%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : BOO073-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:07:05 PM UTC 2026
% Result : Unsatisfiable 40.29s 8.55s
% Output : CNFRefutation 40.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 2
% Syntax : Number of clauses : 96 ( 96 unt; 0 nHn; 5 RR)
% Number of literals : 96 ( 95 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 220 ( 48 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(dn1,axiom,
inverse(add(inverse(add(inverse(add(X1,X2)),X3)),inverse(add(X1,inverse(add(inverse(X3),inverse(add(X3,X4)))))))) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dn1) ).
cnf(huntinton_2,negated_conjecture,
add(add(a,b),c) != add(a,add(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',huntinton_2) ).
cnf(c_0_2,axiom,
inverse(add(inverse(add(inverse(add(X1,X2)),X3)),inverse(add(X1,inverse(add(inverse(X3),inverse(add(X3,X4)))))))) = X3,
dn1 ).
cnf(c_0_3,plain,
inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(X1)),X2)),X1)),X3)),inverse(X1))),X1)) = inverse(X1),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
inverse(add(inverse(add(X1,inverse(X1))),X1)) = inverse(X1),
inference(spm,[status(thm)],[c_0_3,c_0_2]) ).
cnf(c_0_5,plain,
inverse(add(inverse(X1),inverse(add(X1,inverse(add(inverse(X1),inverse(add(X1,X2)))))))) = X1,
inference(spm,[status(thm)],[c_0_2,c_0_4]) ).
cnf(c_0_6,plain,
inverse(add(inverse(add(inverse(add(X1,X2)),X3)),inverse(add(X1,X3)))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_5]) ).
cnf(c_0_7,plain,
inverse(add(inverse(add(X1,X2)),inverse(add(inverse(X1),X2)))) = X2,
inference(spm,[status(thm)],[c_0_6,c_0_5]) ).
cnf(c_0_8,plain,
inverse(add(inverse(X1),inverse(add(X1,X1)))) = X1,
inference(spm,[status(thm)],[c_0_5,c_0_5]) ).
cnf(c_0_9,plain,
inverse(add(inverse(add(X1,inverse(add(X1,X1)))),X1)) = inverse(add(X1,X1)),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,plain,
inverse(add(inverse(add(X1,X1)),inverse(add(X1,X1)))) = X1,
inference(spm,[status(thm)],[c_0_6,c_0_9]) ).
cnf(c_0_11,plain,
inverse(add(inverse(add(add(X1,X1),inverse(add(X1,X1)))),X1)) = inverse(add(X1,X1)),
inference(spm,[status(thm)],[c_0_7,c_0_10]) ).
cnf(c_0_12,plain,
inverse(add(inverse(add(X1,X1)),inverse(add(add(X1,X1),X1)))) = X1,
inference(spm,[status(thm)],[c_0_6,c_0_11]) ).
cnf(c_0_13,plain,
add(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_12]),c_0_12]) ).
cnf(c_0_14,plain,
inverse(add(inverse(add(inverse(add(X1,X2)),X1)),inverse(X1))) = X1,
inference(spm,[status(thm)],[c_0_6,c_0_13]) ).
cnf(c_0_15,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_13]),c_0_13]) ).
cnf(c_0_16,plain,
inverse(add(X1,add(X2,X1))) = inverse(add(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_6]),c_0_15]) ).
cnf(c_0_17,plain,
add(X1,add(X2,X1)) = add(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_16]),c_0_13]),c_0_16]),c_0_13]),c_0_15]) ).
cnf(c_0_18,plain,
add(inverse(add(X1,X2)),inverse(add(inverse(X1),X2))) = inverse(X2),
inference(spm,[status(thm)],[c_0_15,c_0_7]) ).
cnf(c_0_19,plain,
add(inverse(add(inverse(X1),X2)),inverse(X2)) = inverse(X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,plain,
add(inverse(add(inverse(X1),inverse(X2))),X2) = X2,
inference(spm,[status(thm)],[c_0_19,c_0_15]) ).
cnf(c_0_21,plain,
add(inverse(add(X1,inverse(X2))),X2) = X2,
inference(spm,[status(thm)],[c_0_20,c_0_15]) ).
