%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : BOO023-1 : TPTP v9.2.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n023.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 : Tue May 5 04:11:10 PM UTC 2026
% Result : Unsatisfiable 23.83s 14.31s
% Output : CNFRefutation 23.93s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
cnf(pixley1,axiom,
pixley(X1,X1,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley1) ).
cnf(pixley_defn,axiom,
pixley(X1,X2,X3) = add(multiply(X1,inverse(X2)),add(multiply(X1,X3),multiply(inverse(X2),X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley_defn) ).
cnf(multiply_add,axiom,
multiply(add(X1,X2),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_add) ).
cnf(multiply_add_property,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X2,X1),multiply(X3,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_add_property) ).
cnf(pixley3,axiom,
pixley(X1,X2,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley3) ).
cnf(additive_inverse,axiom,
add(X1,inverse(X1)) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse) ).
cnf(pixley2,axiom,
pixley(X1,X2,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley2) ).
cnf(prove_add_multiply_property,negated_conjecture,
add(a,multiply(b,c)) != multiply(add(a,b),add(a,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_add_multiply_property) ).
cnf(c_0_8,axiom,
pixley(X1,X1,X2) = X2,
pixley1 ).
cnf(c_0_9,axiom,
pixley(X1,X2,X3) = add(multiply(X1,inverse(X2)),add(multiply(X1,X3),multiply(inverse(X2),X3))),
pixley_defn ).
cnf(c_0_10,axiom,
multiply(add(X1,X2),X2) = X2,
multiply_add ).
cnf(c_0_11,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X2,X1),multiply(X3,X1)),
multiply_add_property ).
cnf(c_0_12,axiom,
pixley(X1,X2,X1) = X1,
pixley3 ).
cnf(c_0_13,plain,
add(multiply(X1,inverse(X1)),add(multiply(X1,X2),multiply(inverse(X1),X2))) = X2,
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,axiom,
add(X1,inverse(X1)) = n1,
additive_inverse ).
cnf(c_0_15,plain,
multiply(multiply(X1,add(X2,X3)),multiply(X3,X1)) = multiply(X3,X1),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
multiply(X1,add(X2,add(X3,X1))) = add(multiply(X2,X1),X1),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_17,plain,
add(multiply(X1,inverse(X2)),add(multiply(X1,X1),multiply(inverse(X2),X1))) = X1,
inference(rw,[status(thm)],[c_0_12,c_0_9]) ).
cnf(c_0_18,plain,
add(multiply(X1,inverse(X1)),multiply(X2,n1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_11]),c_0_14]) ).
cnf(c_0_19,plain,
multiply(add(X1,X2),add(multiply(X3,X2),X2)) = add(multiply(X3,X2),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_10]),c_0_16]),c_0_16]) ).
cnf(c_0_20,plain,
add(multiply(X1,inverse(X2)),multiply(X1,add(X1,inverse(X2)))) = X1,
inference(rw,[status(thm)],[c_0_17,c_0_11]) ).
cnf(c_0_21,plain,
multiply(n1,inverse(X1)) = inverse(X1),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_22,plain,
add(multiply(X1,inverse(X1)),n1) = add(X2,n1),
inference(spm,[status(thm)],[c_0_18,c_0_10]) ).
cnf(c_0_23,plain,
multiply(add(X1,X2),add(X2,X2)) = add(X2,X2),
inference(spm,[status(thm)],[c_0_19,c_0_10]) ).
cnf(c_0_24,plain,
add(inverse(X1),multiply(n1,add(n1,inverse(X1)))) = n1,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
multiply(X1,add(add(X2,X1),X3)) = add(X1,multiply(X3,X1)),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_26,plain,
add(X1,n1) = add(X2,n1),
inference(spm,[status(thm)],[c_0_22,c_0_22]) ).
cnf(c_0_27,plain,
multiply(n1,multiply(add(n1,inverse(X1)),add(n1,n1))) = multiply(add(n1,inverse(X1)),add(n1,n1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_11]),c_0_11]) ).
