 % -------------------------------------------------
% 0.11/0.46 % User time : 0.023 s
% 0.11/0.46 % System time : 0.003 s
% 0.11/0.47 % Total time : 0.026 s
% 0.11/0.47 % Maximum resident set size: 3648 pages
% 0.11/0.47
% 0.11/0.47 % -------------------------------------------------
% 0.11/0.47 % User time : 0.104 s
% 0.11/0.47 % System time : 0.017 s
% 0.11/0.47 % Total time : 0.122 s
% 0.11/0.47 % Maximum resident set size: 4608 pages
% 0.11/0.47 % E exiting
%------------------------------------------------------------------------------