cnf(c_0_22,plain,
inverse(add(inverse(X1),inverse(add(X2,X1)))) = X1,
inference(spm,[status(thm)],[c_0_6,c_0_21]) ).
cnf(c_0_23,plain,
add(inverse(X1),inverse(add(X2,X1))) = inverse(X1),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_24,plain,
inverse(add(X1,inverse(add(inverse(add(X2,X3)),inverse(add(X2,X1)))))) = inverse(add(X2,X1)),
inference(spm,[status(thm)],[c_0_6,c_0_6]) ).
cnf(c_0_25,plain,
add(X1,inverse(add(X2,inverse(X1)))) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_15]) ).
cnf(c_0_26,plain,
inverse(add(X1,add(X1,X2))) = inverse(add(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_15]),c_0_15]),c_0_13]),c_0_15]) ).
cnf(c_0_27,plain,
inverse(add(inverse(X1),inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(X1)),X2)),X1)),X3)),inverse(add(inverse(X1),inverse(add(X1,X4)))))))) = X1,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_28,plain,
add(X1,add(X1,X2)) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_26]),c_0_15]) ).
cnf(c_0_29,plain,
inverse(add(inverse(X1),inverse(add(X1,X2)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_21]),c_0_15]),c_0_28]) ).
cnf(c_0_30,plain,
add(add(X1,X2),X1) = add(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_29]),c_0_15]),c_0_15]) ).
cnf(c_0_31,plain,
add(X1,inverse(add(inverse(X1),X2))) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_30]) ).
cnf(c_0_32,plain,
inverse(add(X1,X2)) = inverse(add(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_31]),c_0_29]) ).
cnf(c_0_33,plain,
add(X1,X2) = add(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_32]),c_0_15]) ).
cnf(c_0_34,plain,
inverse(add(inverse(add(X1,X2)),inverse(add(inverse(add(inverse(add(X3,X4)),X1)),inverse(add(inverse(X2),inverse(add(X2,X5)))))))) = X2,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_35,plain,
add(X1,inverse(add(X1,inverse(add(X1,X2))))) = add(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_31]),c_0_15]),c_0_15]),c_0_15]),c_0_15]),c_0_33]) ).
cnf(c_0_36,plain,
inverse(add(inverse(add(X1,X2)),inverse(add(inverse(add(X3,X1)),X2)))) = X2,
inference(spm,[status(thm)],[c_0_6,c_0_34]) ).
cnf(c_0_37,plain,
add(X1,inverse(add(X1,inverse(add(X2,X1))))) = add(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_23]),c_0_15]),c_0_15]),c_0_15]) ).
cnf(c_0_38,plain,
add(inverse(add(X1,X2)),inverse(add(X2,inverse(add(X1,X2))))) = add(inverse(add(X1,X2)),inverse(add(inverse(add(X3,X1)),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_33]) ).
cnf(c_0_39,plain,
add(inverse(add(X1,X2)),inverse(add(X2,inverse(add(X1,X2))))) = inverse(X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_23]),c_0_15]),c_0_33]) ).
cnf(c_0_40,plain,
add(inverse(add(X1,X2)),inverse(add(inverse(add(X3,X1)),X2))) = inverse(X2),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_41,plain,
add(inverse(X1),inverse(add(X1,X2))) = inverse(X1),
inference(spm,[status(thm)],[c_0_15,c_0_29]) ).
cnf(c_0_42,plain,
add(X1,inverse(add(inverse(add(X2,inverse(X1))),inverse(add(X1,X3))))) = add(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_15]),c_0_15]) ).
cnf(c_0_43,plain,
inverse(add(inverse(add(X1,X2)),inverse(add(X1,inverse(add(add(X1,X2),X3)))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_23]),c_0_15]),c_0_15]),c_0_33]),c_0_33]) ).
cnf(c_0_44,plain,
add(X1,inverse(add(add(X1,inverse(X1)),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_13]) ).
cnf(c_0_45,plain,
add(add(X1,inverse(X1)),X2) = add(X1,inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_44]),c_0_15]),c_0_33]),c_0_44]),c_0_15]),c_0_33]),c_0_15]),c_0_33]),c_0_15]) ).