cnf(c_0_28,plain,
multiply(X1,add(X2,n1)) = add(X1,multiply(n1,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,plain,
multiply(n1,add(n1,multiply(n1,n1))) = add(n1,multiply(n1,n1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_14]),c_0_28]),c_0_28]) ).
cnf(c_0_30,plain,
multiply(X1,multiply(X1,n1)) = multiply(X1,n1),
inference(spm,[status(thm)],[c_0_10,c_0_18]) ).
cnf(c_0_31,plain,
add(multiply(X1,multiply(X2,n1)),multiply(X2,n1)) = multiply(multiply(X2,n1),add(X1,X2)),
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_32,plain,
multiply(add(n1,multiply(n1,n1)),multiply(multiply(n1,n1),n1)) = multiply(multiply(n1,n1),n1),
inference(spm,[status(thm)],[c_0_15,c_0_29]) ).
cnf(c_0_33,plain,
multiply(add(X1,multiply(X2,X3)),multiply(X3,add(X2,X2))) = multiply(X3,add(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_15]),c_0_11]),c_0_11]) ).
cnf(c_0_34,plain,
multiply(multiply(n1,n1),add(X1,n1)) = add(n1,multiply(n1,n1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_30]),c_0_11]),c_0_28]) ).
cnf(c_0_35,plain,
multiply(add(X1,X1),multiply(X1,add(X2,X1))) = multiply(X1,add(X2,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_23]) ).
cnf(c_0_36,plain,
add(add(X1,multiply(X2,X1)),multiply(X3,add(add(X4,X1),X2))) = multiply(add(add(X4,X1),X2),add(X1,X3)),
inference(spm,[status(thm)],[c_0_11,c_0_25]) ).
cnf(c_0_37,plain,
multiply(multiply(multiply(n1,n1),n1),add(add(n1,multiply(n1,n1)),multiply(n1,n1))) = add(n1,multiply(n1,n1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_11]),c_0_11]),c_0_28]),c_0_29]) ).
cnf(c_0_38,plain,
multiply(add(X1,multiply(n1,n1)),add(n1,multiply(n1,n1))) = add(n1,multiply(n1,n1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_30]) ).
cnf(c_0_39,plain,
multiply(add(X1,multiply(multiply(n1,n1),n1)),add(n1,multiply(n1,n1))) = add(n1,multiply(n1,n1)),
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_19,c_0_32]),c_0_11]),c_0_11]),c_0_28]),c_0_29]),c_0_11]),c_0_11]),c_0_28]),c_0_29]) ).
cnf(c_0_40,plain,
add(inverse(n1),multiply(X1,n1)) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_21]) ).
cnf(c_0_41,plain,
multiply(add(X1,multiply(X2,add(X3,X2))),add(X2,X2)) = add(X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_35]),c_0_11]),c_0_23]),c_0_11]),c_0_23]) ).
cnf(c_0_42,plain,
add(add(multiply(n1,n1),multiply(multiply(n1,n1),multiply(n1,n1))),add(n1,multiply(n1,n1))) = add(n1,multiply(n1,n1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_11]),c_0_29]),c_0_38]) ).
cnf(c_0_43,plain,
add(multiply(X1,n1),multiply(X2,multiply(X1,n1))) = multiply(multiply(X1,n1),add(X1,X2)),
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_44,plain,
multiply(multiply(n1,n1),add(n1,multiply(n1,n1))) = add(n1,multiply(n1,n1)),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,plain,
multiply(add(X1,add(X2,multiply(X2,X2))),add(X2,X2)) = add(X2,X2),
inference(spm,[status(thm)],[c_0_41,c_0_25]) ).
cnf(c_0_46,plain,
multiply(add(n1,multiply(n1,n1)),add(X1,n1)) = add(add(n1,multiply(n1,n1)),add(n1,multiply(n1,n1))),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_47,plain,
add(add(n1,multiply(n1,n1)),add(n1,multiply(n1,n1))) = add(n1,multiply(n1,n1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_48,plain,
add(add(multiply(X1,X2),X2),multiply(X3,add(X1,add(X4,X2)))) = multiply(add(X1,add(X4,X2)),add(X2,X3)),
inference(spm,[status(thm)],[c_0_11,c_0_16]) ).
cnf(c_0_49,axiom,
pixley(X1,X2,X2) = X1,
pixley2 ).
cnf(c_0_50,plain,
add(X1,multiply(inverse(add(X2,X1)),X1)) = multiply(X1,n1),
inference(spm,[status(thm)],[c_0_25,c_0_14]) ).
cnf(c_0_51,plain,
multiply(multiply(add(n1,multiply(n1,n1)),add(X1,n1)),add(n1,n1)) = add(n1,n1),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,plain,
multiply(add(n1,multiply(n1,n1)),add(X1,n1)) = add(n1,multiply(n1,n1)),
inference(rw,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_53,plain,
multiply(X1,multiply(add(X2,add(X3,X1)),add(X1,X4))) = add(X1,multiply(multiply(X4,add(X2,add(X3,X1))),X1)),
inference(spm,[status(thm)],[c_0_25,c_0_48]) ).
cnf(c_0_54,plain,
add(multiply(X1,inverse(X2)),add(multiply(X1,X2),multiply(inverse(X2),X2))) = X1,
inference(rw,[status(thm)],[c_0_49,c_0_9]) ).
cnf(c_0_55,plain,
add(add(n1,multiply(n1,n1)),multiply(inverse(add(n1,multiply(n1,n1))),add(n1,multiply(n1,n1)))) = multiply(add(n1,multiply(n1,n1)),n1),
inference(spm,[status(thm)],[c_0_50,c_0_42]) ).
cnf(c_0_56,plain,
add(n1,multiply(n1,n1)) = add(n1,n1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52]),c_0_52]) ).
cnf(c_0_57,plain,
multiply(X1,add(X1,X1)) = add(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_10]),c_0_16]),c_0_10]) ).
cnf(c_0_58,plain,
add(multiply(X1,inverse(X2)),multiply(X2,add(X1,inverse(X2)))) = X1,
inference(rw,[status(thm)],[c_0_54,c_0_11]) ).
cnf(c_0_59,plain,
add(add(n1,n1),multiply(inverse(add(n1,n1)),add(n1,n1))) = n1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56]),c_0_56]),c_0_56]),c_0_56]),c_0_10]) ).
cnf(c_0_60,plain,
add(add(X1,X1),multiply(X2,add(X1,X1))) = multiply(add(X1,X1),add(X1,X2)),
inference(spm,[status(thm)],[c_0_11,c_0_57]) ).
cnf(c_0_61,plain,
multiply(X1,multiply(X2,add(X1,inverse(X2)))) = multiply(X2,add(X1,inverse(X2))),
inference(spm,[status(thm)],[c_0_10,c_0_58]) ).
cnf(c_0_62,plain,
multiply(add(n1,n1),add(n1,inverse(add(n1,n1)))) = n1,
inference(rw,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_63,plain,
multiply(multiply(X1,X2),add(X3,multiply(X2,add(X4,X1)))) = add(multiply(X3,multiply(X1,X2)),multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_16,c_0_11]) ).
cnf(c_0_64,plain,
add(multiply(X1,inverse(X2)),inverse(X2)) = multiply(inverse(X2),add(X1,n1)),
inference(spm,[status(thm)],[c_0_11,c_0_21]) ).
cnf(c_0_65,plain,
multiply(n1,n1) = n1,
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_66,plain,
multiply(multiply(X1,X2),multiply(multiply(X2,n1),X1)) = multiply(multiply(X2,n1),X1),
inference(spm,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_67,plain,
multiply(inverse(add(n1,n1)),add(add(n1,n1),n1)) = multiply(inverse(add(n1,n1)),n1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_59]),c_0_21]),c_0_21]),c_0_21]),c_0_64]) ).