cnf(c_0_46,plain,
inverse(add(inverse(add(add(X1,inverse(X1)),X1)),inverse(X1))) = X1,
inference(spm,[status(thm)],[c_0_7,c_0_4]) ).
cnf(c_0_47,plain,
add(X1,inverse(add(inverse(add(X2,X3)),inverse(add(X2,X1))))) = add(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_24]),c_0_15]) ).
cnf(c_0_48,plain,
add(X1,inverse(add(X2,inverse(X2)))) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_45]) ).
cnf(c_0_49,plain,
add(X1,inverse(add(inverse(add(X2,X1)),add(inverse(add(X2,X3)),X1)))) = add(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_2]),c_0_15]),c_0_29]),c_0_33]),c_0_33]),c_0_29]) ).
cnf(c_0_50,plain,
inverse(add(X1,inverse(add(add(X1,inverse(X1)),inverse(X1))))) = inverse(X1),
inference(spm,[status(thm)],[c_0_6,c_0_46]) ).
cnf(c_0_51,plain,
add(inverse(X1),add(X1,X2)) = add(X1,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_15]) ).
cnf(c_0_52,plain,
add(inverse(add(X1,inverse(X1))),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_48]),c_0_48]),c_0_41]),c_0_15]),c_0_48]) ).
cnf(c_0_53,plain,
inverse(add(inverse(add(inverse(X1),X2)),inverse(add(X1,X2)))) = X2,
inference(spm,[status(thm)],[c_0_6,c_0_50]) ).
cnf(c_0_54,plain,
add(X1,add(add(X1,X2),X3)) = add(add(X1,X2),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_51]),c_0_41]),c_0_15]),c_0_52]),c_0_15]) ).
cnf(c_0_55,plain,
inverse(add(inverse(add(X1,X2)),inverse(add(inverse(add(X1,X3)),X2)))) = X2,
inference(rw,[status(thm)],[c_0_6,c_0_32]) ).
cnf(c_0_56,plain,
add(inverse(add(add(inverse(X1),X2),inverse(add(X1,X2)))),X2) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_53]),c_0_15]) ).
cnf(c_0_57,plain,
add(X1,add(add(X2,X1),X3)) = add(add(X2,X1),X3),
inference(spm,[status(thm)],[c_0_54,c_0_37]) ).
cnf(c_0_58,plain,
add(inverse(add(X1,X2)),inverse(add(X2,inverse(add(X1,X2))))) = add(inverse(add(X1,X2)),inverse(add(inverse(add(X1,X3)),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_55]),c_0_33]) ).
cnf(c_0_59,plain,
add(X1,inverse(add(add(inverse(X2),X1),inverse(add(X2,X1))))) = add(X2,X1),
inference(rw,[status(thm)],[c_0_56,c_0_33]) ).
cnf(c_0_60,plain,
add(X1,add(X2,add(X3,X1))) = add(X2,add(X3,X1)),
inference(spm,[status(thm)],[c_0_57,c_0_37]) ).
cnf(c_0_61,plain,
add(inverse(add(X1,X2)),inverse(add(inverse(add(X1,X3)),X2))) = inverse(X2),
inference(rw,[status(thm)],[c_0_58,c_0_39]) ).
cnf(c_0_62,plain,
add(inverse(add(X1,X2)),inverse(add(inverse(add(X1,X2)),add(inverse(add(X1,X3)),X2)))) = inverse(X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_2]),c_0_29]),c_0_15]),c_0_29]),c_0_29]),c_0_33]),c_0_33]),c_0_60]),c_0_33]),c_0_61]) ).
cnf(c_0_63,plain,
add(inverse(add(X1,X2)),inverse(add(X2,inverse(X1)))) = inverse(X2),
inference(spm,[status(thm)],[c_0_18,c_0_33]) ).
cnf(c_0_64,plain,
add(inverse(X1),inverse(add(inverse(X1),inverse(X2)))) = add(inverse(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_18]),c_0_31]),c_0_31]),c_0_15]) ).