cnf(c_0_68,plain,
add(inverse(n1),n1) = n1,
inference(spm,[status(thm)],[c_0_40,c_0_65]) ).
cnf(c_0_69,plain,
multiply(multiply(inverse(add(n1,n1)),n1),inverse(add(n1,n1))) = inverse(add(n1,n1)),
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_10]),c_0_21]),c_0_10]),c_0_21]) ).
cnf(c_0_70,plain,
add(X1,n1) = n1,
inference(spm,[status(thm)],[c_0_26,c_0_68]) ).
cnf(c_0_71,plain,
multiply(n1,add(inverse(X1),inverse(X1))) = add(inverse(X1),inverse(X1)),
inference(spm,[status(thm)],[c_0_23,c_0_14]) ).
cnf(c_0_72,plain,
add(inverse(X1),multiply(X2,inverse(X1))) = multiply(inverse(X1),add(n1,X2)),
inference(spm,[status(thm)],[c_0_11,c_0_21]) ).
cnf(c_0_73,plain,
multiply(multiply(inverse(n1),n1),inverse(n1)) = inverse(n1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70]),c_0_70]),c_0_70]) ).
cnf(c_0_74,plain,
add(n1,multiply(inverse(n1),n1)) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_70]),c_0_65]) ).
cnf(c_0_75,plain,
add(multiply(inverse(n1),inverse(n1)),add(inverse(n1),inverse(n1))) = inverse(n1),
inference(spm,[status(thm)],[c_0_58,c_0_71]) ).
cnf(c_0_76,plain,
multiply(inverse(X1),add(X2,n1)) = add(inverse(X1),inverse(X1)),
inference(spm,[status(thm)],[c_0_28,c_0_21]) ).
cnf(c_0_77,plain,
add(inverse(n1),inverse(n1)) = multiply(inverse(n1),n1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]) ).
cnf(c_0_78,plain,
multiply(inverse(n1),inverse(n1)) = add(inverse(n1),inverse(n1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_75]),c_0_64]),c_0_76]) ).
cnf(c_0_79,plain,
multiply(inverse(n1),n1) = inverse(n1),
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_20,c_0_77]),c_0_78]),c_0_77]),c_0_30]),c_0_11]),c_0_71]),c_0_77]) ).
cnf(c_0_80,plain,
multiply(multiply(X1,add(X2,X3)),add(multiply(X4,multiply(X3,X1)),multiply(X3,X1))) = add(multiply(X4,multiply(X3,X1)),multiply(X3,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_11]) ).
cnf(c_0_81,plain,
multiply(inverse(n1),add(X1,inverse(n1))) = inverse(n1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_79]),c_0_64]),c_0_70]),c_0_79]) ).
cnf(c_0_82,plain,
add(inverse(X1),inverse(X1)) = multiply(inverse(X1),n1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_21]),c_0_70]) ).
cnf(c_0_83,plain,
add(multiply(X1,inverse(n1)),inverse(n1)) = inverse(n1),
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_78]),c_0_82]),c_0_79]),c_0_78]),c_0_82]),c_0_79]),c_0_81]),c_0_78]),c_0_82]),c_0_79]),c_0_78]),c_0_82]),c_0_79]) ).
cnf(c_0_84,plain,
multiply(inverse(n1),add(n1,inverse(inverse(n1)))) = inverse(n1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_83]),c_0_72]),c_0_79]) ).
cnf(c_0_85,plain,
add(add(X1,X1),add(X1,X1)) = add(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_57]),c_0_23]) ).
cnf(c_0_86,plain,
add(inverse(inverse(n1)),inverse(n1)) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_84]),c_0_21]) ).
cnf(c_0_87,plain,
multiply(add(X1,X1),add(X2,X2)) = multiply(X2,add(X1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_11]),c_0_11]) ).