cnf(c_0_65,plain,
inverse(add(inverse(add(X1,X2)),inverse(add(inverse(add(X2,X3)),X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_33]),c_0_29]),c_0_33]) ).
cnf(c_0_66,plain,
add(inverse(add(X1,X2)),inverse(add(X2,add(add(inverse(X1),X2),inverse(add(X1,X2)))))) = inverse(X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_59]),c_0_33]),c_0_33]) ).
cnf(c_0_67,plain,
add(X1,inverse(add(X1,inverse(X2)))) = add(X1,X2),
inference(spm,[status(thm)],[c_0_64,c_0_15]) ).
cnf(c_0_68,plain,
add(inverse(add(X1,X2)),inverse(add(X1,inverse(add(X1,X2))))) = add(inverse(add(X1,X2)),inverse(add(inverse(add(X2,X3)),X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_65]),c_0_32]) ).
cnf(c_0_69,plain,
add(inverse(add(X1,X2)),inverse(add(X1,inverse(add(X1,X2))))) = inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_41]),c_0_15]),c_0_32]) ).
cnf(c_0_70,plain,
inverse(add(inverse(add(inverse(add(X1,X2)),inverse(X3))),inverse(add(X1,inverse(add(X3,inverse(add(inverse(X3),X4)))))))) = inverse(X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_8]),c_0_13]),c_0_13]),c_0_13]),c_0_13]),c_0_13]),c_0_13]) ).
cnf(c_0_71,plain,
add(add(X1,X2),inverse(add(X1,inverse(add(X3,add(X1,X2)))))) = add(X3,add(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_25]),c_0_15]),c_0_15]),c_0_15]),c_0_15]),c_0_33]) ).
cnf(c_0_72,plain,
add(X1,inverse(add(X1,X2))) = add(X1,inverse(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_41]),c_0_41]),c_0_33]),c_0_41]),c_0_15]),c_0_33]),c_0_15]) ).
cnf(c_0_73,plain,
add(X1,inverse(add(add(inverse(X2),X1),inverse(add(X1,X2))))) = add(X1,X2),
inference(spm,[status(thm)],[c_0_59,c_0_33]) ).
cnf(c_0_74,plain,
add(inverse(add(X1,X2)),inverse(add(inverse(add(X2,X3)),X1))) = inverse(X1),
inference(rw,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_75,plain,
add(inverse(X1),inverse(add(add(X1,X2),X3))) = inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_33]),c_0_51]),c_0_48]),c_0_15]) ).
cnf(c_0_76,plain,
add(X1,inverse(add(X2,X1))) = add(X1,inverse(X2)),
inference(spm,[status(thm)],[c_0_72,c_0_33]) ).
cnf(c_0_77,plain,
inverse(add(inverse(add(X1,X2)),inverse(add(X2,inverse(add(X1,X3)))))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_33]),c_0_29]),c_0_33]) ).
cnf(c_0_78,plain,
add(add(X1,X2),inverse(add(inverse(add(X2,X3)),X1))) = add(X1,add(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_33]),c_0_75]),c_0_15]),c_0_33]),c_0_76]),c_0_15]),c_0_33]) ).
cnf(c_0_79,plain,
add(inverse(add(X1,X2)),inverse(add(X2,inverse(add(X1,X3))))) = inverse(X2),
inference(spm,[status(thm)],[c_0_15,c_0_77]) ).
cnf(c_0_80,plain,
add(add(X1,X2),add(X1,add(X2,X3))) = add(X1,add(X2,X3)),
inference(spm,[status(thm)],[c_0_28,c_0_78]) ).
cnf(c_0_81,plain,
add(X1,inverse(add(X2,inverse(add(X1,inverse(add(X2,X3))))))) = add(X1,inverse(add(X2,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_79]),c_0_15]),c_0_15]),c_0_33]),c_0_33]) ).
cnf(c_0_82,plain,
add(add(X1,X2),add(X1,add(X3,X2))) = add(X1,add(X3,X2)),
inference(spm,[status(thm)],[c_0_80,c_0_47]) ).
cnf(c_0_83,plain,
add(add(X1,X2),add(X2,X3)) = add(X1,add(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_78]),c_0_23]),c_0_15]) ).