cnf(c_0_88,plain,
inverse(inverse(n1)) = n1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_86]),c_0_65]),c_0_70]) ).
cnf(c_0_89,plain,
multiply(n1,add(X1,X1)) = multiply(X1,n1),
inference(spm,[status(thm)],[c_0_87,c_0_70]) ).
cnf(c_0_90,plain,
multiply(X1,n1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_88]),c_0_70]),c_0_11]),c_0_89]) ).
cnf(c_0_91,plain,
multiply(n1,add(X1,X2)) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_90]),c_0_90]) ).
cnf(c_0_92,plain,
add(multiply(X1,multiply(X2,add(X3,inverse(X2)))),multiply(X2,add(X3,inverse(X2)))) = multiply(multiply(X2,add(X3,inverse(X2))),add(X1,X3)),
inference(spm,[status(thm)],[c_0_16,c_0_58]) ).
cnf(c_0_93,plain,
multiply(X1,multiply(X1,add(X1,inverse(X2)))) = multiply(X1,add(X1,inverse(X2))),
inference(spm,[status(thm)],[c_0_10,c_0_20]) ).
cnf(c_0_94,plain,
multiply(n1,add(n1,X1)) = add(n1,multiply(X1,n1)),
inference(spm,[status(thm)],[c_0_11,c_0_65]) ).
cnf(c_0_95,plain,
multiply(n1,X1) = X1,
inference(spm,[status(thm)],[c_0_91,c_0_58]) ).
cnf(c_0_96,plain,
add(X1,X1) = 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_92,c_0_93]),c_0_14]),c_0_14]),c_0_11]),c_0_14]),c_0_90]),c_0_57]),c_0_89]),c_0_90]) ).
cnf(c_0_97,plain,
add(inverse(X1),add(n1,multiply(inverse(X1),n1))) = n1,
inference(rw,[status(thm)],[c_0_24,c_0_94]) ).
cnf(c_0_98,plain,
add(multiply(X1,X2),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_95]),c_0_70]),c_0_90]) ).
cnf(c_0_99,plain,
multiply(X1,add(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_96]),c_0_10]),c_0_96]) ).
cnf(c_0_100,plain,
multiply(X1,add(X2,X2)) = multiply(X2,add(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_85]),c_0_87]),c_0_87]) ).
cnf(c_0_101,plain,
add(inverse(X1),add(n1,inverse(X1))) = n1,
inference(rw,[status(thm)],[c_0_97,c_0_90]) ).
cnf(c_0_102,plain,
add(X1,add(X2,X1)) = add(X2,X1),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_103,plain,
multiply(X1,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_90]),c_0_90]) ).
cnf(c_0_104,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_96]),c_0_96]) ).
cnf(c_0_105,plain,
add(inverse(n1),X1) = X1,
inference(rw,[status(thm)],[c_0_40,c_0_90]) ).
cnf(c_0_106,plain,
multiply(X1,inverse(n1)) = inverse(n1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_83]),c_0_21]),c_0_83]) ).
cnf(c_0_107,plain,
add(inverse(X1),multiply(X1,add(n1,inverse(X1)))) = n1,
inference(spm,[status(thm)],[c_0_58,c_0_21]) ).
cnf(c_0_108,plain,
add(n1,inverse(X1)) = n1,
inference(rw,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_109,plain,
multiply(add(n1,X1),inverse(X1)) = inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_103]),c_0_82]),c_0_90]),c_0_72]),c_0_104]) ).
cnf(c_0_110,plain,
multiply(X1,inverse(X1)) = inverse(n1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_105]),c_0_11]),c_0_105]),c_0_104]) ).
cnf(c_0_111,plain,
add(X1,inverse(n1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_95]),c_0_106]),c_0_105]) ).
cnf(c_0_112,plain,
add(inverse(X1),X1) = n1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_108]),c_0_90]) ).