cnf(c_0_84,plain,
add(add(X1,X2),add(add(X3,X2),X1)) = add(add(X3,X2),X1),
inference(spm,[status(thm)],[c_0_82,c_0_33]) ).
cnf(c_0_85,plain,
add(add(X1,X2),add(X3,X1)) = add(X3,add(X1,X2)),
inference(spm,[status(thm)],[c_0_33,c_0_83]) ).
cnf(c_0_86,negated_conjecture,
add(add(a,b),c) != add(a,add(b,c)),
inference(fof_simplification,[status(thm)],[huntinton_2]) ).
cnf(c_0_87,plain,
add(add(X1,X2),add(add(X3,X1),X2)) = add(add(X3,X1),X2),
inference(spm,[status(thm)],[c_0_82,c_0_57]) ).
cnf(c_0_88,plain,
add(add(X1,X2),add(X3,X2)) = add(add(X1,X2),X3),
inference(rw,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_89,negated_conjecture,
add(add(a,b),c) != add(a,add(b,c)),
c_0_86 ).
cnf(c_0_90,plain,
add(add(X1,X2),add(add(X1,X3),X2)) = add(add(X1,X3),X2),
inference(spm,[status(thm)],[c_0_82,c_0_54]) ).
cnf(c_0_91,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_88]),c_0_85]) ).
cnf(c_0_92,plain,
add(X1,add(X2,add(X1,X3))) = add(X2,add(X1,X3)),
inference(spm,[status(thm)],[c_0_54,c_0_37]) ).
cnf(c_0_93,negated_conjecture,
add(c,add(a,b)) != add(a,add(b,c)),
inference(rw,[status(thm)],[c_0_89,c_0_33]) ).
cnf(c_0_94,plain,
add(X1,add(X2,X3)) = add(X2,add(X3,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_88]),c_0_91]),c_0_92]),c_0_91]) ).
cnf(c_0_95,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_94]),c_0_33]),c_0_94]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO073-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n018.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 13:54:14 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 40.29/8.55 % Version: 3.5.1
% 40.29/8.55 % Preprocessing class: FSSSSMSSSSSNFFN.
% 40.29/8.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 40.29/8.55 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 40.29/8.55 % Starting new_bool_3 with 300s (1) cores
% 40.29/8.55 % Starting new_bool_1 with 300s (1) cores
% 40.29/8.55 % Starting sh5l with 300s (1) cores
% 40.29/8.55 % new_bool_3 with pid 2059195 completed with status 9
% 40.29/8.55 % new_bool_1 with pid 2059196 completed with status 9
% 40.29/8.55 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2059194 completed with status 0
% 40.29/8.55 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 40.29/8.55 % Preprocessing class: FSSSSMSSSSSNFFN.
% 40.29/8.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 40.29/8.55 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 40.29/8.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 40.29/8.55 % No SInE strategy applied
% 40.29/8.55 % Search class: FUUPF-FFSF21-DFFFFFNN
% 40.29/8.55 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 40.29/8.55 % Starting SubtermCWHack with 136s (1) cores
% 40.29/8.55 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 40.29/8.55 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 40.29/8.55 % Starting new_bool_3 with 136s (1) cores
% 40.29/8.55 % Starting new_bool_1 with 136s (1) cores
% 40.29/8.55 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2059199 completed with status 0
% 40.29/8.55 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 40.29/8.55 % Preprocessing class: FSSSSMSSSSSNFFN.
% 40.29/8.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 40.29/8.55 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 40.29/8.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 40.29/8.55 % No SInE strategy applied
% 40.29/8.55 % Search class: FUUPF-FFSF21-DFFFFFNN
% 40.29/8.55 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 40.29/8.55 % Starting SubtermCWHack with 136s (1) cores
% 40.29/8.55 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 40.29/8.55 % Preprocessing time : 0.001 s
% 40.29/8.55
% 40.29/8.55 % Proof found!