cnf(c_0_113,plain,
add(X1,multiply(X2,X1)) = multiply(X1,add(n1,X2)),
inference(spm,[status(thm)],[c_0_11,c_0_95]) ).
cnf(c_0_114,plain,
add(n1,X1) = n1,
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_58,c_0_109]),c_0_25]),c_0_104]),c_0_110]),c_0_111]),c_0_112]) ).
cnf(c_0_115,plain,
multiply(multiply(X1,X2),multiply(multiply(X3,add(X2,inverse(X3))),X1)) = multiply(multiply(X3,add(X2,inverse(X3))),X1),
inference(spm,[status(thm)],[c_0_15,c_0_58]) ).
cnf(c_0_116,plain,
multiply(add(X1,X2),add(X2,X3)) = add(X2,multiply(X3,add(X1,X2))),
inference(spm,[status(thm)],[c_0_11,c_0_99]) ).
cnf(c_0_117,plain,
add(X1,multiply(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_114]),c_0_90]) ).
cnf(c_0_118,plain,
multiply(X1,multiply(X2,X1)) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_108]),c_0_90]),c_0_90]),c_0_90]) ).
cnf(c_0_119,plain,
multiply(X1,add(multiply(X2,X1),X3)) = multiply(X1,add(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_11]) ).
cnf(c_0_120,plain,
multiply(X1,multiply(X1,X2)) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_118,c_0_104]) ).
cnf(c_0_121,plain,
multiply(X1,add(X2,multiply(X3,X1))) = multiply(X1,add(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_11]),c_0_120]) ).
cnf(c_0_122,plain,
add(inverse(X1),multiply(X1,add(add(X2,inverse(X1)),inverse(X1)))) = add(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_58,c_0_10]) ).
cnf(c_0_123,plain,
add(add(X1,X2),X2) = add(X1,X2),
inference(spm,[status(thm)],[c_0_117,c_0_99]) ).
cnf(c_0_124,plain,
multiply(X1,add(X2,multiply(X1,X3))) = multiply(X1,add(X2,X3)),
inference(spm,[status(thm)],[c_0_121,c_0_104]) ).
cnf(c_0_125,plain,
multiply(X1,add(X1,X2)) = add(X1,multiply(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_90]),c_0_90]),c_0_90]) ).
cnf(c_0_126,plain,
add(inverse(X1),multiply(X1,add(X2,inverse(X1)))) = add(X2,inverse(X1)),
inference(rw,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_127,plain,
multiply(X1,add(X2,inverse(X1))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_110]),c_0_111]) ).
cnf(c_0_128,plain,
multiply(inverse(X1),add(X1,X2)) = multiply(X2,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_110]),c_0_105]) ).
cnf(c_0_129,plain,
multiply(X1,inverse(inverse(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_112]),c_0_90]),c_0_90]),c_0_104]) ).
cnf(c_0_130,plain,
multiply(X1,add(X1,X2)) = X1,
inference(rw,[status(thm)],[c_0_125,c_0_117]) ).
cnf(c_0_131,plain,
add(inverse(X1),multiply(X1,X2)) = add(X2,inverse(X1)),
inference(rw,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_132,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_112]),c_0_90]),c_0_129]) ).
cnf(c_0_133,plain,
add(add(X1,X2),X1) = add(X1,X2),
inference(spm,[status(thm)],[c_0_117,c_0_130]) ).
cnf(c_0_134,plain,
multiply(add(X1,add(X2,X3)),add(X3,X4)) = add(X3,multiply(X4,add(X1,add(X2,X3)))),
inference(rw,[status(thm)],[c_0_48,c_0_98]) ).
cnf(c_0_135,plain,
multiply(inverse(X1),add(X2,X1)) = multiply(X2,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_110]),c_0_111]) ).
cnf(c_0_136,plain,
add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_128]),c_0_132]),c_0_132]),c_0_133]) ).
cnf(c_0_137,plain,
multiply(add(X1,X2),add(X3,add(X1,multiply(X2,add(X4,X1))))) = multiply(add(X1,X2),add(X3,add(X4,X1))),
inference(spm,[status(thm)],[c_0_121,c_0_116]) ).
cnf(c_0_138,plain,
multiply(add(X1,X2),add(X3,add(X4,X1))) = add(X1,multiply(X2,add(X3,add(X4,X1)))),
inference(spm,[status(thm)],[c_0_104,c_0_134]) ).
cnf(c_0_139,plain,
add(X1,X2) = 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_131,c_0_135]),c_0_132]),c_0_136]),c_0_132]),c_0_123]) ).
cnf(c_0_140,plain,
multiply(add(X1,X2),add(X3,add(X1,multiply(X2,add(X4,X1))))) = add(X1,multiply(X2,add(X3,add(X4,X1)))),
inference(rw,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_141,plain,
multiply(X1,add(X2,add(X3,inverse(X1)))) = multiply(X1,add(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_127]),c_0_124]) ).
cnf(c_0_142,plain,
multiply(multiply(X1,add(X2,X3)),multiply(X1,add(X3,X3))) = multiply(X1,add(X3,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_11]),c_0_11]),c_0_11]) ).
cnf(c_0_143,negated_conjecture,
add(a,multiply(b,c)) != multiply(add(a,b),add(a,c)),
prove_add_multiply_property ).
cnf(c_0_144,plain,
multiply(add(X1,X2),add(X1,X3)) = add(X1,multiply(X3,add(X1,X2))),
inference(spm,[status(thm)],[c_0_11,c_0_130]) ).
cnf(c_0_145,plain,
multiply(add(X1,X2),add(X3,X1)) = add(X1,multiply(X3,add(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_130]),c_0_139]) ).
cnf(c_0_146,plain,
add(add(X1,X2),inverse(X3)) = add(X1,add(X2,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_140,c_0_127]),c_0_139]),c_0_14]),c_0_131]),c_0_95]),c_0_141]),c_0_131]) ).
cnf(c_0_147,plain,
multiply(multiply(X1,X2),multiply(X1,add(X3,X2))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_142,c_0_96]),c_0_96]),c_0_104]) ).
cnf(c_0_148,negated_conjecture,
add(a,multiply(c,add(a,b))) != add(a,multiply(b,c)),
inference(rw,[status(thm)],[c_0_143,c_0_144]) ).
cnf(c_0_149,plain,
add(X1,multiply(X2,add(X1,X3))) = add(X1,multiply(X3,add(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_116]),c_0_145]) ).
cnf(c_0_150,plain,
add(add(X1,multiply(X2,X3)),multiply(X2,add(X1,X3))) = add(X1,multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_117,c_0_124]) ).
cnf(c_0_151,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(spm,[status(thm)],[c_0_146,c_0_132]) ).
cnf(c_0_152,plain,
add(multiply(X1,X2),multiply(X1,add(X3,X2))) = multiply(X1,add(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_147]),c_0_139]) ).
cnf(c_0_153,negated_conjecture,
add(a,multiply(b,add(a,c))) != add(a,multiply(b,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_148,c_0_149]),c_0_139]) ).
cnf(c_0_154,plain,
add(X1,multiply(X2,add(X1,X3))) = add(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_151]),c_0_152]) ).
cnf(c_0_155,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_153,c_0_154])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : BOO023-1 : TPTP v9.2.1. Released v2.2.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.35 % Computer : n023.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue May 5 10:45:53 EDT 2026
% 0.15/0.35 % CPUTime :
% 0.18/0.36 % start to proof: theBenchmark
% 23.83/14.31 % Version : CSE_E---1.7
% 23.83/14.31 % Problem : theBenchmark.p
% 23.83/14.31 % SZS status Unsatisfiable for theBenchmark.p
% 23.83/14.31 % SZS output start CNFRefutation
% See solution above
% 23.93/14.42 % Total time : 10.387s
%------------------------------------------------------------------------------