% 40.29/8.55 % SZS status Unsatisfiable
% 40.29/8.55 % SZS output start CNFRefutation
% See solution above
% 40.29/8.55 % Parsed axioms : 2
% 40.29/8.55 % Removed by relevancy pruning/SinE : 0
% 40.29/8.55 % Initial clauses : 2
% 40.29/8.55 % Removed in clause preprocessing : 0
% 40.29/8.55 % Initial clauses in saturation : 2
% 40.29/8.55 % Processed clauses : 4110
% 40.29/8.55 % ...of these trivial : 2049
% 40.29/8.55 % ...subsumed : 1661
% 40.29/8.55 % ...remaining for further processing : 400
% 40.29/8.55 % Other redundant clauses eliminated : 0
% 40.29/8.55 % Clauses deleted for lack of memory : 0
% 40.29/8.55 % Backward-subsumed : 1
% 40.29/8.55 % Backward-rewritten : 219
% 40.29/8.55 % Generated clauses : 214397
% 40.29/8.55 % ...of the previous two non-redundant : 145039
% 40.29/8.55 % ...aggressively subsumed : 0
% 40.29/8.55 % Contextual simplify-reflections : 0
% 40.29/8.55 % Paramodulations : 214397
% 40.29/8.55 % Factorizations : 0
% 40.29/8.55 % NegExts : 0
% 40.29/8.55 % Equation resolutions : 0
% 40.29/8.55 % Disequality decompositions : 0
% 40.29/8.55 % Total rewrite steps : 384634
% 40.29/8.55 % ...of those cached : 350075
% 40.29/8.55 % Propositional unsat checks : 0
% 40.29/8.55 % Propositional check models : 0
% 40.29/8.55 % Propositional check unsatisfiable : 0
% 40.29/8.55 % Propositional clauses : 0
% 40.29/8.55 % Propositional clauses after purity: 0
% 40.29/8.55 % Propositional unsat core size : 0
% 40.29/8.55 % Propositional preprocessing time : 0.000
% 40.29/8.55 % Propositional encoding time : 0.000
% 40.29/8.55 % Propositional solver time : 0.000
% 40.29/8.55 % Success case prop preproc time : 0.000
% 40.29/8.55 % Success case prop encoding time : 0.000
% 40.29/8.55 % Success case prop solver time : 0.000
% 40.29/8.55 % Current number of processed clauses : 180
% 40.29/8.55 % Positive orientable unit clauses : 177
% 40.29/8.55 % Positive unorientable unit clauses: 3
% 40.29/8.55 % Negative unit clauses : 0
% 40.29/8.55 % Non-unit-clauses : 0
% 40.29/8.55 % Current number of unprocessed clauses: 135220
% 40.29/8.55 % ...number of literals in the above : 135220
% 40.29/8.55 % Current number of archived formulas : 0
% 40.29/8.55 % Current number of archived clauses : 220
% 40.29/8.55 % Clause-clause subsumption calls (NU) : 0
% 40.29/8.55 % Rec. Clause-clause subsumption calls : 0
% 40.29/8.55 % Non-unit clause-clause subsumptions : 0
% 40.29/8.55 % Unit Clause-clause subsumption calls : 339
% 40.29/8.55 % Rewrite failures with RHS unbound : 0
% 40.29/8.55 % BW rewrite match attempts : 18293
% 40.29/8.55 % BW rewrite match successes : 389
% 40.29/8.55 % Condensation attempts : 0
% 40.29/8.55 % Condensation successes : 0
% 40.29/8.55 % Termbank termtop insertions : 5489401
% 40.29/8.55 % Search garbage collected termcells : 2
% 40.29/8.55
% 40.29/8.55 % -------------------------------------------------
% 40.29/8.55 % User time : 7.699 s
% 40.29/8.55 % System time : 0.290 s
% 40.29/8.55 % Total time : 7.989 s
% 40.29/8.55 % Maximum resident set size: 3380 pages
% 40.29/8.55
% 40.29/8.55 % -------------------------------------------------
% 40.29/8.55 % User time : 39.056 s
% 40.29/8.55 % System time : 1.144 s
% 40.29/8.55 % Total time : 40.199 s
% 40.29/8.55 % Maximum resident set size: 4608 pages
% 40.29/8.55 % E exiting
%------------------------------------------------------------------------------